- coordinatesRadial coordinates of mesh block boundaries.
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:Radial coordinates of mesh block boundaries.
- mesh_densityA list giving the number of elements in each interval (could be zero for a gap).
C++ Type:std::vector<unsigned int>
Controllable:No
Description:A list giving the number of elements in each interval (could be zero for a gap).
TRISO1DMeshGenerator
Creates a 1D mesh for use with TRISO analysis.
Description
TRISO1DMeshGenerator creates a 1D mesh appropriate for use in TRISO analysis. The user supplies radial coordinates that mark the boundaries of mesh blocks. A list of numbers of radial elements per block is also supplied. A 0 for the elements in the block represents a gap and is typically used for the gap that opens between the buffer and IPyC layers.
Sidesets are created at each mesh boundary. The number that is assigned to the sideset is a function of how many blocks are requested. Numbering starts from the origin and counts outward. The pattern can be seen in Figure 1. If there is a gap, it is assigned the last number and is a union of the left and the right boundaries of the 2 adjacent blocks. See Figure 1 sideset 12 for graphical clarification.
The bias parameter affects mesh density moving from the inner edge to the outer edge. For example, a bias value of 2 for a given block doubles element size from the inner to the outer edge, whereas a bias value of 0.5 cuts element size in half going from inner to outer edge. The dual_bias parameter may be used to affect mesh density on both ends of the block. It is also applied from inner to outer edge. When dual_bias is given, bias affects the first half of the elements, and dual_bias affects the right half of the elements. If the two biases are the same, the result will be the same as the original, single-value bias approach.
Any number of blocks can be made but Figure 1 below is representative of a standard TRISO particle with 5 blocks.
See also TRISO1DFiveLayerMeshGenerator.
The depiction below assumes that the blocks are named fuel, buffer, IPyC, SiC and OPyC in the input file. They can be named anything according to user preferences.

Figure 1: Pictorial line representation of the 1D spherical mesh created by TRISO1DMeshGenerator.
Example Input Syntax
[Mesh<<<{"href": "../../syntax/Mesh/index.html"}>>>]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator<<<{"description": "Creates a 1D mesh for use with TRISO analysis.", "href": "TRISO1DMeshGenerator.html"}>>>
elem_type<<<{"description": "The type of element from libMesh to generate"}>>> = EDGE3
coordinates<<<{"description": "Radial coordinates of mesh block boundaries."}>>> = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
mesh_density<<<{"description": "A list giving the number of elements in each interval (could be zero for a gap)."}>>> = '6 6 0 6 8 6'
block_names<<<{"description": "A list of names to be assigned to the mesh blocks."}>>> = 'fuel buffer IPyC SiC OPyC'
[]
[](examples/TRISO/full_particle/1D/full_particle_1D.i)Input Parameters
- biasMesh bias. Same length as mesh_density, each entry b: 0.5 <= b <= 2.0.
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:Mesh bias. Same length as mesh_density, each entry b: 0.5 <= b <= 2.0.
- block_namesA list of names to be assigned to the mesh blocks.
C++ Type:std::vector<std::string>
Controllable:No
Description:A list of names to be assigned to the mesh blocks.
- dual_biasMesh dual bias. If given, bias must be given. Same length as bias, each entry b: 0.5 <= b <= 2.0.
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:Mesh dual bias. If given, bias must be given. Same length as bias, each entry b: 0.5 <= b <= 2.0.
- elem_typeEDGE3The type of element from libMesh to generate
Default:EDGE3
C++ Type:MooseEnum
Options:EDGE2, EDGE3
Controllable:No
Description:The type of element from libMesh to generate
Optional Parameters
- enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.
- save_with_nameKeep the mesh from this mesh generator in memory with the name specified
C++ Type:std::string
Controllable:No
Description:Keep the mesh from this mesh generator in memory with the name specified
Advanced Parameters
- nemesisFalseWhether or not to output the mesh file in the nemesisformat (only if output = true)
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not to output the mesh file in the nemesisformat (only if output = true)
- outputFalseWhether or not to output the mesh file after generating the mesh
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not to output the mesh file after generating the mesh
- show_infoFalseWhether or not to show mesh info after generating the mesh (bounding box, element types, sidesets, nodesets, subdomains, etc)
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not to show mesh info after generating the mesh (bounding box, element types, sidesets, nodesets, subdomains, etc)
Debugging Parameters
Input Files
- (examples/TRISO/pebble/triso_1d.i)
- (examples/TRISO/correlation_function/h_asphericity/triso_1d.i)
- (test/tests/arrhenius_diffusion_coef/check_jacobian.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_4c/case_4c.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_5a/case_5a.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_8a/case_8a.i)
- (test/tests/triso/UCOFGR/ad_UCOFGR.i)
- (test/tests/triso/mesh/mesh_with_coincident_nodes_1D.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_3c/case_3c.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_2b/case_2b.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_1/case_1_1D.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_4d/case_4d.i)
- (test/tests/triso_pebble/1D_pebble_picard.i)
- (test/tests/triso/UCOFGR/UCOFGR_out_of_pile.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_4b/case_4b_1D.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_6/case_6_1D.i)
- (test/tests/triso/UNFGR/ad_UNFGR.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_4a/case_4a_1D.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_2/case_2_1D.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_6a/case_6a.i)
- (examples/TRISO/parfume/parfume_un.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_10/case_10_1D.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_8/case_8_1D.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_2a/case_2a.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_5b/case_5b.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_7a/case_7a.i)
- (test/tests/triso/UCOFGR/ad_UCOFGR_out_of_pile.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_4b/case_4b.i)
- (test/tests/triso_failure/triso_1d_failure_error.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_3d/case_3d.i)
- (test/tests/triso_failure/triso_failure_diffusivity.i)
- (assessment/verification/TRISO_diffusion/inpile/inpile.i)
- (examples/TRISO/full_particle/1D/full_particle_1D.i)
- (test/tests/triso/UCOFGR/UCOFGR.i)
- (test/tests/triso/UNFGR/UNFGR.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_4c/case_4c_1D.i)
- (test/tests/triso/release_birth_ratio/richards.i)
- (test/tests/triso/kernel_migration/kernel_migration_distance.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_11/case_11.i)
- (test/tests/triso_failure/triso_1d_failure.i)
- (examples/TRISO/accident_simulation/triso1D_accident.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_7b/case_7b.i)
- (examples/TRISO/failure_probability_direct_integration/triso_1d.i)
- (assessment/verification/TRISO_diffusion/inpile_stable/inpile_stable.i)
- (assessment/TRISO/validation/AGR-34/SharedFiles/capsule_dtf.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_8b/case_8b.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_4a/case_4a.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_7/case_7_1D.i)
- (test/tests/triso/mesh/mesh_1D.i)
- (test/tests/triso_pebble/1D_pebble_from_csv.i)
- (test/tests/triso_pebble/triso_1d.i)
- (examples/TRISO/one_layer/1D/one_layer_1D.i)
- (examples/TRISO/parfume/parfume.i)
- (test/tests/triso_failure/ad_triso_1d_weibull_probability.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_4d/case_4d_1D.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_3b/case_3b.i)
- (assessment/TRISO/validation/AGR-34/SharedFiles/capsule_driver.i)
- (test/tests/SiCPdPenetration/palladium_penetration.i)
- (test/tests/triso_failure/triso_1d_weibull_probability.i)
- (test/tests/triso_failure/ad_triso_1d_failure.i)
- (test/tests/triso/mesh/mesh_with_gap_1D.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_9/case_9.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_6b/case_6b.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_3/case_3_1D.i)
- (test/tests/triso_failure/triso_1d_kernel_migration.i)
- (assessment/TRISO/validation/AGR-34/Compacts/AGR-34_dtf_base.i)
- (examples/TRISO/pebble/triso_1d_failed.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_10/case_10.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_3e/case_3e.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_5/case_5_1D.i)
- (test/tests/triso/release_birth_ratio/exposed_kernel.i)
- (test/tests/triso/release_birth_ratio/agr.i)
- (test/tests/triso/release_birth_ratio/uranium_contamination.i)
- (examples/TRISO/two_layers/1D/two_layers_1D.i)
- (test/tests/triso_failure/sub.i)
- (test/tests/void_volume/void_volume.i)
- (test/tests/triso_failure/triso_1d_asphericity_failure.i)
- (test/tests/triso_failure/triso_1d_ipyc_weibull_probability.i)
- (assessment/verification/TRISO_diffusion/outofpile/outofpile.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_11/case_11_1D.i)
- (test/tests/void_volume/ad_void_volume.i)
- (test/tests/triso_failure/ad_triso_1d_ipyc_weibull_probability.i)
- (test/tests/triso_pebble/1D_pebble.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_3a/case_3a.i)
(examples/TRISO/full_particle/1D/full_particle_1D.i)
initial_fuel_density = 10810.0
[GlobalParams]
density = ${initial_fuel_density}
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
mesh_density = '6 6 0 6 8 6'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Variables]
[temperature]
initial_condition = 1346.0
[]
[]
[AuxVariables]
[fission_rate]
block = fuel
[]
[burnup]
block = fuel
[]
[grain_radius]
initial_condition = 5.0e-6
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[fuel]
block = fuel
add_variables = true
strain = FINITE
eigenstrain_names = 'fuel_thermal_strain'
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
[]
[buffer]
block = buffer
add_variables = true
strain = FINITE
eigenstrain_names = 'buffer_thermal_strain buffer_eigenstrain'
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
[]
[IPyC]
block = IPyC
add_variables = true
strain = FINITE
eigenstrain_names = 'IPyC_eigenstrain IPyC_thermal_strain'
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
[]
[SiC]
block = SiC
add_variables = true
strain = FINITE
eigenstrain_names = 'SiC_thermal_strain'
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
[]
[OPyC]
block = OPyC
add_variables = true
strain = FINITE
eigenstrain_names = 'OPyC_eigenstrain OPyC_thermal_strain'
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
[]
[]
[Functions]
[fission_rate]
type = ParsedFunction
expression = 7.75e19
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
[]
[heat]
type = HeatConduction
variable = temperature
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
energy_per_fission = 3.2e-11
fission_rate = fission_rate
[]
[]
[AuxKernels]
[fission_rate]
type = FunctionAux
variable = fission_rate
block = fuel
function = fission_rate
[]
[burnup]
type = BurnupAux
variable = burnup
block = fuel
fission_rate = fission_rate
molecular_weight = 0.270
[]
[grain_radius]
type = GrainRadiusAux
block = fuel
variable = grain_radius
temperature = temperature
execute_on = linear
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
penalty = 1e5
model = frictionless
formulation = kinematic
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
# coupling to a postprocessor
initial_moles = initial_moles
gas_released = 'fis_gas_released co_production'
released_gas_types = 'Kr Xe;
CO'
released_fractions = '0.153 0.847;
1'
tangential_tolerance = 1e-6
[]
[]
[BCs]
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[freesurf_temperature]
type = DirichletBC
variable = temperature
boundary = exterior
value = 1346.0
[]
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure] # apply gas pressure on buffer and IPyC boundaries
[plenumPressure]
boundary = buffer_IPyC_boundary
initial_pressure = 0
startup_time = 1.0e4
R = 8.3143
# couplings to post processor
output_initial_moles = initial_moles
temperature = ave_temperature_interior
volume = volumeGas
material_input = 'fis_gas_released co_production'
output = plenum_pressure
[]
[]
[]
[Materials]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 1.708707e18 # n/m^2-sec
[]
[fuel_thermal]
type = UO2Thermal
block = fuel
temperature = temperature
thermal_conductivity_model = FINK_LUCUTA
initial_porosity = 0.0
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 2.0e8
poissons_ratio = 0.345
[]
[fuel_elastic_stress]
type = ComputeFiniteStrainElasticStress
block = fuel
[]
[fuel_density]
type = StrainAdjustedDensity
block = fuel
strain_free_density = ${initial_fuel_density}
[]
[fuel_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10.0e-6
temperature = temperature
stress_free_temperature = 1346.0
eigenstrain_name = fuel_thermal_strain
[]
[fission_gas_release]
type = UO2Sifgrs
block = fuel
temperature = temperature
fission_rate = fission_rate
grain_radius = grain_radius
[]
[buffer_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 2.0e8
poissons_ratio = 0.345
[]
[buffer_elastic_stress]
type = ComputeFiniteStrainElasticStress
block = buffer
[]
[buffer_temperature]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5
specific_heat = 720.0
[]
[buffer_density]
type = StrainAdjustedDensity
strain_free_density = 1000.0
block = buffer
[]
[buffer_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = buffer
thermal_expansion_coeff = 5.5e-6
temperature = temperature
stress_free_temperature = 1346.0
eigenstrain_name = buffer_thermal_strain
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'IPyC OPyC buffer'
[]
[buffer_irraditation]
type = PyCIrradiationEigenstrain
block = buffer
pyc_type = buffer
eigenstrain_name = buffer_eigenstrain
[]
[IPyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = IPyC
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[IOPyC_stress]
type = PyCCreep
block = 'IPyC OPyC'
temperature = temperature
[]
[IOPyC_thermal]
type = HeatConductionMaterial
block = 'IPyC OPyC'
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IOPyC_density]
type = StrainAdjustedDensity
strain_free_density = 1880.0
block = 'IPyC OPyC'
[]
[IPyC_densification]
type = PyCIrradiationEigenstrain
block = IPyC
pyc_type = dense
eigenstrain_name = IPyC_eigenstrain
[]
[IPyC_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = IPyC
thermal_expansion_coeff = 5.5e-6
temperature = temperature
stress_free_temperature = 1346.0
eigenstrain_name = IPyC_thermal_strain
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_elastic_stress]
type = ComputeFiniteStrainElasticStress
block = SiC
[]
[SiC_temperature]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9
specific_heat = 620.0
[]
[SiC_density]
type = StrainAdjustedDensity
strain_free_density = 3200.0
block = SiC
[]
[SiC_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
temperature = temperature
stress_free_temperature = 1346.0
eigenstrain_name = SiC_thermal_strain
[]
[OPyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = OPyC
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[OPyC_densification]
type = PyCIrradiationEigenstrain
block = OPyC
pyc_type = dense
eigenstrain_name = OPyC_eigenstrain
[]
[OPyC_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = OPyC
thermal_expansion_coeff = 5.5e-6
temperature = temperature
stress_free_temperature = 1346.0
eigenstrain_name = OPyC_thermal_strain
[]
[]
[Dampers]
[temperature]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 3.10176e7
dtmax = 2e5
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 20
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[dt]
type = TimestepSize
[]
[burnup]
type = ElementExtremeValue
block = fuel
variable = burnup
[]
[fis_gas_produced]
type = ElementIntegralFisGasGeneratedSifgrs
block = fuel
[]
[fis_gas_released]
type = ElementIntegralFisGasReleasedSifgrs
block = fuel
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
[]
[volumeFuel]
type = InternalVolume
boundary = fuel_outer_boundary
[]
[volumeGas]
type = InternalVolume
boundary = 'fuel_outer_boundary IPyC_inner_boundary'
addition = -5.53e-11
execute_on = 'initial timestep_end'
[]
[volumeBufferShell]
type = InternalVolume
boundary = buffer_IPyC_boundary
[]
[ave_temperature_interior]
type = SideAverageValue
boundary = buffer_IPyC_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
[]
[avg_surface_temperature]
type = SideAverageValue
variable = temperature
boundary = exterior
[]
[time_int_surf_temperature]
type = TimeIntegratedPostprocessor
value = avg_surface_temperature
[]
[co_production]
type = CarbonMonoxideProduction
total_fissions = total_fissions
time_integrated_triso_temperature = time_int_surf_temperature
initial_enrichment = 0.14029
[]
[tang_SiC]
type = ElementalVariableValue
variable = stress_yy
elementid = 18
[]
[max_xx_IPyC]
type = ElementExtremeValue
variable = stress_xx
block = IPyC
[]
[max_yy_IPyC]
type = ElementExtremeValue
variable = stress_yy
block = IPyC
[]
[min_zz_IPyC]
type = ElementExtremeValue
variable = stress_zz
block = IPyC
value_type = min
[]
[max_xx_SiC]
type = ElementExtremeValue
variable = stress_xx
block = SiC
[]
[max_yy_SiC]
type = ElementExtremeValue
variable = stress_yy
block = SiC
[]
[min_zz_SiC]
type = ElementExtremeValue
variable = stress_zz
block = SiC
value_type = min
[]
[max_xx_OPyC]
type = ElementExtremeValue
variable = stress_xx
block = OPyC
[]
[max_yy_OPyC]
type = ElementExtremeValue
variable = stress_yy
block = OPyC
[]
[min_zz_OPyC]
type = ElementExtremeValue
variable = stress_zz
block = OPyC
value_type = min
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = false
csv = true
perf_graph = true
[chkfile]
type = CSV
execute_on = Final
show = 'max_xx_IPyC max_yy_IPyC min_zz_IPyC max_xx_SiC max_yy_SiC min_zz_SiC'
[]
[]
(examples/TRISO/pebble/triso_1d.i)
kernel_radius = 213.35e-6
buffer_thickness = 98.9e-6
IPyC_thickness = 40.4e-6
SiC_thickness = 35.2e-6
OPyC_thickness = 43.4e-6
coordinates1 = '${fparse kernel_radius}'
coordinates2 = '${fparse coordinates1+buffer_thickness}'
coordinates3 = '${fparse coordinates2+IPyC_thickness}'
coordinates4 = '${fparse coordinates3+SiC_thickness}'
coordinates5 = '${fparse coordinates4+OPyC_thickness}'
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.14029 # [wt-]
energy_per_fission = 3.204e-11 # [J/fission]
O_U = 1.428 # Initial Oxygen to Uranium atom ratio
C_U = 0.392 # Initial Carbon to Uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[mesh]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
mesh_density = '18 14 12 16 16'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = OPyC_outer_boundary
outer_SiC = SiC_outer_boundary
outer_IPyC = IPyC_outer_boundary
inner_IPyC = IPyC_inner_boundary
outer_buffer = buffer_outer_boundary
outer_kernel = fuel_outer_boundary
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temperature]
initial_condition = 773.15
[]
[conc_Cs]
initial_condition = 0.0
scaling = 1e18
[]
[]
[AuxVariables]
[fission_rate]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_flux]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
order = CONSTANT
family = MONOMIAL
[]
[fis_gas_produced]
order = CONSTANT
family = MONOMIAL
[]
[fis_gas_released]
order = CONSTANT
family = MONOMIAL
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[power_history]
type = PiecewiseLinear
x = '0 1e3 4.51008e7' #change time (s) for desired EFPD
y = '0 1 1'
[]
[fission_rate]
type = LinearCombinationFunction
functions = power_history
w = 2.927e18
[]
[temp_bc_func]
type = ParsedFunction
value = temp_bc
symbol_names = temp_bc
symbol_values = temp_bc
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[fissionrate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = fuel
execute_on = timestep_begin
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = fuel
execute_on = timestep_begin
[]
[fast_neutron_flux]
type = MaterialRealAux
variable = fast_neutron_flux
property = fast_neutron_flux
execute_on = timestep_begin
[]
[fast_neutron_fluence]
type = MaterialRealAux
variable = fast_neutron_fluence
property = fast_neutron_fluence
execute_on = timestep_begin
[]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[]
[BCs]
[freesurf_temp]
type = FunctionDirichletBC
variable = temperature
function = temp_bc_func
boundary = exterior
[]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
flux_function = power_history
factor = 1.109e18
[]
[UCO_burnup]
type = TRISOBurnup
initial_density = 10966.0
[]
[UCO_thermal]
type = UCOThermal
block = fuel
temperature = temperature
[]
[UCO_density]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10966.0
[]
[fission_gas_release]
type = UCOFGR
block = fuel
average_grain_radius = 10e-6
temperature = temperature
triso_geometry = particle_geometry
[]
# Arrhenius diffusion coefficients for kernel, PyC, and SiC
# come from IAEA TECDOC-978, French parameters.
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
property_name = Cs_generation
kind = Cs
block = fuel
[]
### Buffer Properties
[buffer_thermal]
type = BufferThermal
block = buffer
initial_density = 1050.0
[]
[Buffer_density]
type = StrainAdjustedDensity
block = buffer
strain_free_density = 1050.0
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0.0
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
### IPyC properties
[IPyC_thermal]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_density]
type = StrainAdjustedDensity
block = IPyC
strain_free_density = 1907.0
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
### SiC properties
[SiC_thermal]
type = MonolithicSiCThermal
block = SiC
temperature = temperature
thermal_conductivity_model = miller
[]
[SiC_density]
type = StrainAdjustedDensity
block = SiC
strain_free_density = 3200.0
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
q1 = 125e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
### OPyC properties
[OPyC_thermal_conductivity]
type = HeatConductionMaterial
block = OPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[OPyC_density]
type = StrainAdjustedDensity
block = OPyC
strain_free_density = 1907.0
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu'
line_search = 'none'
nl_rel_tol = 1e-8
nl_abs_tol = 1e-6
nl_max_its = 20
l_tol = 1e-4
l_max_its = 50
dt = 500000
num_steps = 10
[]
[Postprocessors]
[temp_bc]
type = Receiver
[]
[release_heat_inc]
type = SideIntegralMassFlux
variable = temperature
boundary = exterior
arrhenius_prpty_name = thermal_conductivity
execute_on = 'initial timestep_end'
[]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
[]
[fis_gas_produced]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_produced
block = fuel
execute_on = 'initial timestep_end'
[]
[fis_gas_released]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_released
block = fuel
execute_on = 'initial timestep_end'
[]
### Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
execute_on = 'initial timestep_end'
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
execute_on = 'initial timestep_end'
[]
##### irradiation conditions
[particle_power]
type = ElementIntegralPower
variable = temperature
use_material_fission_rate = true
fission_rate_material = fission_rate
block = fuel
execute_on = 'initial timestep_end'
[]
[max_fluence]
type = ElementExtremeValue
variable = fast_neutron_fluence
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_burnup]
type = ElementExtremeValue
variable = burnup
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[aver_temp_exterior]
type = SideAverageValue
variable = temperature
boundary = exterior
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = true
print_linear_converged_reason = false
print_nonlinear_converged_reason = false
[]
(examples/TRISO/correlation_function/h_asphericity/triso_1d.i)
kernel_radius = 213.35e-6
buffer_thickness = 98.9e-6
IPyC_thickness = 40.4e-6
SiC_thickness = 35.2e-6
OPyC_thickness = 43.4e-6
coordinates1 = '${fparse kernel_radius}'
coordinates2 = '${fparse coordinates1+buffer_thickness}'
coordinates3 = '${fparse coordinates2+IPyC_thickness}'
coordinates4 = '${fparse coordinates3+SiC_thickness}'
coordinates5 = '${fparse coordinates4+OPyC_thickness}'
initial_fuel_density = 10966
[GlobalParams]
order = FIRST
family = LAGRANGE
displacements = 'disp_x'
initial_enrichment = 0.14029 # [wt-]
flux_conversion_factor = 1.0 # convert E>0.10 to E>0.18 MeV
stress_free_temperature = 481 # used for thermal expansion
energy_per_fission = 3.204e-11 # [J/fission]
O_U = 1.428 # Initial Oxygen to Uranium atom ratio
C_U = 0.392 # Initial Carbon to Uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[mesh]
type = TRISO1DMeshGenerator
elem_type = EDGE2
coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
mesh_density = '20 8 0 4 4 4'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = OPyC_outer_boundary
outer_SiC = SiC_outer_boundary
outer_IPyC = IPyC_outer_boundary
inner_IPyC = IPyC_inner_boundary
outer_buffer = buffer_outer_boundary
outer_kernel = fuel_outer_boundary
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temperature]
initial_condition = 481
[]
[]
[AuxVariables]
[fission_rate]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_flux]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temp_bc]
type = PiecewiseLinear
data_file = outer_temp.csv
x_index_in_file = 0
y_index_in_file = 1
format = columns
[]
[fission_rate]
type = ConstantFunction
value = 5.75e19
[]
[]
[Physics/SolidMechanics/QuasiStatic]
generate_output = 'stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz max_principal_stress'
add_variables = true
strain = FINITE
incremental = true
[fuel]
block = fuel
eigenstrain_names = 'UCO_swelling_eigenstrain UCO_TE_strain'
extra_vector_tags = 'ref'
[]
[buffer]
block = buffer
eigenstrain_names = 'Buffer_IIDC_strain Buffer_TE_strain'
extra_vector_tags = 'ref'
[]
[IPyC]
block = IPyC
eigenstrain_names = 'IPyC_IIDC_strain IPyC_TE_strain'
extra_vector_tags = 'ref'
[]
[SiC]
block = SiC
eigenstrain_names = 'SiC_thermal_eigenstrain'
extra_vector_tags = 'ref'
[]
[OPyC]
block = OPyC
eigenstrain_names = 'OPyC_IIDC_strain OPyC_TE_strain'
extra_vector_tags = 'ref'
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[fissionrate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = fuel
execute_on = timestep_begin
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = fuel
execute_on = timestep_begin
[]
[fast_neutron_flux]
type = MaterialRealAux
variable = fast_neutron_flux
property = fast_neutron_flux
execute_on = timestep_begin
[]
[fast_neutron_fluence]
type = MaterialRealAux
variable = fast_neutron_fluence
property = fast_neutron_fluence
execute_on = timestep_begin
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
initial_moles = initial_moles
gas_released = 'fis_gas_released'
released_gas_types = 'Kr Xe'
released_fractions = '0.185 0.815'
tangential_tolerance = 1e-6
quadrature = false
min_gap = 1e-7
max_gap = 50e-6
gap_geometry_type = sphere
[]
[]
[BCs]
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[freesurf_temp]
type = FunctionDirichletBC
variable = temperature
function = temp_bc
boundary = exterior
[]
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure]
[plenumPressure]
boundary = buffer_IPyC_boundary
startup_time = 1e4
initial_pressure = 0
R = 8.3145
output_initial_moles = initial_moles
temperature = ave_gas_temp
volume = 'gap_volume buffer_void_volume kernel_void_volume'
material_input = 'fis_gas_released'
output = gas_pressure
[]
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
block = fuel
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 6.2425e+17
[]
[UCO_burnup]
type = TRISOBurnup
initial_density = ${initial_fuel_density}
block = fuel
[]
[UCO_thermal]
type = UCOThermal
block = fuel
temperature = temperature
[]
[UCO_elasticity_tensor]
type = UCOElasticityTensor
block = fuel
temperature = temperature
[]
[UCO_stress]
type = ComputeFiniteStrainElasticStress
block = fuel
[]
[UCO_VolumetricSwellingEigenstrain]
type = UCOVolumetricSwellingEigenstrain
block = fuel
eigenstrain_name = UCO_swelling_eigenstrain
[]
[fuel_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10.0e-6
temperature = temperature
eigenstrain_name = UCO_TE_strain
[]
[UCO_density]
type = StrainAdjustedDensity
block = fuel
strain_free_density = ${initial_fuel_density}
[]
[fission_gas_release]
type = UCOFGR
block = fuel
average_grain_radius = 10e-6
temperature = temperature
triso_geometry = particle_geometry
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'buffer IPyC OPyC'
[]
[BAF_IPyC]
type = BaconAnisotropyFactor
initial_BAF = 1.0465
block = IPyC
[]
[BAF_OPyC]
type = BaconAnisotropyFactor
initial_BAF = 1.0429
block = OPyC
[]
[buffer_elasticity_tensor]
type = BufferElasticityTensor
block = buffer
temperature = temperature
[]
[buffer_stress]
type = BufferCEGACreep
block = buffer
temperature = temperature
[]
[buffer_thermal]
type = BufferThermal
block = buffer
initial_density = 1050.0
[]
[buffer_density]
type = StrainAdjustedDensity
block = buffer
strain_free_density = 1050.0
[]
[buffer_TE]
type = BufferThermalExpansionEigenstrain
block = buffer
eigenstrain_name = Buffer_TE_strain
temperature = temperature
[]
[buffer_IIDC]
type = BufferCEGAIrradiationEigenstrain
block = buffer
eigenstrain_name = Buffer_IIDC_strain
temperature = temperature
[]
[IPyC_elasticity_tensor]
type = PyCElasticityTensor
block = IPyC
temperature = temperature
[]
[IPyC_stress]
type = PyCCEGACreep
block = IPyC
creep_rate_scale_factor = 1
temperature = temperature
[]
[IPyC_thermal]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_density]
type = GenericConstantMaterial
block = IPyC
prop_names = 'density'
prop_values = 1890
[]
[IPyC_IIDC]
type = PyCCEGAIrradiationEigenstrain
block = IPyC
eigenstrain_name = IPyC_IIDC_strain
temperature = temperature
irradiation_eigenstrain_scale_factor = 1
[]
[IPyC_TE]
type = PyCThermalExpansionEigenstrain
block = IPyC
eigenstrain_name = IPyC_TE_strain
temperature = temperature
[]
[SiC_elasticity_tensor]
type = MonolithicSiCElasticityTensor
block = SiC
temperature = temperature
elastic_modulus_model = miller
[]
[SiC_stress]
type = ComputeFiniteStrainElasticStress
block = SiC
[]
[SiC_thermal]
type = MonolithicSiCThermal
block = SiC
temperature = temperature
thermal_conductivity_model = miller
[]
[SiC_density]
type = StrainAdjustedDensity
block = SiC
strain_free_density = 3200.0
[]
[SiC_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
temperature = temperature
eigenstrain_name = SiC_thermal_eigenstrain
[]
[OPyC_elasticity_tensor]
type = PyCElasticityTensor
block = OPyC
temperature = temperature
initial_BAF = 1.0
[]
[OPyC_stress]
type = PyCCEGACreep
block = OPyC
creep_rate_scale_factor = 1
temperature = temperature
[]
[OPyC_thermal_conductivity]
type = HeatConductionMaterial
block = OPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[OPyC_density]
type = GenericConstantMaterial
block = OPyC
prop_names = 'density'
prop_values = 1900
[]
[OPyC_IIDC]
type = PyCCEGAIrradiationEigenstrain
block = OPyC
eigenstrain_name = OPyC_IIDC_strain
temperature = temperature
irradiation_eigenstrain_scale_factor = 1
[]
[OPyC_TE]
type = PyCThermalExpansionEigenstrain
block = OPyC
eigenstrain_name = OPyC_TE_strain
temperature = temperature
[]
[characteristic_strength_SiC]
type = GenericConstantMaterial
prop_values = '9640000'
block = SiC
prop_names = 'characteristic_strength'
[]
[characteristic_strength_PyC]
type = PyCCharacteristicStrength
temperature = temperature
X = 1.02
block = 'IPyC OPyC'
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temperature
max_increment = 100
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-8
nl_abs_tol = 1e-8
nl_max_its = 20
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 4.831315e7
dtmin = 1e-4
dt = 6e5
[]
[Postprocessors]
[ave_gas_temp]
type = ElementAverageValue
block = buffer
variable = temperature
execute_on = 'initial timestep_end'
[]
[fis_gas_released]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_released
block = fuel
use_displaced_mesh = false
execute_on = 'initial timestep_end'
[]
[gap_volume]
type = InternalVolume
boundary = buffer_IPyC_boundary
execute_on = 'initial linear'
use_displaced_mesh = true
[]
[buffer_void_volume]
type = VoidVolume
block = buffer
theoretical_density = 2250
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[kernel_th_density]
type = UCOTheoreticalDensity
execute_on = initial
[]
[kernel_void_volume]
type = VoidVolume
block = fuel
theoretical_density = kernel_th_density
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[particle_power]
type = ElementIntegralPower
variable = temperature
use_material_fission_rate = true
fission_rate_material = fission_rate
block = fuel
execute_on = 'initial timestep_end'
[]
[max_fluence]
type = ElementExtremeValue
variable = fast_neutron_fluence
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_burnup]
type = ElementExtremeValue
variable = burnup
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[SiC_stress_max]
type = ElementExtremeMaterialProperty
block = SiC
value_type = max
mat_prop = stress_yy
[]
[SiC_stress_min]
type = ElementExtremeMaterialProperty
block = SiC
value_type = min
mat_prop = stress_yy
[]
[strength_SiC]
type = WeibullEffectiveMeanStrength
block = SiC
weibull_modulus = 6
[]
[]
[Outputs]
print_linear_residuals = false
time_step_interval = 1
csv = true
perf_graph = true
exodus = true
[]
(test/tests/arrhenius_diffusion_coef/check_jacobian.i)
[GlobalParams]
order = FIRST
family = LAGRANGE
initial_enrichment = 0.1676
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE2
coordinates = '0 1'
mesh_density = '1'
block_names = 'flubber'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc]
[]
[temperature]
initial_condition = 1373.15
[]
[]
[AuxVariables]
[diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temperature]
type = ParsedFunction
expression = 1373.15
[]
[]
[Kernels]
[mass_dt]
type = TimeDerivative
variable = conc
[]
[mass]
type = ArrheniusDiffusion
variable = conc
arrhenius_prpty_name = arrhenius_diffusion_coef
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source]
type = SpeciesSourceRate
variable = conc
property_name = generation
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = FissionRateHeatSource
variable = temperature
energy_per_fission = 1e-16
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[diff_coef]
type = MaterialRealAux
variable = diff_coef
property = arrhenius_diffusion_coef
execute_on = timestep_end
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
[]
[]
[BCs]
[freesurf_conc]
type = DirichletBC
variable = conc
boundary = exterior
value = 0.0
[]
[temperature]
type = FunctionDirichletBC
variable = temperature
function = temperature
boundary = exterior
[]
[]
[Materials]
[burnup]
type = GenericFunctionMaterial
prop_names = 'burnup'
prop_values = 'if(t<21513600,0.093/21513600*t,0.093)'
[]
[fission_rate]
type = GenericFunctionMaterial
prop_names = 'fission_rate'
prop_values = 1.05e21
[]
[conc]
type = ArrheniusDiffusionCoef
d1 = 5e40
q1 = 1140000
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef
[]
[mass_source_property]
type = SpeciesSourceMaterial
property_name = generation
kind = Ag
[]
[thermal]
type = HeatConductionMaterial
thermal_conductivity = 100
specific_heat = 10
[]
[den]
type = ParsedMaterial
property_name = density
expression = 10850
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'temperature conc'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'NEWTON'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-12
nl_abs_tol = 5e-19
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 24523200
num_steps = 2
dt = 86400
dtmax = 86400
#dtmin = 86400
[TimeStepper]
type = FunctionDT
function = 'if(t<21513600,86400,3600)'
[]
[]
[Outputs]
perf_graph = false
print_linear_residuals = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_4c/case_4c.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.08
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 250e-6 350e-6 390e-6 425e-6 465e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
bias = '1 1.25 1.25 1.25 1.25'
dual_bias = '0.8 0.8 0.8 0.8 1'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[conc_Ag]
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1273.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = 'if(t<4.3200001e7,1273.15,if(t<4.3920001e7,1873.15,2073.15))'
variable = temperature
[]
[fast_neutron_fluence]
type = FunctionAux
function = 'if(t<4.3200001e7,2e25/4.32e7*t,2e25)'
variable = fast_neutron_fluence
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[]
[Materials]
[burnup]
type = GenericFunctionMaterial
block = fuel
prop_names = 'burnup'
prop_values = 'if(t<4.3200001e7,0.1/4.32e7*t,0.1)'
[]
[fission_rate]
type = GenericFunctionMaterial
block = fuel
prop_names = 'fission_rate'
# 5.581219e19 = 0.1/4.32e7*10810/.27*6.0221409e23
prop_values = 'if(t<4.3200001e7,5.581219e19,0)'
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Cs_generation
kind = Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = 'exp(t/5e25)'
d1_function_variable = fast_neutron_fluence
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Ag_generation
kind = Ag
[]
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[SiC_conc_Ag]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs conc_Ag'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 5e-21 #1e-22
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 4.464e7
num_steps = 1000
dt = 86400
dtmax = 86400
#dtmin = 86400
[TimeStepper]
type = FunctionDT
function = 'if(t<4.3200001e7,86400,3600)'
[]
[]
[Postprocessors]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
execute_on = final
[]
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_5a/case_5a.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.08
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 250e-6 350e-6 390e-6 425e-6 465e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
bias = '1 1.25 1.25 1.25 1.25'
dual_bias = '0.8 0.8 0.8 0.8 1'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[conc_Ag]
[]
[]
[AuxVariables]
[temperature]
initial_condition = 873.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temperature]
type = PiecewiseLinear
data_file = temperature_history.dat
format = columns
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = temperature
variable = temperature
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[]
[Materials]
[burnup]
type = GenericFunctionMaterial
block = fuel
prop_names = 'burnup'
prop_values = '0.1/8.64e7*t'
[]
[fission_rate]
type = GenericFunctionMaterial
block = fuel
prop_names = 'fission_rate'
# 2.790610e19 = 0.1/8.64e7*10810/.27*6.0221409e23
prop_values = '2.790610e19'
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Cs_generation
kind = Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = 'exp(2e25/8.64e7*t/5e25)'
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Ag_generation
kind = Ag
[]
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[SiC_conc_Ag]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs conc_Ag'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 5e-21 #1e-22
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 8.64e7
num_steps = 1450
dt = 86400
dtmax = 86400
#dtmin = 86400
[TimeStepper]
type = FunctionDT
function = 'if(t<8.64e7,86400,3600)'
[]
[]
[Postprocessors]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial timestep_end'
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
execute_on = final
[]
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_8a/case_8a.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.0982
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 248.5e-6 342.5e-6 383.5e-6 419.5e-6 459.5e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
bias = '1 1.25 1.25 1.25 1.25'
dual_bias = '0.8 0.8 0.8 0.8 1'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[conc_Ag]
[]
[conc_Sr]
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1391.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Sr_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temperature]
type = PiecewiseLinear
data_file = temperature_history.dat
format = columns
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
[]
[mass_Sr_dt]
type = TimeDerivative
variable = conc_Sr
[]
[mass_Sr]
type = ArrheniusDiffusion
variable = conc_Sr
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Sr]
type = SpeciesSourceRate
variable = conc_Sr
property_name = Sr_generation
block = fuel
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[Sr_diff_coef]
type = MaterialRealAux
variable = Sr_diff_coef
property = arrhenius_diffusion_coef_Sr
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = temperature
variable = temperature
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[freesurf_conc_Sr]
type = DirichletBC
variable = conc_Sr
boundary = exterior
value = 0.0
[]
[]
[Materials]
[burnup]
type = GenericFunctionMaterial
block = fuel
prop_names = 'burnup'
prop_values = 'if(t<31017600,0.075/31017600*t,0.075)'
[]
[fission_rate]
type = GenericFunctionMaterial
block = fuel
prop_names = 'fission_rate'
# 5.83e19 = 0.075/31017600*10810/.27*6.0221409e23
prop_values = 'if(t<31017600,5.83e19,0)'
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Cs_generation
kind = Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = 'if(t<31017600,exp(4.0e25/31017600*t/5e25),exp(4.0e25/5e25))'
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Ag_generation
kind = Ag
[]
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[SiC_conc_Ag]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[fuel_conc_Sr]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 2.2e-3 # m^2/s
q1 = 488e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[mass_source_Sr_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Sr_generation
kind = Sr
[]
[buffer_conc_Sr]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[IPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[SiC_conc_Sr]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 1.2e-9 # m^2/s
q1 = 205e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[OPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs conc_Ag'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 5e-21 #1e-22
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 32965200
num_steps = 1450
dt = 86400
dtmax = 86400
#dtmin = 86400
[TimeStepper]
type = FunctionDT
function = 'if(t<31017600,86400,
if(t<31165200,900,
3600))'
[]
[]
[Postprocessors]
[_temp]
type = NodalExtremeValue
variable = temperature
[]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released_overall]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
start_time = 31017600
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial timestep_end'
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released_overall]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
start_time = 31017600
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
execute_on = 'initial timestep_end'
[]
[release_Sr_inc]
type = SideIntegralMassFlux
variable = conc_Sr
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
execute_on = 'initial timestep_end'
[]
[released_Sr]
type = TimeIntegratedPostprocessor
value = release_Sr_inc
execute_on = 'initial timestep_end'
[]
[total_Sr]
type = ElementIntegralMaterialProperty
mat_prop = Sr_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Sr_released_overall]
type = FractionalRelease
released = released_Sr
total = total_Sr
execute_on = 'initial timestep_end'
[]
[x_Sr_released]
type = FractionalRelease
released = released_Sr
total = total_Sr
execute_on = 'initial timestep_end'
start_time = 31017600
[]
[retained_Sr]
type = ElementIntegralVariablePostprocessor
variable = conc_Sr
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
[]
[out_final]
type = CSV
execute_on = final
[]
[]
(test/tests/triso/UCOFGR/ad_UCOFGR.i)
# Fission Gas Release Model High Temperature
# The geometry is a 1D sphere with a diameter of 425 micrometers and an average
# grain radius of 10 microns.
# The fission gas yield was set to 0.297.
# The temperature is ramped from 673.15 to 3073.15 K.
# The fission rate density is ramped from 0 to 1.1625e21 fission/m^3-s
# (3.72e10 W/m^3) over 1e4 seconds and held constant.
# The density of the kernel is set to 11250 kg/m^3, the Oxygen to Uranium ratio
# is set to 1.5, the Carbon to Uranium ratio is set to 0.4, and the initial
# U-235 enrichment is set to 15%.
#
[GlobalParams]
order = FIRST
family = LAGRANGE
O_U = 1.5
C_U = 0.4
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.125e-4'
mesh_density = '6'
block_names = 'fuel'
[]
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = '2'
outer_SiC = '2'
outer_IPyC = '2'
inner_IPyC = '2'
outer_buffer = '2'
outer_kernel = '2'
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temp]
initial_condition = 673.15
[]
[]
[AuxVariables]
[fission_rate]
block = '1'
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = '1'
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[fission_rate]
type = PiecewiseLinear
x = '0 1e4 1e8'
y = '0 1.1625e21 1.1625e21'
[]
[scaled_time]
type = ParsedFunction
# molar mass / Avogadro's number / density
# 0.266 / 6.022e23 / 11250 = 3.926e-29
expression = '3.926e-29*t'
[]
[burnup]
type = CompositeFunction
functions = 'fission_rate scaled_time'
[]
[temp_function]
type = PiecewiseLinear
x = '0 7.5e6'
y = '673.15 3073.15'
[]
[]
[Kernels]
[heat]
type = ADHeatConduction
variable = temp
[]
[heat_ie]
type = ADHeatConductionTimeDerivative
variable = temp
[]
[]
[AuxKernels]
[fission_rate]
type = ADMaterialRealAux
variable = fission_rate
property = fission_rate
block = '1'
execute_on = timestep_end
[]
[burnup]
type = ADMaterialRealAux
variable = burnup
property = burnup
block = '1'
execute_on = timestep_end
[]
[]
[BCs]
[heat_removal]
type = ADFunctionDirichletBC
variable = temp
boundary = 'xzero exterior'
function = temp_function
[]
[]
[Materials]
[fission_rate]
type = ADGenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[burnup]
type = ADGenericFunctionMaterial
prop_names = burnup
prop_values = burnup
[]
[thermal]
type = ADHeatConductionMaterial
block = '1'
thermal_conductivity = 1.0
specific_heat = 1.0
[]
[fission_gas_release]
type = ADUCOFGR
block = '1'
average_grain_radius = 10e-6
triso_geometry = particle_geometry
temperature = temp
fast_neutron_flux = 1e15
cutoff_neutron_flux = 0.0
[]
[UCO_density]
type = ADParsedMaterial
block = '1'
property_name = density
expression = 11250.0
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 51'
line_search = 'none'
l_max_its = 50
l_tol = 1e-2
nl_max_its = 150
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
start_time = 0.0
#end_time = 7.5e6 # use to test full range of parameters
end_time = 1e4
num_steps = 140
dtmax = 2e6
dtmin = 1.0
[TimeStepper]
type = IterationAdaptiveDT
dt = 1e3
time_t = '1e4 1e5'
time_dt = '1e3 1e5'
[]
[]
[Postprocessors]
[temp]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = temp
execute_on = 'initial timestep_end'
[]
[burnup]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = burnup
execute_on = 'initial timestep_end'
[]
[fission_rate]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = fission_rate
execute_on = 'initial timestep_end'
[]
[_dt]
type = TimestepSize
[]
[FGP]
type = ADElementIntegralMaterialProperty
block = '1'
mat_prop = fis_gas_produced
execute_on = 'initial timestep_end'
[]
[FGR]
type = ADElementIntegralMaterialProperty
block = '1'
mat_prop = fis_gas_released
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
csv = true
[]
(test/tests/triso/mesh/mesh_with_coincident_nodes_1D.i)
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE2
coordinates = '0 .1 .1 .2'
mesh_density = '1 0 2'
block_names = 'fred wilma'
[]
[]
[Variables]
[var_a]
[]
[var_b]
[]
[]
[Kernels]
[Diffusion_a]
type = Diffusion
variable = var_a
[]
[Diffusion_b]
type = Diffusion
variable = var_b
[]
[]
[BCs]
[var_a_1]
type = DirichletBC
variable = var_a
boundary = xzero
value = 0.0
[]
[var_a_2]
type = DirichletBC
variable = var_a
boundary = fred_outer_boundary
value = 1.5
[]
[var_a_3]
type = DirichletBC
variable = var_a
boundary = wilma_inner_boundary
value = 1.5
[]
[var_a_4]
type = DirichletBC
variable = var_a
boundary = exterior
value = 3.0
[]
[var_b_1]
type = DirichletBC
variable = var_b
boundary = fred_inner_boundary
value = 0.0
[]
[var_b_2]
type = DirichletBC
variable = var_b
boundary = fred_wilma_boundary
value = 1.5
[]
[var_b_3]
type = DirichletBC
variable = var_b
boundary = wilma_outer_boundary
value = 3.0
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 51'
start_time = 0.0
end_time = 1.0
dt = 1.0
[]
[Outputs]
# Define output file(s)
time_step_interval = 1
exodus = true
[console]
type = Console
max_rows = 25
[]
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_3c/case_3c.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 250e-6 350e-6 390e-6 425e-6 465e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
[]
[Variables]
[conc_Cs]
[]
[]
[ICs]
[conc_Cs]
type = ConstantIC
block = fuel
value = 1
variable = conc_Cs
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1873.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = 'if(t<720000,1873.15,2073.15)'
variable = temperature
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[]
[Materials]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
# 5.5e-14*exp(2/5) = 8.2e-14
d1 = 8.2e-14 # m^2/s
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 1e-20
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 1440000
num_steps = 1000
dt = 1800
dtmax = 1800
dtmin = 1800
[]
[Postprocessors]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
execute_on = final
[]
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_2b/case_2b.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 250e-6 350e-6 390e-6'
mesh_density = '50 30 15'
block_names = 'fuel buffer IPyC'
[]
[]
[Problem]
[]
[Variables]
[conc_Cs]
[]
[]
[ICs]
[conc_Cs]
type = ConstantIC
block = fuel
value = 1
variable = conc_Cs
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1873.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[]
[Materials]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 1e-20
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 720000
num_steps = 700
dt = 3600
dtmax = 3600
dtmin = 3600
[]
[Postprocessors]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
execute_on = final
[]
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_1/case_1_1D.i)
#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# See also Hales, et al., Multidimensional multiphysics simulation of TRISO
# particle fuel, JNM, 443, 2013. https://doi.org/10.1016/j.jnucmat.2013.07.070
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark. The best way to do this is to compare
# results with information in the JNM article.
#
[GlobalParams]
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
use_displaced_mesh = false
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.5e-4 2.5e-4 3.5e-4 3.85e-4'
mesh_density = '24 0 40 64'
block_names = 'fuel buffer SiC'
[]
[]
[Variables]
[disp_x]
[]
[temp]
initial_condition = 1273.0
[]
[]
[AuxVariables]
[stress_xx]
order = CONSTANT
family = MONOMIAL
[]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[stress_zz]
order = CONSTANT
family = MONOMIAL
[]
[stress_xy]
order = CONSTANT
family = MONOMIAL
[]
[stress_yz]
order = CONSTANT
family = MONOMIAL
[]
[stress_xz]
order = CONSTANT
family = MONOMIAL
[]
[hydrostatic_stress]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
initial_condition = 0.0
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[all]
strain = small
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temp
[]
[heat]
type = HeatConduction
variable = temp
[]
[]
[AuxKernels]
[stress_xx]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xx
index_i = 0
index_j = 0
execute_on = timestep_end
[]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[stress_zz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_zz
index_i = 2
index_j = 2
execute_on = timestep_end
[]
[stress_xy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xy
index_i = 0
index_j = 1
execute_on = timestep_end
[]
[stress_yz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yz
index_i = 1
index_j = 2
execute_on = timestep_end
[]
[stress_xz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xz
index_i = 0
index_j = 2
execute_on = timestep_end
[]
[hydrostatic_stress]
type = RankTwoScalarAux
rank_two_tensor = stress
variable = hydrostatic_stress
scalar_type = hydrostatic
execute_on = timestep_end
[]
[]
[BCs]
# pin particle along symmetry planes
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
# fix temperature on free surface
[freesurf_temp]
type = DirichletBC
variable = temp
boundary = exterior
value = 1273.0
[]
# exterior and internal pressures
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[interior_pressure_x]
type = Pressure
variable = disp_x
boundary = SiC_inner_boundary
factor = 25e6
[]
[]
[Materials]
[stress]
type = ComputeLinearElasticStress
block = 'fuel buffer SiC'
[]
[fuel_thermal] # temperature and burnup dependent thermal properties of UO2 (BISON kernel)
type = UO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temp
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 1
poissons_ratio = 0.345
[]
[fuel_den]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10800.0
[]
[buffer_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 1
poissons_ratio = 0.345
[]
[buffer_temp]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[buffer_den]
type = StrainAdjustedDensity
strain_free_density = 950 #kg/m^3
block = buffer
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_temp]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9 # J/m-s-K
specific_heat = 620.0 # J/kg-K
[]
[SiC_den]
type = StrainAdjustedDensity
strain_free_density = 3200.0 # kg/m^3
block = SiC
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temp
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 1
dt = 1
[]
[Postprocessors]
[max_xx]
type = ElementExtremeValue
variable = stress_xx
[]
[max_yy]
type = ElementExtremeValue
variable = stress_yy
[]
[max_zz]
type = ElementExtremeValue
variable = stress_zz
[]
[]
[PerformanceMetricOutputs]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = true
csv = true
perf_graph = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_4d/case_4d.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.08
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 250e-6 350e-6 390e-6 425e-6 465e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
bias = '1 1.25 1.25 1.25 1.25'
dual_bias = '0.8 0.8 0.8 0.8 1'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[conc_Ag]
[]
[conc_Kr]
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1273.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Kr_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
[]
[mass_Kr_dt]
type = TimeDerivative
variable = conc_Kr
[]
[mass_Kr]
type = ArrheniusDiffusion
variable = conc_Kr
arrhenius_prpty_name = arrhenius_diffusion_coef_Kr
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Kr]
type = SpeciesSourceRate
variable = conc_Kr
property_name = Kr_generation
block = fuel
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[Kr_diff_coef]
type = MaterialRealAux
variable = Kr_diff_coef
property = arrhenius_diffusion_coef_Kr
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = 'if(t<4.3200001e7,1273.15,if(t<4.3920001e7,1873.15,2073.15))'
variable = temperature
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[freesurf_conc_Kr]
type = DirichletBC
variable = conc_Kr
boundary = exterior
value = 0.0
[]
[]
[Materials]
[burnup]
type = GenericFunctionMaterial
block = fuel
prop_names = 'burnup'
prop_values = 'if(t<4.3200001e7,0.1/4.32e7*t,0.1)'
[]
[fission_rate]
type = GenericFunctionMaterial
block = fuel
prop_names = 'fission_rate'
# 5.581219e19 = 0.1/4.32e7*10810/.27*6.0221409e23
prop_values = 'if(t<4.3200001e7,5.581219e19,0)'
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Cs_generation
kind = Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
# 6.22285e6 = 1e-6/6.3e-8/exp(-222e3/8.3145/2073.15)
d1_function = 'if(t<4.3920001e7,1,6.22285e6)'
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = 'if(t<4.3200001e7,exp(2e25/4.32e7*t/5e25),if(t<4.3920001e7,(1e-6-1.6e-2*exp(-514e3/8.3145/1873.15))/5.5e-14/exp(-125e3/8.3145/1873.15),(1e-6-1.6e-2*exp(-514e3/8.3145/2073.15))/5.5e-14/exp(-125e3/8.3145/2073.15)))'
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
# 6.22285e6 = 1e-6/6.3e-8/exp(-222e3/8.3145/2073.15)
d1_function = 'if(t<4.3920001e7,1,6.22285e6)'
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Ag_generation
kind = Ag
[]
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
# 1.431468e6 = 1e-6/5.3e-9/exp(-154e3/8.3145/2073.15)
d1_function = 'if(t<4.3920001e7,1,1.431468e6)'
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[SiC_conc_Ag]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
d1_function = 'if(t<4.3200001e7,1,if(t<4.3920001e7,1e-6/3.6e-9/exp(-215e3/8.3145/1873.15),1e-6/3.6e-9/exp(-215e3/8.3145/2073.15)))'
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
# 1.431468e6 = 1e-6/5.3e-9/exp(-154e3/8.3145/2073.15)
d1_function = 'if(t<4.3920001e7,1,1.431468e6)'
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[fuel_conc_Kr]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 8.8e-15 # m^2/s
q1 = 54e3 # J/mol
d2 = 6.0e-1
q2 = 480e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Kr
[]
[mass_source_Kr_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Kr_generation
kind = custom
additional_function = '0.002717/6.022e23'
additional_function_property = fission_rate
[]
[buffer_conc_Kr]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Kr
[]
[IPyC_conc_Kr]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 2.9e-8 # m^2/s
# 7.40285e8 = 1e-6 / (2.9e-8*exp(-291e3/8.3145/2073.15))
d1_function = 'if(t<4.3920001e7,1,7.40285e8)'
q1 = 291e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Kr
[]
[SiC_conc_Kr]
type = ArrheniusDiffusionCoef
block = SiC
# See "Diffusion Modeling of Fission Product Release during Depressurized Core Conduction Cooldown Conditions,"
# R. C. Martin, https://www.osti.gov/servlets/purl/5719008
d1 = 1.4e-9 # m^2/s
d1_function = 'if(t<4.3200001e7,1,if(t<4.3920001e7,1e-6/1.4e-9/exp(-265.98e3/8.3145/1873.15),1e-6/1.4e-9/exp(-265.98e3/8.3145/2073.15)))'
q1 = 265.98e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Kr
[]
[OPyC_conc_Kr]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 2.9e-8 # m^2/s
# 7.40285e8 = 1e-6 / (2.9e-8*exp(-291e3/8.3145/2073.15))
d1_function = 'if(t<4.3920001e7,1,7.40285e8)'
q1 = 291e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Kr
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs conc_Kr'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 5e-19
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 4.464e7
num_steps = 1000
dt = 86400
dtmax = 86400
#dtmin = 86400
[TimeStepper]
type = FunctionDT
function = 'if(t<4.32e7,86400,3600)'
[]
[]
[Postprocessors]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
[]
[release_Kr_inc]
type = SideIntegralMassFlux
variable = conc_Kr
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Kr
execute_on = 'initial timestep_end'
[]
[released_Kr]
type = TimeIntegratedPostprocessor
value = release_Kr_inc
execute_on = 'initial timestep_end'
[]
[total_Kr]
type = ElementIntegralMaterialProperty
mat_prop = Kr_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Kr_released]
type = FractionalRelease
released = released_Kr
total = total_Kr
[]
[retained_Kr]
type = ElementIntegralVariablePostprocessor
variable = conc_Kr
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
execute_on = final
[]
[]
(test/tests/triso_pebble/1D_pebble_picard.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
flux_conversion_factor = 0.85
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 0.0138 0.018 0.02'
mesh_density = '5 10 10'
block_names = 'core fuel shell'
[]
[]
[Distributions]
[normal_kernel_r]
type = TruncatedNormal
mean = 213.35e-6
standard_deviation = 4.4e-6
lower_bound = 1.9575e-04
upper_bound = 2.3095e-04
[]
[normal_buffer_t]
type = TruncatedNormal
mean = 98.9e-6
standard_deviation = 8.4e-6
lower_bound = 6.53e-05
upper_bound = 1.325e-04
[]
[normal_ipyc_t]
type = TruncatedNormal
mean = 40.4e-6
standard_deviation = 2.5e-6
lower_bound = 3.0400e-05
upper_bound = 5.0400e-05
[]
[normal_sic_t]
type = TruncatedNormal
mean = 35.2e-6
standard_deviation = 1.2e-6
lower_bound = 3.0400e-05
upper_bound = 4.0000e-05
[]
[normal_opyc_t]
type = TruncatedNormal
mean = 43.4e-6
standard_deviation = 2.9e-6
lower_bound = 3.1800e-05
upper_bound = 5.5000e-05
[]
[]
[Samplers]
[sample]
type = MonteCarlo
num_rows = 10
distributions = 'normal_kernel_r normal_buffer_t normal_ipyc_t normal_sic_t normal_opyc_t'
execute_on = 'PRE_MULTIAPP_SETUP'
[]
[]
[MultiApps]
[sub]
type = SamplerTransientMultiApp
input_files = triso_1d.i
sampler = sample
execute_on = 'TIMESTEP_BEGIN'
mode = normal
[]
[]
[DiracKernels]
[vpp_point_source]
type = TRISOMonteCarloPointSource
variable = temperature
point_source_values = released_heat_inc
value_name = released_heat_inc:released_heat_inc
point_source_location = point_source_location
[]
[]
[UserObjects]
[point_source_location]
type = TRISOMonteCarloPointSourceLocation
min_radius = 0.0138
max_radius = 0.018
geometry = SPHERE
sampler = sample
fuel_element_blocks = fuel
execute_on = 'INITIAL'
[]
[]
[Transfers]
[released_heat_inc]
type = SamplerPostprocessorTransfer
from_multi_app = sub
sampler = sample
to_vector_postprocessor = released_heat_inc
from_postprocessor = released_heat_inc
[]
[sub_temp_bc]
type = SamplerPostprocessorTransfer
from_multi_app = sub
sampler = sample
to_vector_postprocessor = temp_bc
from_postprocessor = aver_temp_exterior
[]
[temp_bc]
type = MultiAppVectorPostprocessorTransfer
to_multi_app = sub
vector_postprocessor = sample_points
postprocessor = temp_bc
vector_name = temperature
[]
[]
[Controls]
[cmdline]
type = MultiAppSamplerControl
multi_app = sub
sampler = sample
param_names = 'kernel_radius buffer_thickness IPyC_thickness SiC_thickness OPyC_thickness'
[]
[]
[VectorPostprocessors]
[sample_points]
type = TRISOMonteCarloPointValueSampler
variable = temperature
execute_on = 'INITIAL TIMESTEP_BEGIN'
point_source_location = point_source_location
[]
[sampler_data]
type = SamplerData
execute_on = 'TIMESTEP_BEGIN'
sampler = sample
[]
[released_heat_inc]
type = StochasticResults
execute_on = 'TIMESTEP_BEGIN'
[]
[temp_bc]
type = StochasticResults
execute_on = 'INITIAL TIMESTEP_BEGIN'
[]
[point_source_output]
type = TRISOMonteCarloPointSourceOutput
vector_postprocessor = released_heat_inc
value_name = released_heat_inc:released_heat_inc
point_source_location = point_source_location
[]
[temp_bc_output]
type = TRISOMonteCarloPointSourceOutput
vector_postprocessor = temp_bc
value_name = sub_temp_bc:aver_temp_exterior
point_source_location = point_source_location
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[temperature]
initial_condition = 773.15
[]
[]
[AuxVariables]
[density]
order = CONSTANT
family = MONOMIAL
[]
[thermal_conductivity]
order = CONSTANT
family = MONOMIAL
[]
[specific_heat]
order = CONSTANT
family = MONOMIAL
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = FissionRateHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[density]
type = MaterialRealAux
variable = density
property = density
block = 'core fuel shell'
execute_on = 'initial linear'
[]
[thermal_conductivity]
type = MaterialRealAux
variable = thermal_conductivity
property = thermal_conductivity
block = 'core fuel shell'
execute_on = timestep_end
[]
[specific_heat]
type = MaterialRealAux
variable = specific_heat
property = specific_heat
block = 'core fuel shell'
execute_on = timestep_end
[]
[]
[BCs]
[coolant_temp]
type = DirichletBC
variable = temperature
boundary = exterior
value = 773.15
[]
[]
[Functions]
[power_history]
type = PiecewiseLinear
x = '0 76e6'
y = '1 1'
[]
[fission_rate]
type = LinearCombinationFunction
functions = power_history
w = 5.75e19
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
flux_function = power_history
factor = 6.28e17
[]
[fueled_region_thermal]
type = GraphiteMatrixThermal
block = fuel
graphite_grade = A3_27_1800
packing_fraction = 0.22
temperature = temperature
initial_matrix_density = 1750.0
[]
[fuel_region_density]
type = ParsedMaterial
block = fuel
property_name = density
expression = 1750.0
[]
[shell_region_thermal]
type = GraphiteMatrixThermal
block = shell
graphite_grade = A3_27_1800
packing_fraction = 0.0
temperature = temperature
initial_matrix_density = 1750.0
[]
[shell_region_density]
type = ParsedMaterial
block = shell
property_name = density
expression = 1750.0
[]
[core_region_thermal]
type = GraphiteMatrixThermal
block = core
graphite_grade = A3_27_1800
packing_fraction = 0.0
temperature = temperature
initial_matrix_density = 1400.0
[]
[core_region_density]
type = ParsedMaterial
block = core
property_name = density
expression = 1400.0
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'temperature'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-12
nl_abs_tol = 1e-12
nl_max_its = 15
nl_forced_its = 2
l_tol = 1e-5
l_max_its = 30
start_time = 0.0
dt = 20000
num_steps = 2
fixed_point_max_its = 20
accept_on_max_fixed_point_iteration = true
fixed_point_rel_tol = 1e-8
fixed_point_abs_tol = 1e-10
[]
[Outputs]
exodus = true
[]
(test/tests/triso/UCOFGR/UCOFGR_out_of_pile.i)
# Fission Gas Release Model High Temperature
# The geometry is a 1D sphere with a diameter of 425 micrometers and an average
# grain radius of 10 microns.
# The fission gas yield was set to 0.297.
# Safety testing is hypothetically occurs at 2.5e4.
# The temperature is ramped from 673.15 to 3073.15 K.
# The fission rate density is ramped from 0 to 1.1625e21 fission/m^3-s
# (3.72e10 W/m^3) over 1e4 seconds and held constant.
# The density of the kernel is set to 11250 kg/m^3, the Oxygen to Uranium ratio
# is set to 1.5, the Carbon to Uranium ratio is set to 0.4, and the initial
# U-235 enrichment is set to 15%.
#
[GlobalParams]
order = FIRST
family = LAGRANGE
O_U = 1.5
C_U = 0.4
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.125e-4'
mesh_density = '6'
block_names = 'fuel'
[]
[]
[Functions]
[fast_n_flux_fcn]
type = ParsedFunction
expression = 'if( t>=2.5e4, 0.0, 0.2 * t)'
[]
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = '2'
outer_SiC = '2'
outer_IPyC = '2'
inner_IPyC = '2'
outer_buffer = '2'
outer_kernel = '2'
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temp]
initial_condition = 673.15
[]
[]
[AuxVariables]
[fission_rate]
block = '1'
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = '1'
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[fission_rate]
type = PiecewiseLinear
x = '0 1e3 1.0e6'
y = '0 1.1625e21 0'
[]
[scaled_time]
type = ParsedFunction
# molar mass / Avogadro's number / density
# 0.266 / 6.022e23 / 11250 = 3.926e-29
expression = '3.926e-29*t'
[]
[burnup]
type = CompositeFunction
functions = 'fission_rate scaled_time'
[]
[temp_function]
type = PiecewiseLinear
x = '0 7.5e4'
y = '673.15 3073.15'
[]
[]
[Kernels]
[heat]
type = HeatConduction
variable = temp
[]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temp
[]
[]
[AuxKernels]
[fission_rate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = '1'
execute_on = timestep_end
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = '1'
execute_on = timestep_end
[]
[]
[BCs]
[heat_removal]
type = FunctionDirichletBC
variable = temp
boundary = '1'
function = temp_function
[]
[]
[Materials]
[fast_neutron_flux]
type = GenericFunctionMaterial
prop_names = fast_neutron_flux
prop_values = fast_n_flux_fcn
outputs = all
[]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[burnup]
type = GenericFunctionMaterial
prop_names = burnup
prop_values = burnup
[]
[thermal]
type = HeatConductionMaterial
block = '1'
thermal_conductivity = 1.0
specific_heat = 1.0
[]
[fission_gas_release]
type = UCOFGR
block = '1'
average_grain_radius = 10e-6
triso_geometry = particle_geometry
temperature = temp
cutoff_neutron_flux = 0.0
[]
[UCO_density]
type = ParsedMaterial
block = '1'
property_name = density
expression = 11250.0
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 51'
line_search = 'none'
l_max_its = 50
l_tol = 1e-2
nl_max_its = 150
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
start_time = 0.0
#end_time = 7.5e6 # use to test full range of parameters
end_time = 1e5
num_steps = 140
dtmax = 2e6
dtmin = 1.0
[TimeStepper]
type = IterationAdaptiveDT
dt = 1e3
time_t = '1e4 1e5'
time_dt = '1e3 1e5'
[]
[]
[Postprocessors]
[temp]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = temp
execute_on = 'initial timestep_end'
[]
[burnup]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = burnup
execute_on = 'initial timestep_end'
[]
[fission_rate]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = fission_rate
execute_on = 'initial timestep_end'
[]
[_dt]
type = TimestepSize
[]
[FGP]
type = ElementIntegralMaterialProperty
block = '1'
mat_prop = fis_gas_produced
execute_on = 'initial timestep_end'
[]
[FGR]
type = ElementIntegralMaterialProperty
block = '1'
mat_prop = fis_gas_released
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
csv = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_4b/case_4b_1D.i)
#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# See also Hales, et al., Multidimensional multiphysics simulation of TRISO
# particle fuel, JNM, 443, 2013. https://doi.org/10.1016/j.jnucmat.2013.07.070
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark. The best way to do this is to compare
# results with information in the JNM article.
#
[GlobalParams]
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
use_displaced_mesh = false
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.5e-4 2.5e-4 3.5e-4 3.5e-4 3.9e-4 4.25e-4'
mesh_density = '12 0 20 0 16 16'
block_names = 'fuel buffer IPyC SiC'
[]
[]
[Variables]
[disp_x]
[]
[temperature]
initial_condition = 1273.0
[]
[]
[Functions]
[eigenstrain]
type = ParsedFunction
expression = '-0.005*t'
[]
[fluence]
type = ParsedFunction
expression = '3.75e17*t'
[]
[k_function]
type = ParsedFunction
expression = '2.715e-29'
[]
[]
[AuxVariables]
[stress_xx]
order = CONSTANT
family = MONOMIAL
[]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[stress_zz]
order = CONSTANT
family = MONOMIAL
[]
[stress_xy]
order = CONSTANT
family = MONOMIAL
[]
[stress_yz]
order = CONSTANT
family = MONOMIAL
[]
[stress_xz]
order = CONSTANT
family = MONOMIAL
[]
[hydrostatic_stress]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
initial_condition = 0.0
[]
[fluence]
initial_condition = 0.0
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[IPyC]
block = IPyC
strain = small
incremental = true
[]
[rest]
block = 'fuel buffer SiC'
strain = small
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
[]
[heat]
type = HeatConduction
variable = temperature
[]
[]
[AuxKernels]
[stress_xx]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xx
index_i = 0
index_j = 0
execute_on = timestep_end
[]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[stress_zz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_zz
index_i = 2
index_j = 2
execute_on = timestep_end
[]
[stress_xy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xy
index_i = 0
index_j = 1
execute_on = timestep_end
[]
[stress_yz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yz
index_i = 1
index_j = 2
execute_on = timestep_end
[]
[stress_xz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xz
index_i = 0
index_j = 2
execute_on = timestep_end
[]
[hydrostatic_stress]
type = RankTwoScalarAux
rank_two_tensor = stress
variable = hydrostatic_stress
scalar_type = hydrostatic
execute_on = timestep_end
[]
[fluence]
type = FunctionAux
variable = fluence
function = fluence
execute_on = timestep_begin
[]
[]
[BCs]
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[freesurf_temperature]
type = DirichletBC
variable = temperature
boundary = exterior
value = 1273.0
[]
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[interior_pressure_x]
type = Pressure
variable = disp_x
boundary = IPyC_inner_boundary
factor = 25e6
[]
[]
[Materials]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 3.75e17 # n/m^2-sec
[]
[stress]
type = ComputeLinearElasticStress
block = 'fuel buffer SiC'
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
[]
[IPyC_stress]
type = PyCCreep
block = IPyC
k = k_function
temperature = temperature
[]
[fuel_thermal]
type = UO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temperature
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 1
poissons_ratio = 0.345
[]
[fuel_den]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10800.0
[]
[buffer_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 1
poissons_ratio = 0.345
[]
[buffer_temperature]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5
specific_heat = 720.0
[]
[buffer_den]
type = StrainAdjustedDensity
strain_free_density = 950
block = buffer
[]
[IPyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = IPyC
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[IPyC_temperature]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_den]
type = StrainAdjustedDensity
strain_free_density = 1900.0
block = IPyC
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_temperature]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9
specific_heat = 620.0
[]
[SiC_den]
type = StrainAdjustedDensity
strain_free_density = 3180.0
block = SiC
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Dampers]
[temperature]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 8e7
dt = 1.0
dtmax = 5e6
dtmin = 1.0e4
[TimeStepper]
type = IterationAdaptiveDT
dt = 1
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[max_xx_IPyC]
type = ElementExtremeValue
variable = stress_xx
block = IPyC
[]
[max_yy_IPyC]
type = ElementExtremeValue
variable = stress_yy
block = IPyC
[]
[max_zz_IPyC]
type = ElementExtremeValue
variable = stress_zz
block = IPyC
[]
[max_xx_SiC]
type = ElementExtremeValue
variable = stress_xx
block = SiC
[]
[max_yy_SiC]
type = ElementExtremeValue
variable = stress_yy
block = SiC
[]
[max_zz_SiC]
type = ElementExtremeValue
variable = stress_zz
block = SiC
[]
[]
[PerformanceMetricOutputs]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = true
csv = true
perf_graph = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_6/case_6_1D.i)
#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# See also Hales, et al., Multidimensional multiphysics simulation of TRISO
# particle fuel, JNM, 443, 2013. https://doi.org/10.1016/j.jnucmat.2013.07.070
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark. The best way to do this is to compare
# results with information in the JNM article.
#
[GlobalParams]
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '3.50e-4 3.90e-4 4.25e-4 4.65e-4'
mesh_density = '4 4 4'
block_names = 'IPyC SiC OPyC'
[]
[]
[Variables]
[disp_x]
[]
[]
[Functions]
[radial_eigenstrain]
type = ParsedFunction
expression = 't*(1.36334e-3/4.0*t*t*t - 7.77024e-3/3.0*t*t + 2.00861e-2/2.0*t - 2.22642e-2)'
[]
[tangential_eigenstrain]
type = ParsedFunction
expression = 't*(-3.53804e-4/4.0*t*t*t + 1.69251e-3/3.0*t*t + 2.63307e-3/2.0*t - 1.91253e-2)'
[]
[pressure]
type = ParsedFunction
expression = '26.2e6/8e7*t'
[]
[k_function]
type = ParsedFunction
expression = '2.715e-29'
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1273.0
[]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[stress_zz]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
initial_condition = 0.0
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[IPyC_OPyC]
block = 'IPyC OPyC'
strain = finite
eigenstrain_names = pyc_eigenstrain
[]
[SiC]
block = SiC
strain = finite
[]
[]
[AuxKernels]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[stress_zz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_zz
index_i = 2
index_j = 2
execute_on = timestep_end
[]
[]
[BCs]
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[interior_pressure_x]
type = Pressure
variable = disp_x
boundary = IPyC_inner_boundary
factor = 1.0
function = pressure
[]
[]
[Materials]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 3.75e17 # n/m^2-sec
[]
[stress]
type = ComputeFiniteStrainElasticStress
block = 'SiC'
[]
[PyC_stress]
type = PyCCreep
block = 'IPyC OPyC'
k = k_function
temperature = temperature
[]
[PyC_density]
type = StrainAdjustedDensity
block = 'IPyC OPyC'
strain_free_density = 1900.0
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'IPyC OPyC'
[]
[PyC_eigenstrain]
type = PyCIrradiationEigenstrain
block = 'IPyC OPyC'
radial_eigenstrain_function = radial_eigenstrain
tangential_eigenstrain_function = tangential_eigenstrain
eigenstrain_name = pyc_eigenstrain
[]
[PyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = 'IPyC OPyC'
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 8e7
dt = 1.0
dtmax = 1e6
dtmin = 1.0e4
[TimeStepper]
type = IterationAdaptiveDT
dt = 1
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[max_yy_IPyC]
type = ElementExtremeValue
variable = stress_yy
block = IPyC
[]
[max_yy_SiC]
type = ElementExtremeValue
variable = stress_yy
block = SiC
[]
[]
[PerformanceMetricOutputs]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = true
csv = true
perf_graph = true
[]
(test/tests/triso/UNFGR/ad_UNFGR.i)
[GlobalParams]
order = FIRST
family = LAGRANGE
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.125e-4'
mesh_density = '6'
block_names = 'fuel'
[]
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = '2'
outer_SiC = '2'
outer_IPyC = '2'
inner_IPyC = '2'
outer_buffer = '2'
outer_kernel = '2'
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temp]
initial_condition = 673.15
[]
[]
[AuxVariables]
[fission_rate]
block = '1'
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = '1'
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[fission_rate]
type = PiecewiseLinear
x = '0 1e4 1e8'
y = '0 1.1625e21 1.1625e21'
[]
[scaled_time]
type = ParsedFunction
# molar mass / Avogadro's number / density
# 0.266 / 6.022e23 / 11250 = 3.926e-29
expression = '3.926e-29*t'
[]
[burnup]
type = CompositeFunction
functions = 'fission_rate scaled_time'
[]
[temp_function]
type = PiecewiseLinear
x = '0 7.5e6'
y = '673.15 3073.15'
[]
[]
[Kernels]
[heat]
type = ADHeatConduction
variable = temp
[]
[heat_ie]
type = ADHeatConductionTimeDerivative
variable = temp
[]
[]
[AuxKernels]
[fission_rate]
type = ADMaterialRealAux
variable = fission_rate
property = fission_rate
block = '1'
execute_on = timestep_end
[]
[burnup]
type = ADMaterialRealAux
variable = burnup
property = burnup
block = '1'
execute_on = timestep_end
[]
[]
[BCs]
[heat_removal]
type = ADFunctionDirichletBC
variable = temp
boundary = '1'
function = temp_function
[]
[]
[Materials]
[fission_rate]
type = ADGenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[burnup]
type = ADGenericFunctionMaterial
prop_names = burnup
prop_values = burnup
[]
[thermal]
type = ADHeatConductionMaterial
block = '1'
thermal_conductivity = 1.0
specific_heat = 1.0
[]
[fission_gas_release]
type = ADUNFGR
block = '1'
average_grain_radius = 10e-6
triso_geometry = particle_geometry
temperature = temp
[]
[UN_density]
type = ADParsedMaterial
block = '1'
property_name = density
expression = 13760
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 51'
line_search = 'none'
l_max_its = 50
l_tol = 1e-2
nl_max_its = 150
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
start_time = 0.0
#end_time = 7.5e6 # use to test full range of parameters
end_time = 1e4
num_steps = 140
dtmax = 2e6
dtmin = 1.0
[TimeStepper]
type = IterationAdaptiveDT
dt = 1e3
time_t = '1e4 1e5'
time_dt = '1e3 1e5'
[]
[]
[Postprocessors]
[temp]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = temp
execute_on = 'initial timestep_end'
[]
[burnup]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = burnup
execute_on = 'initial timestep_end'
[]
[fission_rate]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = fission_rate
execute_on = 'initial timestep_end'
[]
[_dt]
type = TimestepSize
[]
[FGP]
type = ADElementIntegralMaterialProperty
block = '1'
mat_prop = fis_gas_produced
execute_on = 'initial timestep_end'
[]
[FGR]
type = ADElementIntegralMaterialProperty
block = '1'
mat_prop = fis_gas_released
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
csv = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_4a/case_4a_1D.i)
#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# See also Hales, et al., Multidimensional multiphysics simulation of TRISO
# particle fuel, JNM, 443, 2013. https://doi.org/10.1016/j.jnucmat.2013.07.070
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark. The best way to do this is to compare
# results with information in the JNM article.
#
[GlobalParams]
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
use_displaced_mesh = false
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.5e-4 2.5e-4 3.5e-4 3.5e-4 3.9e-4 4.25e-4'
mesh_density = '12 0 20 0 16 16'
block_names = 'fuel buffer IPyC SiC'
[]
[]
[Variables]
[disp_x]
[]
[temp]
initial_condition = 1273.0
[]
[]
[Functions]
[eigenstrain]
type = ParsedFunction
expression = '-0.005*t'
[]
[fluence]
type = ParsedFunction
expression = '3.75e17*t'
[]
[]
[AuxVariables]
[stress_xx]
order = CONSTANT
family = MONOMIAL
[]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[stress_zz]
order = CONSTANT
family = MONOMIAL
[]
[stress_xy]
order = CONSTANT
family = MONOMIAL
[]
[stress_yz]
order = CONSTANT
family = MONOMIAL
[]
[stress_xz]
order = CONSTANT
family = MONOMIAL
[]
[hydrostatic_stress]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
initial_condition = 0.0
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[IPyC]
block = IPyC
strain = small
eigenstrain_names = ipyc_eigenstrain
[]
[rest]
block = 'fuel buffer SiC'
strain = small
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temp
[]
[heat]
type = HeatConduction
variable = temp
[]
[]
[AuxKernels]
[stress_xx]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xx
index_i = 0
index_j = 0
execute_on = timestep_end
[]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[stress_zz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_zz
index_i = 2
index_j = 2
execute_on = timestep_end
[]
[stress_xy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xy
index_i = 0
index_j = 1
execute_on = timestep_end
[]
[stress_yz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yz
index_i = 1
index_j = 2
execute_on = timestep_end
[]
[stress_xz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xz
index_i = 0
index_j = 2
execute_on = timestep_end
[]
[hydrostatic_stress]
type = RankTwoScalarAux
rank_two_tensor = stress
variable = hydrostatic_stress
scalar_type = hydrostatic
execute_on = timestep_end
[]
[]
[BCs]
# pin particle along symmetry planes
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
# fix temperature on free surface
[freesurf_temp]
type = DirichletBC
variable = temp
boundary = exterior
value = 1273.0
[]
# exterior and internal pressures
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[interior_pressure_x]
type = Pressure
variable = disp_x
boundary = IPyC_inner_boundary
factor = 25e6
[]
[]
[Materials]
[fluence]
type = GenericFunctionMaterial
prop_names = fast_neutron_fluence
prop_values = fluence
[]
[stress]
type = ComputeLinearElasticStress
block = 'fuel buffer IPyC SiC'
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
[]
[IPyC_eigenstrain]
type = PyCIrradiationEigenstrain
radial_eigenstrain_function = eigenstrain
tangential_eigenstrain_function = eigenstrain
eigenstrain_name = ipyc_eigenstrain
[]
[fuel_thermal] # temperature and burnup dependent thermal properties of UO2 (BISON kernel)
type = UO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temp
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 1
poissons_ratio = 0.345
[]
[fuel_den]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10800.0
[]
[buffer_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 1
poissons_ratio = 0.345
[]
[buffer_temp]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[buffer_den]
type = StrainAdjustedDensity
strain_free_density = 950 #kg/m^3
block = buffer
[]
[IPyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = IPyC
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[IPyC_temp]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[IPyC_den]
type = StrainAdjustedDensity
strain_free_density = 1900.0 # kg/m^3
block = IPyC
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_temp]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9 # J/m-s-K
specific_heat = 620.0 # J/kg-K
[]
[SiC_den]
type = StrainAdjustedDensity
strain_free_density = 3180.0 # kg/m^3
block = SiC
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temp
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 8e7
dt = 1.0
dtmax = 5e6
dtmin = 1.0e4
[TimeStepper]
type = IterationAdaptiveDT
dt = 1
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[max_xx_IPyC]
type = ElementExtremeValue
variable = stress_xx
block = IPyC
[]
[max_yy_IPyC]
type = ElementExtremeValue
variable = stress_yy
block = IPyC
[]
[max_zz_IPyC]
type = ElementExtremeValue
variable = stress_zz
block = IPyC
[]
[max_xx_SiC]
type = ElementExtremeValue
variable = stress_xx
block = SiC
[]
[max_yy_SiC]
type = ElementExtremeValue
variable = stress_yy
block = SiC
value_type = min
[]
[max_zz_SiC]
type = ElementExtremeValue
variable = stress_zz
block = SiC
value_type = min
[]
[]
[PerformanceMetricOutputs]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = true
csv = true
perf_graph = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_2/case_2_1D.i)
#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# See also Hales, et al., Multidimensional multiphysics simulation of TRISO
# particle fuel, JNM, 443, 2013. https://doi.org/10.1016/j.jnucmat.2013.07.070
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark. The best way to do this is to compare
# results with information in the JNM article.
#
[GlobalParams]
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
use_displaced_mesh = false
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.5e-4 2.5e-4 3.5e-4 4.4e-4'
mesh_density = '24 0 40 64'
block_names = 'fuel buffer IPyC'
[]
[]
[Variables]
[disp_x]
[]
[temp]
initial_condition = 1273.0
[]
[]
[AuxVariables]
[stress_xx]
order = CONSTANT
family = MONOMIAL
[]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[stress_zz]
order = CONSTANT
family = MONOMIAL
[]
[stress_xy]
order = CONSTANT
family = MONOMIAL
[]
[stress_yz]
order = CONSTANT
family = MONOMIAL
[]
[stress_xz]
order = CONSTANT
family = MONOMIAL
[]
[hydrostatic_stress]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
initial_condition = 0.0
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[all]
strain = small
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temp
[]
[heat]
type = HeatConduction
variable = temp
[]
[]
[AuxKernels]
[stress_xx]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xx
index_i = 0
index_j = 0
execute_on = timestep_end
[]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[stress_zz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_zz
index_i = 2
index_j = 2
execute_on = timestep_end
[]
[stress_xy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xy
index_i = 0
index_j = 1
execute_on = timestep_end
[]
[stress_yz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yz
index_i = 1
index_j = 2
execute_on = timestep_end
[]
[stress_xz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xz
index_i = 0
index_j = 2
execute_on = timestep_end
[]
[hydrostatic_stress]
type = RankTwoScalarAux
rank_two_tensor = stress
variable = hydrostatic_stress
scalar_type = hydrostatic
execute_on = timestep_end
[]
[]
[BCs]
# pin particle along symmetry planes
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
# fix temperature on free surface
[freesurf_temp]
type = DirichletBC
variable = temp
boundary = exterior
value = 1273.0
[]
# exterior and internal pressures
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[interior_pressure_x]
type = Pressure
variable = disp_x
boundary = IPyC_inner_boundary
factor = 25e6
[]
[]
[Materials]
[stress]
type = ComputeLinearElasticStress
block = 'fuel buffer IPyC'
[]
[fuel_thermal] # temperature and burnup dependent thermal properties of UO2 (BISON kernel)
type = UO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temp
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 1
poissons_ratio = 0.345
[]
[fuel_den]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10800.0
[]
[buffer_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 1
poissons_ratio = 0.345
[]
[buffer_temp]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[buffer_den]
type = StrainAdjustedDensity
strain_free_density = 950 #kg/m^3
block = buffer
[]
[IPyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = IPyC
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[IPyC_temp]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[IPyC_den]
type = StrainAdjustedDensity
strain_free_density = 1900.0 # kg/m^3
block = IPyC
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temp
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 1.0
dt = 1.0
[]
[Postprocessors]
[max_xx]
type = ElementExtremeValue
variable = stress_xx
[]
[max_yy]
type = ElementExtremeValue
variable = stress_yy
[]
[max_zz]
type = ElementExtremeValue
variable = stress_zz
[]
[]
[PerformanceMetricOutputs]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = true
csv = true
perf_graph = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_6a/case_6a.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.0982
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 248.5e-6 342.5e-6 383.5e-6 419.5e-6 459.5e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
bias = '1 1.25 1.25 1.25 1.25'
dual_bias = '0.8 0.8 0.8 0.8 1'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[conc_Ag]
[]
[conc_Sr]
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1213.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Sr_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temperature]
type = PiecewiseLinear
data_file = temperature_history.dat
format = columns
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
[]
[mass_Sr_dt]
type = TimeDerivative
variable = conc_Sr
[]
[mass_Sr]
type = ArrheniusDiffusion
variable = conc_Sr
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Sr]
type = SpeciesSourceRate
variable = conc_Sr
property_name = Sr_generation
block = fuel
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[Sr_diff_coef]
type = MaterialRealAux
variable = Sr_diff_coef
property = arrhenius_diffusion_coef_Sr
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = temperature
variable = temperature
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[freesurf_conc_Sr]
type = DirichletBC
variable = conc_Sr
boundary = exterior
value = 0.0
[]
[]
[Materials]
[burnup]
type = GenericFunctionMaterial
block = fuel
prop_names = 'burnup'
prop_values = 'if(t<30326400,0.111/30326400*t,0.111)'
[]
[fission_rate]
type = GenericFunctionMaterial
block = fuel
prop_names = 'fission_rate'
# 8.825e19 = 0.111/30326400*10810/.27*6.0221409e23
prop_values = 'if(t<30326400,8.825e19,0)'
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Cs_generation
kind = Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = 'if(t<30326400,exp(5.5e25/30326400*t/5e25),exp(5.5e25/5e25))'
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Ag_generation
kind = Ag
[]
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[SiC_conc_Ag]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[fuel_conc_Sr]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 2.2e-3 # m^2/s
q1 = 488e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[mass_source_Sr_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Sr_generation
kind = Sr
[]
[buffer_conc_Sr]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[IPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[SiC_conc_Sr]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 1.2e-9 # m^2/s
q1 = 205e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[OPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs conc_Ag conc_Sr'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
automatic_scaling = true
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 5e-5
nl_abs_tol = 1e-13
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 31525200
num_steps = 1450
dt = 86400
dtmax = 86400
#dtmin = 86400
[TimeStepper]
type = FunctionDT
function = 'if(t<30326400,86400,
if(t<30430800,1800,
3600))'
[]
[]
[Postprocessors]
[_temp]
type = NodalExtremeValue
variable = temperature
[]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released_overall]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
start_time = 30326400
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial timestep_end'
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released_overall]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
start_time = 30326400
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
execute_on = 'initial timestep_end'
[]
[release_Sr_inc]
type = SideIntegralMassFlux
variable = conc_Sr
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
execute_on = 'initial timestep_end'
[]
[released_Sr]
type = TimeIntegratedPostprocessor
value = release_Sr_inc
execute_on = 'initial timestep_end'
[]
[total_Sr]
type = ElementIntegralMaterialProperty
mat_prop = Sr_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Sr_released_overall]
type = FractionalRelease
released = released_Sr
total = total_Sr
execute_on = 'initial timestep_end'
[]
[x_Sr_released]
type = FractionalRelease
released = released_Sr
total = total_Sr
execute_on = 'initial timestep_end'
start_time = 30326400
[]
[retained_Sr]
type = ElementIntegralVariablePostprocessor
variable = conc_Sr
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
[]
[out_final]
type = CSV
execute_on = final
[]
[]
(examples/TRISO/parfume/parfume_un.i)
# UN TRISO particle using several PARFUME models
[GlobalParams]
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
initial_enrichment = 0.1955 # [wt-]
flux_conversion_factor = 1.0 # convert E>0.10 to E>0.18 MeV
stress_free_temperature = 923.15 # used for thermal expansion
energy_per_fission = 3.204e-11 # [J/fission]
O_U = 1.5 # Initial Oxygen to Uranium atom ratio
C_U = 0.4 # Initial Carbon to Uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.125e-4 3.125e-4 3.125e-4 3.525e-4 3.875e-4 4.275e-4'
mesh_density = '6 6 0 6 8 6'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
[]
[]
[Variables]
[temperature]
initial_condition = 923.15
[]
[conc]
initial_condition = 0.0
scaling = 1e18
[]
[]
[AuxVariables]
[disp_y]
[]
[disp_z]
[]
[fission_rate]
block = fuel
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = fuel
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_flux]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
order = CONSTANT
family = MONOMIAL
[]
[gap_condSlave]
order = CONSTANT
family = MONOMIAL
[]
[density]
order = CONSTANT
family = MONOMIAL
[]
[thermal_conductivity]
order = CONSTANT
family = MONOMIAL
[]
[swelling]
order = CONSTANT
family = MONOMIAL
[]
[specific_heat]
order = CONSTANT
family = MONOMIAL
[]
[volumetric_IIDC_strain]
order = CONSTANT
family = MONOMIAL
[]
[radial_IIDC_strain]
order = CONSTANT
family = MONOMIAL
[]
[tangential_IIDC_strain]
order = CONSTANT
family = MONOMIAL
[]
[BAF]
order = CONSTANT
family = MONOMIAL
[]
[fis_gas_produced]
order = CONSTANT
family = MONOMIAL
[]
[fis_gas_released]
order = CONSTANT
family = MONOMIAL
[]
[gap_HTC]
order = CONSTANT
family = MONOMIAL
[]
[gap_distance]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[power_history]
type = PiecewiseLinear
x = '0 76e6 76.001e6'
y = '1 1 0'
[]
[fission_rate]
type = LinearCombinationFunction
functions = power_history
w = 3.89e19
[]
[temp_bc]
type = PiecewiseLinear
# A final temperature ramp is not possible with the UNThermal model since
# its range of applicability ends at 1800 K
# To use the model beyond its limit but get a warning, add
# value_range_behavior = WARN in the GlobalParams block.
x = '0 76e6 76.001e6 84.641e6 84.6482e6'
y = '1500 1500 300 300 2073'
[]
[k_function]
type = PiecewiseLinear
x = '0 200e6'
y = '4e-37 4e-37'
[]
[d1_function]
type = ParsedFunction
expression = 'exp(t/4.5e25)'
[]
[d_gap]
type = PiecewiseLinear
x = '1500 2100'
y = '1e-14 1e-12'
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[fuel]
block = fuel
add_variables = true
strain = FINITE
incremental = true
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
eigenstrain_names = 'UN_swelling_eigenstrain UN_thermal_strain'
extra_vector_tags = 'ref'
[]
[buffer]
block = buffer
add_variables = true
strain = FINITE
incremental = true
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
eigenstrain_names = 'buffer_IIDC_strain buffer_thermal_strain'
extra_vector_tags = 'ref'
[]
[IPyC]
block = IPyC
add_variables = true
strain = FINITE
incremental = true
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
eigenstrain_names = 'IPyC_IIDC_strain IPyC_thermal_strain'
extra_vector_tags = 'ref'
[]
[SiC]
block = SiC
add_variables = true
strain = FINITE
incremental = true
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
eigenstrain_names = 'SiC_thermal_eigenstrain'
extra_vector_tags = 'ref'
[]
[OPyC]
block = OPyC
add_variables = true
strain = FINITE
incremental = true
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
eigenstrain_names = 'OPyC_IIDC_strain OPyC_thermal_strain'
extra_vector_tags = 'ref'
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[mass_ie]
type = TimeDerivative
variable = conc
extra_vector_tags = 'ref'
[]
[mass]
type = ArrheniusDiffusion
variable = conc
extra_vector_tags = 'ref'
[]
[mass_source]
type = BodyForce
variable = conc
function = power_history
value = 1.22e-5 # units of mol/m**3-s
block = fuel
extra_vector_tags = 'ref'
[]
[mass_decay]
type = Decay
variable = conc
radioactive_decay_constant = 7.297e-10 # units:(1/sec) The constant for Cesium
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[fissionrate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = fuel
execute_on = timestep_begin
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = fuel
execute_on = timestep_begin
[]
[fast_neutron_flux]
type = MaterialRealAux
variable = fast_neutron_flux
property = fast_neutron_flux
block = 'fuel buffer IPyC SiC OPyC'
execute_on = timestep_begin
[]
[fast_neutron_fluence]
type = MaterialRealAux
variable = fast_neutron_fluence
property = fast_neutron_fluence
block = 'fuel buffer IPyC SiC OPyC'
execute_on = timestep_begin
[]
[conductanceSlave]
type = MaterialRealAux
property = gap_conductance
variable = gap_condSlave
boundary = buffer_outer_boundary
execute_on = 'initial timestep_end'
[]
[density]
type = MaterialRealAux
variable = density
property = density
block = 'fuel buffer IPyC SiC OPyC'
execute_on = 'initial linear'
[]
[thermal_conductivity]
type = MaterialRealAux
variable = thermal_conductivity
property = thermal_conductivity
block = 'fuel buffer IPyC SiC OPyC'
execute_on = timestep_end
[]
[specific_heat]
type = MaterialRealAux
variable = specific_heat
property = specific_heat
block = 'fuel buffer IPyC SiC OPyC'
execute_on = timestep_end
[]
[swelling]
type = MaterialRealAux
variable = swelling
property = swelling
block = fuel
execute_on = linear
[]
[volumetric_IIDC_strain]
type = MaterialRealAux
variable = volumetric_IIDC_strain
property = volumetric_IIDC_strain
block = 'IPyC OPyC'
execute_on = timestep_end
[]
[radial_IIDC_strain]
type = MaterialRealAux
variable = radial_IIDC_strain
property = radial_IIDC_strain
block = 'IPyC OPyC'
execute_on = timestep_end
[]
[tangential_IIDC_strain]
type = MaterialRealAux
variable = tangential_IIDC_strain
property = tangential_IIDC_strain
block = 'IPyC OPyC'
execute_on = timestep_end
[]
[BAF]
type = MaterialRealAux
variable = BAF
property = BAF
block = 'IPyC OPyC'
execute_on = timestep_end
[]
[fis_gas_produced]
type = MaterialRealAux
variable = fis_gas_produced
property = fis_gas_produced
block = fuel
execute_on = linear
[]
[fis_gas_released]
type = MaterialRealAux
variable = fis_gas_released
property = fis_gas_released
block = fuel
execute_on = linear
[]
[gap_HTC]
type = MaterialRealAux
property = gap_conductance
variable = gap_HTC
boundary = buffer_outer_boundary
execute_on = 'initial timestep_end'
[]
[gap_distance]
type = PenetrationAux
variable = gap_distance
boundary = buffer_outer_boundary
paired_boundary = IPyC_inner_boundary
quantity = distance
tangential_tolerance = 1e-6
execute_on = 'initial timestep_end'
[]
[]
[Contact]
[mechanical]
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
penalty = 1e5
model = frictionless
formulation = kinematic
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
initial_gas_types = 'Kr Xe'
initial_fractions = '0.185 0.815'
gas_released = 'fis_gas_released'
released_gas_types = 'Kr Xe'
released_fractions = '0.185 0.815'
tangential_tolerance = 1e-6
roughness_primary = 0e-6
roughness_secondary = 0e-6
jumpdistance_primary = 0
jumpdistance_secondary = 0
quadrature = true
emissivity_secondary = 0.0
emissivity_primary = 0.0
min_gap = 1e-7
max_gap = 50e-6
gap_geometry_type = sphere
[]
[cesium_contact]
type = GapHeatTransfer
variable = conc
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
tangential_tolerance = 1e-6
gap_conductivity_function = d_gap
gap_conductivity_function_variable = temperature
appended_property_name = _conc
quadrature = true
gap_geometry_type = sphere
emissivity_primary = 0.0
emissivity_secondary = 0.0
min_gap = 1e-7
[]
[]
[BCs]
# pin particle along symmetry planes
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
# fix temperature on free surface
[freesurf_temp]
type = FunctionDirichletBC
variable = temperature
function = temp_bc
boundary = exterior
[]
# fix concentration on free surface
[freesurf_conc]
type = DirichletBC
variable = conc
boundary = exterior
value = 0.0
[]
# exterior and internal pressures
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure] # apply gas pressure on buffer and IPyC boundaries
[plenumPressure]
boundary = buffer_IPyC_boundary
initial_pressure = 100.0
startup_time = 0
R = 8.3145
output_initial_moles = initial_moles
temperature = ave_gas_temp
volume = 'gap_volume buffer_void_volume kernel_void_volume'
material_input = 'fis_gas_released'
output = gas_pressure
[]
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
flux_function = power_history
factor = 5e17
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'buffer IPyC OPyC'
[]
### UN properties
[UN_burnup]
type = TRISOBurnup
initial_density = 13760.0
kernel_type = UN
[]
[UN_thermal]
type = MNThermal
block = fuel
temperature = temperature
formulation = COLLIN_BAUER
[]
[UN_elasticity_tensor]
type = UNElasticityTensor
block = fuel
temperature = temperature
[]
[UN_stress]
type = ComputeFiniteStrainElasticStress
block = fuel
[]
[UN_VolumetricSwellingEigenstrain]
type = BurnupDependentEigenstrain
block = fuel
swelling_name = swelling
eigenstrain_name = UN_swelling_eigenstrain
swelling_factor = 0.8
[]
[UN_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10e-6 # check this value for UN
eigenstrain_name = UN_thermal_strain
temperature = temperature
[]
[UN_density]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 13760.0
[]
[fission_gas_release]
type = UNFGR
block = fuel
average_grain_radius = 10e-6
temperature = temperature
triso_geometry = particle_geometry
[]
[fuel_conc]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209.0e+3 # J/mol
d2 = 5.2e-4 # m^2/s
q2 = 362.0e+3 # J/mol
temperature = temperature
[]
### Buffer Properties
[buffer_elasticity_tensor]
type = BufferElasticityTensor
block = buffer
temperature = temperature
[]
[buffer_stress]
type = BufferCEGACreep
block = buffer
temperature = temperature
[]
[buffer_thermal]
type = BufferThermal
block = buffer
initial_density = 1050.0
[]
[buffer_density]
type = StrainAdjustedDensity
block = buffer
strain_free_density = 1050.0
[]
[buffer_thermal_strain]
type = BufferThermalExpansionEigenstrain
block = buffer
eigenstrain_name = buffer_thermal_strain
temperature = temperature
[]
[buffer_IIDC_strain]
type = BufferCEGAIrradiationEigenstrain
block = buffer
eigenstrain_name = buffer_IIDC_strain
temperature = temperature
[]
[buffer_conc]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1.0e-12 # m^2/s
q1 = 0.0
d2 = 0.0
q2 = 0.0
temperature = temperature
[]
### IPyC properties
[IPyC_elasticity_tensor]
type = PyCElasticityTensor
block = IPyC
temperature = temperature
initial_BAF = 1.045
poissons_ratio = 0.23
[]
[IPyC_stress]
type = PyCCEGACreep
block = IPyC
temperature = temperature
[]
[IPyC_thermal]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_density]
type = GenericConstantMaterial
block = IPyC
prop_names = 'density'
prop_values = 1900.0
[]
[IPyC_IIDC_strain]
type = PyCCEGAIrradiationEigenstrain
block = IPyC
eigenstrain_name = IPyC_IIDC_strain
temperature = temperature
[]
[BAF_IPyC]
type = BaconAnisotropyFactor
initial_BAF = 1.045
block = IPyC
[]
[BAF_OPyC]
type = BaconAnisotropyFactor
initial_BAF = 1.045
block = OPyC
[]
[IPyC_thermal_strain]
type = PyCThermalExpansionEigenstrain
block = IPyC
eigenstrain_name = IPyC_thermal_strain
temperature = temperature
[]
[IPyC_conc]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222.0e+3 # J/mol
d2 = 0.0
q2 = 0.0
temperature = temperature
[]
### SiC properties
[SiC_elasticity_tensor]
type = MonolithicSiCElasticityTensor
block = SiC
temperature = temperature
elastic_modulus_model = miller
[]
[SiC_stress]
type = ComputeFiniteStrainElasticStress
block = SiC
[]
[SiC_thermal]
type = MonolithicSiCThermal
block = SiC
temperature = temperature
thermal_conductivity_model = miller
[]
[SiC_density]
type = GenericConstantMaterial
block = SiC
prop_names = 'density'
prop_values = 3200.0
[]
[SiC_thermal_strain]
type = MonolithicSiCThermalExpansionEigenstrain
block = SiC
temperature = temperature
eigenstrain_name = SiC_thermal_eigenstrain
[]
[SiC_conc]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = d1_function
d1_function_variable = fast_neutron_fluence
q1 = 125.0e+3 # J/mol
d2 = 1.6e-2 # m^2/s
q2 = 514.0e+3 # J/mol
temperature = temperature
[]
### OPyC properties
[OPyC_elasticity_tensor]
type = PyCElasticityTensor
block = OPyC
temperature = temperature
initial_BAF = 1.045
poissons_ratio = 0.23
[]
[OPyC_stress]
type = PyCCEGACreep
block = OPyC
temperature = temperature
[]
[OPyC_thermal_conductivity]
type = HeatConductionMaterial
block = OPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[OPyC_density]
type = GenericConstantMaterial
block = OPyC
prop_names = 'density'
prop_values = 1900.0
[]
[OPyC_IIDC_strain]
type = PyCCEGAIrradiationEigenstrain
block = OPyC
eigenstrain_name = OPyC_IIDC_strain
temperature = temperature
[]
[OPyC_thermal_strain]
type = PyCThermalExpansionEigenstrain
block = OPyC
eigenstrain_name = OPyC_thermal_strain
temperature = temperature
[]
[OPyC_conc]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222.0e+3 # J/mol
d2 = 0.0
q2 = 0.0
temperature = temperature
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[disp_x]
type = MaxIncrement
variable = disp_x
max_increment = 1e-6
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'disp_x temperature conc'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-8
nl_abs_tol = 1e-7
nl_max_its = 15
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 84.641e6 #85.3682e6
num_steps = 1000
dtmax = 2e6
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 20
growth_factor = 1.5
optimal_iterations = 8 #6
linear_iteration_ratio = 100
time_t = '0 76e6 76.001e6 84.641e6 84.6482e6'
time_dt = '20 20 20 20 20'
[]
[Quadrature]
order = THIRD
[]
[]
[Postprocessors]
[_dt]
type = TimestepSize
execute_on = timestep_end
[]
[cs_release]
type = SideIntegralMassFlux
variable = conc
boundary = exterior
[]
[int_cs_release]
type = TimeIntegratedPostprocessor
value = cs_release
[]
[cs_release_fuel]
type = SideIntegralMassFlux
variable = conc
boundary = fuel_outer_boundary
[]
[int_cs_release_fuel]
type = TimeIntegratedPostprocessor
value = cs_release_fuel
[]
[cs_release_PyCGapBndry]
type = SideIntegralMassFlux
variable = conc
boundary = IPyC_inner_boundary
[]
[int_cs_release_PyCGapBndry]
type = TimeIntegratedPostprocessor
value = cs_release_PyCGapBndry
[]
[ave_gas_temp]
type = ElementAverageValue
block = buffer
variable = temperature
execute_on = 'initial timestep_end'
[]
[ave_gap_temp]
type = SideAverageValue
boundary = buffer_IPyC_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
[fis_gas_produced]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_produced
block = fuel
execute_on = 'initial timestep_end'
[]
[fis_gas_released]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_released
block = fuel
execute_on = 'initial timestep_end'
[]
[gap_volume]
type = InternalVolume
boundary = buffer_IPyC_boundary
execute_on = 'initial linear'
use_displaced_mesh = true
[]
[buffer_void_volume]
type = VoidVolume
block = buffer
theoretical_density = 2250
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[kernel_void_volume]
type = VoidVolume
block = fuel
theoretical_density = 14330
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
execute_on = 'initial timestep_end'
scale_factor = -1
[]
[volumeFuel]
type = InternalVolume
boundary = fuel_outer_boundary
execute_on = 'initial timestep_end'
scale_factor = -1
[]
[volumeGas]
type = InternalVolume
boundary = buffer_outer_boundary
execute_on = 'initial timestep_end'
scale_factor = -1
addition = 4.67e-11
[]
[volumeBufferShell]
type = InternalVolume
boundary = buffer_outer_boundary
execute_on = 'initial timestep_end'
[]
[ave_temp_interior]
type = SideAverageValue
boundary = buffer_outer_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
[gap_HTC]
type = ElementExtremeValue
variable = gap_HTC
block = buffer
value_type = 'max'
execute_on = 'initial timestep_end'
[]
### Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
outputs = exodus
execute_on = 'initial timestep_end'
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
outputs = exodus
execute_on = 'initial timestep_end'
[]
[avg_surface_temp]
type = SideAverageValue
variable = temperature
boundary = exterior
outputs = exodus
execute_on = 'initial timestep_end'
[]
[time_int_surf_temp]
type = TimeIntegratedPostprocessor
value = avg_surface_temp
outputs = exodus
execute_on = 'initial timestep_end'
[]
##### irradiation conditions
[particle_power]
type = ElementIntegralPower
variable = temperature
use_material_fission_rate = true
fission_rate_material = fission_rate
block = fuel
execute_on = 'initial timestep_end'
[]
[max_fluence]
type = ElementExtremeValue
variable = fast_neutron_fluence
block = 'fuel buffer IPyC SiC OPyC'
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_burnup]
type = ElementExtremeValue
variable = burnup
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
#### II strain
[OPyC_radial_IIDC_strain]
type = ElementExtremeValue
variable = radial_IIDC_strain
block = OPyC
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[OPyC_tangential_IIDC_strain]
type = ElementExtremeValue
variable = tangential_IIDC_strain
block = OPyC
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[IPyC_radial_IIDC_strain]
type = ElementExtremeValue
variable = radial_IIDC_strain
block = IPyC
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[IPyC_tangential_IIDC_strain]
type = ElementExtremeValue
variable = tangential_IIDC_strain
block = IPyC
value_type = 'max'
execute_on = 'initial timestep_end'
[]
#### temperatures
[max_T_kernel]
type = NodalExtremeValue
variable = temperature
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_T_buffer]
type = NodalExtremeValue
variable = temperature
block = buffer
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[min_T_buffer]
type = NodalExtremeValue
variable = temperature
block = buffer
value_type = 'min'
execute_on = 'initial timestep_end'
[]
[max_T_IPyC]
type = NodalExtremeValue
variable = temperature
block = IPyC
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_T_SiC]
type = NodalExtremeValue
variable = temperature
block = SiC
value_type = 'max'
execute_on = 'initial timestep_end'
[]
#### displacement BCs
[max_disp_kernel]
type = NodalExtremeValue
variable = disp_x
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[min_disp_buffer]
type = NodalExtremeValue
variable = disp_x
block = buffer
value_type = 'min'
execute_on = 'initial timestep_end'
[]
[max_disp_IPyC]
type = NodalExtremeValue
variable = disp_x
block = IPyC
value_type = 'max'
execute_on = 'initial timestep_end'
[]
#### hoop stresses
[hoop_opyc_max]
type = ElementExtremeValue
variable = stress_yy
block = OPyC
execute_on = 'initial timestep_end'
[]
[hoop_sic_max]
type = ElementExtremeValue
variable = stress_yy
block = SiC
execute_on = 'initial timestep_end'
[]
[hoop_ipyc_max]
type = ElementExtremeValue
variable = stress_yy
block = IPyC
execute_on = 'initial timestep_end'
[]
[hoop_buffer_max]
type = ElementExtremeValue
variable = stress_yy
block = buffer
execute_on = 'initial timestep_end'
[]
[hoop_opyc_min]
type = ElementExtremeValue
variable = stress_yy
block = OPyC
value_type = min
execute_on = 'initial timestep_end'
[]
[hoop_sic_min]
type = ElementExtremeValue
variable = stress_yy
block = SiC
value_type = min
execute_on = 'initial timestep_end'
[]
[hoop_ipyc_min]
type = ElementExtremeValue
variable = stress_yy
block = IPyC
value_type = min
execute_on = 'initial timestep_end'
[]
[hoop_buffer_min]
type = ElementExtremeValue
variable = stress_yy
block = buffer
value_type = min
execute_on = 'initial timestep_end'
[]
### Check warning for Density
[oPyC_density]
type = ElementExtremeValue
variable = density
block = OPyC
execute_on = 'initial timestep_end'
[]
[sic_density]
type = ElementExtremeValue
variable = density
block = SiC
execute_on = 'initial timestep_end'
[]
[IPyC_density]
type = ElementExtremeValue
variable = density
block = IPyC
execute_on = 'initial timestep_end'
[]
[buffer_density]
type = ElementExtremeValue
variable = density
block = buffer
execute_on = 'initial timestep_end'
[]
[kernel_density]
type = ElementExtremeValue
variable = density
block = fuel
execute_on = 'initial timestep_end'
[]
[pd_penetration]
type = PdPenetration
boundary = SiC_inner_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = true
csv = true
perf_graph = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_10/case_10_1D.i)
#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# See also Hales, et al., Multidimensional multiphysics simulation of TRISO
# particle fuel, JNM, 443, 2013. https://doi.org/10.1016/j.jnucmat.2013.07.070
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark. The best way to do this is to compare
# results with information in the JNM article.
#
[GlobalParams]
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
mesh_density = '6 6 0 6 8 6'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Variables]
[disp_x]
[]
[temperature]
initial_condition = 1346.0
[]
[]
[Functions]
[radial_eigenstrain]
type = ParsedFunction
expression = 't*(4.52013e-4/6.0*t*t*t*t*t - 8.36313e-3/5.0*t*t*t*t + 5.67549e-2/4.0*t*t*t - 1.74247e-1/3.0*t*t + 2.62692e-1/2.0*t - 1.43234e-1)'
[]
[tangential_eigenstrain]
type = ParsedFunction
expression = 't*(1.30457e-4/4.0*t*t*t - 2.10029e-3/3.0*t*t + 9.07826e-3/2.0*t - 3.24737e-2)'
[]
[fission_rate]
type = ParsedFunction
expression = 7.75e19 # units of fissions/m**3
[]
[k_function]
type = ParsedFunction
expression = '4.93e-29'
[]
[]
[AuxVariables]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = fuel
initial_condition = 0.0
[]
[fission_rate]
block = fuel
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[IPyC_OPyC]
block = 'IPyC OPyC'
strain = finite
eigenstrain_names = 'thermal_strain pyc_eigenstrain'
[]
[rest]
block = 'fuel buffer SiC'
strain = finite
eigenstrain_names = thermal_strain
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
[]
[heat]
type = HeatConduction
variable = temperature
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
energy_per_fission = 3.2e-11 # units of J/fission
fission_rate = fission_rate
[]
[]
[AuxKernels]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[fission_rate]
type = FunctionAux
variable = fission_rate
block = fuel
function = fission_rate
[]
[burnup]
type = BurnupAux
variable = burnup
block = fuel
fission_rate = fission_rate
density = 10810.0
molecular_weight = 0.270 # units of kg/mole
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
penalty = 1e5
model = frictionless
formulation = kinematic
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
gas_released = 'fis_gas_released co_production' # coupling to postprocessors which supply the fission gas addition, co addition
released_gas_types = 'Kr Xe;
CO'
released_fractions = '0.153 0.847;
1'
tangential_tolerance = 1e-6
# contact_pressure_input = 10e6
# quadrature = true
[]
[]
[BCs]
# pin particle along symmetry planes
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
# fix temperature on free surface
[freesurf_temperature]
type = DirichletBC
variable = temperature
boundary = exterior
value = 1346.0
[]
# exterior and internal pressures
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure] # apply gas pressure on buffer and IPyC boundaries
[plenumPressure]
boundary = buffer_IPyC_boundary
initial_pressure = 0
startup_time = 1.0e4
R = 8.3143
output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
volume = volumeGas # coupling to post processor to get gas volume
material_input = 'fis_gas_released co_production' # coupling to post processor to get fission gas added, co added
output = plenum_pressure # coupling to post processor to output plenum/gap pressure
[]
[]
[]
[Materials]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 1.708707e18 # n/m^2-sec
[]
[fission_gas_release] # Sifgr fission gas release mode
type = UO2Sifgrs
block = fuel
temperature = temperature
fission_rate = fission_rate # coupling to fission_rate aux variable
grain_radius_const = 5.0e-6
[]
[stress]
type = ComputeFiniteStrainElasticStress
block = 'fuel buffer SiC'
[]
[PyC_stress]
type = PyCCreep
block = 'IPyC OPyC'
k = k_function
poissons_ratio = 0.4
temperature = temperature
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'IPyC OPyC'
[]
[PyC_eigenstrain]
type = PyCIrradiationEigenstrain
block = 'IPyC OPyC'
radial_eigenstrain_function = radial_eigenstrain
tangential_eigenstrain_function = tangential_eigenstrain
eigenstrain_name = pyc_eigenstrain
[]
[fuel_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[PyC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = 'buffer IPyC OPyC'
thermal_expansion_coeff = 5.5e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[SiC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[fuel_thermal] # temperature and burnup dependent thermal properties of UO2 (BISON kernel)
type = UO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temperature
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[fuel_den]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10810.0
[]
[buffer_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[buffer_temperature]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[buffer_den]
type = StrainAdjustedDensity
strain_free_density = 1000 #kg/m^3
block = buffer
[]
[PyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = 'IPyC OPyC'
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[PyC_temperature]
type = HeatConductionMaterial
block = 'IPyC OPyC'
thermal_conductivity = 4.0 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[PyC_den]
type = StrainAdjustedDensity
strain_free_density = 1880.0 # kg/m^3
block = 'IPyC OPyC'
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_temperature]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9 # J/m-s-K
specific_heat = 620.0 # J/kg-K
[]
[SiC_den]
type = StrainAdjustedDensity
strain_free_density = 3200.0 # kg/m^3
block = SiC
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Dampers]
[temperature]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 1e-7
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 3.10176e7
dtmax = 2e5
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 20
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[burnup]
type = ElementExtremeValue
block = fuel
variable = burnup
[]
[fis_gas_produced] # fission gas produced (moles)
type = ElementIntegralFisGasGeneratedSifgrs
block = fuel
[]
[fis_gas_released] # fission gas released to plenum (moles)
type = ElementIntegralFisGasReleasedSifgrs
block = fuel
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
[]
[volumeFuel]
type = InternalVolume
boundary = fuel_outer_boundary
[]
[volumeGas]
type = InternalVolume
boundary = 'fuel_outer_boundary IPyC_inner_boundary'
addition = -5.53e-11
execute_on = 'initial timestep_end'
[]
[volumeBufferShell]
type = InternalVolume
boundary = buffer_IPyC_boundary
[]
[ave_temp_interior]
type = SideAverageValue
boundary = buffer_IPyC_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
# Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
[]
[avg_surface_temp]
type = SideAverageValue
variable = temperature
boundary = exterior
[]
[time_int_surf_temp]
type = TimeIntegratedPostprocessor
value = avg_surface_temp
[]
[co_production]
type = CarbonMonoxideProduction
total_fissions = total_fissions
time_integrated_triso_temperature = time_int_surf_temp
initial_enrichment = 0.14029
[]
[tang_SiC]
type = ElementalVariableValue
variable = stress_yy
elementid = 18
[]
[]
[PerformanceMetricOutputs]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = true
csv = true
perf_graph = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_8/case_8_1D.i)
#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# See also Hales, et al., Multidimensional multiphysics simulation of TRISO
# particle fuel, JNM, 443, 2013. https://doi.org/10.1016/j.jnucmat.2013.07.070
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark. The best way to do this is to compare
# results with information in the JNM article.
#
[GlobalParams]
order = SECOND
family = LAGRANGE
flux_conversion_factor = 1.0
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '3.50e-4 3.90e-4 4.25e-4 4.65e-4'
mesh_density = '6 6 6'
block_names = 'IPyC SiC OPyC'
[]
[]
[Variables]
[disp_x]
[]
[]
[Functions]
[radial_eigenstrain]
type = ParsedFunction
expression = 't*(4.03266e-4/4.0*t*t*t - 2.25937e-3/3.0*t*t + 9.82884e-3/2.0*t - 1.80613e-2)'
[]
[tangential_eigenstrain]
type = ParsedFunction
expression = 't*(-4.91648e-4/4.0*t*t*t + 2.32979e-3/3.0*t*t + 1.71315e-3/2.0*t - 1.78392e-2)'
[]
[pressure]
type = PiecewiseLinear
data_file = pressure_history.dat
format = columns
[]
[temperature]
type = PiecewiseLinear
data_file = temperature_history.dat
format = columns
[]
[k_function]
type = ParsedFunction
expression = '(4.386e-4 - 9.70e-7*(t-273.15) + 8.0294e-10*(t-273.15)*(t-273.15))*1e-25'
[]
[]
[AuxVariables]
[temperature]
initial_condition = 873.0
[]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
initial_condition = 0.0
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[IPyC_OPyC]
block = 'IPyC OPyC'
strain = finite
eigenstrain_names = 'thermal_strain pyc_eigenstrain'
[]
[SiC]
block = SiC
strain = finite
eigenstrain_names = thermal_strain
[]
[]
[AuxKernels]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
# fix temperature on free surface
[freesurf_temperature]
type = FunctionAux
variable = temperature
function = temperature
[]
[]
[BCs]
# exterior and internal pressures
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[interior_pressure_x]
type = Pressure
variable = disp_x
boundary = IPyC_inner_boundary
factor = 1.0
function = pressure
[]
[]
[Materials]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 3.472222222e17 # n/m^2-sec
[]
[stress]
type = ComputeFiniteStrainElasticStress
block = 'SiC'
[]
[PyC_stress]
type = PyCCreep
block = 'IPyC OPyC'
k = k_function
temperature = temperature
[]
[IPyC_den]
type = StrainAdjustedDensity
strain_free_density = 1900.0
block = 'IPyC OPyC'
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'IPyC OPyC'
[]
[PyC_eigenstrain]
type = PyCIrradiationEigenstrain
block = 'IPyC OPyC'
radial_eigenstrain_function = radial_eigenstrain
tangential_eigenstrain_function = tangential_eigenstrain
eigenstrain_name = pyc_eigenstrain
[]
[PyC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
thermal_expansion_coeff = 5.35e-6
block = 'IPyC OPyC'
stress_free_temperature = 873.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[SiC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
thermal_expansion_coeff = 4.9e-6
block = SiC
stress_free_temperature = 873.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[PyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = 'IPyC OPyC'
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 8.64e7
dt = 1.0
dtmax = 2e5
dtmin = 5e3
[TimeStepper]
type = IterationAdaptiveDT
dt = 1
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
time_t = '0 0.864e7 1.728e7 2.592e7 3.456e7 4.320e7 5.184e7 6.048e7 6.912e7 7.776e7'
time_dt = '5e3 5e3 5e3 5e3 5e3 5e3 5e3 5e3 5e3 5e3'
[]
[]
[Postprocessors]
[tang_IPyC]
type = ElementalVariableValue
variable = stress_yy
elementid = 0
[]
[tang_SiC]
type = ElementalVariableValue
variable = stress_yy
elementid = 6
[]
[]
[PerformanceMetricOutputs]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
csv = true
exodus = true
perf_graph = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_2a/case_2a.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 250e-6 350e-6 390e-6'
mesh_density = '50 30 15'
block_names = 'fuel buffer IPyC'
[]
[]
[Problem]
[]
[Variables]
[conc_Cs]
[]
[]
[ICs]
[conc_Cs]
type = ConstantIC
block = fuel
value = 1
variable = conc_Cs
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1473.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[]
[Materials]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 1e-20
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 720000
num_steps = 700
dt = 3600
dtmax = 3600
dtmin = 3600
[]
[Postprocessors]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
execute_on = final
[]
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_5b/case_5b.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.08
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 250e-6 350e-6 390e-6 425e-6 465e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
bias = '1 1.25 1.25 1.25 1.25'
dual_bias = '0.8 0.8 0.8 0.8 1'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[conc_Ag]
[]
[]
[AuxVariables]
[temperature]
initial_condition = 873.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temperature]
type = PiecewiseLinear
data_file = temperature_history.dat
format = columns
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = temperature
variable = temperature
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[]
[Materials]
[burnup]
type = GenericFunctionMaterial
block = fuel
prop_names = 'burnup'
prop_values = '0.1/8.64e7*t'
[]
[fission_rate]
type = GenericFunctionMaterial
block = fuel
prop_names = 'fission_rate'
# 2.790610e19 = 0.1/8.64e7*10810/.27*6.0221409e23
prop_values = '2.790610e19'
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Cs_generation
kind = Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = 'exp(2e25/8.64e7*t/5e25)'
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Ag_generation
kind = Ag
[]
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[SiC_conc_Ag]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs conc_Ag'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 5e-21 #1e-22
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 8.712e7
num_steps = 1450
dt = 86400
dtmax = 86400
#dtmin = 86400
[TimeStepper]
type = FunctionDT
function = 'if(t<8.64e7,86400,3600)'
[]
[]
[Postprocessors]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial timestep_end'
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
execute_on = final
[]
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_7a/case_7a.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.0407
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 272e-6 396e-6 402e-6 436e-6 475e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
bias = '1 1.25 1.25 1.25 1.25'
dual_bias = '0.8 0.8 0.8 0.8 1'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[conc_Ag]
[]
[conc_Sr]
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1304.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Sr_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temperature]
type = PiecewiseLinear
data_file = temperature_history.dat
format = columns
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
[]
[mass_Sr_dt]
type = TimeDerivative
variable = conc_Sr
[]
[mass_Sr]
type = ArrheniusDiffusion
variable = conc_Sr
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Sr]
type = SpeciesSourceRate
variable = conc_Sr
property_name = Sr_generation
block = fuel
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[Sr_diff_coef]
type = MaterialRealAux
variable = Sr_diff_coef
property = arrhenius_diffusion_coef_Sr
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = temperature
variable = temperature
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[freesurf_conc_Sr]
type = DirichletBC
variable = conc_Sr
boundary = exterior
value = 0.0
[]
[]
[Materials]
[burnup]
type = GenericFunctionMaterial
block = fuel
prop_names = 'burnup'
prop_values = 'if(t<7682400,0.048/7682400*t,0.048)'
[]
[fission_rate]
type = GenericFunctionMaterial
block = fuel
prop_names = 'fission_rate'
# 1.699e20 = 0.048/7682400*10840/.27*6.0221409e23
prop_values = 'if(t<7682400,1.699e20,0)'
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Cs_generation
kind = Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = 'if(t<7682400,exp(2.1e25/7682400*t/5e25),exp(2.1e25/5e25))'
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Ag_generation
kind = Ag
[]
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[SiC_conc_Ag]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[fuel_conc_Sr]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 2.2e-3 # m^2/s
q1 = 488e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[mass_source_Sr_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Sr_generation
kind = Sr
[]
[buffer_conc_Sr]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[IPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[SiC_conc_Sr]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 1.2e-9 # m^2/s
q1 = 205e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[OPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs conc_Ag'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 5e-21 #1e-22
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 8679600
num_steps = 1450
dt = 86400
dtmax = 86400
#dtmin = 86400
[TimeStepper]
type = FunctionDT
function = 'if(t<7682400,86400,
if(t<7707600,720,
3600))'
[]
[]
[Postprocessors]
[_temp]
type = NodalExtremeValue
variable = temperature
[]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released_overall]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
start_time = 7682400
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial timestep_end'
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released_overall]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
start_time = 7682400
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
execute_on = 'initial timestep_end'
[]
[release_Sr_inc]
type = SideIntegralMassFlux
variable = conc_Sr
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
execute_on = 'initial timestep_end'
[]
[released_Sr]
type = TimeIntegratedPostprocessor
value = release_Sr_inc
execute_on = 'initial timestep_end'
[]
[total_Sr]
type = ElementIntegralMaterialProperty
mat_prop = Sr_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Sr_released_overall]
type = FractionalRelease
released = released_Sr
total = total_Sr
execute_on = 'initial timestep_end'
[]
[x_Sr_released]
type = FractionalRelease
released = released_Sr
total = total_Sr
execute_on = 'initial timestep_end'
start_time = 7682400
[]
[retained_Sr]
type = ElementIntegralVariablePostprocessor
variable = conc_Sr
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
[]
[out_final]
type = CSV
execute_on = final
[]
[]
(test/tests/triso/UCOFGR/ad_UCOFGR_out_of_pile.i)
# Fission Gas Release Model High Temperature
# The geometry is a 1D sphere with a diameter of 425 micrometers and an average
# grain radius of 10 microns.
# The fission gas yield was set to 0.297.
# Safety testing is hypothetically occurs at 2.5e4.
# The temperature is ramped from 673.15 to 3073.15 K.
# The fission rate density is ramped from 0 to 1.1625e21 fission/m^3-s
# (3.72e10 W/m^3) over 1e4 seconds and held constant.
# The density of the kernel is set to 11250 kg/m^3, the Oxygen to Uranium ratio
# is set to 1.5, the Carbon to Uranium ratio is set to 0.4, and the initial
# U-235 enrichment is set to 15%.
#
[GlobalParams]
order = FIRST
family = LAGRANGE
O_U = 1.5
C_U = 0.4
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.125e-4'
mesh_density = '6'
block_names = 'fuel'
[]
[]
[Functions]
[fast_n_flux_fcn]
type = ParsedFunction
expression = 'if( t>=2.5e4, 0.0, 0.2 * t)'
[]
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = '2'
outer_SiC = '2'
outer_IPyC = '2'
inner_IPyC = '2'
outer_buffer = '2'
outer_kernel = '2'
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temp]
initial_condition = 673.15
[]
[]
[AuxVariables]
[fission_rate]
block = '1'
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = '1'
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[fission_rate]
type = PiecewiseLinear
x = '0 1e3 1.0e6'
y = '0 1.1625e21 0'
[]
[scaled_time]
type = ParsedFunction
# molar mass / Avogadro's number / density
# 0.266 / 6.022e23 / 11250 = 3.926e-29
expression = '3.926e-29*t'
[]
[burnup]
type = CompositeFunction
functions = 'fission_rate scaled_time'
[]
[temp_function]
type = PiecewiseLinear
x = '0 7.5e4'
y = '673.15 3073.15'
[]
[]
[Kernels]
[heat]
type = ADHeatConduction
variable = temp
[]
[heat_ie]
type = ADHeatConductionTimeDerivative
variable = temp
[]
[]
[AuxKernels]
[fission_rate]
type = ADMaterialRealAux
variable = fission_rate
property = fission_rate
block = '1'
execute_on = timestep_end
[]
[burnup]
type = ADMaterialRealAux
variable = burnup
property = burnup
block = '1'
execute_on = timestep_end
[]
[]
[BCs]
[heat_removal]
type = ADFunctionDirichletBC
variable = temp
boundary = '1'
function = temp_function
[]
[]
[Materials]
[fast_neutron_flux]
type = ADGenericFunctionMaterial
prop_names = fast_neutron_flux
prop_values = fast_n_flux_fcn
outputs = all
[]
[fission_rate]
type = ADGenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[burnup]
type = ADGenericFunctionMaterial
prop_names = burnup
prop_values = burnup
[]
[thermal]
type = ADHeatConductionMaterial
block = '1'
thermal_conductivity = 1.0
specific_heat = 1.0
[]
[fission_gas_release]
type = ADUCOFGR
block = '1'
average_grain_radius = 10e-6
triso_geometry = particle_geometry
temperature = temp
cutoff_neutron_flux = 0.0
[]
[UCO_density]
type = ADParsedMaterial
block = '1'
property_name = density
expression = 11250.0
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 51'
line_search = 'none'
l_max_its = 50
l_tol = 1e-2
nl_max_its = 150
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
start_time = 0.0
#end_time = 7.5e6 # use to test full range of parameters
end_time = 1e5
num_steps = 140
dtmax = 2e6
dtmin = 1.0
[TimeStepper]
type = IterationAdaptiveDT
dt = 1e3
time_t = '1e4 1e5'
time_dt = '1e3 1e5'
[]
[]
[Postprocessors]
[temp]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = temp
execute_on = 'initial timestep_end'
[]
[burnup]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = burnup
execute_on = 'initial timestep_end'
[]
[fission_rate]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = fission_rate
execute_on = 'initial timestep_end'
[]
[_dt]
type = TimestepSize
[]
[FGP]
type = ADElementIntegralMaterialProperty
block = '1'
mat_prop = fis_gas_produced
execute_on = 'initial timestep_end'
[]
[FGR]
type = ADElementIntegralMaterialProperty
block = '1'
mat_prop = fis_gas_released
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
csv = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_4b/case_4b.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.08
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 250e-6 350e-6 390e-6 425e-6 465e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
bias = '1 1.25 1.25 1.25 1.25'
dual_bias = '0.8 0.8 0.8 0.8 1'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[conc_Ag]
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1273.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = 'if(t<4.3200001e7,1273.15,2073.15)'
variable = temperature
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[]
[Materials]
[burnup]
type = GenericFunctionMaterial
block = fuel
prop_names = 'burnup'
prop_values = '0.1/4.32e7*t'
[]
[fission_rate]
type = GenericFunctionMaterial
block = fuel
prop_names = 'fission_rate'
# 5.581219e19 = 0.1/4.32e7*10810/.27*6.0221409e23
prop_values = '5.581219e19'
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Cs_generation
kind = Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = 'exp(2e25/4.32e7*t/5e25)'
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Ag_generation
kind = Ag
[]
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[SiC_conc_Ag]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs conc_Ag'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 5e-21 #1e-22
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 4.392e7
num_steps = 700
dt = 86400
dtmax = 86400
#dtmin = 86400
[TimeStepper]
type = FunctionDT
function = 'if(t<4.3200001e7,86400,3600)'
[]
[]
[Postprocessors]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
execute_on = final
[]
[]
(test/tests/triso_failure/triso_1d_failure_error.i)
[GlobalParams]
density = 10810.0
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
mesh_density = '6 6 0 6 8 6'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Variables]
[disp_x]
[]
[temperature]
initial_condition = 1346.0
[]
[]
[Functions]
[radial_eigenstrain]
type = ParsedFunction
expression = 't*(4.52013e-4/6.0*t*t*t*t*t - 8.36313e-3/5.0*t*t*t*t + 5.67549e-2/4.0*t*t*t - 1.74247e-1/3.0*t*t + 2.62692e-1/2.0*t - 1.43234e-1)'
[]
[tangential_eigenstrain]
type = ParsedFunction
expression = 't*(1.30457e-4/4.0*t*t*t - 2.10029e-3/3.0*t*t + 9.07826e-3/2.0*t - 3.24737e-2)'
[]
[fission_rate]
type = ParsedFunction
expression = 7.75e19 # units of fissions/m**3
[]
[k_function]
type = ParsedFunction
expression = '4.93e-29'
[]
[high_fidelity_strength_crackedIPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1000000 1000000'
[]
[high_fidelity_strength_crackedOPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1000000 1000000'
[]
[stress_correlation_crackedOPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[stress_correlation_crackedIPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[high_fidelity_strength_asphericity]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1000000 1000000'
[]
[stress_correlation_asphericity]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[stress_change_correlation_asphericity]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[]
[AuxVariables]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = fuel
initial_condition = 0.0
[]
[fast_neutron_flux]
[]
[fast_neutron_fluence]
initial_condition = 0.0
[]
[fission_rate]
block = fuel
[]
[]
[Physics/SolidMechanics/QuasiStatic]
strain = small
[fuel_buffer_sic]
block = 'fuel buffer SiC'
eigenstrain_names = thermal_strain
[]
[ipyc_opyc]
block = 'IPyC OPyC'
incremental = true
eigenstrain_names = 'thermal_strain pyc_eigenstrain'
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
[]
[heat]
type = HeatConduction
variable = temperature
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
energy_per_fission = 3.2e-11
fission_rate = fission_rate
[]
[]
[AuxKernels]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[fast_neutron_flux]
type = FastNeutronFluxAux
variable = fast_neutron_flux
factor = 1.708707e18 # n/m^2-sec
[]
[fast_neutron_fluence]
type = FastNeutronFluenceAux
variable = fast_neutron_fluence
fast_neutron_flux = fast_neutron_flux
[]
[fission_rate]
type = FunctionAux
variable = fission_rate
block = fuel
function = fission_rate
[]
[burnup]
type = BurnupAux
variable = burnup
block = fuel
fission_rate = fission_rate
molecular_weight = 0.270
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
penalty = 1e5
model = frictionless
formulation = kinematic
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
# coupling to a postprocessor
initial_moles = initial_moles
gas_released = 'fis_gas_released co_production'
released_gas_types = 'Kr Xe;
CO'
released_fractions = '0.153 0.847;
1'
tangential_tolerance = 1e-6
# contact_pressure_input = 10e6
# quadrature = true
[]
[]
[BCs]
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[freesurf_temperature]
type = DirichletBC
variable = temperature
boundary = exterior
value = 1346.0
[]
[exterior_pressure_x]
type = Pressure
use_displaced_mesh = false
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure]
# apply gas pressure on buffer and IPyC boundaries
[plenumPressure]
use_displaced_mesh = false
boundary = buffer_IPyC_boundary
initial_pressure = 0
startup_time = 1.0e4
# coupling to post processor
output_initial_moles = initial_moles
temperature = ave_temperature_interior
volume = volumeGas
material_input = 'fis_gas_released co_production'
output = plenum_pressure
[]
[]
[]
[Materials]
[fission_gas_release]
type = UO2Sifgrs
block = fuel
temperature = temperature
fission_rate = fission_rate
grain_radius_const = 5.0e-6
[]
[stress]
type = ComputeLinearElasticStress
block = 'fuel buffer SiC'
[]
[PyC_stress]
type = PyCCreep
block = 'IPyC OPyC'
k = k_function
poissons_ratio = 0.4
flux = fast_neutron_flux
temperature = temperature
[]
[PyC_den]
type = StrainAdjustedDensity
strain_free_density = 1880.0
block = 'IPyC OPyC'
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'IPyC OPyC'
[]
[PyC_eigenstrain]
type = PyCIrradiationEigenstrain
block = 'IPyC OPyC'
fluence = fast_neutron_fluence
radial_eigenstrain_function = radial_eigenstrain
tangential_eigenstrain_function = tangential_eigenstrain
eigenstrain_name = pyc_eigenstrain
[]
[fuel_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[PyC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = 'buffer IPyC OPyC'
thermal_expansion_coeff = 5.5e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[SiC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[fuel_thermal]
type = UO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temperature
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[fuel_den]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10810.0
[]
[buffer_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[buffer_temperature]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5
specific_heat = 720.0
[]
[buffer_den]
type = StrainAdjustedDensity
strain_free_density = 1000
block = buffer
[]
[PyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = 'IPyC OPyC'
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[PyC_thermal]
type = HeatConductionMaterial
block = 'IPyC OPyC'
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_temperature]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9
specific_heat = 620.0
[]
[SiC_den]
type = StrainAdjustedDensity
strain_free_density = 3200.0
block = SiC
[]
[characteristic_strength]
type = GenericConstantMaterial
prop_values = '9640000 9640000 9640000'
prop_names = 'characteristic_strength_SiC characteristic_strength_IPyC characteristic_strength_OPyC'
[]
[]
[Dampers]
[temperature]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
num_steps = 10
dtmax = 2e5
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 20
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[dt]
type = TimestepSize
[]
[burnup]
type = ElementExtremeValue
block = fuel
variable = burnup
[]
[fis_gas_produced]
type = ElementIntegralFisGasGeneratedSifgrs
block = fuel
[]
[fis_gas_released]
type = ElementIntegralFisGasReleasedSifgrs
block = fuel
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
[]
[volumeFuel]
type = InternalVolume
boundary = fuel_outer_boundary
[]
[volumeGas]
type = InternalVolume
boundary = 'fuel_outer_boundary IPyC_inner_boundary'
addition = -5.53e-11
execute_on = 'initial timestep_end'
[]
[volumeBufferShell]
type = InternalVolume
boundary = buffer_IPyC_boundary
[]
[ave_temperature_interior]
type = SideAverageValue
boundary = buffer_IPyC_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
[]
[avg_surface_temperature]
type = SideAverageValue
variable = temperature
boundary = exterior
[]
[time_int_surf_temperature]
type = TimeIntegratedPostprocessor
value = avg_surface_temperature
[]
[co_production]
type = CarbonMonoxideProduction
total_fissions = total_fissions
time_integrated_triso_temperature = time_int_surf_temperature
initial_enrichment = 0.14029
[]
[tang_SiC]
type = ElementalVariableValue
variable = stress_yy
elementid = 18
[]
[strength_SiC]
type = WeibullEffectiveMeanStrength
block = SiC
weibull_modulus = 6
characteristic_strength = characteristic_strength_SiC
[]
[failure_indicator_SiC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
[]
[strength_IPyC]
type = WeibullEffectiveMeanStrength
block = IPyC
weibull_modulus = 6
characteristic_strength = characteristic_strength_IPyC
[]
[failure_indicator_IPyC]
type = WeibullFailureOutputUsingCorrelation
block = IPyC
weibull_modulus = 6
stress_type = scalar_quantity
scalar_type = MaxPrincipal
effective_mean_strength = strength_IPyC
[]
[strength_OPyC]
type = WeibullEffectiveMeanStrength
block = OPyC
weibull_modulus = 6
characteristic_strength = characteristic_strength_OPyC
[]
[failure_indicator_OPyC]
type = WeibullFailureOutputUsingCorrelation
block = OPyC
weibull_modulus = 6
stress_type = scalar_quantity
scalar_type = MaxPrincipal
effective_mean_strength = strength_OPyC
[]
[failure_indicator_SiC_crackedIPyC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_type = scalar_quantity
scalar_type = MaxPrincipal
high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
stress_correlation_function = 'stress_correlation_crackedIPyC'
[]
[failure_indicator_SiC_crackedOPyC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_type = scalar_quantity
scalar_type = MaxPrincipal
high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
stress_correlation_function = 'stress_correlation_crackedOPyC'
[]
[triso_failure]
type = TRISOFailureEvaluation
IPyC_failure = failure_indicator_IPyC
OPyC_failure = failure_indicator_OPyC
SiC_failure = failure_indicator_SiC
SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
SiC_failure_crackedOPyC = failure_indicator_SiC_crackedOPyC
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
csv = true
perf_graph = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_3d/case_3d.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 250e-6 350e-6 390e-6 425e-6 465e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[]
[ICs]
[conc_Cs]
type = ConstantIC
block = fuel
value = 1
variable = conc_Cs
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1873.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = 'if(t<720000,1873.15,2073.15)'
variable = temperature
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[]
[Materials]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
# 5.5e-14*exp(2/5) = 8.2e-14
d1 = 8.2e-14 # m^2/s
# 1.7202e10 = 1e-6 / (8.2e-14*exp(-125e3/8.3145/2073.15))
d1_function = 'if(t<720000,1,1.7202e10)'
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 1e-22
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 1440000
num_steps = 1000
dt = 3600
dtmax = 3600
dtmin = 3600
[]
[Postprocessors]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
execute_on = final
[]
[]
(test/tests/triso_failure/triso_failure_diffusivity.i)
kernel_radius = 213.35e-6
buffer_thickness = 98.9e-6
IPyC_thickness = 40.4e-6
SiC_thickness = 35.2e-6
OPyC_thickness = 43.4e-6
coordinates1 = '${fparse kernel_radius}'
coordinates2 = '${fparse coordinates1+buffer_thickness}'
coordinates3 = '${fparse coordinates2+IPyC_thickness}'
coordinates4 = '${fparse coordinates3+SiC_thickness}'
coordinates5 = '${fparse coordinates4+OPyC_thickness}'
[GlobalParams]
order = FIRST
family = LAGRANGE
displacements = 'disp_x'
initial_enrichment = 0.14029 # [wt-]
flux_conversion_factor = 1.0 # convert E>0.10 to E>0.18 MeV
stress_free_temperature = 481 # used for thermal expansion
energy_per_fission = 3.204e-11 # [J/fission]
O_U = 1.428 # Initial Oxygen to Uranium atom ratio
C_U = 0.392 # Initial Carbon to Uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[mesh]
type = TRISO1DMeshGenerator
elem_type = EDGE2
coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
mesh_density = '18 14 0 12 16 16'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Physics/SolidMechanics/QuasiStatic]
generate_output = 'stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz max_principal_stress'
add_variables = true
strain = FINITE
incremental = true
[fuel]
block = fuel
eigenstrain_names = 'UCO_swelling_eigenstrain UCO_TE_strain'
extra_vector_tags = 'ref'
[]
[buffer]
block = buffer
eigenstrain_names = 'Buffer_IIDC_strain Buffer_TE_strain'
extra_vector_tags = 'ref'
[]
[IPyC]
block = IPyC
eigenstrain_names = 'IPyC_IIDC_strain IPyC_TE_strain'
extra_vector_tags = 'ref'
[]
[SiC]
block = SiC
eigenstrain_names = 'SiC_thermal_eigenstrain'
extra_vector_tags = 'ref'
[]
[OPyC]
block = OPyC
eigenstrain_names = 'OPyC_IIDC_strain OPyC_TE_strain'
extra_vector_tags = 'ref'
[]
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = OPyC_outer_boundary
outer_SiC = SiC_outer_boundary
outer_IPyC = IPyC_outer_boundary
inner_IPyC = IPyC_inner_boundary
outer_buffer = buffer_outer_boundary
outer_kernel = fuel_outer_boundary
include_particle = true
include_pebble = false
IPyC_thickness_mean = ${IPyC_thickness}
SiC_thickness_mean = ${SiC_thickness}
OPyC_thickness_mean = ${OPyC_thickness}
[]
[]
[Variables]
[temperature]
initial_condition = 873.15
[]
[conc_Ag]
initial_condition = 0.0
scaling = 1e12
[]
[]
[AuxVariables]
[bounds_dummy]
order = FIRST
family = LAGRANGE
[]
[fission_rate]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_flux]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
order = CONSTANT
family = MONOMIAL
[]
[fis_gas_produced]
order = CONSTANT
family = MONOMIAL
[]
[fis_gas_released]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[power_history]
type = PiecewiseLinear
x = '0 76e6'
y = '1 1'
[]
[fission_rate]
type = LinearCombinationFunction
functions = power_history
w = 7.78e19
[]
[high_fidelity_strength_crackedIPyC]
type = ConstantFunction
value = '1403604095.5707'
[]
[stress_correlation_crackedIPyC]
type = TRISOStressCorrelationFunction
triso_geometry = particle_geometry
polynomial_coefficients_IPyC = '1 0 0'
polynomial_coefficients_SiC = '1 0 0'
polynomial_coefficients_OPyC = '1 0 0'
correlation_factor = -4.0
[]
[high_fidelity_strength_asphericity]
type = ConstantFunction
value = '1371700766.8875'
[]
[stress_correlation_asphericity]
type = TRISOStressCorrelationFunction
triso_geometry = particle_geometry
polynomial_coefficients_IPyC = '1 0 0'
polynomial_coefficients_SiC = '1 0 0'
polynomial_coefficients_OPyC = '1 0 0'
correlation_factor = 1.5191967987843993
[]
[stress_change_correlation_asphericity]
type = TRISOStressCorrelationFunction
triso_geometry = particle_geometry
polynomial_coefficients_IPyC = '1 0 0'
polynomial_coefficients_SiC = '1 0 0'
polynomial_coefficients_OPyC = '1 0 0'
correlation_factor = 1.391516859626456
[]
[d_gap]
type = PiecewiseLinear
x = '1500 2100'
y = '1e-14 1e-12'
[]
[ag_d1]
type = ParsedFunction
symbol_values = 'sic_failure_overall'
symbol_names = 'failure'
expression = 'if(failure > 0.5,1e-6,3.6e-9)'
[]
[ag_q1]
type = ParsedFunction
symbol_values = 'sic_failure_overall'
symbol_names = 'failure'
expression = 'if(failure > 0.5,0,215e3)'
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[fissionrate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = fuel
execute_on = timestep_begin
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = fuel
execute_on = timestep_begin
[]
[fast_neutron_flux]
type = MaterialRealAux
variable = fast_neutron_flux
property = fast_neutron_flux
execute_on = timestep_begin
[]
[fast_neutron_fluence]
type = MaterialRealAux
variable = fast_neutron_fluence
property = fast_neutron_fluence
execute_on = timestep_begin
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[]
[BCs]
[freesurf_temp]
type = FunctionDirichletBC
variable = temperature
function = 873.15
boundary = exterior
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure]
[plenumPressure]
boundary = buffer_IPyC_boundary
startup_time = 1e4
initial_pressure = 0
output_initial_moles = initial_moles
temperature = ave_gas_temp
volume = 'gap_volume buffer_void_volume kernel_void_volume'
material_input = 'fis_gas_released'
output = gas_pressure
[]
[]
[]
[Controls]
[ag_d1]
type = RealFunctionControl
parameter = 'Materials/SiC_conc_Ag/d1'
function = 'ag_d1'
execute_on = 'INITIAL TIMESTEP_BEGIN'
[]
[ag_q1]
type = RealFunctionControl
parameter = 'Materials/SiC_conc_Ag/q1'
function = 'ag_q1'
execute_on = 'INITIAL TIMESTEP_BEGIN'
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
#block = fuel
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
flux_function = power_history
factor = 1.16e18
[]
# Arrhenius diffusion coefficients for kernel, PyC, and SiC
# come from IAEA TECDOC-978, French parameters.
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
property_name = Ag_generation
kind = Ag
block = fuel
[]
### Buffer Properties
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0.0
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
### IPyC properties
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
### SiC properties
[SiC_conc_Ag]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
### OPyC properties
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[UCO_burnup]
type = TRISOBurnup
initial_density = 10966
block = fuel
[]
[UCO_thermal]
type = UCOThermal
block = fuel
temperature = temperature
[]
[UCO_elasticity_tensor]
type = UCOElasticityTensor
block = fuel
temperature = temperature
[]
[UCO_stress]
type = ComputeFiniteStrainElasticStress
block = fuel
[]
[UCO_VolumetricSwellingEigenstrain]
type = UCOVolumetricSwellingEigenstrain
block = fuel
eigenstrain_name = UCO_swelling_eigenstrain
[]
[fuel_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10.0e-6
temperature = temperature
eigenstrain_name = UCO_TE_strain
[]
[UCO_density]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10966
[]
[fission_gas_release]
type = UCOFGR
block = fuel
average_grain_radius = 10e-6
temperature = temperature
triso_geometry = particle_geometry
cutoff_neutron_flux = 0.0
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'buffer IPyC OPyC'
[]
[BAF_IPyC]
type = BaconAnisotropyFactor
initial_BAF = 1.0465
block = IPyC
[]
[BAF_OPyC]
type = BaconAnisotropyFactor
initial_BAF = 1.0429
block = OPyC
[]
[buffer_elasticity_tensor]
type = BufferElasticityTensor
block = buffer
temperature = temperature
[]
[buffer_stress]
type = BufferCEGACreep
block = buffer
temperature = temperature
[]
[buffer_thermal]
type = BufferThermal
block = buffer
initial_density = 1050.0
[]
[buffer_density]
type = StrainAdjustedDensity
block = buffer
strain_free_density = 1050.0
[]
[buffer_TE]
type = BufferThermalExpansionEigenstrain
block = buffer
eigenstrain_name = Buffer_TE_strain
temperature = temperature
[]
[buffer_IIDC]
type = BufferCEGAIrradiationEigenstrain
block = buffer
eigenstrain_name = Buffer_IIDC_strain
temperature = temperature
[]
[IPyC_elasticity_tensor]
type = PyCElasticityTensor
block = IPyC
temperature = temperature
[]
[IPyC_stress]
type = PyCCEGACreep
block = IPyC
creep_rate_scale_factor = 1
temperature = temperature
[]
[IPyC_thermal]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_density]
type = GenericConstantMaterial
block = IPyC
prop_names = 'density'
prop_values = 1890
[]
[IPyC_IIDC]
type = PyCCEGAIrradiationEigenstrain
block = IPyC
eigenstrain_name = IPyC_IIDC_strain
temperature = temperature
irradiation_eigenstrain_scale_factor = 1
[]
[IPyC_TE]
type = PyCThermalExpansionEigenstrain
block = IPyC
eigenstrain_name = IPyC_TE_strain
temperature = temperature
[]
[SiC_elasticity_tensor]
type = MonolithicSiCElasticityTensor
block = SiC
temperature = temperature
elastic_modulus_model = miller
[]
[SiC_stress]
type = ComputeFiniteStrainElasticStress
block = SiC
[]
[SiC_thermal]
type = MonolithicSiCThermal
block = SiC
temperature = temperature
thermal_conductivity_model = miller
[]
[SiC_density]
type = StrainAdjustedDensity
block = SiC
strain_free_density = 3200.0
[]
[SiC_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
temperature = temperature
eigenstrain_name = SiC_thermal_eigenstrain
[]
[OPyC_elasticity_tensor]
type = PyCElasticityTensor
block = OPyC
temperature = temperature
initial_BAF = 1.0
[]
[OPyC_stress]
type = PyCCEGACreep
block = OPyC
creep_rate_scale_factor = 1
temperature = temperature
[]
[OPyC_thermal_conductivity]
type = HeatConductionMaterial
block = OPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[OPyC_density]
type = GenericConstantMaterial
block = OPyC
prop_names = 'density'
prop_values = 1900
[]
[OPyC_IIDC]
type = PyCCEGAIrradiationEigenstrain
block = OPyC
eigenstrain_name = OPyC_IIDC_strain
temperature = temperature
irradiation_eigenstrain_scale_factor = 1
[]
[OPyC_TE]
type = PyCThermalExpansionEigenstrain
block = OPyC
eigenstrain_name = OPyC_TE_strain
temperature = temperature
[]
[characteristic_strength_SiC]
type = GenericConstantMaterial
prop_values = '9640000'
block = SiC
prop_names = 'characteristic_strength'
[]
[characteristic_strength_PyC]
type = PyCCharacteristicStrength
temperature = temperature
X = 1.02
block = 'IPyC OPyC'
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
initial_gas_types = 'Kr Xe'
initial_fractions = '0.185 0.815'
gas_released = 'fis_gas_released'
released_gas_types = 'Kr Xe'
released_fractions = '0.185 0.815'
tangential_tolerance = 1e-6
roughness_primary = 0e-6
roughness_secondary = 0e-6
jumpdistance_primary = 0
jumpdistance_secondary = 0
quadrature = true
emissivity_secondary = 0.0
emissivity_primary = 0.0
min_gap = 1e-7
max_gap = 50e-6
gap_geometry_type = sphere
[]
[conc_Ag]
type = GapHeatTransfer
variable = conc_Ag
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
tangential_tolerance = 1e-6
gap_conductivity_function = d_gap
gap_conductivity_function_variable = temperature
appended_property_name = _conc_Ag
quadrature = true
gap_geometry_type = sphere
emissivity_primary = 0.0
emissivity_secondary = 0.0
min_gap = 1e-7
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu'
line_search = 'none'
nl_rel_tol = 1e-7
nl_abs_tol = 1e-7
nl_max_its = 20
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 4.831315e7
dtmin = 1e-4
[TimeStepper]
type = IterationAdaptiveDT
dt = 20
growth_factor = 1.5
optimal_iterations = 8 #6
linear_iteration_ratio = 100
time_t = '0 76e6 76.001e6 84.641e6 84.6482e6'
time_dt = '20 20 20 20 20'
[]
[]
[Postprocessors]
[ave_gas_temp]
type = ElementAverageValue
block = buffer
variable = temperature
execute_on = 'initial timestep_end'
[]
[gap_volume]
type = InternalVolume
boundary = buffer_IPyC_boundary
execute_on = 'initial linear'
use_displaced_mesh = true
[]
[buffer_void_volume]
type = VoidVolume
block = buffer
theoretical_density = 2250
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[kernel_th_density]
type = UCOTheoreticalDensity
execute_on = initial
[]
[kernel_void_volume]
type = VoidVolume
block = fuel
theoretical_density = kernel_th_density
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[release_heat_inc]
type = SideIntegralMassFlux
variable = temperature
boundary = exterior
arrhenius_prpty_name = thermal_conductivity
execute_on = 'initial timestep_end'
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor # computes time integration of value
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
[]
[fis_gas_produced]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_produced
block = fuel
execute_on = 'initial timestep_end'
[]
[fis_gas_released]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_released
block = fuel
execute_on = 'initial linear timestep_end'
[]
### Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
execute_on = 'initial timestep_end'
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
execute_on = 'initial timestep_end'
[]
##### irradiation conditions
[particle_power]
type = ElementIntegralPower
variable = temperature
use_material_fission_rate = true
fission_rate_material = fission_rate
block = fuel
execute_on = 'initial timestep_end'
[]
[max_fluence]
type = ElementExtremeValue
variable = fast_neutron_fluence
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_burnup]
type = ElementExtremeValue
variable = burnup
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[SiC_stress]
type = ElementExtremeMaterialProperty
block = SiC
value_type = min
mat_prop = stress_yy
[]
[strength_SiC]
type = WeibullEffectiveMeanStrength
block = SiC
weibull_modulus = 6
[]
[failure_indicator_SiC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = stress_yy
high_fidelity_analysis_strength = 'high_fidelity_strength_asphericity'
stress_correlation_function = 'stress_correlation_asphericity'
stress_change_correlation_function = 'stress_change_correlation_asphericity'
[]
[strength_IPyC]
type = WeibullEffectiveMeanStrength
block = IPyC
weibull_modulus = 9.5
[]
[failure_indicator_IPyC]
type = WeibullFailureOutputUsingCorrelation
block = IPyC
weibull_modulus = 9.5
stress_name = max_principal_stress
effective_mean_strength = strength_IPyC
[]
[failure_indicator_SiC_crackedIPyC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = stress_yy
high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
stress_correlation_function = 'stress_correlation_crackedIPyC'
[]
[sic_failure_overall]
type = TRISOFailureEvaluation
IPyC_failure = failure_indicator_IPyC
SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
SiC_failure = failure_indicator_SiC
SiC_failure_pd_penetration = failure_indicator_pd_penetration
failure_type = SIC_FAILURE_OVERALL
[]
[ipyc_cracking]
type = TRISOFailureEvaluation
IPyC_failure = failure_indicator_IPyC
SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
SiC_failure = failure_indicator_SiC
failure_type = IPYC_CRACKING
[]
[sic_failure_due_to_pressure]
type = TRISOFailureEvaluation
IPyC_failure = failure_indicator_IPyC
SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
SiC_failure = failure_indicator_SiC
failure_type = SIC_FAILURE_DUE_TO_PRESSURE
[]
[sic_failure_due_to_ipyc_cracking]
type = TRISOFailureEvaluation
IPyC_failure = failure_indicator_IPyC
SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
SiC_failure = failure_indicator_SiC
failure_type = SIC_FAILURE_DUE_TO_IPYC_CRACKING
[]
[weibull_failure_probability_IPyC]
type = WeibullFailureProbability
block = IPyC
weibull_modulus = 9.5
characteristic_strength = characteristic_strength
[]
[weibull_failure_probability_SiC]
type = WeibullFailureProbability
block = SiC
weibull_modulus = 6
characteristic_strength = characteristic_strength
[]
[pd_penetration]
type = PdPenetration
boundary = SiC_inner_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
[failure_indicator_pd_penetration]
type = PdPenetrationFailureIndicator
triso_geometry = particle_geometry
pd_penetration = pd_penetration
[]
[]
[Outputs]
csv = true
[]
(assessment/verification/TRISO_diffusion/inpile/inpile.i)
#
# TRISO kernel in 1D spherical
#
# In-pile, a decaying fission product
# -------------------------------
# Non-zero source, p/=0
# Decaying fission product, decay_const/=0
# Zero initial concentration, C0=0
#
timestep = 100
p = 1.0
C0 = 0.0
decay_const = 1e-5
Dprime = 1e-4
kernel_radius = 212.5e-6
[GlobalParams]
order = SECOND
family = LAGRANGE
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 ${kernel_radius}'
mesh_density = 100
block_names = 'fuel'
bias = 1
dual_bias = 0.8
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc]
initial_condition = '${C0}'
[]
[]
[Kernels]
[mass_dt]
type = TimeDerivative
variable = conc
[]
[mass]
type = MatDiffusion
variable = conc
diffusivity = diffusion_coef
extra_vector_tags = 'ref'
[]
[mass_source]
type = BodyForce
variable = conc
value = '${p}'
extra_vector_tags = 'ref'
[]
[decay]
type = Decay
variable = conc
radioactive_decay_constant = ${decay_const}
extra_vector_tags = 'ref'
[]
[]
[BCs]
[freesurf_conc]
type = DirichletBC
variable = conc
boundary = exterior
value = 0.0
[]
[]
[Materials]
[fuel_conc]
type = GenericConstantMaterial
block = fuel
prop_names = diffusion_coef
prop_values = '${fparse Dprime*kernel_radius^2}'
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-10
nl_abs_tol = 1e-20
nl_max_its = 20
l_tol = 1e-8
l_max_its = 30
start_time = 0.0
end_time = '${fparse 1/Dprime}'
num_steps = 100
dtmax = '${timestep}'
dtmin = '${timestep}'
[Predictor]
type = SimplePredictor
scale = 1.0
[]
[]
[Functions]
[analytic]
type = ParsedFunction
symbol_names = 'mu'
symbol_values = '${fparse decay_const/Dprime}'
expression = '1-sinh(x*sqrt(mu))/(x*sinh(sqrt(mu)))'
[]
[]
[Postprocessors]
[dt]
type = TimestepSize
execute_on = timestep_end
[]
# Release rate
[release_inc]
type = SideIntegralMassFlux
variable = conc
boundary = exterior
arrhenius_prpty_name = diffusion_coef
execute_on = 'initial timestep_end'
[]
[released]
type = TimeIntegratedPostprocessor
value = release_inc
execute_on = 'initial timestep_end'
[]
[total]
type = ElementIntegralVariablePostprocessor
variable = conc
execute_on = 'initial timestep_end'
[]
[x_released]
type = FractionalRelease
released = released
retained = retained
[]
[retained]
type = ElementIntegralVariablePostprocessor
variable = conc
[]
[conc_point_25]
type = PointValue
variable = conc
point = '${fparse 0.25*kernel_radius} 0 0'
execute_on = 'initial timestep_end'
[]
[conc_point_50]
type = PointValue
variable = conc
point = '${fparse 0.50*kernel_radius} 0 0'
execute_on = 'initial timestep_end'
[]
[conc_point_75]
type = PointValue
variable = conc
point = '${fparse 0.75*kernel_radius} 0 0'
execute_on = 'initial timestep_end'
[]
[conc_point_95]
type = PointValue
variable = conc
point = '${fparse 0.95*kernel_radius} 0 0'
execute_on = 'initial timestep_end'
[]
[bison_dimensionless_25]
type = ParsedPostprocessor
expression = 'conc_point_25 / (p / lambda)'
pp_names = conc_point_25
constant_names = 'p lambda'
constant_expressions = '${p} ${decay_const}'
execute_on = 'initial timestep_end'
[]
[bison_dimensionless_50]
type = ParsedPostprocessor
expression = 'conc_point_50 / (p / lambda)'
pp_names = conc_point_50
constant_names = 'p lambda'
constant_expressions = '${p} ${decay_const}'
execute_on = 'initial timestep_end'
[]
[bison_dimensionless_75]
type = ParsedPostprocessor
expression = 'conc_point_75 / (p / lambda)'
pp_names = conc_point_75
constant_names = 'p lambda'
constant_expressions = '${p} ${decay_const}'
execute_on = 'initial timestep_end'
[]
[bison_dimensionless_95]
type = ParsedPostprocessor
expression = 'conc_point_95 / (p / lambda)'
pp_names = conc_point_95
constant_names = 'p lambda'
constant_expressions = '${p} ${decay_const}'
execute_on = 'initial timestep_end'
[]
[analytic_dimensionless_25]
type = FunctionValuePostprocessor
function = analytic
point = '0.25 0 0'
execute_on = 'initial timestep_end'
[]
[analytic_dimensionless_50]
type = FunctionValuePostprocessor
function = analytic
point = '0.50 0 0'
execute_on = 'initial timestep_end'
[]
[analytic_dimensionless_75]
type = FunctionValuePostprocessor
function = analytic
point = '0.75 0 0'
execute_on = 'initial timestep_end'
[]
[analytic_dimensionless_95]
type = FunctionValuePostprocessor
function = analytic
point = '0.95 0 0'
execute_on = 'initial timestep_end'
[]
[error_25]
type = ParsedPostprocessor
pp_names = 'bison_dimensionless_25 analytic_dimensionless_25'
expression = '(bison_dimensionless_25 - analytic_dimensionless_25)/analytic_dimensionless_25*100'
execute_on = 'initial timestep_end'
[]
[error_50]
type = ParsedPostprocessor
pp_names = 'bison_dimensionless_50 analytic_dimensionless_50'
expression = '(bison_dimensionless_50 - analytic_dimensionless_50)/analytic_dimensionless_50*100'
execute_on = 'initial timestep_end'
[]
[error_75]
type = ParsedPostprocessor
pp_names = 'bison_dimensionless_75 analytic_dimensionless_75'
expression = '(bison_dimensionless_75 - analytic_dimensionless_75)/analytic_dimensionless_75*100'
execute_on = 'initial timestep_end'
[]
[error_95]
type = ParsedPostprocessor
pp_names = 'bison_dimensionless_95 analytic_dimensionless_95'
expression = '(bison_dimensionless_95 - analytic_dimensionless_95)/analytic_dimensionless_95*100'
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
time_step_interval = 1
exodus = false
print_linear_converged_reason = false
print_linear_residuals = false
print_nonlinear_converged_reason = false
[console]
type = Console
show = 'analytic_dimensionless_25 analytic_dimensionless_50 analytic_dimensionless_75 analytic_dimensionless_95
bison_dimensionless_25 bison_dimensionless_50 bison_dimensionless_75 bison_dimensionless_95
error_25 error_50 error_75 error_95 released x_released'
[]
[out]
type = CSV
execute_on = final
[]
[]
(examples/TRISO/full_particle/1D/full_particle_1D.i)
initial_fuel_density = 10810.0
[GlobalParams]
density = ${initial_fuel_density}
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
mesh_density = '6 6 0 6 8 6'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Variables]
[temperature]
initial_condition = 1346.0
[]
[]
[AuxVariables]
[fission_rate]
block = fuel
[]
[burnup]
block = fuel
[]
[grain_radius]
initial_condition = 5.0e-6
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[fuel]
block = fuel
add_variables = true
strain = FINITE
eigenstrain_names = 'fuel_thermal_strain'
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
[]
[buffer]
block = buffer
add_variables = true
strain = FINITE
eigenstrain_names = 'buffer_thermal_strain buffer_eigenstrain'
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
[]
[IPyC]
block = IPyC
add_variables = true
strain = FINITE
eigenstrain_names = 'IPyC_eigenstrain IPyC_thermal_strain'
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
[]
[SiC]
block = SiC
add_variables = true
strain = FINITE
eigenstrain_names = 'SiC_thermal_strain'
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
[]
[OPyC]
block = OPyC
add_variables = true
strain = FINITE
eigenstrain_names = 'OPyC_eigenstrain OPyC_thermal_strain'
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
[]
[]
[Functions]
[fission_rate]
type = ParsedFunction
expression = 7.75e19
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
[]
[heat]
type = HeatConduction
variable = temperature
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
energy_per_fission = 3.2e-11
fission_rate = fission_rate
[]
[]
[AuxKernels]
[fission_rate]
type = FunctionAux
variable = fission_rate
block = fuel
function = fission_rate
[]
[burnup]
type = BurnupAux
variable = burnup
block = fuel
fission_rate = fission_rate
molecular_weight = 0.270
[]
[grain_radius]
type = GrainRadiusAux
block = fuel
variable = grain_radius
temperature = temperature
execute_on = linear
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
penalty = 1e5
model = frictionless
formulation = kinematic
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
# coupling to a postprocessor
initial_moles = initial_moles
gas_released = 'fis_gas_released co_production'
released_gas_types = 'Kr Xe;
CO'
released_fractions = '0.153 0.847;
1'
tangential_tolerance = 1e-6
[]
[]
[BCs]
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[freesurf_temperature]
type = DirichletBC
variable = temperature
boundary = exterior
value = 1346.0
[]
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure] # apply gas pressure on buffer and IPyC boundaries
[plenumPressure]
boundary = buffer_IPyC_boundary
initial_pressure = 0
startup_time = 1.0e4
R = 8.3143
# couplings to post processor
output_initial_moles = initial_moles
temperature = ave_temperature_interior
volume = volumeGas
material_input = 'fis_gas_released co_production'
output = plenum_pressure
[]
[]
[]
[Materials]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 1.708707e18 # n/m^2-sec
[]
[fuel_thermal]
type = UO2Thermal
block = fuel
temperature = temperature
thermal_conductivity_model = FINK_LUCUTA
initial_porosity = 0.0
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 2.0e8
poissons_ratio = 0.345
[]
[fuel_elastic_stress]
type = ComputeFiniteStrainElasticStress
block = fuel
[]
[fuel_density]
type = StrainAdjustedDensity
block = fuel
strain_free_density = ${initial_fuel_density}
[]
[fuel_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10.0e-6
temperature = temperature
stress_free_temperature = 1346.0
eigenstrain_name = fuel_thermal_strain
[]
[fission_gas_release]
type = UO2Sifgrs
block = fuel
temperature = temperature
fission_rate = fission_rate
grain_radius = grain_radius
[]
[buffer_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 2.0e8
poissons_ratio = 0.345
[]
[buffer_elastic_stress]
type = ComputeFiniteStrainElasticStress
block = buffer
[]
[buffer_temperature]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5
specific_heat = 720.0
[]
[buffer_density]
type = StrainAdjustedDensity
strain_free_density = 1000.0
block = buffer
[]
[buffer_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = buffer
thermal_expansion_coeff = 5.5e-6
temperature = temperature
stress_free_temperature = 1346.0
eigenstrain_name = buffer_thermal_strain
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'IPyC OPyC buffer'
[]
[buffer_irraditation]
type = PyCIrradiationEigenstrain
block = buffer
pyc_type = buffer
eigenstrain_name = buffer_eigenstrain
[]
[IPyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = IPyC
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[IOPyC_stress]
type = PyCCreep
block = 'IPyC OPyC'
temperature = temperature
[]
[IOPyC_thermal]
type = HeatConductionMaterial
block = 'IPyC OPyC'
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IOPyC_density]
type = StrainAdjustedDensity
strain_free_density = 1880.0
block = 'IPyC OPyC'
[]
[IPyC_densification]
type = PyCIrradiationEigenstrain
block = IPyC
pyc_type = dense
eigenstrain_name = IPyC_eigenstrain
[]
[IPyC_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = IPyC
thermal_expansion_coeff = 5.5e-6
temperature = temperature
stress_free_temperature = 1346.0
eigenstrain_name = IPyC_thermal_strain
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_elastic_stress]
type = ComputeFiniteStrainElasticStress
block = SiC
[]
[SiC_temperature]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9
specific_heat = 620.0
[]
[SiC_density]
type = StrainAdjustedDensity
strain_free_density = 3200.0
block = SiC
[]
[SiC_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
temperature = temperature
stress_free_temperature = 1346.0
eigenstrain_name = SiC_thermal_strain
[]
[OPyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = OPyC
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[OPyC_densification]
type = PyCIrradiationEigenstrain
block = OPyC
pyc_type = dense
eigenstrain_name = OPyC_eigenstrain
[]
[OPyC_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = OPyC
thermal_expansion_coeff = 5.5e-6
temperature = temperature
stress_free_temperature = 1346.0
eigenstrain_name = OPyC_thermal_strain
[]
[]
[Dampers]
[temperature]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 3.10176e7
dtmax = 2e5
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 20
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[dt]
type = TimestepSize
[]
[burnup]
type = ElementExtremeValue
block = fuel
variable = burnup
[]
[fis_gas_produced]
type = ElementIntegralFisGasGeneratedSifgrs
block = fuel
[]
[fis_gas_released]
type = ElementIntegralFisGasReleasedSifgrs
block = fuel
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
[]
[volumeFuel]
type = InternalVolume
boundary = fuel_outer_boundary
[]
[volumeGas]
type = InternalVolume
boundary = 'fuel_outer_boundary IPyC_inner_boundary'
addition = -5.53e-11
execute_on = 'initial timestep_end'
[]
[volumeBufferShell]
type = InternalVolume
boundary = buffer_IPyC_boundary
[]
[ave_temperature_interior]
type = SideAverageValue
boundary = buffer_IPyC_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
[]
[avg_surface_temperature]
type = SideAverageValue
variable = temperature
boundary = exterior
[]
[time_int_surf_temperature]
type = TimeIntegratedPostprocessor
value = avg_surface_temperature
[]
[co_production]
type = CarbonMonoxideProduction
total_fissions = total_fissions
time_integrated_triso_temperature = time_int_surf_temperature
initial_enrichment = 0.14029
[]
[tang_SiC]
type = ElementalVariableValue
variable = stress_yy
elementid = 18
[]
[max_xx_IPyC]
type = ElementExtremeValue
variable = stress_xx
block = IPyC
[]
[max_yy_IPyC]
type = ElementExtremeValue
variable = stress_yy
block = IPyC
[]
[min_zz_IPyC]
type = ElementExtremeValue
variable = stress_zz
block = IPyC
value_type = min
[]
[max_xx_SiC]
type = ElementExtremeValue
variable = stress_xx
block = SiC
[]
[max_yy_SiC]
type = ElementExtremeValue
variable = stress_yy
block = SiC
[]
[min_zz_SiC]
type = ElementExtremeValue
variable = stress_zz
block = SiC
value_type = min
[]
[max_xx_OPyC]
type = ElementExtremeValue
variable = stress_xx
block = OPyC
[]
[max_yy_OPyC]
type = ElementExtremeValue
variable = stress_yy
block = OPyC
[]
[min_zz_OPyC]
type = ElementExtremeValue
variable = stress_zz
block = OPyC
value_type = min
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = false
csv = true
perf_graph = true
[chkfile]
type = CSV
execute_on = Final
show = 'max_xx_IPyC max_yy_IPyC min_zz_IPyC max_xx_SiC max_yy_SiC min_zz_SiC'
[]
[]
(test/tests/triso/UCOFGR/UCOFGR.i)
# Fission Gas Release Model High Temperature
# The geometry is a 1D sphere with a diameter of 425 micrometers and an average
# grain radius of 10 microns.
# The fission gas yield was set to 0.297.
# The temperature is ramped from 673.15 to 3073.15 K.
# The fission rate density is ramped from 0 to 1.1625e21 fission/m^3-s
# (3.72e10 W/m^3) over 1e4 seconds and held constant.
# The density of the kernel is set to 11250 kg/m^3, the Oxygen to Uranium ratio
# is set to 1.5, the Carbon to Uranium ratio is set to 0.4, and the initial
# U-235 enrichment is set to 15%.
#
[GlobalParams]
order = FIRST
family = LAGRANGE
O_U = 1.5
C_U = 0.4
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.125e-4'
mesh_density = '6'
block_names = 'fuel'
[]
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = '2'
outer_SiC = '2'
outer_IPyC = '2'
inner_IPyC = '2'
outer_buffer = '2'
outer_kernel = '2'
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temp]
initial_condition = 673.15
[]
[]
[AuxVariables]
[fission_rate]
block = '1'
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = '1'
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[fission_rate]
type = PiecewiseLinear
x = '0 1e4 1e8'
y = '0 1.1625e21 1.1625e21'
[]
[scaled_time]
type = ParsedFunction
# molar mass / Avogadro's number / density
# 0.266 / 6.022e23 / 11250 = 3.926e-29
expression = '3.926e-29*t'
[]
[burnup]
type = CompositeFunction
functions = 'fission_rate scaled_time'
[]
[temp_function]
type = PiecewiseLinear
x = '0 7.5e6'
y = '673.15 3073.15'
[]
[]
[Kernels]
[heat]
type = HeatConduction
variable = temp
[]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temp
[]
[]
[AuxKernels]
[fission_rate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = '1'
execute_on = timestep_end
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = '1'
execute_on = timestep_end
[]
[]
[BCs]
[heat_removal]
type = FunctionDirichletBC
variable = temp
boundary = 'xzero exterior'
function = temp_function
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[burnup]
type = GenericFunctionMaterial
prop_names = burnup
prop_values = burnup
[]
[thermal]
type = HeatConductionMaterial
block = '1'
thermal_conductivity = 1.0
specific_heat = 1.0
[]
[fission_gas_release]
type = UCOFGR
block = '1'
average_grain_radius = 10e-6
triso_geometry = particle_geometry
temperature = temp
fast_neutron_flux = 1e15
cutoff_neutron_flux = 0.0
[]
[UCO_density]
type = ParsedMaterial
block = '1'
property_name = density
expression = 11250.0
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 51'
line_search = 'none'
l_max_its = 50
l_tol = 1e-2
nl_max_its = 150
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
start_time = 0.0
#end_time = 7.5e6 # use to test full range of parameters
end_time = 1e4
num_steps = 140
dtmax = 2e6
dtmin = 1.0
[TimeStepper]
type = IterationAdaptiveDT
dt = 1e3
time_t = '1e4 1e5'
time_dt = '1e3 1e5'
[]
[]
[Postprocessors]
[temp]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = temp
execute_on = 'initial timestep_end'
[]
[burnup]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = burnup
execute_on = 'initial timestep_end'
[]
[fission_rate]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = fission_rate
execute_on = 'initial timestep_end'
[]
[_dt]
type = TimestepSize
[]
[FGP]
type = ElementIntegralMaterialProperty
block = '1'
mat_prop = fis_gas_produced
execute_on = 'initial timestep_end'
[]
[FGR]
type = ElementIntegralMaterialProperty
block = '1'
mat_prop = fis_gas_released
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
csv = true
[]
(test/tests/triso/UNFGR/UNFGR.i)
[GlobalParams]
order = FIRST
family = LAGRANGE
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.125e-4'
mesh_density = '6'
block_names = 'fuel'
[]
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = '2'
outer_SiC = '2'
outer_IPyC = '2'
inner_IPyC = '2'
outer_buffer = '2'
outer_kernel = '2'
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temp]
initial_condition = 673.15
[]
[]
[AuxVariables]
[fission_rate]
block = '1'
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = '1'
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[fission_rate]
type = PiecewiseLinear
x = '0 1e4 1e8'
y = '0 1.1625e21 1.1625e21'
[]
[scaled_time]
type = ParsedFunction
# molar mass / Avogadro's number / density
# 0.266 / 6.022e23 / 11250 = 3.926e-29
expression = '3.926e-29*t'
[]
[burnup]
type = CompositeFunction
functions = 'fission_rate scaled_time'
[]
[temp_function]
type = PiecewiseLinear
x = '0 7.5e6'
y = '673.15 3073.15'
[]
[]
[Kernels]
[heat]
type = HeatConduction
variable = temp
[]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temp
[]
[]
[AuxKernels]
[fission_rate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = '1'
execute_on = timestep_end
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = '1'
execute_on = timestep_end
[]
[]
[BCs]
[heat_removal]
type = FunctionDirichletBC
variable = temp
boundary = '1'
function = temp_function
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[burnup]
type = GenericFunctionMaterial
prop_names = burnup
prop_values = burnup
[]
[thermal]
type = HeatConductionMaterial
block = '1'
thermal_conductivity = 1.0
specific_heat = 1.0
[]
[fission_gas_release]
type = UNFGR
block = '1'
average_grain_radius = 10e-6
triso_geometry = particle_geometry
temperature = temp
[]
[UN_density]
type = ParsedMaterial
block = '1'
property_name = density
expression = 13760
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 51'
line_search = 'none'
l_max_its = 50
l_tol = 1e-2
nl_max_its = 150
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
start_time = 0.0
#end_time = 7.5e6 # use to test full range of parameters
end_time = 1e4
num_steps = 140
dtmax = 2e6
dtmin = 1.0
[TimeStepper]
type = IterationAdaptiveDT
dt = 1e3
time_t = '1e4 1e5'
time_dt = '1e3 1e5'
[]
[]
[Postprocessors]
[temp]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = temp
execute_on = 'initial timestep_end'
[]
[burnup]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = burnup
execute_on = 'initial timestep_end'
[]
[fission_rate]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = fission_rate
execute_on = 'initial timestep_end'
[]
[_dt]
type = TimestepSize
[]
[FGP]
type = ElementIntegralMaterialProperty
block = '1'
mat_prop = fis_gas_produced
execute_on = 'initial timestep_end'
[]
[FGR]
type = ElementIntegralMaterialProperty
block = '1'
mat_prop = fis_gas_released
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
csv = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_4c/case_4c_1D.i)
#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# See also Hales, et al., Multidimensional multiphysics simulation of TRISO
# particle fuel, JNM, 443, 2013. https://doi.org/10.1016/j.jnucmat.2013.07.070
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark. The best way to do this is to compare
# results with information in the JNM article.
#
[GlobalParams]
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
use_displaced_mesh = false
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.5e-4 2.5e-4 3.5e-4 3.5e-4 3.9e-4 4.25e-4'
mesh_density = '12 0 20 0 16 16'
block_names = 'fuel buffer IPyC SiC'
[]
[]
[Variables]
[disp_x]
[]
[temperature]
initial_condition = 1273.0
[]
[]
[Functions]
[eigenstrain]
type = ParsedFunction
expression = '-0.005*t'
[]
[k_function]
type = ParsedFunction
expression = '2.715e-29'
[]
[]
[AuxVariables]
[stress_xx]
order = CONSTANT
family = MONOMIAL
[]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[stress_zz]
order = CONSTANT
family = MONOMIAL
[]
[stress_xy]
order = CONSTANT
family = MONOMIAL
[]
[stress_yz]
order = CONSTANT
family = MONOMIAL
[]
[stress_xz]
order = CONSTANT
family = MONOMIAL
[]
[hydrostatic_stress]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
initial_condition = 0.0
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[IPyC]
block = IPyC
strain = small
incremental = true
eigenstrain_names = ipyc_eigenstrain
[]
[rest]
block = 'fuel buffer SiC'
strain = small
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
[]
[heat]
type = HeatConduction
variable = temperature
[]
[]
[AuxKernels]
[stress_xx]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xx
index_i = 0
index_j = 0
execute_on = timestep_end
[]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[stress_zz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_zz
index_i = 2
index_j = 2
execute_on = timestep_end
[]
[stress_xy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xy
index_i = 0
index_j = 1
execute_on = timestep_end
[]
[stress_yz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yz
index_i = 1
index_j = 2
execute_on = timestep_end
[]
[stress_xz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xz
index_i = 0
index_j = 2
execute_on = timestep_end
[]
[hydrostatic_stress]
type = RankTwoScalarAux
rank_two_tensor = stress
variable = hydrostatic_stress
scalar_type = hydrostatic
execute_on = timestep_end
[]
[]
[BCs]
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[freesurf_temperature]
type = DirichletBC
variable = temperature
boundary = exterior
value = 1273.0
[]
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[interior_pressure_x]
type = Pressure
variable = disp_x
boundary = IPyC_inner_boundary
factor = 25e6
[]
[]
[Materials]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 3.75e17 # n/m^2-sec
[]
[stress]
type = ComputeLinearElasticStress
block = 'fuel buffer SiC'
[]
[IPyC_stress]
type = PyCCreep
block = IPyC
k = k_function
temperature = temperature
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
[]
[IPyC_eigenstrain]
type = PyCIrradiationEigenstrain
radial_eigenstrain_function = eigenstrain
tangential_eigenstrain_function = eigenstrain
eigenstrain_name = ipyc_eigenstrain
[]
[fuel_thermal]
type = UO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temperature
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 1
poissons_ratio = 0.345
[]
[fuel_den]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10800.0
[]
[buffer_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 1
poissons_ratio = 0.345
[]
[buffer_temperature]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5
specific_heat = 720.0
[]
[buffer_den]
type = StrainAdjustedDensity
strain_free_density = 950
block = buffer
[]
[IPyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = IPyC
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[IPyC_temperature]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_den]
type = StrainAdjustedDensity
strain_free_density = 1900.0
block = IPyC
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_temperature]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9
specific_heat = 620.0
[]
[SiC_den]
type = StrainAdjustedDensity
strain_free_density = 3180.0
block = SiC
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Dampers]
[temperature]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 8e7
dt = 1.0
dtmax = 5e6
dtmin = 1.0e4
[TimeStepper]
type = IterationAdaptiveDT
dt = 1
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[max_xx_IPyC]
type = ElementExtremeValue
variable = stress_xx
block = IPyC
[]
[max_yy_IPyC]
type = ElementExtremeValue
variable = stress_yy
block = IPyC
[]
[min_zz_IPyC]
type = ElementExtremeValue
variable = stress_zz
block = IPyC
value_type = min
[]
[max_xx_SiC]
type = ElementExtremeValue
variable = stress_xx
block = SiC
[]
[max_yy_SiC]
type = ElementExtremeValue
variable = stress_yy
block = SiC
[]
[min_zz_SiC]
type = ElementExtremeValue
variable = stress_zz
block = SiC
value_type = min
[]
[]
[PerformanceMetricOutputs]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = true
csv = true
perf_graph = true
[]
(test/tests/triso/release_birth_ratio/richards.i)
# Release rate to birth rate ratio (R/B) of short-lived Kr and Xe isotopes from exposed kernels.
# The geometry is a sphere with a diameter of 700 micrometers.
# The temperature is ramped from 773 to 2073 K.
# This test uses the Richards model.
#
[GlobalParams]
U_contamination_fraction = 0.0
exposed_kernel_fraction = 1.0
outside_temperature = 1250
fission_rate = 1.872e18 # fissions/m^3/s
O_U = 1.5
C_U = 0.4
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 350e-6'
mesh_density = '6'
block_names = 'particle'
[]
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = '2'
outer_SiC = '2'
outer_IPyC = '2'
inner_IPyC = '2'
outer_buffer = '2'
outer_kernel = '2'
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temperature]
initial_condition = 773
[]
[]
[Functions]
[temp_function]
type = PiecewiseLinear
x = '0 13'
y = '773 2073'
[]
[]
[Kernels]
[heat]
type = HeatConduction
variable = temperature
[]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
[]
[]
[BCs]
[heat_removal]
type = FunctionDirichletBC
variable = temperature
boundary = '2'
function = temp_function
[]
[]
[Materials]
[thermal]
type = HeatConductionMaterial
block = '1'
thermal_conductivity = 1.0
specific_heat = 1.0
[]
[density]
type = ParsedMaterial
block = '1'
property_name = density
expression = 11250.0
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 51'
line_search = 'none'
l_max_its = 50
l_tol = 1e-2
nl_max_its = 150
nl_rel_tol = 1e-8
start_time = 0
end_time = 13
num_steps = 13
dtmax = 1
dtmin = 1
[]
[Postprocessors]
[temperature]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = temperature
execute_on = 'initial timestep_end'
[]
[average_kernel_temperature]
type = ElementAverageValue
block = '1'
variable = temperature
execute_on = 'initial timestep_end'
[]
[average_matrix_temperature]
type = ElementAverageValue
block = '1'
variable = temperature
execute_on = 'initial timestep_end'
[]
[_dt]
type = TimestepSize
[]
[Kr83m_RB_ratio]
type = ReleaseBirthRatio
model = Richards
isotope = Kr83m
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
mol_weight_gas_medium = 12
initial_density = 11250.0
void_fraction = 0.29
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr85m_RB_ratio]
type = ReleaseBirthRatio
model = Richards
isotope = Kr85m
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
mol_weight_gas_medium = 12
initial_density = 11250.0
void_fraction = 0.29
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr85_RB_ratio]
type = ReleaseBirthRatio
model = Richards
isotope = Kr85
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
mol_weight_gas_medium = 12
initial_density = 11250.0
void_fraction = 0.29
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr87_RB_ratio]
type = ReleaseBirthRatio
model = Richards
isotope = Kr87
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
mol_weight_gas_medium = 12
initial_density = 11250.0
void_fraction = 0.29
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr88_RB_ratio]
type = ReleaseBirthRatio
model = Richards
isotope = Kr88
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
mol_weight_gas_medium = 12
initial_density = 11250.0
void_fraction = 0.29
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr89_RB_ratio]
type = ReleaseBirthRatio
model = Richards
isotope = Kr89
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
mol_weight_gas_medium = 12
initial_density = 11250.0
void_fraction = 0.29
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr90_RB_ratio]
type = ReleaseBirthRatio
model = Richards
isotope = Kr90
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
mol_weight_gas_medium = 12
initial_density = 11250.0
void_fraction = 0.29
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe131m_RB_ratio]
type = ReleaseBirthRatio
model = Richards
isotope = Xe131m
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
mol_weight_gas_medium = 12
initial_density = 11250.0
void_fraction = 0.29
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe133_RB_ratio]
type = ReleaseBirthRatio
model = Richards
isotope = Xe133
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
mol_weight_gas_medium = 12
initial_density = 11250.0
void_fraction = 0.29
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe135_RB_ratio]
type = ReleaseBirthRatio
model = Richards
isotope = Xe135
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
mol_weight_gas_medium = 12
initial_density = 11250.0
void_fraction = 0.29
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe135m_RB_ratio]
type = ReleaseBirthRatio
model = Richards
isotope = Xe135m
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
mol_weight_gas_medium = 12
initial_density = 11250.0
void_fraction = 0.29
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe137_RB_ratio]
type = ReleaseBirthRatio
model = Richards
isotope = Xe137
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
mol_weight_gas_medium = 12
initial_density = 11250.0
void_fraction = 0.29
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe138_RB_ratio]
type = ReleaseBirthRatio
model = Richards
isotope = Xe138
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
mol_weight_gas_medium = 12
initial_density = 11250.0
void_fraction = 0.29
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe139_RB_ratio]
type = ReleaseBirthRatio
model = Richards
isotope = Xe139
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
mol_weight_gas_medium = 12
initial_density = 11250.0
void_fraction = 0.29
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
csv = true
exodus = false
[console]
type = Console
[]
[]
(test/tests/triso/kernel_migration/kernel_migration_distance.i)
kernel_radius = 213.35e-6
buffer_thickness = 98.9e-6
IPyC_thickness = 40.4e-6
SiC_thickness = 35.2e-6
OPyC_thickness = 43.4e-6
coordinates1 = '${fparse kernel_radius}'
coordinates2 = '${fparse coordinates1+buffer_thickness}'
coordinates3 = '${fparse coordinates2+IPyC_thickness}'
coordinates4 = '${fparse coordinates3+SiC_thickness}'
coordinates5 = '${fparse coordinates4+OPyC_thickness}'
[GlobalParams]
order = FIRST
family = LAGRANGE
displacements = 'disp_x'
initial_enrichment = 0.14029 # [wt-]
flux_conversion_factor = 1.0 # convert E>0.10 to E>0.18 MeV
stress_free_temperature = 1573 # used for thermal expansion
energy_per_fission = 3.204e-11 # [J/fission]
O_U = 1.428 # Initial Oxygen to Uranium atom ratio
C_U = 0.392 # Initial Carbon to Uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[mesh]
type = TRISO1DMeshGenerator
elem_type = EDGE2
coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
mesh_density = '20 8 0 4 4 4'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = OPyC_outer_boundary
outer_SiC = SiC_outer_boundary
outer_IPyC = IPyC_outer_boundary
inner_IPyC = IPyC_inner_boundary
outer_buffer = buffer_outer_boundary
outer_kernel = fuel_outer_boundary
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temperature]
initial_condition = 1573
[]
[]
[AuxVariables]
[fission_rate]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_flux]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[fission_rate]
type = ConstantFunction
value = 5.75e19
[]
[]
[Physics/SolidMechanics/QuasiStatic]
generate_output = 'stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz max_principal_stress'
add_variables = true
strain = FINITE
incremental = true
[fuel]
block = fuel
eigenstrain_names = 'UCO_swelling_eigenstrain UCO_TE_strain'
extra_vector_tags = 'ref'
[]
[buffer]
block = buffer
eigenstrain_names = 'Buffer_IIDC_strain Buffer_TE_strain'
extra_vector_tags = 'ref'
[]
[IPyC]
block = IPyC
eigenstrain_names = 'IPyC_IIDC_strain IPyC_TE_strain'
extra_vector_tags = 'ref'
[]
[SiC]
block = SiC
eigenstrain_names = 'SiC_thermal_eigenstrain'
extra_vector_tags = 'ref'
[]
[OPyC]
block = OPyC
eigenstrain_names = 'OPyC_IIDC_strain OPyC_TE_strain'
extra_vector_tags = 'ref'
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[fissionrate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = fuel
execute_on = timestep_begin
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = fuel
execute_on = timestep_begin
[]
[fast_neutron_flux]
type = MaterialRealAux
variable = fast_neutron_flux
property = fast_neutron_flux
execute_on = timestep_begin
[]
[fast_neutron_fluence]
type = MaterialRealAux
variable = fast_neutron_fluence
property = fast_neutron_fluence
execute_on = timestep_begin
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
initial_moles = initial_moles
gas_released = 'fis_gas_released'
released_gas_types = 'Kr Xe'
released_fractions = '0.185 0.815'
tangential_tolerance = 1e-6
quadrature = false
min_gap = 1e-7
max_gap = 50e-6
gap_geometry_type = sphere
[]
[]
[BCs]
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[freesurf_temp]
type = DirichletBC
variable = temperature
value = 1573
boundary = exterior
[]
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure]
[plenumPressure]
boundary = buffer_IPyC_boundary
startup_time = 1e4
initial_pressure = 0
R = 8.3145
output_initial_moles = initial_moles
temperature = ave_gas_temp
volume = 'gap_volume buffer_void_volume kernel_void_volume'
material_input = 'fis_gas_released'
output = gas_pressure
[]
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
block = fuel
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 6.2425e+17
[]
[UCO_burnup]
type = TRISOBurnup
initial_density = 10966
block = fuel
[]
[UCO_thermal]
type = UCOThermal
block = fuel
temperature = temperature
[]
[UCO_elasticity_tensor]
type = UCOElasticityTensor
block = fuel
temperature = temperature
[]
[UCO_stress]
type = ComputeFiniteStrainElasticStress
block = fuel
[]
[UCO_VolumetricSwellingEigenstrain]
type = UCOVolumetricSwellingEigenstrain
block = fuel
eigenstrain_name = UCO_swelling_eigenstrain
[]
[fuel_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10.0e-6
temperature = temperature
eigenstrain_name = UCO_TE_strain
[]
[UCO_density]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10966
[]
[fission_gas_release]
type = UCOFGR
block = fuel
average_grain_radius = 10e-6
temperature = temperature
triso_geometry = particle_geometry
cutoff_neutron_flux = 0.0
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'buffer IPyC OPyC'
[]
[BAF_IPyC]
type = BaconAnisotropyFactor
initial_BAF = 1.0465
block = IPyC
[]
[BAF_OPyC]
type = BaconAnisotropyFactor
initial_BAF = 1.0429
block = OPyC
[]
[buffer_elasticity_tensor]
type = BufferElasticityTensor
block = buffer
temperature = temperature
[]
[buffer_stress]
type = BufferCEGACreep
block = buffer
temperature = temperature
[]
[buffer_thermal]
type = BufferThermal
block = buffer
initial_density = 1050.0
[]
[buffer_density]
type = StrainAdjustedDensity
block = buffer
strain_free_density = 1050.0
[]
[buffer_TE]
type = BufferThermalExpansionEigenstrain
block = buffer
eigenstrain_name = Buffer_TE_strain
temperature = temperature
[]
[buffer_IIDC]
type = BufferCEGAIrradiationEigenstrain
block = buffer
eigenstrain_name = Buffer_IIDC_strain
temperature = temperature
[]
[IPyC_elasticity_tensor]
type = PyCElasticityTensor
block = IPyC
temperature = temperature
[]
[IPyC_stress]
type = PyCCEGACreep
block = IPyC
creep_rate_scale_factor = 1
temperature = temperature
[]
[IPyC_thermal]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_density]
type = GenericConstantMaterial
block = IPyC
prop_names = 'density'
prop_values = 1890
[]
[IPyC_IIDC]
type = PyCCEGAIrradiationEigenstrain
block = IPyC
eigenstrain_name = IPyC_IIDC_strain
temperature = temperature
irradiation_eigenstrain_scale_factor = 1
[]
[IPyC_TE]
type = PyCThermalExpansionEigenstrain
block = IPyC
eigenstrain_name = IPyC_TE_strain
temperature = temperature
[]
[SiC_elasticity_tensor]
type = MonolithicSiCElasticityTensor
block = SiC
temperature = temperature
elastic_modulus_model = miller
[]
[SiC_stress]
type = ComputeFiniteStrainElasticStress
block = SiC
[]
[SiC_thermal]
type = MonolithicSiCThermal
block = SiC
temperature = temperature
thermal_conductivity_model = miller
[]
[SiC_density]
type = StrainAdjustedDensity
block = SiC
strain_free_density = 3200.0
[]
[SiC_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
temperature = temperature
eigenstrain_name = SiC_thermal_eigenstrain
[]
[OPyC_elasticity_tensor]
type = PyCElasticityTensor
block = OPyC
temperature = temperature
initial_BAF = 1.0
[]
[OPyC_stress]
type = PyCCEGACreep
block = OPyC
creep_rate_scale_factor = 1
temperature = temperature
[]
[OPyC_thermal_conductivity]
type = HeatConductionMaterial
block = OPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[OPyC_density]
type = GenericConstantMaterial
block = OPyC
prop_names = 'density'
prop_values = 1900
[]
[OPyC_IIDC]
type = PyCCEGAIrradiationEigenstrain
block = OPyC
eigenstrain_name = OPyC_IIDC_strain
temperature = temperature
irradiation_eigenstrain_scale_factor = 1
[]
[OPyC_TE]
type = PyCThermalExpansionEigenstrain
block = OPyC
eigenstrain_name = OPyC_TE_strain
temperature = temperature
[]
[characteristic_strength_SiC]
type = GenericConstantMaterial
prop_values = '9640000'
block = SiC
prop_names = 'characteristic_strength'
[]
[characteristic_strength_PyC]
type = PyCCharacteristicStrength
temperature = temperature
X = 1.02
block = 'IPyC OPyC'
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temperature
max_increment = 100
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-10
nl_abs_tol = 1e-9
nl_max_its = 20
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
num_steps = 10
dtmin = 1e-4
dt = 1e4
[]
[Postprocessors]
[ave_gas_temp]
type = ElementAverageValue
block = buffer
variable = temperature
execute_on = 'initial timestep_end'
[]
[fis_gas_released]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_released
block = fuel
use_displaced_mesh = false
execute_on = 'initial timestep_end'
[]
[gap_volume]
type = InternalVolume
boundary = buffer_IPyC_boundary
execute_on = 'initial linear'
use_displaced_mesh = true
[]
[buffer_void_volume]
type = VoidVolume
block = buffer
theoretical_density = 2250
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[kernel_th_density]
type = UCOTheoreticalDensity
execute_on = initial
[]
[kernel_void_volume]
type = VoidVolume
block = fuel
theoretical_density = kernel_th_density
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[particle_power]
type = ElementIntegralPower
variable = temperature
use_material_fission_rate = true
fission_rate_material = fission_rate
block = fuel
execute_on = 'initial timestep_end'
[]
[max_fluence]
type = ElementExtremeValue
variable = fast_neutron_fluence
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_burnup]
type = ElementExtremeValue
variable = burnup
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[SiC_stress_max]
type = ElementExtremeMaterialProperty
block = SiC
value_type = max
mat_prop = stress_yy
[]
[SiC_stress_min]
type = ElementExtremeMaterialProperty
block = SiC
value_type = min
mat_prop = stress_yy
[]
[strength_SiC]
type = WeibullEffectiveMeanStrength
block = SiC
weibull_modulus = 6
[]
[kernel_migration_distance]
type = KernelMigrationDistance
block = 'fuel buffer IPyC SiC OPyC'
variable = temperature
temperature_gradient = 15000
kernel_type = UO2
[]
[]
[Outputs]
show = 'kernel_migration_distance'
print_linear_residuals = false
time_step_interval = 1
csv = true
perf_graph = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_11/case_11.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.089
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 250e-6 345e-6 385e-6 420e-6 460e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
bias = '1 1.25 1.25 1.25 1.25'
dual_bias = '0.8 0.8 0.8 0.8 1'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1273.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temperature]
type = PiecewiseLinear
data_file = temperature_history.dat
format = columns
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
extra_vector_tags = 'ref'
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = temperature
variable = temperature
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[]
[Materials]
[burnup]
type = GenericFunctionMaterial
block = fuel
prop_names = 'burnup'
prop_values = 'if(t<86400000,0.09/86400000*t,0.09)'
[]
[fission_rate]
type = GenericFunctionMaterial
block = fuel
prop_names = 'fission_rate'
# 2.42e19 = 0.09/86400000*10400/.27*6.0221409e23
prop_values = 'if(t<86400000,2.42e19,0)'
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Cs_generation
kind = Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = 'if(t<86400000,exp(5.0e25/86400000*t/5e25),exp(5.0e25/5e25))'
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 5e-19
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 89366400
num_steps = 5000
dt = 86400
dtmax = 86400
[TimeStepper]
type = FunctionDT
function = 'if(t<86400000,86400,1800)'
[]
[]
[Postprocessors]
[_temp]
type = NodalExtremeValue
variable = temperature
[]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released_overall]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
start_time = 86400000
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
[]
[out_final]
type = CSV
execute_on = final
[]
[]
(test/tests/triso_failure/triso_1d_failure.i)
[GlobalParams]
density = 10810.0
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
mesh_density = '6 6 0 6 8 6'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Variables]
[disp_x]
[]
[temperature]
initial_condition = 1346.0
[]
[]
[Functions]
[radial_eigenstrain]
type = ParsedFunction
expression = 't*(4.52013e-4/6.0*t*t*t*t*t - 8.36313e-3/5.0*t*t*t*t + 5.67549e-2/4.0*t*t*t - 1.74247e-1/3.0*t*t + 2.62692e-1/2.0*t - 1.43234e-1)'
[]
[tangential_eigenstrain]
type = ParsedFunction
expression = 't*(1.30457e-4/4.0*t*t*t - 2.10029e-3/3.0*t*t + 9.07826e-3/2.0*t - 3.24737e-2)'
[]
[fission_rate]
type = ParsedFunction
expression = 7.75e19
[]
[k_function]
type = ParsedFunction
expression = '4.93e-29'
[]
[high_fidelity_strength_crackedIPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1000000 1000000'
[]
[high_fidelity_strength_crackedOPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1000000 1000000'
[]
[stress_correlation_crackedOPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[stress_correlation_crackedIPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[]
[AuxVariables]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = fuel
initial_condition = 0.0
[]
[fission_rate]
block = fuel
[]
[]
[Physics/SolidMechanics/QuasiStatic]
strain = small
[fuel_buffer_sic]
block = 'fuel buffer SiC'
eigenstrain_names = thermal_strain
[]
[ipyc_opyc]
block = 'IPyC OPyC'
incremental = true
eigenstrain_names = 'thermal_strain pyc_eigenstrain'
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
[]
[heat]
type = HeatConduction
variable = temperature
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
energy_per_fission = 3.2e-11
fission_rate = fission_rate
[]
[]
[AuxKernels]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[fission_rate]
type = FunctionAux
variable = fission_rate
block = fuel
function = fission_rate
[]
[burnup]
type = BurnupAux
variable = burnup
block = fuel
fission_rate = fission_rate
molecular_weight = 0.270
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
penalty = 1e5
model = frictionless
formulation = kinematic
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
# coupling to a postprocessor
initial_moles = initial_moles
gas_released = 'fis_gas_released co_production'
released_gas_types = 'Kr Xe;
CO'
released_fractions = '0.153 0.847;
1'
tangential_tolerance = 1e-6
[]
[]
[BCs]
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[freesurf_temperature]
type = DirichletBC
variable = temperature
boundary = exterior
value = 1346.0
[]
[exterior_pressure_x]
type = Pressure
use_displaced_mesh = false
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure]
# apply gas pressure on buffer and IPyC boundaries
[plenumPressure]
use_displaced_mesh = false
boundary = buffer_IPyC_boundary
initial_pressure = 0
startup_time = 1.0e4
R = 8.3143
# coupling to post processor
output_initial_moles = initial_moles
temperature = ave_temp_interior
volume = volumeGas
material_input = 'fis_gas_released co_production'
output = plenum_pressure
[]
[]
[]
[Materials]
[radial_stress]
type = RankTwoCylindricalComponent
rank_two_tensor = stress
cylindrical_axis_point1 = '0 0 0'
cylindrical_axis_point2 = '0 0 1'
cylindrical_component = RadialStress
property_name = radial_stress
outputs = all
[]
[max_principal_stress]
type = RankTwoInvariant
property_name = max_principal_stress
rank_two_tensor = stress
invariant = MaxPrincipal
[]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 1.708707e18
[]
[fission_gas_release]
type = UO2Sifgrs
block = fuel
temperature = temperature
fission_rate = fission_rate
grain_radius_const = 5.0e-6
[]
[stress]
type = ComputeLinearElasticStress
block = 'fuel buffer SiC'
[]
[PyC_stress]
type = PyCCreep
block = 'IPyC OPyC'
k = k_function
poissons_ratio = 0.4
temperature = temperature
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'IPyC OPyC'
[]
[PyC_eigenstrain]
type = PyCIrradiationEigenstrain
block = 'IPyC OPyC'
radial_eigenstrain_function = radial_eigenstrain
tangential_eigenstrain_function = tangential_eigenstrain
eigenstrain_name = pyc_eigenstrain
[]
[fuel_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[PyC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = 'buffer IPyC OPyC'
thermal_expansion_coeff = 5.5e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[SiC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[fuel_thermal]
type = UO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temperature
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[fuel_den]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10810.0
[]
[buffer_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[buffer_thermal]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5
specific_heat = 720.0
[]
[buffer_den]
type = StrainAdjustedDensity
strain_free_density = 1000
block = buffer
[]
[PyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = 'IPyC OPyC'
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[PyC_thermal]
type = HeatConductionMaterial
block = 'IPyC OPyC'
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[PyC_den]
type = StrainAdjustedDensity
strain_free_density = 1880.0
block = 'IPyC OPyC'
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_thermal]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9
specific_heat = 620.0
[]
[SiC_den]
type = StrainAdjustedDensity
strain_free_density = 3200.0
block = SiC
[]
[characteristic_strength_SiC]
type = GenericConstantMaterial
prop_values = '9640000'
prop_names = 'characteristic_strength'
block = SiC
[]
[characteristic_strength_PyC]
type = GenericConstantMaterial
prop_values = '964000'
prop_names = 'characteristic_strength'
block = 'IPyC OPyC'
[]
[]
[Dampers]
[temperature]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 1e-10
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
num_steps = 10
dtmax = 2e5
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 20
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[dt]
type = TimestepSize
[]
[burnup]
type = ElementExtremeValue
block = fuel
variable = burnup
[]
[fis_gas_produced]
type = ElementIntegralFisGasGeneratedSifgrs
block = fuel
[]
[fis_gas_released]
type = ElementIntegralFisGasReleasedSifgrs
block = fuel
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
[]
[volumeFuel]
type = InternalVolume
boundary = fuel_outer_boundary
[]
[volumeGas]
type = InternalVolume
boundary = 'fuel_outer_boundary IPyC_inner_boundary'
addition = -5.53e-11
execute_on = 'initial timestep_end'
[]
[volumeBufferShell]
type = InternalVolume
boundary = buffer_IPyC_boundary
[]
[ave_temp_interior]
type = SideAverageValue
boundary = buffer_IPyC_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
# Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
[]
[avg_surface_temperature]
type = SideAverageValue
variable = temperature
boundary = exterior
[]
[time_int_surf_temperature]
type = TimeIntegratedPostprocessor
value = avg_surface_temperature
[]
[co_production]
type = CarbonMonoxideProduction
total_fissions = total_fissions
time_integrated_triso_temperature = time_int_surf_temperature
initial_enrichment = 0.14029
[]
[tang_SiC]
type = ElementalVariableValue
variable = stress_yy
elementid = 18
[]
[strength_SiC]
type = WeibullEffectiveMeanStrength
block = SiC
weibull_modulus = 6
[]
[failure_indicator_SiC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_SiC
[]
[strength_IPyC]
type = WeibullEffectiveMeanStrength
block = IPyC
weibull_modulus = 6
[]
[failure_indicator_IPyC]
type = WeibullFailureOutputUsingCorrelation
block = IPyC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_IPyC
[]
[failure_indicator_debonding]
type = TRISODebondingFailureIndicator
boundary = IPyC_outer_boundary
bond_strength = 1e5
stress_name = radial_stress
[]
[strength_OPyC]
type = WeibullEffectiveMeanStrength
block = OPyC
weibull_modulus = 6
[]
[failure_indicator_OPyC]
type = WeibullFailureOutputUsingCorrelation
block = OPyC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_OPyC
[]
[failure_indicator_SiC_crackedIPyC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = max_principal_stress
high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
stress_correlation_function = 'stress_correlation_crackedIPyC'
[]
[failure_indicator_SiC_crackedOPyC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = max_principal_stress
high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
stress_correlation_function = 'stress_correlation_crackedOPyC'
[]
[triso_failure]
type = TRISOFailureEvaluation
IPyC_failure = failure_indicator_IPyC
OPyC_failure = failure_indicator_OPyC
SiC_failure = failure_indicator_SiC
SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
SiC_failure_crackedOPyC = failure_indicator_SiC_crackedOPyC
SiC_failure_debonding = failure_indicator_debonding
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
csv = true
perf_graph = true
[]
(examples/TRISO/accident_simulation/triso1D_accident.i)
# This example is 1D spherical analysis of a TRISO fuel particle. Fully coupled
# heat transfer and solid mechanics, plus diffusion of the fission product
# species cesium (Cs) are simulated. The mesh includes contact surfaces
# between the buffer and IPyC layers to facilitate a gap opening between
# these layers. These surfaces are initially in mechanical contact but
# are assumed to have no strength in tension. A coarse mesh is used to
# provide a short run time.
# The calculation simulates fuel-life in three steps. The first step is an
# irradiation period, where constant power and a fixed particle surface
# temperature (1500 K) are assumed over a lifetime of 76 Ms (2.4 yrs).
# For the second step, fuel removal and storage are simulated by setting
# the reactor power and Cs source terms to zero, reducing the particle
# surface temperature to ambient (300 K), and then holding it
# for 100 days. A third and final step simulates accident
# behavior by increasing the particle surface temperature from ambient
# to 2073 K over 2 hrs, and then holding it at this elevated temperature
# for an additional 200 hrs. At the particle outer boundary, the Cs
# concentration is held at zero and the pressure at ambient during the
# entire simulation. The particle is assumed to be stress-free at an
# initial temperature of 1500 K.
#
# Details about this simulation are given in Section 4 of the following
# article: J. D. Hales, R. L. Williamson, S. R. Novascone, D. M. Perez,
# B. W. Spencer and G. Pastore, "Multidimensional multiphysics simulation
# of TRISO particle fuel", Journal of Nuclear Materials, Vol. 443, p. 531,
# 2013.
# This is a version using an interface kernel to model gap mass transfer.
# Sorption constants are given in Table 1 of the following article: A.
# Londono-Hurtado, I. Szlufarska, R. Bratton and D. Morgan, "A review of
# fission product sorption in carbon structures", Journal of Nuclear
# Materials, Vol. 426, p. 254, 2012.
initial_fuel_density = 11000
[GlobalParams]
order = SECOND
family = LAGRANGE
displacements = disp_x
flux_conversion_factor = 0.85
[]
[Mesh]
coord_type = RSPHERICAL
[gen] # exclude gap to establish buffer-IPyC neighbor relationships for the sorption interface kernel
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.125e-4 3.125e-4 3.525e-4 3.875e-4 4.275e-4'
mesh_density = '10 5 2 2 2'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[break] # create gap between buffer and IPyC to model mechanical and thermal contact
type = BreakMeshByBlockGenerator
input = gen
block_pairs = 'buffer IPyC'
split_interface = true
add_interface_on_two_sides = true
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[disp_x]
[]
[temp]
initial_condition = 1500.0
[]
[conc]
initial_condition = 0.0
[]
[]
[AuxVariables]
[fission_rate]
block = fuel
order = CONSTANT
family = MONOMIAL
[]
[fluence]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = fuel
order = CONSTANT
family = MONOMIAL
[]
[gap_cond]
order = CONSTANT
family = MONOMIAL
[]
[creep_xx]
order = CONSTANT
family = MONOMIAL
[]
[creep_yy]
order = CONSTANT
family = MONOMIAL
[]
[creep_zz]
order = CONSTANT
family = MONOMIAL
[]
[gap_HTC]
order = CONSTANT
family = MONOMIAL
[]
[gap_distance]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[power_history]
type = PiecewiseLinear
x = '0 76e6 76.001e6'
y = '1 1 0'
[]
[temp_bc]
type = PiecewiseLinear
x = '0 76e6 76.001e6 84.641e6 84.6482e6'
y = '1500 1500 300 300 2073'
[]
[k_function]
type = PiecewiseLinear
x = '0 200e6'
y = '4e-37 4e-37'
[]
[d1_function]
type = ParsedFunction
expression = 'exp(t/4.5e25)'
[]
[integral_flux_error]
type = ParsedFunction
symbol_names = 'buffer_integral_flux IPyC_integral_flux'
symbol_values = 'buffer_integral_flux IPyC_integral_flux'
expression = 'IPyC_integral_flux + buffer_integral_flux'
[]
[partial_pressure_error]
type = ParsedFunction
symbol_names = 'buffer_partial_pressure IPyC_partial_pressure'
symbol_values = 'buffer_partial_pressure IPyC_partial_pressure'
expression = 'IPyC_partial_pressure - buffer_partial_pressure'
[]
[]
[Physics/SolidMechanics/QuasiStatic]
generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_yz stress_zx hydrostatic_stress'
strain = FINITE
incremental = true
add_variables = false
[default]
block = 'fuel buffer IPyC OPyC'
eigenstrain_names = 'thermal_strain swelling_strain'
extra_vector_tags = 'ref'
[]
[SiC]
block = 'SiC'
eigenstrain_names = 'thermal_strain'
extra_vector_tags = 'ref'
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temp
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temp
extra_vector_tags = 'ref'
[]
[heat_source]
type = NeutronHeatSource
variable = temp
block = fuel
energy_per_fission = 3.2e-11 # units of J/fission
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[mass_ie]
type = TimeDerivative
variable = conc
extra_vector_tags = 'ref'
[]
[mass]
type = ArrheniusDiffusion
variable = conc
extra_vector_tags = 'ref'
[]
[mass_source]
type = BodyForce
variable = conc
function = power_history
value = 1.22e-5 # units of moles/m**3-s
block = fuel
extra_vector_tags = 'ref'
[]
[mass_decay]
type = Decay
variable = conc
radioactive_decay_constant = 7.297e-10 # units:(1/sec) The constant for Cesium
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[fission_rate]
type = FissionRateGeneral
fission_rate_formulation = GENERIC
variable = fission_rate
block = fuel
fission_rate_function = power_history
value = 3.89e19
execute_on = timestep_begin
[]
[fluence]
type = MaterialRealAux
property = fast_neutron_fluence
variable = fluence
[]
[burnup]
type = BurnupAux
variable = burnup
block = fuel
fission_rate = fission_rate
molecular_weight = 0.270 # units of kg/mole
execute_on = timestep_begin
density = ${initial_fuel_density}
[]
[creep_xx]
type = RankTwoAux
rank_two_tensor = creep_strain
variable = creep_xx
index_i = 0
index_j = 0
block = 'buffer IPyC SiC OPyC'
execute_on = timestep_end
[]
[creep_yy]
type = RankTwoAux
rank_two_tensor = creep_strain
variable = creep_yy
index_i = 1
index_j = 1
block = 'buffer IPyC SiC OPyC'
execute_on = timestep_end
[]
[creep_zz]
type = RankTwoAux
rank_two_tensor = creep_strain
variable = creep_zz
index_i = 2
index_j = 2
block = 'buffer IPyC SiC OPyC'
execute_on = timestep_end
[]
[conductance]
type = MaterialRealAux
property = gap_conductance
variable = gap_cond
boundary = buffer_IPyC
execute_on = linear
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = IPyC_buffer
secondary = buffer_IPyC
penalty = 1e5
model = frictionless
formulation = penalty
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temp
primary = IPyC_buffer
secondary = buffer_IPyC
initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
gas_released = 'fis_gas_released co_production' # coupling to postprocessors which supply the fission gas addition, co addition
released_gas_types = 'Kr Xe;
CO'
released_fractions = '0.153 0.847;
1'
gap_geometry_type = SPHERE
tangential_tolerance = 1e-6
roughness_coef = 0.0
quadrature = true
[]
[]
[InterfaceKernels]
[cesium_gap]
type = SorptionIsothermGapInterface
variable = conc
neighbor_var = conc
partial_pressure_name = partial_pressure
sorption_penalty = 1e5
diffusivity = arrhenius_diffusion_coef
use_flux_penalty = true
flux_penalty = 1e3
boundary = buffer_IPyC
extra_vector_tags = 'ref'
[]
[]
[BCs]
# pin particle along symmetry planes
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
extra_vector_tags = 'ref'
[]
# fix temperature on free surface
[freesurf_temp]
type = FunctionDirichletBC
variable = temp
boundary = exterior
function = temp_bc
extra_vector_tags = 'ref'
[]
# fix concentration on free surface
[freesurf_conc]
type = DirichletBC
variable = conc
boundary = exterior
value = 0.0
extra_vector_tags = 'ref'
[]
[PlenumPressure] # apply plenum pressure on clad inner walls and pellet surfaces
[plenumPressure]
boundary = 'buffer_IPyC IPyC_buffer'
initial_pressure = 0
startup_time = 1.0e4
R = 8.3145
output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
volume = volumeGas # coupling to post processor to get gas volume
material_input = 'fis_gas_released co_production' # coupling to post processor to get fission gas added, co added
output = plenum_pressure # coupling to post processor to output plenum/gap pressure
[]
[]
[]
[Materials]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 5e17
[]
[fission_gas_release] # Sifgrs fission gas release mode
type = UO2Sifgrs
block = fuel
temperature = temp
fission_rate = fission_rate # coupling to fission_rate aux variable
grain_radius_const = 5.0e-6
[]
[fuel_thermal]
type = UO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temp
burnup = burnup
initial_porosity = 0.0
[]
[fuel_swelling]
type = UO2VolumetricSwellingEigenstrain
gas_swelling_model_type = MATPRO
block = fuel
temperature = temp
burnup = burnup
eigenstrain_name = 'swelling_strain'
initial_fuel_density = ${initial_fuel_density}
[]
[fuel_stress]
type = ComputeFiniteStrainElasticStress
block = 'fuel'
[]
[fuel_elasticity]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 2.2e11
poissons_ratio = .345
[]
[fuel_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10e-6
stress_free_temperature = 1500.0
eigenstrain_name = thermal_strain
temperature = temp
[]
[fuel_den]
type = StrainAdjustedDensity
block = fuel
strain_free_density = ${initial_fuel_density} # kg/m^3
[]
[fuel_conc]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209.0e+3 # J/mol
d2 = 5.2e-4 # m^2/s
q2 = 362.0e+3 # J/mol
gas_constant = 8.3143 # J/K-mol
temperature = temp
[]
[buffer_eigenstrain]
type = PyCIrradiationEigenstrain
block = buffer
pyc_type = buffer
eigenstrain_name = 'swelling_strain'
[]
[buffer_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = buffer
thermal_expansion_coeff = 5.65e-6
stress_free_temperature = 1500.0
eigenstrain_name = thermal_strain
temperature = temp
[]
[buffer_elasticity]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 2e10
poissons_ratio = .23
[]
[buffer_stress]
type = PyCCreep
block = buffer
temperature = temp
[]
[buffer_temp]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[buffer_den]
type = StrainAdjustedDensity
strain_free_density = 1000.0 #kg/m^3
block = buffer
[]
[buffer_conc]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1.0e-12 # m^2/s
q1 = 0.0
d2 = 0.0
q2 = 0.0
gas_constant = 8.3143 # J/K-mol
temperature = temp
[]
[buffer_partial_pressure]
type = SorptionPartialPressure
A = 19.33
B = -47290
D = 1.518
E = 4338
d1 = 3.397
d2 = 6.15e-4
unit_scale = 1e3 # convert from mol to mmol
density = density # convert from mmol/m^3 to mmol/kg
concentration = conc
temperature = temp
block = 'buffer IPyC'
outputs = 'all'
output_properties = partial_pressure
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'IPyC OPyC buffer'
[]
[IPyC_eigenstrain]
type = PyCIrradiationEigenstrain
block = IPyC
pyc_type = dense
eigenstrain_name = 'swelling_strain'
[]
[IPyC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = IPyC
thermal_expansion_coeff = 5.65e-6
stress_free_temperature = 1500.0
eigenstrain_name = thermal_strain
temperature = temp
[]
[IPyC_elasticity]
type = ComputeIsotropicElasticityTensor
block = IPyC
youngs_modulus = 4.74e10
poissons_ratio = .23
[]
[IPyC_disp]
type = PyCCreep
block = 'IPyC OPyC'
temperature = temp
[]
[IPyC_temp]
type = HeatConductionMaterial
block = 'IPyC OPyC'
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_den]
type = StrainAdjustedDensity
block = 'IPyC OPyC'
strain_free_density = 1900.0
[]
[IPyC_conc]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8
q1 = 222.0e+3
d2 = 0.0
q2 = 0.0
gas_constant = 8.3143 # J/K-mol
temperature = temp
[]
[SiC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
stress_free_temperature = 1500.0
eigenstrain_name = thermal_strain
temperature = temp
[]
[SiC_elasticity]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.4e11
poissons_ratio = .13
[]
[SiC_creep]
type = MonolithicSiCCreepUpdate
block = SiC
temperature = temp
k_function = k_function
[]
[SiC_stress]
type = ComputeMultipleInelasticStress
block = SiC
tangent_operator = elastic
inelastic_models = 'SiC_creep'
[]
[SiC_temp]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9 # J/m-s-K
specific_heat = 620.0 # J/kg-K
[]
[SiC_den]
type = StrainAdjustedDensity
strain_free_density = 3180.0 # kg/m^3
block = SiC
[]
[SiC_conc]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = d1_function
d1_function_variable = fluence
q1 = 125.0e+3 # J/mol
d2 = 1.6e-2 # m^2/s
q2 = 514.0e+3 # J/mol
gas_constant = 8.3143 # J/K-mol
temperature = temp
[]
[OPyC_eigenstrain]
type = PyCIrradiationEigenstrain
block = OPyC
pyc_type = dense
eigenstrain_name = 'swelling_strain'
[]
[OPyC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = OPyC
thermal_expansion_coeff = 5.65e-6
stress_free_temperature = 1500.0
eigenstrain_name = thermal_strain
temperature = temp
[]
[OPyC_elasticity]
type = ComputeIsotropicElasticityTensor
block = OPyC
youngs_modulus = 4.74e10
poissons_ratio = .23
[]
[OPyC_conc]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222.0e+3 # J/mol
d2 = 0.0
q2 = 0.0
gas_constant = 8.3143 # J/K-mol
temperature = temp
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temp
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 5e-4
nl_abs_tol = 1e-9
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 85.3682e6
dt = 100
dtmax = 2e6
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 100
optimal_iterations = 6
growth_factor = 1.5
linear_iteration_ratio = 100
time_t = '0 76e6 76.001e6 84.641e6 84.6482e6'
time_dt = '20 20 20 20 20'
[]
[Predictor]
type = SimplePredictor
scale = 1
skip_times_old = '0 76e6 76.001e6 84.641e6 84.6482e6'
[]
[]
[Outputs]
perf_graph = true
exodus = true
[console]
type = Console
max_rows = 25
[]
[csv]
type = CSV
sync_times = '100 6308007 75696087'
sync_only = true
[]
[]
[Postprocessors]
[Cs_release]
type = SideIntegralMassFlux
variable = conc
boundary = exterior
execute_on = timestep_end
[]
[dt]
type = TimestepSize
execute_on = timestep_end
[]
[fis_gas_produced] # fission gas produced (moles)
type = ElementIntegralFisGasGeneratedSifgrs
block = fuel
execute_on = 'initial linear nonlinear timestep_begin timestep_end'
[]
[fis_gas_released] # fission gas released to plenum (moles)
type = ElementIntegralFisGasReleasedSifgrs
block = fuel
execute_on = 'initial linear nonlinear timestep_begin timestep_end'
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
scale_factor = -1
execute_on = 'initial timestep_end'
[]
[volumeFuel]
type = InternalVolume
boundary = fuel_outer_boundary
scale_factor = -1
execute_on = 'initial timestep_end'
[]
[volumeGas]
type = InternalVolume
boundary = 'buffer_IPyC IPyC_buffer'
# ro = 3.125e-4
# ri = 2.125e-4
# vb = 4/3*pi*(ro^3-ri^3) = 8.76e-11
# buffer density = 1000
# PyC density = 1900
# fill ratio = 10/19
# vb*10/19 = 4.6e-11
# Must remove 4.6e-11 m^3 from the volume
addition = -4.6e-11
execute_on = 'initial linear nonlinear timestep_begin timestep_end'
[]
[volumeBufferShell]
type = InternalVolume
boundary = 'buffer_IPyC IPyC_buffer'
execute_on = 'initial timestep_end'
[]
[ave_temp_interior]
type = SideAverageValue
boundary = 'buffer_IPyC IPyC_buffer'
variable = temp
execute_on = 'initial linear nonlinear timestep_begin timestep_end'
[]
# Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temp
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
execute_on = 'initial linear nonlinear timestep_begin timestep_end'
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
execute_on = 'initial linear nonlinear timestep_begin timestep_end'
[]
[avg_surface_temp]
type = SideAverageValue
variable = temp
boundary = exterior
execute_on = 'initial linear nonlinear timestep_begin timestep_end'
[]
[time_int_surf_temp]
type = TimeIntegratedPostprocessor
value = avg_surface_temp
execute_on = 'initial linear nonlinear timestep_begin timestep_end'
[]
[co_production]
type = CarbonMonoxideProduction
total_fissions = total_fissions
time_integrated_triso_temperature = time_int_surf_temp
initial_enrichment = 0.14029
execute_on = 'initial linear nonlinear timestep_begin timestep_end'
[]
[num_lin_it]
type = NumLinearIterations
[]
[num_nonlin_it]
type = NumNonlinearIterations
[]
[tot_lin_it]
type = CumulativeValuePostprocessor
postprocessor = num_lin_it
[]
[tot_nonlin_it]
type = CumulativeValuePostprocessor
postprocessor = num_nonlin_it
[]
[alive_time]
type = PerfGraphData
section_name = Root
data_type = TOTAL
[]
[buffer_integral_flux]
type = SideDiffusiveFluxIntegral
variable = conc
boundary = buffer_IPyC
diffusivity = arrhenius_diffusion_coef
[]
[IPyC_integral_flux]
type = SideDiffusiveFluxIntegral
variable = conc
boundary = IPyC_buffer
diffusivity = arrhenius_diffusion_coef
[]
[buffer_partial_pressure]
type = SideAverageMaterialProperty
property = partial_pressure
boundary = buffer_IPyC
[]
[IPyC_partial_pressure]
type = SideAverageMaterialProperty
property = partial_pressure
boundary = IPyC_buffer
[]
[integral_flux_error]
type = FunctionValuePostprocessor
function = integral_flux_error
[]
[partial_pressure_error]
type = FunctionValuePostprocessor
function = partial_pressure_error
[]
[integral_Cs_release]
type = TimeIntegratedPostprocessor
value = Cs_release
[]
[Cs_production]
type = FunctionValuePostprocessor
function = power_history
scale_factor = 1.22e-5 # units of moles/m**3-s
[]
[time_integral_Cs_production]
type = TimeIntegratedPostprocessor
value = Cs_production
[]
[volumeFuel_initial]
type = InternalVolume
boundary = fuel_outer_boundary
scale_factor = -1
execute_on = initial
[]
[integral_Cs_production]
type = ParsedPostprocessor
pp_names = 'time_integral_Cs_production volumeFuel_initial'
expression = 'time_integral_Cs_production * volumeFuel_initial'
[]
[Cs_release_fraction]
type = ParsedPostprocessor
pp_names = 'integral_Cs_release integral_Cs_production'
expression = 'integral_Cs_release / integral_Cs_production'
[]
[]
[VectorPostprocessors]
[temperaturevpp]
type = SideValueSampler
boundary = 11
variable = temp
sort_by = x
outputs = 'csv'
use_displaced_mesh = true
[]
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_7b/case_7b.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.0407
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 272e-6 396e-6 402e-6 436e-6 475e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
bias = '1 1.25 1.25 1.25 1.25'
dual_bias = '0.8 0.8 0.8 0.8 1'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[conc_Ag]
[]
[conc_Sr]
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1304.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Sr_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temperature]
type = PiecewiseLinear
data_file = temperature_history.dat
format = columns
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
[]
[mass_Sr_dt]
type = TimeDerivative
variable = conc_Sr
[]
[mass_Sr]
type = ArrheniusDiffusion
variable = conc_Sr
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Sr]
type = SpeciesSourceRate
variable = conc_Sr
property_name = Sr_generation
block = fuel
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[Sr_diff_coef]
type = MaterialRealAux
variable = Sr_diff_coef
property = arrhenius_diffusion_coef_Sr
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = temperature
variable = temperature
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[freesurf_conc_Sr]
type = DirichletBC
variable = conc_Sr
boundary = exterior
value = 0.0
[]
[]
[Materials]
[burnup]
type = GenericFunctionMaterial
block = fuel
prop_names = 'burnup'
prop_values = 'if(t<7682400,0.048/7682400*t,0.048)'
[]
[fission_rate]
type = GenericFunctionMaterial
block = fuel
prop_names = 'fission_rate'
# 1.699e20 = 0.048/7682400*10840/.27*6.0221409e23
prop_values = 'if(t<7682400,1.699e20,0)'
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Cs_generation
kind = Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = 'if(t<7682400,exp(2.1e25/7682400*t/5e25),exp(2.1e25/5e25))'
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Ag_generation
kind = Ag
[]
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[SiC_conc_Ag]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[fuel_conc_Sr]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 2.2e-3 # m^2/s
q1 = 488e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[mass_source_Sr_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Sr_generation
kind = Sr
[]
[buffer_conc_Sr]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[IPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[SiC_conc_Sr]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 1.2e-9 # m^2/s
q1 = 205e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[OPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs conc_Ag'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 5e-21 #1e-22
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 8506800
num_steps = 1450
dt = 86400
dtmax = 86400
#dtmin = 86400
[TimeStepper]
type = FunctionDT
function = 'if(t<7682400,86400,
if(t<7707600,720,
3600))'
[]
[]
[Postprocessors]
[_temp]
type = NodalExtremeValue
variable = temperature
[]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released_overall]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
start_time = 7682400
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial timestep_end'
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released_overall]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
start_time = 7682400
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
execute_on = 'initial timestep_end'
[]
[release_Sr_inc]
type = SideIntegralMassFlux
variable = conc_Sr
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
execute_on = 'initial timestep_end'
[]
[released_Sr]
type = TimeIntegratedPostprocessor
value = release_Sr_inc
execute_on = 'initial timestep_end'
[]
[total_Sr]
type = ElementIntegralMaterialProperty
mat_prop = Sr_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Sr_released_overall]
type = FractionalRelease
released = released_Sr
total = total_Sr
execute_on = 'initial timestep_end'
[]
[x_Sr_released]
type = FractionalRelease
released = released_Sr
total = total_Sr
execute_on = 'initial timestep_end'
start_time = 7682400
[]
[retained_Sr]
type = ElementIntegralVariablePostprocessor
variable = conc_Sr
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
[]
[out_final]
type = CSV
execute_on = final
[]
[]
(examples/TRISO/failure_probability_direct_integration/triso_1d.i)
kernel_radius = 213.35e-6
buffer_thickness = 98.9e-6
IPyC_thickness = 40.4e-6
SiC_thickness = 35.2e-6
OPyC_thickness = 43.4e-6
coordinates1 = '${fparse kernel_radius}'
coordinates2 = '${fparse coordinates1+buffer_thickness}'
coordinates3 = '${fparse coordinates2+IPyC_thickness}'
coordinates4 = '${fparse coordinates3+SiC_thickness}'
coordinates5 = '${fparse coordinates4+OPyC_thickness}'
initial_fuel_density = 10966
[GlobalParams]
order = FIRST
family = LAGRANGE
displacements = 'disp_x'
initial_enrichment = 0.14029 # [wt-]
flux_conversion_factor = 1.0 # convert E>0.10 to E>0.18 MeV
stress_free_temperature = 481 # used for thermal expansion
energy_per_fission = 3.204e-11 # [J/fission]
O_U = 1.428 # Initial Oxygen to Uranium atom ratio
C_U = 0.392 # Initial Carbon to Uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
mesh_density = '5 3 0 5 3 4'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = OPyC_outer_boundary
outer_SiC = SiC_outer_boundary
outer_IPyC = IPyC_outer_boundary
inner_IPyC = IPyC_inner_boundary
outer_buffer = buffer_outer_boundary
outer_kernel = fuel_outer_boundary
include_particle = true
include_pebble = false
IPyC_thickness_mean = 40.4e-6
SiC_thickness_mean = 35.2e-6
OPyC_thickness_mean = 43.4e-6
[]
[]
[Variables]
[temperature]
initial_condition = 481
[]
[]
[AuxVariables]
[fission_rate]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_flux]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temp_bc]
type = PiecewiseLinear
data_file = outer_temp.csv
x_index_in_file = 0
y_index_in_file = 1
format = columns
[]
[fission_rate]
type = ConstantFunction
value = 5.75e19
[]
[high_fidelity_strength_crackedIPyC]
type = ConstantFunction
value = '1363350801.3058'
[]
[stress_correlation_crackedIPyC]
type = TRISOStressCorrelationFunction
triso_geometry = particle_geometry
polynomial_coefficients_IPyC = '1 7017 -2.368e8'
polynomial_coefficients_SiC = '1 1.492e4 -3.802e7'
polynomial_coefficients_OPyC = '1 -1.273e4 1.849e8'
correlation_factor = -1.1824630660785265
[]
[high_fidelity_strength_asphericity]
type = ConstantFunction
value = '1086690814.283'
[]
[stress_correlation_asphericity]
type = TRISOStressCorrelationFunction
triso_geometry = particle_geometry
polynomial_coefficients_IPyC = '1 -2070 3.458e7'
polynomial_coefficients_SiC = '1 -868.9 -1.368e7'
polynomial_coefficients_OPyC = '1 1734 -1.988e7'
correlation_factor = 1.0626986695756293
[]
[stress_change_correlation_asphericity]
type = TRISOStressCorrelationFunction
triso_geometry = particle_geometry
polynomial_coefficients_IPyC = '1 -856 1.593e7'
polynomial_coefficients_SiC = '1 1774 -5.253e7'
polynomial_coefficients_OPyC = '1 456.4 -1.459e7'
correlation_factor = 1.0113764663823708
[]
[]
[Physics/SolidMechanics/QuasiStatic]
generate_output = 'stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz max_principal_stress'
add_variables = true
strain = FINITE
incremental = true
[fuel]
block = fuel
eigenstrain_names = 'UCO_swelling_eigenstrain UCO_TE_strain'
extra_vector_tags = 'ref'
[]
[buffer]
block = buffer
eigenstrain_names = 'Buffer_IIDC_strain Buffer_TE_strain'
extra_vector_tags = 'ref'
[]
[IPyC]
block = IPyC
eigenstrain_names = 'IPyC_IIDC_strain IPyC_TE_strain'
extra_vector_tags = 'ref'
[]
[SiC]
block = SiC
eigenstrain_names = 'SiC_thermal_eigenstrain'
extra_vector_tags = 'ref'
[]
[OPyC]
block = OPyC
eigenstrain_names = 'OPyC_IIDC_strain OPyC_TE_strain'
extra_vector_tags = 'ref'
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[fissionrate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = fuel
execute_on = timestep_begin
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = fuel
execute_on = timestep_begin
[]
[fast_neutron_flux]
type = MaterialRealAux
variable = fast_neutron_flux
property = fast_neutron_flux
execute_on = timestep_begin
[]
[fast_neutron_fluence]
type = MaterialRealAux
variable = fast_neutron_fluence
property = fast_neutron_fluence
execute_on = timestep_begin
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
initial_moles = initial_moles
gas_released = 'fis_gas_released'
released_gas_types = 'Kr Xe'
released_fractions = '0.185 0.815'
tangential_tolerance = 1e-6
quadrature = false
min_gap = 1e-7
max_gap = 50e-6
gap_geometry_type = sphere
[]
[]
[BCs]
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[freesurf_temp]
type = FunctionDirichletBC
variable = temperature
function = temp_bc
boundary = exterior
[]
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure]
[plenumPressure]
boundary = buffer_IPyC_boundary
startup_time = 1e4
initial_pressure = 0
R = 8.3145
output_initial_moles = initial_moles
temperature = ave_gas_temp
volume = 'gap_volume buffer_void_volume kernel_void_volume'
material_input = 'fis_gas_released'
output = gas_pressure
[]
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
block = fuel
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 6.2425e+17
[]
[UCO_burnup]
type = TRISOBurnup
initial_density = ${initial_fuel_density}
block = fuel
[]
[UCO_thermal]
type = UCOThermal
block = fuel
temperature = temperature
[]
[UCO_elasticity_tensor]
type = UCOElasticityTensor
block = fuel
temperature = temperature
[]
[UCO_stress]
type = ComputeFiniteStrainElasticStress
block = fuel
[]
[UCO_VolumetricSwellingEigenstrain]
type = UCOVolumetricSwellingEigenstrain
block = fuel
eigenstrain_name = UCO_swelling_eigenstrain
[]
[fuel_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10.0e-6
temperature = temperature
eigenstrain_name = UCO_TE_strain
[]
[UCO_density]
type = StrainAdjustedDensity
block = fuel
strain_free_density = ${initial_fuel_density}
[]
[fission_gas_release]
type = UCOFGR
block = fuel
average_grain_radius = 10e-6
temperature = temperature
triso_geometry = particle_geometry
cutoff_neutron_flux = 0.0
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'buffer IPyC OPyC'
[]
[BAF_IPyC]
type = BaconAnisotropyFactor
initial_BAF = 1.0465
block = IPyC
[]
[BAF_OPyC]
type = BaconAnisotropyFactor
initial_BAF = 1.0429
block = OPyC
[]
[buffer_elasticity_tensor]
type = BufferElasticityTensor
block = buffer
temperature = temperature
[]
[buffer_stress]
type = BufferCEGACreep
block = buffer
temperature = temperature
[]
[buffer_thermal]
type = BufferThermal
block = buffer
initial_density = 1050.0
[]
[buffer_density]
type = StrainAdjustedDensity
block = buffer
strain_free_density = 1050.0
[]
[buffer_TE]
type = BufferThermalExpansionEigenstrain
block = buffer
eigenstrain_name = Buffer_TE_strain
temperature = temperature
[]
[buffer_IIDC]
type = BufferCEGAIrradiationEigenstrain
block = buffer
eigenstrain_name = Buffer_IIDC_strain
temperature = temperature
[]
[IPyC_elasticity_tensor]
type = PyCElasticityTensor
block = IPyC
temperature = temperature
[]
[IPyC_stress]
type = PyCCEGACreep
block = IPyC
creep_rate_scale_factor = 1
temperature = temperature
[]
[IPyC_thermal]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_density]
type = GenericConstantMaterial
block = IPyC
prop_names = 'density'
prop_values = 1890
[]
[IPyC_IIDC]
type = PyCCEGAIrradiationEigenstrain
block = IPyC
eigenstrain_name = IPyC_IIDC_strain
temperature = temperature
irradiation_eigenstrain_scale_factor = 1
[]
[IPyC_TE]
type = PyCThermalExpansionEigenstrain
block = IPyC
eigenstrain_name = IPyC_TE_strain
temperature = temperature
[]
[SiC_elasticity_tensor]
type = MonolithicSiCElasticityTensor
block = SiC
temperature = temperature
elastic_modulus_model = miller
[]
[SiC_stress]
type = ComputeFiniteStrainElasticStress
block = SiC
[]
[SiC_thermal]
type = MonolithicSiCThermal
block = SiC
temperature = temperature
thermal_conductivity_model = miller
[]
[SiC_density]
type = StrainAdjustedDensity
block = SiC
strain_free_density = 3200.0
[]
[SiC_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
temperature = temperature
eigenstrain_name = SiC_thermal_eigenstrain
[]
[OPyC_elasticity_tensor]
type = PyCElasticityTensor
block = OPyC
temperature = temperature
initial_BAF = 1.0
[]
[OPyC_stress]
type = PyCCEGACreep
block = OPyC
creep_rate_scale_factor = 1
temperature = temperature
[]
[OPyC_thermal_conductivity]
type = HeatConductionMaterial
block = OPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[OPyC_density]
type = GenericConstantMaterial
block = OPyC
prop_names = 'density'
prop_values = 1900
[]
[OPyC_IIDC]
type = PyCCEGAIrradiationEigenstrain
block = OPyC
eigenstrain_name = OPyC_IIDC_strain
temperature = temperature
irradiation_eigenstrain_scale_factor = 1
[]
[OPyC_TE]
type = PyCThermalExpansionEigenstrain
block = OPyC
eigenstrain_name = OPyC_TE_strain
temperature = temperature
[]
[characteristic_strength_SiC]
type = GenericConstantMaterial
prop_values = '9640000'
block = SiC
prop_names = 'characteristic_strength'
[]
[characteristic_strength_PyC]
type = PyCCharacteristicStrength
temperature = temperature
X = 1.02
block = 'IPyC OPyC'
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temperature
max_increment = 100
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-8
nl_max_its = 20
l_tol = 1e-4
l_max_its = 50
#num_steps = 1
start_time = 0.0
end_time = 4.831315e7
dtmin = 1e-4
dt = 5e5
[]
[Postprocessors]
[ave_gas_temp]
type = ElementAverageValue
block = buffer
variable = temperature
execute_on = 'initial timestep_end'
[]
[fis_gas_released]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_released
block = fuel
use_displaced_mesh = false
execute_on = 'initial timestep_end'
[]
[gap_volume]
type = InternalVolume
boundary = buffer_IPyC_boundary
execute_on = 'initial linear'
use_displaced_mesh = true
[]
[buffer_void_volume]
type = VoidVolume
block = buffer
theoretical_density = 2250
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[kernel_th_density]
type = UCOTheoreticalDensity
execute_on = initial
[]
[kernel_void_volume]
type = VoidVolume
block = fuel
theoretical_density = kernel_th_density
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[particle_power]
type = ElementIntegralPower
variable = temperature
use_material_fission_rate = true
fission_rate_material = fission_rate
block = fuel
execute_on = 'initial timestep_end'
[]
[max_fluence]
type = ElementExtremeValue
variable = fast_neutron_fluence
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_burnup]
type = ElementExtremeValue
variable = burnup
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[SiC_stress]
type = ElementExtremeMaterialProperty
block = SiC
value_type = min
mat_prop = stress_yy
[]
[weibull_failure_probability_IPyC]
type = WeibullFailureProbability
block = IPyC
weibull_modulus = 9.5
characteristic_strength = characteristic_strength
[]
[weibull_failure_probability_SiC_crackedIPyC]
type = WeibullFailureProbabilityUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = stress_yy
high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
stress_correlation_function = 'stress_correlation_crackedIPyC'
[]
[weibull_failure_probability_SiC]
type = WeibullFailureProbabilityUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = stress_yy
high_fidelity_analysis_strength = 'high_fidelity_strength_asphericity'
stress_correlation_function = 'stress_correlation_asphericity'
stress_change_correlation_function = 'stress_change_correlation_asphericity'
[]
[]
[Outputs]
show = 'weibull_failure_probability_IPyC weibull_failure_probability_SiC weibull_failure_probability_SiC_crackedIPyC'
print_linear_residuals = false
time_step_interval = 1
csv = false
exodus = false
perf_graph = true
print_linear_converged_reason = false
print_nonlinear_converged_reason = false
[]
(assessment/verification/TRISO_diffusion/inpile_stable/inpile_stable.i)
#
# TRISO kernel in 1D spherical
#
# In-pile, a stable fission product
# -------------------------------
# Non-zero source, p/=0
# Stable fission product, decay_const=0
# Zero initial concentration, C0=0
#
timestep = 100
p = 1.0
C0 = 0.0
decay_const = 0
kernel_radius = 212.5e-6
Dprime = 1e-4
[GlobalParams]
order = SECOND
family = LAGRANGE
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 ${kernel_radius}'
mesh_density = 100
block_names = 'fuel'
bias = 1
dual_bias = 0.8
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc]
initial_condition = '${C0}'
[]
[]
[Kernels]
[mass_dt]
type = TimeDerivative
variable = conc
[]
[mass]
type = MatDiffusion
variable = conc
diffusivity = diffusion_coef
extra_vector_tags = 'ref'
[]
[mass_source]
type = BodyForce
variable = conc
value = '${p}'
extra_vector_tags = 'ref'
[]
[decay]
type = Decay
variable = conc
radioactive_decay_constant = ${decay_const}
extra_vector_tags = 'ref'
[]
[]
[BCs]
[freesurf_conc]
type = DirichletBC
variable = conc
boundary = exterior
value = 0.0
[]
[]
[Materials]
[fuel_conc]
type = GenericConstantMaterial
block = fuel
prop_names = diffusion_coef
prop_values = '${fparse Dprime*kernel_radius^2}'
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-10
nl_abs_tol = 1e-20
nl_max_its = 20
l_tol = 1e-8
l_max_its = 30
start_time = 0.0
end_time = '${fparse 1/Dprime}'
num_steps = 100
dtmax = '${timestep}'
dtmin = '${timestep}'
[Predictor]
type = SimplePredictor
scale = 1.0
[]
[]
[Functions]
[analytic]
type = ParsedFunction
expression = '1 - x*x'
[]
[]
[Postprocessors]
[dt]
type = TimestepSize
execute_on = timestep_end
[]
# Release rate
[release_inc]
type = SideIntegralMassFlux
variable = conc
boundary = exterior
arrhenius_prpty_name = diffusion_coef
execute_on = 'initial timestep_end'
[]
[released]
type = TimeIntegratedPostprocessor
value = release_inc
execute_on = 'initial timestep_end'
[]
[total]
type = ElementIntegralVariablePostprocessor
variable = conc
execute_on = 'initial timestep_end'
[]
[x_released]
type = FractionalRelease
released = released
retained = retained
[]
[retained]
type = ElementIntegralVariablePostprocessor
variable = conc
[]
[conc_point_25]
type = PointValue
variable = conc
point = '${fparse 0.25*kernel_radius} 0 0'
execute_on = 'initial timestep_end'
[]
[conc_point_50]
type = PointValue
variable = conc
point = '${fparse 0.50*kernel_radius} 0 0'
execute_on = 'initial timestep_end'
[]
[conc_point_75]
type = PointValue
variable = conc
point = '${fparse 0.75*kernel_radius} 0 0'
execute_on = 'initial timestep_end'
[]
[conc_point_95]
type = PointValue
variable = conc
point = '${fparse 0.95*kernel_radius} 0 0'
execute_on = 'initial timestep_end'
[]
[bison_dimensionless_25]
type = ParsedPostprocessor
expression = 'conc_point_25 / (p / (6 * Dprime))'
pp_names = conc_point_25
constant_names = 'p Dprime'
constant_expressions = '${p} ${Dprime}'
execute_on = 'initial timestep_end'
[]
[bison_dimensionless_50]
type = ParsedPostprocessor
expression = 'conc_point_50 / (p / (6 * Dprime))'
pp_names = conc_point_50
constant_names = 'p Dprime'
constant_expressions = '${p} ${Dprime}'
execute_on = 'initial timestep_end'
[]
[bison_dimensionless_75]
type = ParsedPostprocessor
expression = 'conc_point_75 / (p / (6 * Dprime))'
pp_names = conc_point_75
constant_names = 'p Dprime'
constant_expressions = '${p} ${Dprime}'
execute_on = 'initial timestep_end'
[]
[bison_dimensionless_95]
type = ParsedPostprocessor
expression = 'conc_point_95 / (p / (6 * Dprime))'
pp_names = conc_point_95
constant_names = 'p Dprime'
constant_expressions = '${p} ${Dprime}'
execute_on = 'initial timestep_end'
[]
[analytic_dimensionless_25]
type = FunctionValuePostprocessor
function = analytic
point = '0.25 0 0'
execute_on = 'initial timestep_end'
[]
[analytic_dimensionless_50]
type = FunctionValuePostprocessor
function = analytic
point = '0.50 0 0'
execute_on = 'initial timestep_end'
[]
[analytic_dimensionless_75]
type = FunctionValuePostprocessor
function = analytic
point = '0.75 0 0'
execute_on = 'initial timestep_end'
[]
[analytic_dimensionless_95]
type = FunctionValuePostprocessor
function = analytic
point = '0.95 0 0'
execute_on = 'initial timestep_end'
[]
[error_25]
type = ParsedPostprocessor
pp_names = 'bison_dimensionless_25 analytic_dimensionless_25'
expression = '(bison_dimensionless_25 - analytic_dimensionless_25)/analytic_dimensionless_25*100'
execute_on = 'initial timestep_end'
[]
[error_50]
type = ParsedPostprocessor
pp_names = 'bison_dimensionless_50 analytic_dimensionless_50'
expression = '(bison_dimensionless_50 - analytic_dimensionless_50)/analytic_dimensionless_50*100'
execute_on = 'initial timestep_end'
[]
[error_75]
type = ParsedPostprocessor
pp_names = 'bison_dimensionless_75 analytic_dimensionless_75'
expression = '(bison_dimensionless_75 - analytic_dimensionless_75)/analytic_dimensionless_75*100'
execute_on = 'initial timestep_end'
[]
[error_95]
type = ParsedPostprocessor
pp_names = 'bison_dimensionless_95 analytic_dimensionless_95'
expression = '(bison_dimensionless_95 - analytic_dimensionless_95)/analytic_dimensionless_95*100'
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
time_step_interval = 1
exodus = false
print_linear_converged_reason = false
print_linear_residuals = false
print_nonlinear_converged_reason = false
[console]
type = Console
show = 'analytic_dimensionless_25 analytic_dimensionless_50 analytic_dimensionless_75 analytic_dimensionless_95
bison_dimensionless_25 bison_dimensionless_50 bison_dimensionless_75 bison_dimensionless_95
error_25 error_50 error_75 error_95 released x_released'
[]
[out]
type = CSV
execute_on = final
[]
[]
(assessment/TRISO/validation/AGR-34/SharedFiles/capsule_dtf.i)
kernel_radius = 178.65e-6
PyC_thickness = 20e-6
coordinates1 = '${fparse kernel_radius}'
coordinates2 = '${fparse coordinates1+PyC_thickness}'
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.19717 # [wt-]
energy_per_fission = 3.204e-11 # [J/fission]
O_U = 1.430 # Initial oxygen to uranium atom ratio
C_U = 0.361 # Initial carbon to uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[mesh]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 ${coordinates1} ${coordinates2}'
mesh_density = '18 14'
block_names = 'fuel PyC'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = PyC_outer_boundary
outer_SiC = PyC_outer_boundary
outer_IPyC = PyC_outer_boundary
inner_IPyC = PyC_outer_boundary
outer_buffer = PyC_outer_boundary
outer_kernel = fuel_outer_boundary
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temperature]
initial_condition = 1200
[]
[conc_Ag]
initial_condition = 0.0
scaling = 1e12 #1e18
[]
[conc_Cs]
initial_condition = 0.0
scaling = 1e12 #1e18
[]
[conc_Sr]
initial_condition = 0.0
scaling = 1e12 #1e18
[]
[]
[AuxVariables]
[fission_rate]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_flux]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
order = CONSTANT
family = MONOMIAL
[]
[fis_gas_produced]
order = CONSTANT
family = MONOMIAL
[]
[fis_gas_released]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Sr_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temp_bc]
type = PiecewiseLinear
x_index_in_file = 0
y_index_in_file = 1
xy_in_file_only = false
format = columns
data_file='AGR-34_capsule_daily_data/Cap1Temps.csv'
[]
[power_history]
type = PiecewiseLinear
x = '0 76e6'
y = '1 1'
[]
[fission_rate]
type = LinearCombinationFunction
functions = power_history
w = 4.8156e+19
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
extra_vector_tags = 'ref'
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
extra_vector_tags = 'ref'
[]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
extra_vector_tags = 'ref'
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
extra_vector_tags = 'ref'
[]
[mass_Sr_dt]
type = TimeDerivative
variable = conc_Sr
extra_vector_tags = 'ref'
[]
[mass_Sr]
type = ArrheniusDiffusion
variable = conc_Sr
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
extra_vector_tags = 'ref'
[]
[mass_source_Sr]
type = SpeciesSourceRate
variable = conc_Sr
property_name = Sr_generation
block = fuel
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[fissionrate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = fuel
execute_on = timestep_begin
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = fuel
execute_on = timestep_begin
[]
[fast_neutron_flux]
type = MaterialRealAux
variable = fast_neutron_flux
property = fast_neutron_flux
execute_on = timestep_begin
[]
[fast_neutron_fluence]
type = MaterialRealAux
variable = fast_neutron_fluence
property = fast_neutron_fluence
execute_on = timestep_begin
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Sr_diff_coef]
type = MaterialRealAux
variable = Sr_diff_coef
property = arrhenius_diffusion_coef_Sr
execute_on = timestep_end
[]
[]
[BCs]
[freesurf_temp]
type = FunctionDirichletBC
variable = temperature
function = temp_bc
boundary = exterior
extra_vector_tags = 'ref'
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Sr]
type = DirichletBC
variable = conc_Sr
boundary = exterior
value = 0.0
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
flux_function = power_history
factor = 0.5519e+18
[]
[UCO_burnup]
type = TRISOBurnup
initial_density = ${initial_fuel_density}
[]
[UCO_thermal]
type = UCOThermal
block = fuel
temperature = temperature
[]
[UCO_density]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 11098.0
[]
[fission_gas_release]
type = UCOFGR
block = fuel
average_grain_radius = 10e-6
temperature = temperature
triso_geometry = particle_geometry
[]
# Arrhenius diffusion coefficients for kernel, PyC, and SiC
# come from IAEA TECDOC-978, French parameters.
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 1.0e-6 # m^2/s
q1 = 0.0
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 1.0e-6 # m^2/s
q1 = 0.0
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Sr]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 1.0e-6 # m^2/s
q1 = 0.0
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
property_name = Ag_generation
kind = Ag
block = fuel
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
property_name = Cs_generation
kind = Cs
block = fuel
[]
[mass_source_Sr_property]
type = SpeciesSourceMaterial
property_name = Sr_generation
kind = Sr
block = fuel
[]
### PyC properties
[PyC_thermal]
type = HeatConductionMaterial
block = PyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[PyC_density]
type = StrainAdjustedDensity
block = PyC
density = 1988.0
[]
[PyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = PyC
d1 = 1.0e-6 # m^2/s
q1 = 0.0
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[PyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = PyC
d1 = 1.0e-6 # m^2/s
q1 = 0.0
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[PyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = PyC
d1 = 1.0e-6 # m^2/s
q1 = 0.0
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'temperature conc_Ag conc_Cs conc_Sr'
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu'
line_search = 'none'
nl_rel_tol = 1e-9
nl_abs_tol = 1e-9
nl_max_its = 20
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 31890240
dt = 86400
[]
[Postprocessors]
[release_heat_inc]
type = SideIntegralMassFlux
variable = temperature
boundary = exterior
arrhenius_prpty_name = thermal_conductivity
execute_on = 'initial timestep_end'
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor # computes time integration of value
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
[]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
[]
[release_Sr_inc]
type = SideIntegralMassFlux
variable = conc_Sr
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
execute_on = 'initial timestep_end'
[]
[released_Sr]
type = TimeIntegratedPostprocessor
value = release_Sr_inc
execute_on = 'initial timestep_end'
[]
[total_Sr]
type = ElementIntegralMaterialProperty
mat_prop = Sr_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Sr_released]
type = FractionalRelease
released = released_Sr
total = total_Sr
[]
[retained_Sr]
type = ElementIntegralVariablePostprocessor
variable = conc_Sr
[]
[fis_gas_produced]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_produced
block = fuel
execute_on = 'initial timestep_end'
[]
[fis_gas_released]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_released
block = fuel
execute_on = 'initial timestep_end'
[]
### Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
execute_on = 'initial timestep_end'
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
execute_on = 'initial timestep_end'
[]
##### irradiation conditions
[particle_power]
type = ElementIntegralPower
variable = temperature
use_material_fission_rate = true
fission_rate_material = fission_rate
block = fuel
execute_on = 'initial timestep_end'
[]
[max_fluence]
type = ElementExtremeValue
variable = fast_neutron_fluence
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_burnup]
type = ElementExtremeValue
variable = burnup
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
print_linear_converged_reason = false
print_nonlinear_converged_reason = false
exodus = false
csv = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_8b/case_8b.i)
#
# Particle failure at 50, 55, 65, 70, 75, 80, 85, 89, 92, and 97h after 1800 C.
# A failure-free analysis is also needed (eleven in all).
# The compact has 16350 particles.
#
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.0982
constant_expressions = 31690800.0
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 248.5e-6 342.5e-6 383.5e-6 419.5e-6 459.5e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
bias = '1 1.25 1.25 1.25 1.25'
dual_bias = '0.8 0.8 0.8 0.8 1'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[conc_Ag]
[]
[conc_Sr]
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1114.65
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Sr_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temperature]
type = PiecewiseLinear
data_file = temperature_history.dat
format = columns
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
[]
[mass_Sr_dt]
type = TimeDerivative
variable = conc_Sr
[]
[mass_Sr]
type = ArrheniusDiffusion
variable = conc_Sr
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Sr]
type = SpeciesSourceRate
variable = conc_Sr
property_name = Sr_generation
block = fuel
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[Sr_diff_coef]
type = MaterialRealAux
variable = Sr_diff_coef
property = arrhenius_diffusion_coef_Sr
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = temperature
variable = temperature
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[freesurf_conc_Sr]
type = DirichletBC
variable = conc_Sr
boundary = exterior
value = 0.0
[]
[]
[Materials]
[burnup]
type = GenericFunctionMaterial
block = fuel
prop_names = 'burnup'
prop_values = 'if(t<31017600,0.106/31017600*t,0.106)'
[]
[fission_rate]
type = GenericFunctionMaterial
block = fuel
prop_names = 'fission_rate'
# 8.24e19 = 0.106/31017600*10810/.27*6.0221409e23
prop_values = 'if(t<31017600,8.24e19,0)'
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Cs_generation
kind = Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs_intact]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = 'if(t<31017600,exp(5.9e25/31017600*t/5e25),exp(5.9e25/5e25))'
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs_intact
[]
[time]
type = TimeStepMaterial
[]
[SiC_conc_Cs]
type = ParsedMaterial
block = SiC
property_name = arrhenius_diffusion_coef_Cs
coupled_variables = 'temperature'
material_property_names = 'time arrhenius_diffusion_coef_Cs_intact'
constant_names = 'failure_time'
expression = 'if(time<=failure_time, arrhenius_diffusion_coef_Cs_intact, 1e-6)'
[]
[SiC_conc_Cs_dT]
type = ParsedMaterial
block = SiC
property_name = arrhenius_diffusion_coef_Cs_dT
coupled_variables = 'temperature'
material_property_names = 'time arrhenius_diffusion_coef_Cs_intact_dT'
constant_names = 'failure_time'
expression = 'if(time<=failure_time, arrhenius_diffusion_coef_Cs_intact_dT, 0)'
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Ag_generation
kind = Ag
[]
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[SiC_conc_Ag_intact]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag_intact
[]
[SiC_conc_Ag]
type = ParsedMaterial
block = SiC
property_name = arrhenius_diffusion_coef_Ag
coupled_variables = 'temperature'
material_property_names = 'time arrhenius_diffusion_coef_Ag_intact'
constant_names = 'failure_time'
expression = 'if(time<=failure_time, arrhenius_diffusion_coef_Ag_intact, 1e-6)'
[]
[SiC_conc_Ag_dT]
type = ParsedMaterial
block = SiC
property_name = arrhenius_diffusion_coef_Ag_dT
coupled_variables = 'temperature'
material_property_names = 'time arrhenius_diffusion_coef_Ag_intact_dT'
constant_names = 'failure_time'
expression = 'if(time<=failure_time, arrhenius_diffusion_coef_Ag_intact_dT, 0)'
[]
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[fuel_conc_Sr]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 2.2e-3 # m^2/s
q1 = 488e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[mass_source_Sr_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Sr_generation
kind = Sr
[]
[buffer_conc_Sr]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[IPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[SiC_conc_Sr_intact]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 1.2e-9 # m^2/s
q1 = 205e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr_intact
[]
[SiC_conc_Sr]
type = ParsedMaterial
block = SiC
property_name = arrhenius_diffusion_coef_Sr
coupled_variables = 'temperature'
material_property_names = 'time arrhenius_diffusion_coef_Sr_intact'
constant_names = 'failure_time'
expression = 'if(time<=failure_time, arrhenius_diffusion_coef_Sr_intact, 1e-6)'
[]
[SiC_conc_Sr_dT]
type = ParsedMaterial
block = SiC
property_name = arrhenius_diffusion_coef_Sr_dT
coupled_variables = 'temperature'
material_property_names = 'time arrhenius_diffusion_coef_Sr_intact_dT'
constant_names = 'failure_time'
expression = 'if(time<=failure_time, arrhenius_diffusion_coef_Sr_intact_dT, 0)'
[]
[OPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs conc_Ag conc_Sr'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 5e-21
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 31690800
num_steps = 1450
dt = 86400
dtmax = 86400
#dtmin = 86400
[TimeStepper]
type = FunctionDT
function = 'if(t<31017600,86400,1800)'
[]
[]
[Postprocessors]
[_temp]
type = NodalExtremeValue
variable = temperature
[]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released_overall]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
start_time = 31017600
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial timestep_end'
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released_overall]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
start_time = 31017600
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
execute_on = 'initial timestep_end'
[]
[release_Sr_inc]
type = SideIntegralMassFlux
variable = conc_Sr
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
execute_on = 'initial timestep_end'
[]
[released_Sr]
type = TimeIntegratedPostprocessor
value = release_Sr_inc
execute_on = 'initial timestep_end'
[]
[total_Sr]
type = ElementIntegralMaterialProperty
mat_prop = Sr_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Sr_released_overall]
type = FractionalRelease
released = released_Sr
total = total_Sr
execute_on = 'initial timestep_end'
[]
[x_Sr_released]
type = FractionalRelease
released = released_Sr
total = total_Sr
execute_on = 'initial timestep_end'
start_time = 31017600
[]
[retained_Sr]
type = ElementIntegralVariablePostprocessor
variable = conc_Sr
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
[]
[out_final]
type = CSV
execute_on = final
[]
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_4a/case_4a.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.08
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 250e-6 350e-6 390e-6 425e-6 465e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
bias = '1 1.25 1.25 1.25 1.25'
dual_bias = '0.8 0.8 0.8 0.8 1'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[conc_Ag]
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1273.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = 'if(t<4.3200001e7,1273.15,1873.15)'
variable = temperature
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[]
[Materials]
[burnup]
type = GenericFunctionMaterial
block = fuel
prop_names = 'burnup'
prop_values = '0.1/4.32e7*t'
[]
[fission_rate]
type = GenericFunctionMaterial
block = fuel
prop_names = 'fission_rate'
# 5.581219e19 = 0.1/4.32e7*10810/.27*6.0221409e23
prop_values = '5.581219e19'
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Cs_generation
kind = Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = 'exp(2e25/4.32e7*t/5e25)'
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Ag_generation
kind = Ag
[]
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[SiC_conc_Ag]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs conc_Ag'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 5e-21 #1e-22
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 4.392e7
num_steps = 700
dt = 86400
dtmax = 86400
#dtmin = 86400
[TimeStepper]
type = FunctionDT
function = 'if(t<4.3200001e7,86400,3600)'
[]
[]
[Postprocessors]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
execute_on = final
[]
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_7/case_7_1D.i)
#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# See also Hales, et al., Multidimensional multiphysics simulation of TRISO
# particle fuel, JNM, 443, 2013. https://doi.org/10.1016/j.jnucmat.2013.07.070
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark. The best way to do this is to compare
# results with information in the JNM article.
#
[GlobalParams]
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '3.50e-4 3.90e-4 4.25e-4 4.65e-4'
mesh_density = '4 4 4'
block_names = 'IPyC SiC OPyC'
[]
[]
[Variables]
[disp_x]
[]
[]
[Functions]
[radial_eigenstrain]
type = ParsedFunction
expression = 't*(7.27026e-4/4.0*t*t*t - 5.05553e-3/3.0*t*t + 1.83715e-2/2.0*t - 2.12522e-2)'
[]
[tangential_eigenstrain]
type = ParsedFunction
expression = 't*(-8.88086e-4/4.0*t*t*t + 5.03465e-3/3.0*t*t - 3.42182e-3/2.0*t - 1.79113e-2)'
[]
[pressure]
type = ParsedFunction
expression = '26.2e6/8e7*t'
[]
[k_function]
type = ParsedFunction
expression = '2.715e-29'
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1273.0
[]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
initial_condition = 0.0
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[IPyC_OPyC]
block = 'IPyC OPyC'
strain = finite
eigenstrain_names = pyc_eigenstrain
[]
[SiC]
block = SiC
strain = finite
[]
[]
[AuxKernels]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[]
[BCs]
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[interior_pressure_x]
type = Pressure
variable = disp_x
boundary = IPyC_inner_boundary
factor = 1.0
function = pressure
[]
[]
[Materials]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 3.75e17 # n/m^2-sec
[]
[stress]
type = ComputeFiniteStrainElasticStress
block = 'SiC'
[]
[PyC_stress]
type = PyCCreep
block = 'IPyC OPyC'
k = k_function
temperature = temperature
[]
[PyC_density]
type = StrainAdjustedDensity
block = 'IPyC OPyC'
strain_free_density = 1900.0
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'IPyC OPyC'
[]
[PyC_eigenstrain]
type = PyCIrradiationEigenstrain
block = 'IPyC OPyC'
radial_eigenstrain_function = radial_eigenstrain
tangential_eigenstrain_function = tangential_eigenstrain
eigenstrain_name = pyc_eigenstrain
[]
[PyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = 'IPyC OPyC'
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 8e7
dt = 1.0
dtmax = 1e6
dtmin = 1.0e4
[TimeStepper]
type = IterationAdaptiveDT
dt = 1
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[max_yy_IPyC]
type = ElementExtremeValue
variable = stress_yy
block = IPyC
[]
[max_yy_SiC]
type = ElementExtremeValue
variable = stress_yy
block = SiC
[]
[]
[PerformanceMetricOutputs]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
csv = true
perf_graph = true
[]
(test/tests/triso/mesh/mesh_1D.i)
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE2
coordinates = '0 .1 .2'
mesh_density = '7 7'
block_names = 'fred wilma'
bias = '2.0 2.0'
[]
[]
[Variables]
[var_a]
[]
[var_b]
[]
[]
[Kernels]
[Diffusion_a]
type = Diffusion
variable = var_a
[]
[Diffusion_b]
type = Diffusion
variable = var_b
[]
[]
[BCs]
[var_a_left]
type = DirichletBC
variable = var_a
boundary = xzero
value = 0.0
[]
[var_a_right]
type = DirichletBC
variable = var_a
boundary = exterior
value = 1.0
[]
[var_b_left]
type = DirichletBC
variable = var_b
boundary = fred_inner_boundary
value = 0.0
[]
[var_b_right]
type = DirichletBC
variable = var_b
boundary = wilma_outer_boundary
value = 100.0
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 51'
start_time = 0.0
end_time = 1.0
dt = 1.0
[]
[Outputs]
# Define output file(s)
time_step_interval = 1
exodus = true
[console]
type = Console
max_rows = 25
[]
[]
(test/tests/triso_pebble/1D_pebble_from_csv.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
flux_conversion_factor = 0.85
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 0.0138 0.018 0.02'
mesh_density = '5 10 10'
block_names = 'core fuel shell'
[]
[]
[Distributions]
[normal_kernel_r]
type = TruncatedNormal
mean = 213.35e-6
standard_deviation = 4.4e-6
lower_bound = 1.9575e-04
upper_bound = 2.3095e-04
[]
[normal_buffer_t]
type = TruncatedNormal
mean = 98.9e-6
standard_deviation = 8.4e-6
lower_bound = 6.53e-05
upper_bound = 1.325e-04
[]
[normal_ipyc_t]
type = TruncatedNormal
mean = 40.4e-6
standard_deviation = 2.5e-6
lower_bound = 3.0400e-05
upper_bound = 5.0400e-05
[]
[normal_sic_t]
type = TruncatedNormal
mean = 35.2e-6
standard_deviation = 1.2e-6
lower_bound = 3.0400e-05
upper_bound = 4.0000e-05
[]
[normal_opyc_t]
type = TruncatedNormal
mean = 43.4e-6
standard_deviation = 2.9e-6
lower_bound = 3.1800e-05
upper_bound = 5.5000e-05
[]
[]
[DiracKernels]
[vpp_point_source]
type = TRISOMonteCarloPointSource
variable = temperature
point_source_values = heat_source
value_name = heat_inc
point_source_location = point_source_location
[]
[]
[UserObjects]
[point_source_location]
type = TRISOMonteCarloPointSourceLocation
min_radius = 0.0138
max_radius = 0.018
geometry = SPHERE
fuel_element_blocks = fuel
execute_on = 'INITIAL'
num_particles = 100
[]
[]
[VectorPostprocessors]
[heat_source]
type = TRISOMonteCarloPointSourceFromFile
file_base_time = monte_carlo_out_time
file_base_source = monte_carlo_out_release_heat_inc
x_header_in_file = 'time:time'
y_header_in_file = 'release_heat_inc:release_heat_inc'
source_name = heat_inc
num_files = 2
num_particles = 100
format = columns
execute_on = 'INITIAL TIMESTEP_BEGIN'
[]
[point_source_output]
type = TRISOMonteCarloPointSourceOutput
vector_postprocessor = heat_source
value_name = heat_inc
point_source_location = point_source_location
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[temperature]
initial_condition = 773.15
[]
[]
[AuxVariables]
[density]
order = CONSTANT
family = MONOMIAL
[]
[thermal_conductivity]
order = CONSTANT
family = MONOMIAL
[]
[specific_heat]
order = CONSTANT
family = MONOMIAL
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[density]
type = MaterialRealAux
variable = density
property = density
block = 'core fuel shell'
execute_on = 'initial linear'
[]
[thermal_conductivity]
type = MaterialRealAux
variable = thermal_conductivity
property = thermal_conductivity
block = 'core fuel shell'
execute_on = timestep_end
[]
[specific_heat]
type = MaterialRealAux
variable = specific_heat
property = specific_heat
block = 'core fuel shell'
execute_on = timestep_end
[]
[]
[BCs]
[coolant_temp]
type = DirichletBC
variable = temperature
boundary = exterior
value = 773.15
[]
[]
[Functions]
[power_history]
type = PiecewiseLinear
x = '0 76e6'
y = '1 1'
[]
[fission_rate]
type = LinearCombinationFunction
functions = power_history
w = 5.75e19
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
flux_function = power_history
factor = 6.28e17
[]
[fueled_region_thermal]
type = GraphiteMatrixThermal
block = fuel
graphite_grade = A3_27_1800
packing_fraction = 0.22
temperature = temperature
initial_matrix_density = 1750.0
[]
[fuel_region_density]
type = ParsedMaterial
block = fuel
property_name = density
expression = 1750.0
[]
[shell_region_thermal]
type = GraphiteMatrixThermal
block = shell
graphite_grade = A3_27_1800
packing_fraction = 0.0
temperature = temperature
initial_matrix_density = 1750.0
[]
[shell_region_density]
type = ParsedMaterial
block = shell
property_name = density
expression = 1750.0
[]
[core_region_thermal]
type = GraphiteMatrixThermal
block = core
graphite_grade = A3_27_1800
packing_fraction = 0.0
temperature = temperature
initial_matrix_density = 1400.0
[]
[core_region_density]
type = ParsedMaterial
block = core
property_name = density
expression = 1400.0
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'temperature'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-9
nl_abs_tol = 1e-9
nl_max_its = 15
l_tol = 1e-5
l_max_its = 30
start_time = 0.0
dt = 10
num_steps = 2
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = true
perf_graph = true
[]
(test/tests/triso_pebble/triso_1d.i)
kernel_radius = 213.35e-6
buffer_thickness = 98.9e-6
IPyC_thickness = 40.4e-6
SiC_thickness = 35.2e-6
OPyC_thickness = 43.4e-6
coordinates1 = '${fparse kernel_radius}'
coordinates2 = '${fparse coordinates1+buffer_thickness}'
coordinates3 = '${fparse coordinates2+IPyC_thickness}'
coordinates4 = '${fparse coordinates3+SiC_thickness}'
coordinates5 = '${fparse coordinates4+OPyC_thickness}'
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.14029 # [wt-]
energy_per_fission = 3.204e-11 # [J/fission]
O_U = 1.428 # Initial Oxygen to Uranium atom ratio
C_U = 0.392 # Initial Carbon to Uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[mesh]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
mesh_density = '18 14 12 16 16'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = OPyC_outer_boundary
outer_SiC = SiC_outer_boundary
outer_IPyC = IPyC_outer_boundary
inner_IPyC = IPyC_inner_boundary
outer_buffer = buffer_outer_boundary
outer_kernel = fuel_outer_boundary
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temperature]
initial_condition = 773.15
[]
[conc_Ag]
initial_condition = 0.0
scaling = 1e14
[]
[conc_Cs]
initial_condition = 0.0
scaling = 1e14
[]
[conc_Sr]
initial_condition = 0.0
scaling = 1e14
[]
[]
[AuxVariables]
[fission_rate]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_flux]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
order = CONSTANT
family = MONOMIAL
[]
[fis_gas_produced]
order = CONSTANT
family = MONOMIAL
[]
[fis_gas_released]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Sr_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[power_history]
type = PiecewiseLinear
x = '0 76e6'
y = '1 1'
[]
[fission_rate]
type = LinearCombinationFunction
functions = power_history
w = 5.75e19
[]
[d1_function]
type = ParsedFunction
expression = 'exp(t/4.5e25)'
[]
[temp_bc_func]
type = ParsedFunction
expression = temp_bc
symbol_names = temp_bc
symbol_values = temp_bc
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
extra_vector_tags = 'ref'
[]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
extra_vector_tags = 'ref'
[]
[mass_Sr_dt]
type = MassLumpedTimeDerivative
variable = conc_Sr
[]
[mass_Sr]
type = ArrheniusDiffusion
variable = conc_Sr
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
extra_vector_tags = 'ref'
[]
[mass_source_Sr]
type = SpeciesSourceRate
variable = conc_Sr
property_name = Sr_generation
block = fuel
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[fissionrate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = fuel
execute_on = timestep_begin
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = fuel
execute_on = timestep_begin
[]
[fast_neutron_flux]
type = MaterialRealAux
variable = fast_neutron_flux
property = fast_neutron_flux
execute_on = timestep_begin
[]
[fast_neutron_fluence]
type = MaterialRealAux
variable = fast_neutron_fluence
property = fast_neutron_fluence
execute_on = timestep_begin
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Sr_diff_coef]
type = MaterialRealAux
variable = Sr_diff_coef
property = arrhenius_diffusion_coef_Sr
execute_on = timestep_end
[]
[]
[BCs]
[freesurf_temp]
type = FunctionDirichletBC
variable = temperature
function = temp_bc_func
boundary = exterior
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Sr]
type = DirichletBC
variable = conc_Sr
boundary = exterior
value = 0.0
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
flux_function = power_history
factor = 6.28e17
[]
[UCO_burnup]
type = TRISOBurnup
initial_density = 10966.0
[]
[UCO_thermal]
type = UCOThermal
block = fuel
temperature = temperature
[]
[UCO_density]
type = ParsedMaterial
block = fuel
property_name = density
expression = 10966.0
[]
[fission_gas_release]
type = UCOFGR
block = fuel
average_grain_radius = 10e-6
temperature = temperature
triso_geometry = particle_geometry
cutoff_neutron_flux = 0.0
[]
# Arrhenius diffusion coefficients for kernel, PyC, and SiC
# come from IAEA TECDOC-978, French parameters.
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Sr]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 2.2e-3 # m^2/s
q1 = 488e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
property_name = Ag_generation
kind = Ag
block = fuel
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
property_name = Cs_generation
kind = Cs
block = fuel
[]
[mass_source_Sr_property]
type = SpeciesSourceMaterial
property_name = Sr_generation
kind = Sr
block = fuel
[]
### Buffer Properties
[buffer_thermal]
type = BufferThermal
block = buffer
initial_density = 1050.0
[]
[Buffer_density]
type = ParsedMaterial
block = buffer
property_name = density
expression = 1050.0
[]
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0.0
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0.0
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[buffer_conc_Sr]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0.0
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
### IPyC properties
[IPyC_thermal]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_density]
type = ParsedMaterial
block = IPyC
property_name = density
expression = 1907.0
[]
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
### SiC properties
[SiC_thermal]
type = MonolithicSiCThermal
block = SiC
temperature = temperature
thermal_conductivity_model = miller
[]
[SiC_density]
type = ParsedMaterial
block = SiC
property_name = density
expression = 3200.0
[]
[SiC_conc_Ag]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
q1 = 125e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Sr]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 1.2e-9 # m^2/s
q1 = 205e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
### OPyC properties
[OPyC_thermal_conductivity]
type = HeatConductionMaterial
block = OPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[OPyC_density]
type = ParsedMaterial
block = OPyC
property_name = density
expression = 1907.0
[]
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'temperature conc_Ag conc_Cs conc_Sr'
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu'
line_search = 'none'
automatic_scaling = true
nl_rel_tol = 1e-12
nl_abs_tol = 1e-12
nl_max_its = 20
nl_forced_its = 2
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
dt = 20000
num_steps = 2
[]
[Postprocessors]
[temp_bc]
type = Receiver
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor # computes time integration of value
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
[]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
[]
[release_Sr_inc]
type = SideIntegralMassFlux
variable = conc_Sr
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
execute_on = 'initial timestep_end'
[]
[released_Sr]
type = TimeIntegratedPostprocessor
value = release_Sr_inc
execute_on = 'initial timestep_end'
[]
[released_heat_inc]
type = SideIntegralMassFlux
variable = temperature
boundary = exterior
arrhenius_prpty_name = thermal_conductivity
execute_on = 'initial timestep_end'
[]
[total_Sr]
type = ElementIntegralMaterialProperty
mat_prop = Sr_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Sr_released]
type = FractionalRelease
released = released_Sr
total = total_Sr
[]
[retained_Sr]
type = ElementIntegralVariablePostprocessor
variable = conc_Sr
[]
[fis_gas_produced]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_produced
block = fuel
execute_on = 'initial timestep_end'
[]
[fis_gas_released]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_released
block = fuel
execute_on = 'initial timestep_end'
[]
### Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
execute_on = 'initial timestep_end'
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
execute_on = 'initial timestep_end'
[]
##### irradiation conditions
[particle_power]
type = ElementIntegralPower
variable = temperature
use_material_fission_rate = true
fission_rate_material = fission_rate
block = fuel
execute_on = 'initial timestep_end'
[]
[max_fluence]
type = ElementExtremeValue
variable = fast_neutron_fluence
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_burnup]
type = ElementExtremeValue
variable = burnup
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[aver_temp_exterior]
type = SideAverageValue
variable = temperature
boundary = exterior
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
print_linear_residuals = false
[]
(examples/TRISO/one_layer/1D/one_layer_1D.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '3.5e-4 3.85e-4'
mesh_density = '64'
block_names = 'SiC'
[]
[]
[Variables]
[temp]
initial_condition = 1273.0
[]
[]
[AuxVariables]
[burnup]
initial_condition = 0
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[SiC]
block = SiC
add_variables = true
strain = FINITE
eigenstrain_names = ''
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temp
[]
[heat]
type = HeatConduction
variable = temp
[]
[]
[BCs]
# fix temperature on free surface
[freesurf_temp]
type = DirichletBC
variable = temp
boundary = exterior
value = 1273.0
[]
# exterior and internal pressures
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[interior_pressure_x]
type = Pressure
variable = disp_x
boundary = SiC_inner_boundary
factor = 25e6
[]
[]
[Materials]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_elastic_stress]
type = ComputeFiniteStrainElasticStress
block = SiC
[]
[SiC_temp]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9 # J/m-s-K
specific_heat = 620.0 # J/kg-K
[]
[SiC_den]
type = StrainAdjustedDensity
strain_free_density = 3180.0 # kg/m^3
block = SiC
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temp
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 1
dt = 1
[]
[Postprocessors]
[dt]
type = TimestepSize
[]
[max_xx]
type = ElementExtremeValue
variable = stress_xx
[]
[max_yy]
type = ElementExtremeValue
variable = stress_yy
[]
[max_zz]
type = ElementExtremeValue
variable = stress_zz
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = true
csv = true
perf_graph = true
[]
(examples/TRISO/parfume/parfume.i)
# UCO TRISO particle using several PARFUME models
initial_fuel_density = 10400
[GlobalParams]
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
initial_enrichment = 0.1955 # [wt-]
flux_conversion_factor = 1.0 # convert E>0.10 to E>0.18 MeV
stress_free_temperature = 923.15 # used for thermal expansion
energy_per_fission = 3.204e-11 # [J/fission]
O_U = 1.5 # Initial Oxygen to Uranium atom ratio
C_U = 0.4 # Initial Carbon to Uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.125e-4 3.125e-4 3.125e-4 3.525e-4 3.875e-4 4.275e-4'
mesh_density = '6 6 0 6 8 6'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
[]
[]
[Variables]
[temperature]
initial_condition = 923.15
[]
[conc]
initial_condition = 0.0
scaling = 1e18
[]
[]
[AuxVariables]
[disp_y]
[]
[disp_z]
[]
[fission_rate]
block = fuel
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = fuel
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_flux]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
order = CONSTANT
family = MONOMIAL
[]
[gap_condSlave]
order = CONSTANT
family = MONOMIAL
[]
[density]
order = CONSTANT
family = MONOMIAL
[]
[thermal_conductivity]
order = CONSTANT
family = MONOMIAL
[]
[swelling]
order = CONSTANT
family = MONOMIAL
[]
[specific_heat]
order = CONSTANT
family = MONOMIAL
[]
[volumetric_IIDC_strain]
order = CONSTANT
family = MONOMIAL
[]
[radial_IIDC_strain]
order = CONSTANT
family = MONOMIAL
[]
[tangential_IIDC_strain]
order = CONSTANT
family = MONOMIAL
[]
[BAF]
order = CONSTANT
family = MONOMIAL
[]
[fis_gas_produced]
order = CONSTANT
family = MONOMIAL
[]
[fis_gas_released]
order = CONSTANT
family = MONOMIAL
[]
[gap_HTC]
order = CONSTANT
family = MONOMIAL
[]
[gap_distance]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[power_history]
type = PiecewiseLinear
x = '0 76e6 76.001e6'
y = '1 1 0'
[]
[fission_rate]
type = LinearCombinationFunction
functions = power_history
w = 3.89e19
[]
[temp_bc]
type = PiecewiseLinear
x = '0 76e6 76.001e6 84.641e6 84.6482e6'
y = '1500 1500 300 300 2073'
[]
[k_function]
type = PiecewiseLinear
x = '0 200e6'
y = '4e-37 4e-37'
[]
[d1_function]
type = ParsedFunction
expression = 'exp(t/4.5e25)'
[]
[d_gap]
type = PiecewiseLinear
x = '1500 2100'
y = '1e-14 1e-12'
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[fuel]
block = fuel
add_variables = true
strain = FINITE
incremental = true
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
eigenstrain_names = 'UCO_swelling_eigenstrain UCO_thermal_strain'
extra_vector_tags = 'ref'
[]
[buffer]
block = buffer
add_variables = true
strain = FINITE
incremental = true
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
eigenstrain_names = 'buffer_IIDC_strain buffer_thermal_strain'
extra_vector_tags = 'ref'
[]
[IPyC]
block = IPyC
add_variables = true
strain = FINITE
incremental = true
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
eigenstrain_names = 'IPyC_IIDC_strain IPyC_thermal_strain'
extra_vector_tags = 'ref'
[]
[SiC]
block = SiC
add_variables = true
strain = FINITE
incremental = true
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
eigenstrain_names = 'SiC_thermal_eigenstrain'
extra_vector_tags = 'ref'
[]
[OPyC]
block = OPyC
add_variables = true
strain = FINITE
incremental = true
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
eigenstrain_names = 'OPyC_IIDC_strain OPyC_thermal_strain'
extra_vector_tags = 'ref'
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[mass_ie]
type = TimeDerivative
variable = conc
extra_vector_tags = 'ref'
[]
[mass]
type = ArrheniusDiffusion
variable = conc
extra_vector_tags = 'ref'
[]
[mass_source]
type = BodyForce
variable = conc
function = power_history
value = 1.22e-5 # units of mol/m**3-s
block = fuel
extra_vector_tags = 'ref'
[]
[mass_decay]
type = Decay
variable = conc
radioactive_decay_constant = 7.297e-10 # units:(1/sec) The constant for Cesium
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[fissionrate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = fuel
execute_on = timestep_begin
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = fuel
execute_on = timestep_begin
[]
[fast_neutron_flux]
type = MaterialRealAux
variable = fast_neutron_flux
property = fast_neutron_flux
block = 'fuel buffer IPyC SiC OPyC'
execute_on = timestep_begin
[]
[fast_neutron_fluence]
type = MaterialRealAux
variable = fast_neutron_fluence
property = fast_neutron_fluence
block = 'fuel buffer IPyC SiC OPyC'
execute_on = timestep_begin
[]
[conductanceSlave]
type = MaterialRealAux
property = gap_conductance
variable = gap_condSlave
boundary = buffer_outer_boundary
execute_on = 'initial timestep_end'
[]
[density]
type = MaterialRealAux
variable = density
property = density
block = 'fuel buffer IPyC SiC OPyC'
execute_on = 'initial linear'
[]
[thermal_conductivity]
type = MaterialRealAux
variable = thermal_conductivity
property = thermal_conductivity
block = 'fuel buffer IPyC SiC OPyC'
execute_on = timestep_end
[]
[specific_heat]
type = MaterialRealAux
variable = specific_heat
property = specific_heat
block = 'fuel buffer IPyC SiC OPyC'
execute_on = timestep_end
[]
[swelling]
type = MaterialRealAux
variable = swelling
property = swelling
block = fuel
execute_on = linear
[]
[volumetric_IIDC_strain]
type = MaterialRealAux
variable = volumetric_IIDC_strain
property = volumetric_IIDC_strain
block = 'IPyC OPyC'
execute_on = timestep_end
[]
[radial_IIDC_strain]
type = MaterialRealAux
variable = radial_IIDC_strain
property = radial_IIDC_strain
block = 'IPyC OPyC'
execute_on = timestep_end
[]
[tangential_IIDC_strain]
type = MaterialRealAux
variable = tangential_IIDC_strain
property = tangential_IIDC_strain
block = 'IPyC OPyC'
execute_on = timestep_end
[]
[BAF]
type = MaterialRealAux
variable = BAF
property = BAF
block = 'IPyC OPyC'
execute_on = timestep_end
[]
[fis_gas_produced]
type = MaterialRealAux
variable = fis_gas_produced
property = fis_gas_produced
block = fuel
execute_on = linear
[]
[fis_gas_released]
type = MaterialRealAux
variable = fis_gas_released
property = fis_gas_released
block = fuel
execute_on = linear
[]
[gap_HTC]
type = MaterialRealAux
property = gap_conductance
variable = gap_HTC
boundary = buffer_outer_boundary
execute_on = 'initial timestep_end'
[]
[gap_distance]
type = PenetrationAux
variable = gap_distance
boundary = buffer_outer_boundary
paired_boundary = IPyC_inner_boundary
quantity = distance
tangential_tolerance = 1e-6
execute_on = 'initial timestep_end'
[]
[]
[Contact]
[mechanical]
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
penalty = 1e5
model = frictionless
formulation = kinematic
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
initial_gas_types = 'Kr Xe'
initial_fractions = '0.185 0.815'
gas_released = 'fis_gas_released'
released_gas_types = 'Kr Xe'
released_fractions = '0.185 0.815'
tangential_tolerance = 1e-6
roughness_primary = 0e-6
roughness_secondary = 0e-6
jumpdistance_primary = 0
jumpdistance_secondary = 0
quadrature = true
emissivity_secondary = 0.0
emissivity_primary = 0.0
min_gap = 1e-7
max_gap = 50e-6
gap_geometry_type = sphere
[]
[cesium_contact]
type = GapHeatTransfer
variable = conc
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
tangential_tolerance = 1e-6
gap_conductivity_function = d_gap
gap_conductivity_function_variable = temperature
appended_property_name = _conc
quadrature = true
gap_geometry_type = sphere
emissivity_primary = 0.0
emissivity_secondary = 0.0
min_gap = 1e-7
[]
[]
[BCs]
# pin particle along symmetry planes
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
# fix temperature on free surface
[freesurf_temp]
type = FunctionDirichletBC
variable = temperature
function = temp_bc
boundary = exterior
[]
# fix concentration on free surface
[freesurf_conc]
type = DirichletBC
variable = conc
boundary = exterior
value = 0.0
[]
# exterior and internal pressures
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure] # apply gas pressure on buffer and IPyC boundaries
[plenumPressure]
boundary = buffer_IPyC_boundary
initial_pressure = 100.0
startup_time = 0
R = 8.3145
output_initial_moles = initial_moles
temperature = ave_gas_temp
volume = 'gap_volume buffer_void_volume kernel_void_volume'
material_input = 'fis_gas_released'
output = gas_pressure
[]
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
flux_function = power_history
factor = 5e17
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'buffer IPyC OPyC'
[]
### UCO properties
[UCO_burnup]
type = TRISOBurnup
initial_density = ${initial_fuel_density}
[]
[UCO_thermal]
type = UCOThermal
block = fuel
temperature = temperature
[]
[UCO_elasticity_tensor]
type = UCOElasticityTensor
block = fuel
temperature = temperature
[]
[UCO_stress]
type = ComputeFiniteStrainElasticStress
block = fuel
[]
[UCO_VolumetricSwellingEigenstrain]
type = UCOVolumetricSwellingEigenstrain
block = fuel
eigenstrain_name = UCO_swelling_eigenstrain
[]
[UCO_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10e-6 # check this value for UCO
eigenstrain_name = UCO_thermal_strain
temperature = temperature
[]
[UCO_density]
type = StrainAdjustedDensity
block = fuel
strain_free_density = ${initial_fuel_density}
[]
[fission_gas_release]
type = UCOFGR
block = fuel
average_grain_radius = 10e-6
temperature = temperature
triso_geometry = particle_geometry
cutoff_neutron_flux = 0.0
[]
[fuel_conc]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209.0e+3 # J/mol
d2 = 5.2e-4 # m^2/s
q2 = 362.0e+3 # J/mol
temperature = temperature
[]
### Buffer Properties
[buffer_elasticity_tensor]
type = BufferElasticityTensor
block = buffer
temperature = temperature
[]
[buffer_stress]
type = BufferCEGACreep
block = buffer
temperature = temperature
[]
[buffer_thermal]
type = BufferThermal
block = buffer
initial_density = 1050.0
[]
[buffer_density]
type = StrainAdjustedDensity
block = buffer
strain_free_density = 1050.0
[]
[buffer_thermal_strain]
type = BufferThermalExpansionEigenstrain
block = buffer
eigenstrain_name = buffer_thermal_strain
temperature = temperature
[]
[buffer_IIDC_strain]
type = BufferCEGAIrradiationEigenstrain
block = buffer
eigenstrain_name = buffer_IIDC_strain
temperature = temperature
[]
[buffer_conc]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1.0e-12 # m^2/s
q1 = 0.0
d2 = 0.0
q2 = 0.0
temperature = temperature
[]
### IPyC properties
[IPyC_elasticity_tensor]
type = PyCElasticityTensor
block = IPyC
temperature = temperature
initial_BAF = 1.045
[]
[IPyC_stress]
type = PyCCEGACreep
block = IPyC
temperature = temperature
[]
[IPyC_thermal]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_density]
type = GenericConstantMaterial
block = IPyC
prop_names = 'density'
prop_values = 1900.0
[]
[IPyC_IIDC_strain]
type = PyCCEGAIrradiationEigenstrain
block = IPyC
eigenstrain_name = IPyC_IIDC_strain
temperature = temperature
[]
[BAF_IPyC]
type = BaconAnisotropyFactor
initial_BAF = 1.045
block = IPyC
[]
[BAF_OPyC]
type = BaconAnisotropyFactor
initial_BAF = 1.045
block = OPyC
[]
[IPyC_thermal_strain]
type = PyCThermalExpansionEigenstrain
block = IPyC
eigenstrain_name = IPyC_thermal_strain
temperature = temperature
[]
[IPyC_conc]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222.0e+3 # J/mol
d2 = 0.0
q2 = 0.0
temperature = temperature
[]
### SiC properties
[SiC_elasticity_tensor]
type = MonolithicSiCElasticityTensor
block = SiC
temperature = temperature
elastic_modulus_model = miller
[]
[SiC_stress]
type = ComputeFiniteStrainElasticStress
block = SiC
[]
[SiC_thermal]
type = MonolithicSiCThermal
block = SiC
temperature = temperature
thermal_conductivity_model = miller
[]
[SiC_density]
type = GenericConstantMaterial
block = SiC
prop_names = 'density'
prop_values = 3200.0
[]
[SiC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
temperature = temperature
eigenstrain_name = SiC_thermal_eigenstrain
[]
[SiC_conc]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = d1_function
d1_function_variable = fast_neutron_fluence
q1 = 125.0e+3 # J/mol
d2 = 1.6e-2 # m^2/s
q2 = 514.0e+3 # J/mol
temperature = temperature
[]
### OPyC properties
[OPyC_elasticity_tensor]
type = PyCElasticityTensor
block = OPyC
temperature = temperature
initial_BAF = 1.045
[]
[OPyC_stress]
type = PyCCEGACreep
block = OPyC
temperature = temperature
[]
[OPyC_thermal_conductivity]
type = HeatConductionMaterial
block = OPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[OPyC_density]
type = GenericConstantMaterial
block = OPyC
prop_names = 'density'
prop_values = 1900.0
[]
[OPyC_IIDC_strain]
type = PyCCEGAIrradiationEigenstrain
block = OPyC
eigenstrain_name = OPyC_IIDC_strain
temperature = temperature
[]
[OPyC_thermal_strain]
type = PyCThermalExpansionEigenstrain
block = OPyC
eigenstrain_name = OPyC_thermal_strain
temperature = temperature
[]
[OPyC_conc]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222.0e+3 # J/mol
d2 = 0.0
q2 = 0.0
temperature = temperature
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[disp_x]
type = MaxIncrement
variable = disp_x
max_increment = 1e-6
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'disp_x temperature conc'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-8
nl_abs_tol = 1e-7 #1e-12
nl_max_its = 15
l_tol = 1e-4 #1e-8
l_max_its = 50
start_time = 0.0
end_time = 85.3682e6 #5.0e7
num_steps = 1000
dtmax = 2e6
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 20
growth_factor = 1.5
optimal_iterations = 8 #6
linear_iteration_ratio = 100
time_t = '0 76e6 76.001e6 84.641e6 84.6482e6'
time_dt = '20 20 20 20 20'
[]
[Quadrature]
order = THIRD
[]
[]
[Postprocessors]
[_dt]
type = TimestepSize
execute_on = timestep_end
[]
[cs_release]
type = SideIntegralMassFlux
variable = conc
boundary = exterior
[]
[int_cs_release]
type = TimeIntegratedPostprocessor
value = cs_release
[]
[cs_release_fuel]
type = SideIntegralMassFlux
variable = conc
boundary = fuel_outer_boundary
[]
[int_cs_release_fuel]
type = TimeIntegratedPostprocessor
value = cs_release_fuel
[]
[cs_release_PyCGapBndry]
type = SideIntegralMassFlux
variable = conc
boundary = IPyC_inner_boundary
[]
[int_cs_release_PyCGapBndry]
type = TimeIntegratedPostprocessor
value = cs_release_PyCGapBndry
[]
[ave_gas_temp]
type = ElementAverageValue
block = buffer
variable = temperature
execute_on = 'initial timestep_end'
[]
[ave_gap_temp]
type = SideAverageValue
boundary = buffer_IPyC_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
[fis_gas_produced]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_produced
block = fuel
execute_on = 'initial timestep_end'
[]
[fis_gas_released]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_released
block = fuel
execute_on = 'initial timestep_end'
[]
[gap_volume]
type = InternalVolume
boundary = buffer_IPyC_boundary
execute_on = 'initial linear'
use_displaced_mesh = true
[]
[buffer_void_volume]
type = VoidVolume
block = buffer
theoretical_density = 2250
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[kernel_th_density]
type = UCOTheoreticalDensity
execute_on = initial
[]
[kernel_void_volume]
type = VoidVolume
block = fuel
theoretical_density = kernel_th_density
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
execute_on = 'initial timestep_end'
scale_factor = -1
[]
[volumeFuel]
type = InternalVolume
boundary = fuel_outer_boundary
execute_on = 'initial timestep_end'
scale_factor = -1
[]
[volumeGas]
type = InternalVolume
boundary = buffer_outer_boundary
execute_on = 'initial timestep_end'
scale_factor = -1
addition = 4.67e-11
[]
[volumeBufferShell]
type = InternalVolume
boundary = buffer_outer_boundary
execute_on = 'initial timestep_end'
[]
[ave_temp_interior]
type = SideAverageValue
boundary = buffer_outer_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
[gap_HTC]
type = ElementExtremeValue
variable = gap_HTC
block = buffer
value_type = 'max'
execute_on = 'initial timestep_end'
[]
### Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
outputs = exodus
execute_on = 'initial timestep_end'
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
outputs = exodus
execute_on = 'initial timestep_end'
[]
[avg_surface_temp]
type = SideAverageValue
variable = temperature
boundary = exterior
outputs = exodus
execute_on = 'initial timestep_end'
[]
[time_int_surf_temp]
type = TimeIntegratedPostprocessor
value = avg_surface_temp
outputs = exodus
execute_on = 'initial timestep_end'
[]
##### irradiation conditions
[particle_power]
type = ElementIntegralPower
variable = temperature
use_material_fission_rate = true
fission_rate_material = fission_rate
block = fuel
execute_on = 'initial timestep_end'
[]
[max_fluence]
type = ElementExtremeValue
variable = fast_neutron_fluence
block = 'fuel buffer IPyC SiC OPyC'
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_burnup]
type = ElementExtremeValue
variable = burnup
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
#### II strain
[OPyC_radial_IIDC_strain]
type = ElementExtremeValue
variable = radial_IIDC_strain
block = OPyC
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[OPyC_tangential_IIDC_strain]
type = ElementExtremeValue
variable = tangential_IIDC_strain
block = OPyC
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[IPyC_radial_IIDC_strain]
type = ElementExtremeValue
variable = radial_IIDC_strain
block = IPyC
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[IPyC_tangential_IIDC_strain]
type = ElementExtremeValue
variable = tangential_IIDC_strain
block = IPyC
value_type = 'max'
execute_on = 'initial timestep_end'
[]
#### temperatures
[max_T_kernel]
type = NodalExtremeValue
variable = temperature
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_T_buffer]
type = NodalExtremeValue
variable = temperature
block = buffer
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[min_T_buffer]
type = NodalExtremeValue
variable = temperature
block = buffer
value_type = 'min'
execute_on = 'initial timestep_end'
[]
[max_T_IPyC]
type = NodalExtremeValue
variable = temperature
block = IPyC
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_T_SiC]
type = NodalExtremeValue
variable = temperature
block = SiC
value_type = 'max'
execute_on = 'initial timestep_end'
[]
#### displacement BCs
[max_disp_kernel]
type = NodalExtremeValue
variable = disp_x
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[min_disp_buffer]
type = NodalExtremeValue
variable = disp_x
block = buffer
value_type = 'min'
execute_on = 'initial timestep_end'
[]
[max_disp_IPyC]
type = NodalExtremeValue
variable = disp_x
block = IPyC
value_type = 'max'
execute_on = 'initial timestep_end'
[]
#### hoop stresses
[hoop_opyc_max]
type = ElementExtremeValue
variable = stress_yy
block = OPyC
execute_on = 'initial timestep_end'
[]
[hoop_sic_max]
type = ElementExtremeValue
variable = stress_yy
block = SiC
execute_on = 'initial timestep_end'
[]
[hoop_ipyc_max]
type = ElementExtremeValue
variable = stress_yy
block = IPyC
execute_on = 'initial timestep_end'
[]
[hoop_buffer_max]
type = ElementExtremeValue
variable = stress_yy
block = buffer
execute_on = 'initial timestep_end'
[]
[hoop_opyc_min]
type = ElementExtremeValue
variable = stress_yy
block = OPyC
value_type = min
execute_on = 'initial timestep_end'
[]
[hoop_sic_min]
type = ElementExtremeValue
variable = stress_yy
block = SiC
value_type = min
execute_on = 'initial timestep_end'
[]
[hoop_ipyc_min]
type = ElementExtremeValue
variable = stress_yy
block = IPyC
value_type = min
execute_on = 'initial timestep_end'
[]
[hoop_buffer_min]
type = ElementExtremeValue
variable = stress_yy
block = buffer
value_type = min
execute_on = 'initial timestep_end'
[]
### Check warning for Density
[oPyC_density]
type = ElementExtremeValue
variable = density
block = OPyC
execute_on = 'initial timestep_end'
[]
[sic_density]
type = ElementExtremeValue
variable = density
block = SiC
execute_on = 'initial timestep_end'
[]
[IPyC_density]
type = ElementExtremeValue
variable = density
block = IPyC
execute_on = 'initial timestep_end'
[]
[buffer_density]
type = ElementExtremeValue
variable = density
block = buffer
execute_on = 'initial timestep_end'
[]
[kernel_density]
type = ElementExtremeValue
variable = density
block = fuel
execute_on = 'initial timestep_end'
[]
[pd_penetration]
type = PdPenetration
boundary = SiC_inner_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = true
csv = true
perf_graph = true
[]
(test/tests/triso_failure/ad_triso_1d_weibull_probability.i)
[GlobalParams]
density = 10810.0
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
mesh_density = '6 6 0 6 8 6'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Variables]
[disp_x]
[]
[temperature]
initial_condition = 1346.0
[]
[]
[Functions]
[radial_eigenstrain]
type = ParsedFunction
expression = 't*(4.52013e-4/6.0*t*t*t*t*t - 8.36313e-3/5.0*t*t*t*t + 5.67549e-2/4.0*t*t*t - 1.74247e-1/3.0*t*t + 2.62692e-1/2.0*t - 1.43234e-1)'
[]
[tangential_eigenstrain]
type = ParsedFunction
expression = 't*(1.30457e-4/4.0*t*t*t - 2.10029e-3/3.0*t*t + 9.07826e-3/2.0*t - 3.24737e-2)'
[]
[fission_rate]
type = ParsedFunction
expression = 7.75e19
[]
[k_function]
type = ParsedFunction
expression = '4.93e-29'
[]
[high_fidelity_strength_crackedIPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1000000 1000000'
[]
[high_fidelity_strength_crackedOPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1000000 1000000'
[]
[stress_correlation_crackedOPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[stress_correlation_crackedIPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[]
[AuxVariables]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = fuel
initial_condition = 0.0
[]
[fission_rate]
block = fuel
[]
[]
[Physics/SolidMechanics/QuasiStatic]
strain = small
[fuel_buffer_sic]
block = 'fuel buffer SiC'
eigenstrain_names = thermal_strain
use_automatic_differentiation = true
[]
[ipyc_opyc]
block = 'IPyC OPyC'
incremental = true
eigenstrain_names = 'thermal_strain pyc_eigenstrain'
use_automatic_differentiation = true
[]
[]
[Kernels]
[heat_ie]
type = ADHeatConductionTimeDerivative
variable = temperature
[]
[heat]
type = ADHeatConduction
variable = temperature
[]
[heat_source]
type = ADNeutronHeatSource
variable = temperature
block = fuel
energy_per_fission = 3.2e-11
fission_rate = fission_rate
[]
[]
[AuxKernels]
[stress_yy]
type = ADRankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[fission_rate]
type = FunctionAux
variable = fission_rate
block = fuel
function = fission_rate
[]
[burnup]
type = ADBurnupAux
variable = burnup
block = fuel
fission_rate = fission_rate
molecular_weight = 0.270
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
penalty = 1e5
model = frictionless
formulation = kinematic
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
# coupling to a postprocessor
initial_moles = initial_moles
gas_released = 'fis_gas_released co_production'
released_gas_types = 'Kr Xe;
CO'
released_fractions = '0.153 0.847;
1'
tangential_tolerance = 1e-6
use_automatic_differentiation = true
[]
[]
[BCs]
[no_disp_x]
type = ADDirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[freesurf_temperature]
type = ADDirichletBC
variable = temperature
boundary = exterior
value = 1346.0
[]
[exterior_pressure_x]
type = ADPressure
use_displaced_mesh = false
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure]
# apply gas pressure on buffer and IPyC boundaries
[plenumPressure]
use_displaced_mesh = false
boundary = buffer_IPyC_boundary
initial_pressure = 0
startup_time = 1.0e4
R = 8.3143
# coupling to post processor
output_initial_moles = initial_moles
temperature = ave_temp_interior
volume = volumeGas
material_input = 'fis_gas_released co_production'
output = plenum_pressure
use_automatic_differentiation = true
[]
[]
[]
[Materials]
[flux]
type = ADFastNeutronFlux
calculate_fluence = true
factor = 1.708707e18
[]
[fission_gas_release]
type = ADUO2Sifgrs
block = fuel
temperature = temperature
fission_rate = fission_rate
grain_radius_const = 5.0e-6
[]
[stress]
type = ADComputeLinearElasticStress
block = 'fuel buffer SiC'
[]
[PyC_stress]
type = ADPyCCreep
block = 'IPyC OPyC'
k = k_function
poissons_ratio = 0.4
temperature = temperature
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'buffer IPyC OPyC'
[]
[PyC_eigenstrain]
type = ADPyCIrradiationEigenstrain
block = 'IPyC OPyC'
radial_eigenstrain_function = radial_eigenstrain
tangential_eigenstrain_function = tangential_eigenstrain
eigenstrain_name = pyc_eigenstrain
[]
[fuel_thermal_strain]
type = ADComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[PyC_thermal_strain]
type = ADComputeThermalExpansionEigenstrain
block = 'buffer IPyC OPyC'
thermal_expansion_coeff = 5.5e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[SiC_thermal_strain]
type = ADComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[fuel_thermal]
type = ADUO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temperature
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ADComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[fuel_den]
type = ADStrainAdjustedDensity
block = fuel
strain_free_density = 10810.0
[]
[buffer_elasticity_tensor]
type = ADComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[buffer_thermal]
type = ADHeatConductionMaterial
block = buffer
thermal_conductivity = 0.5
specific_heat = 720.0
[]
[buffer_den]
type = ADStrainAdjustedDensity
strain_free_density = 1000
block = buffer
[]
[PyC_elasticity_tensor]
type = ADComputeIsotropicElasticityTensor
block = 'IPyC OPyC'
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[PyC_thermal]
type = ADHeatConductionMaterial
block = 'IPyC OPyC'
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[PyC_den]
type = ADStrainAdjustedDensity
strain_free_density = 1880.0
block = 'IPyC OPyC'
[]
[SiC_elasticity_tensor]
type = ADComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_thermal]
type = ADHeatConductionMaterial
block = SiC
thermal_conductivity = 13.9
specific_heat = 620.0
[]
[SiC_den]
type = ADStrainAdjustedDensity
strain_free_density = 3200.0
block = SiC
[]
[characteristic_strength]
type = ADGenericConstantMaterial
prop_values = '1000 1000 1000'
prop_names = 'characteristic_strength_SiC characteristic_strength_IPyC characteristic_strength_OPyC'
[]
[]
[Dampers]
[temperature]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 1e-10
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-6
l_max_its = 50
start_time = 0.0
num_steps = 10
dtmax = 2e5
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 20
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[burnup]
type = ElementExtremeValue
block = fuel
variable = burnup
[]
[fis_gas_produced]
type = ADElementIntegralFisGasGeneratedSifgrs
block = fuel
[]
[fis_gas_released]
type = ADElementIntegralFisGasReleasedSifgrs
block = fuel
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
[]
[volumeFuel]
type = InternalVolume
boundary = fuel_outer_boundary
[]
[volumeGas]
type = InternalVolume
boundary = 'fuel_outer_boundary IPyC_inner_boundary'
addition = -5.53e-11
execute_on = 'initial timestep_end'
[]
[volumeBufferShell]
type = InternalVolume
boundary = buffer_IPyC_boundary
[]
[ave_temp_interior]
type = SideAverageValue
boundary = buffer_IPyC_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
# Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
[]
[avg_surface_temperature]
type = SideAverageValue
variable = temperature
boundary = exterior
[]
[time_int_surf_temperature]
type = TimeIntegratedPostprocessor
value = avg_surface_temperature
[]
[co_production]
type = CarbonMonoxideProduction
total_fissions = total_fissions
time_integrated_triso_temperature = time_int_surf_temperature
initial_enrichment = 0.14029
[]
[tang_SiC]
type = ElementalVariableValue
variable = stress_yy
elementid = 18
[]
[Weibull_failure_probability_OPyC]
type = ADWeibullFailureProbability
block = OPyC
weibull_modulus = 6
characteristic_strength = characteristic_strength_OPyC
[]
[Weibull_failure_probability_IPyC]
type = ADWeibullFailureProbability
block = IPyC
weibull_modulus = 6
characteristic_strength = characteristic_strength_IPyC
[]
[Weibull_failure_probability_SiC]
type = ADWeibullFailureProbability
block = SiC
weibull_modulus = 6
characteristic_strength = characteristic_strength_SiC
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
csv = true
perf_graph = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_4d/case_4d_1D.i)
#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# See also Hales, et al., Multidimensional multiphysics simulation of TRISO
# particle fuel, JNM, 443, 2013. https://doi.org/10.1016/j.jnucmat.2013.07.070
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark. The best way to do this is to compare
# results with information in the JNM article.
#
[GlobalParams]
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '3.5e-4 3.9e-4 4.25e-4'
mesh_density = '4 4'
block_names = 'IPyC SiC'
[]
[]
[Variables]
[disp_x]
[]
[]
[Functions]
[radial_eigenstrain]
type = ParsedFunction
expression = 't*(1.36334e-3/4.0*t*t*t - 7.77024e-3/3.0*t*t + 2.00861e-2/2.0*t - 2.22642e-2)'
[]
[tangential_eigenstrain]
type = ParsedFunction
expression = 't*(-3.53804e-4/4.0*t*t*t + 1.69251e-3/3.0*t*t + 2.63307e-3/2.0*t - 1.91253e-2)'
[]
[k_function]
type = ParsedFunction
expression = '2.715e-29'
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1273.0
[]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[stress_zz]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
initial_condition = 0.0
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[IPyC]
block = IPyC
incremental = true
strain = small
eigenstrain_names = ipyc_eigenstrain
[]
[SiC]
block = SiC
strain = small
[]
[]
[AuxKernels]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[stress_zz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_zz
index_i = 2
index_j = 2
execute_on = timestep_end
[]
[]
[BCs]
[exterior_pressure_x]
use_displaced_mesh = false
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[interior_pressure_x]
type = Pressure
use_displaced_mesh = false
variable = disp_x
boundary = IPyC_inner_boundary
factor = 25e6
[]
[]
[Materials]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 3.75e17 # n/m^2-sec
[]
[stress]
type = ComputeLinearElasticStress
block = 'SiC'
[]
[IPyC_stress]
type = PyCCreep
block = IPyC
k = k_function
temperature = temperature
[]
[IPyC_density]
type = StrainAdjustedDensity
strain_free_density = 1900.0
block = IPyC
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
[]
[IPyC_eigenstrain]
type = PyCIrradiationEigenstrain
radial_eigenstrain_function = radial_eigenstrain
tangential_eigenstrain_function = tangential_eigenstrain
eigenstrain_name = ipyc_eigenstrain
[]
[IPyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = IPyC
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[IPyC_temperature]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_temperature]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9
specific_heat = 620.0
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 8e7
dt = 1.0
dtmax = 1e6
dtmin = 1.0e4
[TimeStepper]
type = IterationAdaptiveDT
dt = 1
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[max_yy_IPyC]
type = ElementExtremeValue
variable = stress_yy
block = IPyC
[]
[max_yy_SiC]
type = ElementExtremeValue
variable = stress_yy
block = SiC
[]
[]
[PerformanceMetricOutputs]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = true
csv = true
perf_graph = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_3b/case_3b.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 250e-6 350e-6 390e-6 425e-6 465e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
[]
[Variables]
[conc_Cs]
[]
[]
[ICs]
[conc_Cs]
type = ConstantIC
block = fuel
value = 1
variable = conc_Cs
[]
[]
[AuxVariables]
[temperature]
initial_condition = 2073.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[]
[Materials]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
# 5.5e-14*exp(2/5) = 8.2e-14
d1 = 8.2e-14 # m^2/s
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 1e-20
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 720000
num_steps = 700
dt = 1800
dtmax = 1800
dtmin = 1800
[]
[Postprocessors]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
execute_on = final
[]
[]
(assessment/TRISO/validation/AGR-34/SharedFiles/capsule_driver.i)
kernel_radius = 178.65e-6
buffer_thickness = 109.7e-6
IPyC_thickness = 40.4e-6
SiC_thickness = 33.5e-6
OPyC_thickness = 41.3e-6
buffer_density = 1100
ipyc_density = 1904
opyc_density = 1901
sic_density = 3203
coordinates1 = '${fparse kernel_radius}'
coordinates2 = '${fparse coordinates1+buffer_thickness}'
coordinates3 = '${fparse coordinates2+IPyC_thickness}'
coordinates4 = '${fparse coordinates3+SiC_thickness}'
coordinates5 = '${fparse coordinates4+OPyC_thickness}'
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.19717 # [wt-]
energy_per_fission = 3.204e-11 # [J/fission]
O_U = 1.430 # Initial Oxygen to Uranium atom ratio
C_U = 0.361 # Initial Carbon to Uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[mesh]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
mesh_density = '18 14 12 16 16'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = OPyC_outer_boundary
outer_SiC = SiC_outer_boundary
outer_IPyC = IPyC_outer_boundary
inner_IPyC = IPyC_inner_boundary
outer_buffer = buffer_outer_boundary
outer_kernel = fuel_outer_boundary
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temperature]
initial_condition = 1200
[]
[conc_Ag]
initial_condition = 0.0
scaling = 1e12 #1e18
[]
[conc_Cs]
initial_condition = 0.0
scaling = 1e12 #1e18
[]
[conc_Sr]
initial_condition = 0.0
scaling = 1e12 #1e18
[]
[]
[AuxVariables]
[fission_rate]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_flux]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
order = CONSTANT
family = MONOMIAL
[]
[fis_gas_produced]
order = CONSTANT
family = MONOMIAL
[]
[fis_gas_released]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Sr_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temp_bc]
type = PiecewiseLinear
x_index_in_file = 0
y_index_in_file = 1
xy_in_file_only = false
format = columns
data_file='AGR-34_capsule_daily_data/Cap1Temps.csv'
[]
[power_history]
type = PiecewiseLinear
x = '0 76e6'
y = '1 1'
[]
[fission_rate]
type = LinearCombinationFunction
functions = power_history
w = 4.8156e+19
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
extra_vector_tags = 'ref'
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
extra_vector_tags = 'ref'
[]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
extra_vector_tags = 'ref'
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
extra_vector_tags = 'ref'
[]
[mass_Sr_dt]
type = TimeDerivative
variable = conc_Sr
extra_vector_tags = 'ref'
[]
[mass_Sr]
type = ArrheniusDiffusion
variable = conc_Sr
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
extra_vector_tags = 'ref'
[]
[mass_source_Sr]
type = SpeciesSourceRate
variable = conc_Sr
property_name = Sr_generation
block = fuel
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[fissionrate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = fuel
execute_on = timestep_begin
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = fuel
execute_on = timestep_begin
[]
[fast_neutron_flux]
type = MaterialRealAux
variable = fast_neutron_flux
property = fast_neutron_flux
execute_on = timestep_begin
[]
[fast_neutron_fluence]
type = MaterialRealAux
variable = fast_neutron_fluence
property = fast_neutron_fluence
execute_on = timestep_begin
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Sr_diff_coef]
type = MaterialRealAux
variable = Sr_diff_coef
property = arrhenius_diffusion_coef_Sr
execute_on = timestep_end
[]
[]
[BCs]
[freesurf_temp]
type = FunctionDirichletBC
variable = temperature
function = temp_bc
boundary = exterior
extra_vector_tags = 'ref'
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Sr]
type = DirichletBC
variable = conc_Sr
boundary = exterior
value = 0.0
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
flux_function = power_history
factor = 0.5519e+18
[]
[UCO_burnup]
type = TRISOBurnup
initial_density = ${initial_fuel_density}
[]
[UCO_thermal]
type = UCOThermal
block = fuel
temperature = temperature
[]
[UCO_density]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 11098.0
[]
[fission_gas_release]
type = UCOFGR
block = fuel
average_grain_radius = 10e-6
temperature = temperature
triso_geometry = particle_geometry
[]
# Arrhenius diffusion coefficients for kernel, PyC, and SiC
# come from IAEA TECDOC-978, French parameters.
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Sr]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 2.2e-3 # m^2/s
q1 = 488e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
property_name = Ag_generation
kind = Ag
block = fuel
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
property_name = Cs_generation
kind = Cs
block = fuel
[]
[mass_source_Sr_property]
type = SpeciesSourceMaterial
property_name = Sr_generation
kind = Sr
block = fuel
[]
### Buffer Properties
[buffer_thermal]
type = BufferThermal
block = buffer
initial_density = ${buffer_density}
[]
[Buffer_density]
type = StrainAdjustedDensity
block = buffer
strain_free_density = ${buffer_density}
[]
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0.0
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0.0
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[buffer_conc_Sr]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0.0
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
### IPyC properties
[IPyC_thermal]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_density]
type = StrainAdjustedDensity
block = IPyC
strain_free_density = ${ipyc_density}
[]
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
### SiC properties
[SiC_thermal]
type = MonolithicSiCThermal
block = SiC
temperature = temperature
thermal_conductivity_model = miller
[]
[SiC_density]
type = StrainAdjustedDensity
block = SiC
strain_free_density = ${sic_density}
[]
[SiC_conc_Ag]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
q1 = 125e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Sr]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 1.2e-9 # m^2/s
q1 = 205e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
### OPyC properties
[OPyC_thermal_conductivity]
type = HeatConductionMaterial
block = OPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[OPyC_density]
type = StrainAdjustedDensity
block = OPyC
strain_free_density = ${opyc_density}
[]
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'temperature conc_Ag conc_Cs conc_Sr'
[]
[Executioner]
type = Transient
solve_type = 'NEWTON'
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu'
line_search = 'none'
nl_rel_tol = 1e-8
nl_abs_tol = 1e-8
nl_max_its = 20
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
dt = 86400
end_time = 31890240
[]
[Postprocessors]
[release_heat_inc]
type = SideIntegralMassFlux
variable = temperature
boundary = exterior
arrhenius_prpty_name = thermal_conductivity
execute_on = 'initial timestep_end'
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor # computes time integration of value
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
[]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
[]
[release_Sr_inc]
type = SideIntegralMassFlux
variable = conc_Sr
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
execute_on = 'initial timestep_end'
[]
[released_Sr]
type = TimeIntegratedPostprocessor
value = release_Sr_inc
execute_on = 'initial timestep_end'
[]
[total_Sr]
type = ElementIntegralMaterialProperty
mat_prop = Sr_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Sr_released]
type = FractionalRelease
released = released_Sr
total = total_Sr
[]
[retained_Sr]
type = ElementIntegralVariablePostprocessor
variable = conc_Sr
[]
[fis_gas_produced]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_produced
block = fuel
execute_on = 'initial timestep_end'
[]
[fis_gas_released]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_released
block = fuel
execute_on = 'initial timestep_end'
[]
### Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
execute_on = 'initial timestep_end'
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
execute_on = 'initial timestep_end'
[]
##### irradiation conditions
[particle_power]
type = ElementIntegralPower
variable = temperature
use_material_fission_rate = true
fission_rate_material = fission_rate
block = fuel
execute_on = 'initial timestep_end'
[]
[max_fluence]
type = ElementExtremeValue
variable = fast_neutron_fluence
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_burnup]
type = ElementExtremeValue
variable = burnup
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
print_linear_converged_reason = false
print_nonlinear_converged_reason = false
exodus = false
csv = true
[]
(test/tests/SiCPdPenetration/palladium_penetration.i)
# This test verifies the implementation of the palladium peneteration model
# for SiC in TRISO fuel particles. The geometry is a 2D spherical shell of
# inner and outer diameters of 215 and 250 micrometers, respectively. The
# temperature is ramped linearly from 673.15 to 1673.15 K over 5.0e6 seconds
# using 5.0e5 second timesteps.
#
# The rate of palladium penetration (microns/day) is calculated by:
#
# P_{Pd}_dot = 38.232 * exp(-11342.3 / T) / 86400.0
#
# where T is the temperature. An incremental form is used to compute the total
# penetration thickness of the palladium. Therefore, the average temperature
# over the timestep is used for T. The current penetration thickness is given by:
#
# P_{Pd} = P_{Pd}_old + P_{Pd}_dot * dt
#
# The palladium penetration for the 10 timesteps compared to the analytical
# calculation is provided below:
#
# Current BISON Pd Analytical Pd
# Temperature (K) Penetration (m) Penetration (m)
# 673.15 0 0
# 773.15 3.4132E-11 3.4132E-11
# 873.15 2.6358E-10 2.6358E-10
# 973.15 1.2843E-09 1.2843E-09
# 1073.15 4.6762E-09 4.6762E-09
# 1173.15 1.3777E-08 1.3777E-08
# 1273.15 3.4558E-08 3.4558E-08
# 1373.15 7.6440E-08 7.6440E-08
# 1473.15 1.5293E-07 1.5293E-07
# 1573.15 2.8201E-07 2.8201E-07
# 1673.15 4.8624E-07 4.8624E-07
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE2
coordinates = '215e-6 250e-6'
mesh_density = '4'
block_names = 'sic'
[]
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = '1'
outer_SiC = '1'
outer_IPyC = '2'
inner_IPyC = '1'
outer_buffer = '1'
outer_kernel = '1'
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temperature]
order = FIRST
family = LAGRANGE
initial_condition = 673.15
[]
[]
[Functions]
[temp_function] # reads and interpolates input data defining amplitude curve for fill gas pressure
type = PiecewiseLinear
x = '0 5.0e6'
y = '673.15 1673.15'
[]
[]
[Kernels]
[heat]
type = HeatConduction
variable = temperature
[]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
[]
[]
[BCs]
[heat_removal]
type = FunctionDirichletBC
variable = temperature
boundary = 2
function = temp_function
[]
[]
[Materials]
[thermal]
type = MonolithicSiCThermal
block = sic
temperature = temperature
thermal_conductivity_model = MILLER
[]
[SiC_density]
type = ParsedMaterial
block = sic
property_name = density
expression = 3200.0
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 51'
line_search = 'none'
l_tol = 1e-5
nl_rel_tol = 1e-10
nl_abs_tol = 1e-12
start_time = 0.0
end_time = 5.0e6
num_steps = 10
dt = 5.0e5
[]
[Postprocessors]
[temperature]
type = ElementExtremeValue
block = sic
value_type = 'max'
variable = temperature
execute_on = 'initial timestep_end'
[]
[pd_penetration]
type = PdPenetration
boundary = 1
variable = temperature
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
csv = true
[]
(test/tests/triso_failure/triso_1d_weibull_probability.i)
[GlobalParams]
density = 10810.0
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
mesh_density = '6 6 0 6 8 6'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Variables]
[disp_x]
[]
[temperature]
initial_condition = 1346.0
[]
[]
[Functions]
[radial_eigenstrain]
type = ParsedFunction
expression = 't*(4.52013e-4/6.0*t*t*t*t*t - 8.36313e-3/5.0*t*t*t*t + 5.67549e-2/4.0*t*t*t - 1.74247e-1/3.0*t*t + 2.62692e-1/2.0*t - 1.43234e-1)'
[]
[tangential_eigenstrain]
type = ParsedFunction
expression = 't*(1.30457e-4/4.0*t*t*t - 2.10029e-3/3.0*t*t + 9.07826e-3/2.0*t - 3.24737e-2)'
[]
[fission_rate]
type = ParsedFunction
expression = 7.75e19
[]
[k_function]
type = ParsedFunction
expression = '4.93e-29'
[]
[high_fidelity_strength_crackedIPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1000000 1000000'
[]
[high_fidelity_strength_crackedOPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1000000 1000000'
[]
[stress_correlation_crackedOPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[stress_correlation_crackedIPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[]
[AuxVariables]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = fuel
initial_condition = 0.0
[]
[fission_rate]
block = fuel
[]
[]
[Physics/SolidMechanics/QuasiStatic]
strain = small
[fuel_buffer_sic]
block = 'fuel buffer SiC'
eigenstrain_names = thermal_strain
[]
[ipyc_opyc]
block = 'IPyC OPyC'
incremental = true
eigenstrain_names = 'thermal_strain pyc_eigenstrain'
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
[]
[heat]
type = HeatConduction
variable = temperature
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
energy_per_fission = 3.2e-11
fission_rate = fission_rate
[]
[]
[AuxKernels]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[fission_rate]
type = FunctionAux
variable = fission_rate
block = fuel
function = fission_rate
[]
[burnup]
type = BurnupAux
variable = burnup
block = fuel
fission_rate = fission_rate
molecular_weight = 0.270
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
penalty = 1e5
model = frictionless
formulation = kinematic
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
# coupling to a postprocessor
initial_moles = initial_moles
gas_released = 'fis_gas_released co_production'
released_gas_types = 'Kr Xe;
CO'
released_fractions = '0.153 0.847;
1'
tangential_tolerance = 1e-6
[]
[]
[BCs]
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[freesurf_temperature]
type = DirichletBC
variable = temperature
boundary = exterior
value = 1346.0
[]
[exterior_pressure_x]
type = Pressure
use_displaced_mesh = false
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure]
# apply gas pressure on buffer and IPyC boundaries
[plenumPressure]
use_displaced_mesh = false
boundary = buffer_IPyC_boundary
initial_pressure = 0
startup_time = 1.0e4
R = 8.3143
# coupling to post processor
output_initial_moles = initial_moles
temperature = ave_temp_interior
volume = volumeGas
material_input = 'fis_gas_released co_production'
output = plenum_pressure
[]
[]
[]
[Materials]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 1.708707e18
[]
[fission_gas_release]
type = UO2Sifgrs
block = fuel
temperature = temperature
fission_rate = fission_rate
grain_radius_const = 5.0e-6
[]
[stress]
type = ComputeLinearElasticStress
block = 'fuel buffer SiC'
[]
[PyC_stress]
type = PyCCreep
block = 'IPyC OPyC'
k = k_function
poissons_ratio = 0.4
temperature = temperature
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'buffer IPyC OPyC'
[]
[PyC_eigenstrain]
type = PyCIrradiationEigenstrain
block = 'IPyC OPyC'
radial_eigenstrain_function = radial_eigenstrain
tangential_eigenstrain_function = tangential_eigenstrain
eigenstrain_name = pyc_eigenstrain
[]
[fuel_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[PyC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = 'buffer IPyC OPyC'
thermal_expansion_coeff = 5.5e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[SiC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[fuel_thermal]
type = UO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temperature
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[fuel_den]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10810.0
[]
[buffer_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[buffer_thermal]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5
specific_heat = 720.0
[]
[buffer_den]
type = StrainAdjustedDensity
strain_free_density = 1000
block = buffer
[]
[PyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = 'IPyC OPyC'
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[PyC_thermal]
type = HeatConductionMaterial
block = 'IPyC OPyC'
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[PyC_den]
type = StrainAdjustedDensity
strain_free_density = 1880.0
block = 'IPyC OPyC'
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_thermal]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9
specific_heat = 620.0
[]
[SiC_den]
type = StrainAdjustedDensity
strain_free_density = 3200.0
block = SiC
[]
[characteristic_strength]
type = GenericConstantMaterial
prop_values = '1000 1000 1000'
prop_names = 'characteristic_strength_SiC characteristic_strength_IPyC characteristic_strength_OPyC'
[]
[]
[Dampers]
[temperature]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 1e-10
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
num_steps = 10
dtmax = 2e5
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 20
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[burnup]
type = ElementExtremeValue
block = fuel
variable = burnup
[]
[fis_gas_produced]
type = ElementIntegralFisGasGeneratedSifgrs
block = fuel
[]
[fis_gas_released]
type = ElementIntegralFisGasReleasedSifgrs
block = fuel
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
[]
[volumeFuel]
type = InternalVolume
boundary = fuel_outer_boundary
[]
[volumeGas]
type = InternalVolume
boundary = 'fuel_outer_boundary IPyC_inner_boundary'
addition = -5.53e-11
execute_on = 'initial timestep_end'
[]
[volumeBufferShell]
type = InternalVolume
boundary = buffer_IPyC_boundary
[]
[ave_temp_interior]
type = SideAverageValue
boundary = buffer_IPyC_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
# Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
[]
[avg_surface_temperature]
type = SideAverageValue
variable = temperature
boundary = exterior
[]
[time_int_surf_temperature]
type = TimeIntegratedPostprocessor
value = avg_surface_temperature
[]
[co_production]
type = CarbonMonoxideProduction
total_fissions = total_fissions
time_integrated_triso_temperature = time_int_surf_temperature
initial_enrichment = 0.14029
[]
[tang_SiC]
type = ElementalVariableValue
variable = stress_yy
elementid = 18
[]
[Weibull_failure_probability_OPyC]
type = WeibullFailureProbability
block = OPyC
weibull_modulus = 6
characteristic_strength = characteristic_strength_OPyC
[]
[Weibull_failure_probability_IPyC]
type = WeibullFailureProbability
block = IPyC
weibull_modulus = 6
characteristic_strength = characteristic_strength_IPyC
[]
[Weibull_failure_probability_SiC]
type = WeibullFailureProbability
block = SiC
weibull_modulus = 6
characteristic_strength = characteristic_strength_SiC
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
csv = true
perf_graph = true
[]
(test/tests/triso_failure/ad_triso_1d_failure.i)
[GlobalParams]
density = 10810.0
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
mesh_density = '6 6 0 6 8 6'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Variables]
[disp_x]
[]
[temperature]
initial_condition = 1346.0
[]
[]
[Functions]
[radial_eigenstrain]
type = ParsedFunction
expression = 't*(4.52013e-4/6.0*t*t*t*t*t - 8.36313e-3/5.0*t*t*t*t + 5.67549e-2/4.0*t*t*t - 1.74247e-1/3.0*t*t + 2.62692e-1/2.0*t - 1.43234e-1)'
[]
[tangential_eigenstrain]
type = ParsedFunction
expression = 't*(1.30457e-4/4.0*t*t*t - 2.10029e-3/3.0*t*t + 9.07826e-3/2.0*t - 3.24737e-2)'
[]
[fission_rate]
type = ParsedFunction
expression = 7.75e19
[]
[k_function]
type = ParsedFunction
expression = '4.93e-29'
[]
[high_fidelity_strength_crackedIPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1000000 1000000'
[]
[high_fidelity_strength_crackedOPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1000000 1000000'
[]
[stress_correlation_crackedOPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[stress_correlation_crackedIPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[]
[AuxVariables]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = fuel
initial_condition = 0.0
[]
[fission_rate]
block = fuel
[]
[]
[Physics/SolidMechanics/QuasiStatic]
strain = small
[fuel_buffer_sic]
block = 'fuel buffer SiC'
eigenstrain_names = thermal_strain
use_automatic_differentiation = true
[]
[ipyc_opyc]
block = 'IPyC OPyC'
incremental = true
eigenstrain_names = 'thermal_strain pyc_eigenstrain'
use_automatic_differentiation = true
[]
[]
[Kernels]
[heat_ie]
type = ADHeatConductionTimeDerivative
variable = temperature
[]
[heat]
type = ADHeatConduction
variable = temperature
[]
[heat_source]
type = ADNeutronHeatSource
variable = temperature
block = fuel
energy_per_fission = 3.2e-11
fission_rate = fission_rate
[]
[]
[AuxKernels]
[stress_yy]
type = ADRankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[fission_rate]
type = FunctionAux
variable = fission_rate
block = fuel
function = fission_rate
[]
[burnup]
type = ADBurnupAux
variable = burnup
block = fuel
fission_rate = fission_rate
molecular_weight = 0.270
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
penalty = 1e5
model = frictionless
formulation = kinematic
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
# coupling to a postprocessor
initial_moles = initial_moles
gas_released = 'fis_gas_released co_production'
released_gas_types = 'Kr Xe;
CO'
released_fractions = '0.153 0.847;
1'
tangential_tolerance = 1e-6
use_automatic_differentiation = true
[]
[]
[BCs]
[no_disp_x]
type = ADDirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[freesurf_temperature]
type = ADDirichletBC
variable = temperature
boundary = exterior
value = 1346.0
[]
[exterior_pressure_x]
type = ADPressure
use_displaced_mesh = false
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure]
# apply gas pressure on buffer and IPyC boundaries
[plenumPressure]
use_displaced_mesh = false
boundary = buffer_IPyC_boundary
initial_pressure = 0
startup_time = 1.0e4
R = 8.3143
# coupling to post processor
output_initial_moles = initial_moles
temperature = ave_temp_interior
volume = volumeGas
material_input = 'fis_gas_released co_production'
output = plenum_pressure
use_automatic_differentiation = true
[]
[]
[]
[Materials]
[radial_stress]
type = ADRankTwoCylindricalComponent
rank_two_tensor = stress
cylindrical_axis_point1 = '0 0 0'
cylindrical_axis_point2 = '0 0 1'
cylindrical_component = RadialStress
property_name = radial_stress
outputs = all
[]
[max_principal_stress]
type = ADRankTwoInvariant
property_name = max_principal_stress
rank_two_tensor = stress
invariant = MaxPrincipal
[]
[flux]
type = ADFastNeutronFlux
calculate_fluence = true
factor = 1.708707e18
[]
[fission_gas_release]
type = ADUO2Sifgrs
block = fuel
temperature = temperature
fission_rate = fission_rate
grain_radius_const = 5.0e-6
[]
[stress]
type = ADComputeLinearElasticStress
block = 'fuel buffer SiC'
[]
[PyC_stress]
type = ADPyCCreep
block = 'IPyC OPyC'
k = k_function
poissons_ratio = 0.4
temperature = temperature
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'IPyC OPyC'
[]
[PyC_eigenstrain]
type = ADPyCIrradiationEigenstrain
block = 'IPyC OPyC'
radial_eigenstrain_function = radial_eigenstrain
tangential_eigenstrain_function = tangential_eigenstrain
eigenstrain_name = pyc_eigenstrain
[]
[fuel_thermal_strain]
type = ADComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[PyC_thermal_strain]
type = ADComputeThermalExpansionEigenstrain
block = 'buffer IPyC OPyC'
thermal_expansion_coeff = 5.5e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[SiC_thermal_strain]
type = ADComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[fuel_thermal]
type = ADUO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temperature
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ADComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[fuel_den]
type = ADStrainAdjustedDensity
block = fuel
strain_free_density = 10810.0
[]
[buffer_elasticity_tensor]
type = ADComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[buffer_thermal]
type = ADHeatConductionMaterial
block = buffer
thermal_conductivity = 0.5
specific_heat = 720.0
[]
[buffer_den]
type = ADStrainAdjustedDensity
strain_free_density = 1000
block = buffer
[]
[PyC_elasticity_tensor]
type = ADComputeIsotropicElasticityTensor
block = 'IPyC OPyC'
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[PyC_thermal]
type = ADHeatConductionMaterial
block = 'IPyC OPyC'
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[PyC_den]
type = ADStrainAdjustedDensity
strain_free_density = 1880.0
block = 'IPyC OPyC'
[]
[SiC_elasticity_tensor]
type = ADComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_thermal]
type = ADHeatConductionMaterial
block = SiC
thermal_conductivity = 13.9
specific_heat = 620.0
[]
[SiC_den]
type = ADStrainAdjustedDensity
strain_free_density = 3200.0
block = SiC
[]
[characteristic_strength_SiC]
type = ADGenericConstantMaterial
prop_values = '9640000'
prop_names = 'characteristic_strength'
block = SiC
[]
[characteristic_strength_PyC]
type = ADGenericConstantMaterial
prop_values = '964000'
prop_names = 'characteristic_strength'
block = 'IPyC OPyC'
[]
[]
[Dampers]
[temperature]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 1e-10
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
num_steps = 10
dtmax = 2e5
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 20
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[dt]
type = TimestepSize
[]
[burnup]
type = ElementExtremeValue
block = fuel
variable = burnup
[]
[fis_gas_produced]
type = ADElementIntegralFisGasGeneratedSifgrs
block = fuel
[]
[fis_gas_released]
type = ADElementIntegralFisGasReleasedSifgrs
block = fuel
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
[]
[volumeFuel]
type = InternalVolume
boundary = fuel_outer_boundary
[]
[volumeGas]
type = InternalVolume
boundary = 'fuel_outer_boundary IPyC_inner_boundary'
addition = -5.53e-11
execute_on = 'initial timestep_end'
[]
[volumeBufferShell]
type = InternalVolume
boundary = buffer_IPyC_boundary
[]
[ave_temp_interior]
type = SideAverageValue
boundary = buffer_IPyC_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
# Postprocessors for CO production
[total_fission_rate]
type = ADElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
[]
[avg_surface_temperature]
type = SideAverageValue
variable = temperature
boundary = exterior
[]
[time_int_surf_temperature]
type = TimeIntegratedPostprocessor
value = avg_surface_temperature
[]
[co_production]
type = CarbonMonoxideProduction
total_fissions = total_fissions
time_integrated_triso_temperature = time_int_surf_temperature
initial_enrichment = 0.14029
[]
[tang_SiC]
type = ElementalVariableValue
variable = stress_yy
elementid = 18
[]
[strength_SiC]
type = ADWeibullEffectiveMeanStrength
block = SiC
weibull_modulus = 6
[]
[failure_indicator_SiC]
type = ADWeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_SiC
[]
[strength_IPyC]
type = ADWeibullEffectiveMeanStrength
block = IPyC
weibull_modulus = 6
[]
[failure_indicator_IPyC]
type = ADWeibullFailureOutputUsingCorrelation
block = IPyC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_IPyC
[]
[failure_indicator_debonding]
type = ADTRISODebondingFailureIndicator
boundary = IPyC_outer_boundary
bond_strength = 1e5
stress_name = radial_stress
[]
[strength_OPyC]
type = ADWeibullEffectiveMeanStrength
block = OPyC
weibull_modulus = 6
[]
[failure_indicator_OPyC]
type = ADWeibullFailureOutputUsingCorrelation
block = OPyC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_OPyC
[]
[failure_indicator_SiC_crackedIPyC]
type = ADWeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = max_principal_stress
high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
stress_correlation_function = 'stress_correlation_crackedIPyC'
[]
[failure_indicator_SiC_crackedOPyC]
type = ADWeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = max_principal_stress
high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
stress_correlation_function = 'stress_correlation_crackedOPyC'
[]
[triso_failure]
type = TRISOFailureEvaluation
IPyC_failure = failure_indicator_IPyC
OPyC_failure = failure_indicator_OPyC
SiC_failure = failure_indicator_SiC
SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
SiC_failure_crackedOPyC = failure_indicator_SiC_crackedOPyC
SiC_failure_debonding = failure_indicator_debonding
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
csv = true
perf_graph = true
[]
(test/tests/triso/mesh/mesh_with_gap_1D.i)
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE2
coordinates = '0 .1 .2 .3'
mesh_density = '1 0 2'
block_names = 'fred wilma'
[]
[]
[Variables]
[var_a]
[]
[var_b]
[]
[]
[Kernels]
[Diffusion_a]
type = Diffusion
variable = var_a
[]
[Diffusion_b]
type = Diffusion
variable = var_b
[]
[]
[BCs]
[var_a_1]
type = DirichletBC
variable = var_a
boundary = xzero
value = 0.0
[]
[var_a_2]
type = DirichletBC
variable = var_a
boundary = fred_outer_boundary
value = 1.5
[]
[var_a_3]
type = DirichletBC
variable = var_a
boundary = wilma_inner_boundary
value = 1.5
[]
[var_a_4]
type = DirichletBC
variable = var_a
boundary = exterior
value = 3.0
[]
[var_b_1]
type = DirichletBC
variable = var_b
boundary = fred_inner_boundary
value = 0.0
[]
[var_b_2]
type = DirichletBC
variable = var_b
boundary = fred_wilma_boundary
value = 1.5
[]
[var_b_3]
type = DirichletBC
variable = var_b
boundary = wilma_outer_boundary
value = 3.0
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 51'
start_time = 0.0
end_time = 1.0
dt = 1.0
[]
[Outputs]
# Define output file(s)
time_step_interval = 1
exodus = true
[console]
type = Console
max_rows = 25
[]
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_9/case_9.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.106
constant_expressions = 57294000.0
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 254e-6 356e-6 395e-6 431e-6 469e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
bias = '1 1.25 1.25 1.25 1.25'
dual_bias = '0.8 0.8 0.8 0.8 1'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[conc_Ag]
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1391.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temperature]
type = PiecewiseLinear
data_file = temperature_history.dat
format = columns
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = temperature
variable = temperature
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[]
[Materials]
[burnup]
type = GenericFunctionMaterial
block = fuel
prop_names = 'burnup'
prop_values = 'if(t<54777600,0.109/54777600*t,0.109)'
[]
[fission_rate]
type = GenericFunctionMaterial
block = fuel
prop_names = 'fission_rate'
# 4.76e19 = 0.109/54777600*10720/.27*6.0221409e23
prop_values = 'if(t<54777600,4.76e19,0)'
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Cs_generation
kind = Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs_intact]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = 'if(t<31017600,exp(4.8e25/54777600*t/5e25),exp(4.8e25/5e25))'
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs_intact
[]
[time]
type = TimeStepMaterial
[]
[SiC_conc_Cs]
type = ParsedMaterial
block = SiC
property_name = arrhenius_diffusion_coef_Cs
coupled_variables = 'temperature'
material_property_names = 'time arrhenius_diffusion_coef_Cs_intact'
constant_names = 'failure_time'
expression = 'if(time<=failure_time, arrhenius_diffusion_coef_Cs_intact, 1e-6)'
[]
[SiC_conc_Cs_dT]
type = ParsedMaterial
block = SiC
property_name = arrhenius_diffusion_coef_Cs_dT
coupled_variables = 'temperature'
material_property_names = 'time arrhenius_diffusion_coef_Cs_intact_dT'
constant_names = 'failure_time'
expression = 'if(time<=failure_time, arrhenius_diffusion_coef_Cs_intact_dT, 0)'
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Ag_generation
kind = Ag
[]
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[SiC_conc_Ag_intact]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag_intact
[]
[SiC_conc_Ag]
type = ParsedMaterial
block = SiC
property_name = arrhenius_diffusion_coef_Ag
material_property_names = 'time arrhenius_diffusion_coef_Ag_intact'
constant_names = 'failure_time'
expression = 'if(time<=failure_time, arrhenius_diffusion_coef_Ag_intact, 1e-6)'
[]
[SiC_conc_Ag_dT]
type = ParsedMaterial
block = SiC
property_name = arrhenius_diffusion_coef_Ag_dT
material_property_names = 'time arrhenius_diffusion_coef_Ag_intact_dT'
constant_names = 'failure_time'
expression = 'if(time<=failure_time, arrhenius_diffusion_coef_Ag_intact_dT, 0)'
[]
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs conc_Ag'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 1e-20
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 57294000
num_steps = 2600
dt = 86400
dtmax = 86400
#dtmin = 86400
[TimeStepper]
type = FunctionDT
function = 'if(t<54777600,86400,
if(t<56214000,900,
3600))'
[]
[]
[Postprocessors]
[_temp]
type = NodalExtremeValue
variable = temperature
[]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released_overall]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
start_time = 54777600
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial timestep_end'
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released_overall]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
start_time = 54777600
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
[]
[out_final]
type = CSV
execute_on = final
[]
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_6b/case_6b.i)
#
# Particle failure at 49, 115, and 200h after 1600 C (30430800 s).
# So, particle failure at 30607200, 30844800, and 31150800 s.
# A failure-free analysis is also needed (four in all).
# The compact has 1631 particles.
#
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.0982
constant_expressions = 31525200.0
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 248.5e-6 342.5e-6 383.5e-6 419.5e-6 459.5e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
bias = '1 1.25 1.25 1.25 1.25'
dual_bias = '0.8 0.8 0.8 0.8 1'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[conc_Ag]
[]
[conc_Sr]
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1348.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Sr_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temperature]
type = PiecewiseLinear
data_file = temperature_history.dat
format = columns
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
[]
[mass_Sr_dt]
type = TimeDerivative
variable = conc_Sr
[]
[mass_Sr]
type = ArrheniusDiffusion
variable = conc_Sr
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Sr]
type = SpeciesSourceRate
variable = conc_Sr
property_name = Sr_generation
block = fuel
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[Sr_diff_coef]
type = MaterialRealAux
variable = Sr_diff_coef
property = arrhenius_diffusion_coef_Sr
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = temperature
variable = temperature
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[freesurf_conc_Sr]
type = DirichletBC
variable = conc_Sr
boundary = exterior
value = 0.0
[]
[]
[Materials]
[burnup]
type = GenericFunctionMaterial
block = fuel
prop_names = 'burnup'
prop_values = 'if(t<30326400,0.139/30326400*t,0.139)'
[]
[fission_rate]
type = GenericFunctionMaterial
block = fuel
prop_names = 'fission_rate'
# 1.105e20 = 0.139/30326400*10810/.27*6.0221409e23
prop_values = 'if(t<30326400,1.105e20,0)'
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Cs_generation
kind = Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs_intact]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = 'if(t<30326400,exp(7.5e25/30326400*t/5e25),exp(7.5e25/5e25))'
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs_intact
[]
[time]
type = TimeStepMaterial
[]
[SiC_conc_Cs]
type = ParsedMaterial
block = SiC
property_name = arrhenius_diffusion_coef_Cs
coupled_variables = 'temperature'
material_property_names = 'time arrhenius_diffusion_coef_Cs_intact'
constant_names = 'failure_time'
expression = 'if(time<=failure_time, arrhenius_diffusion_coef_Cs_intact, 1e-6)'
[]
[SiC_conc_Cs_dT]
type = ParsedMaterial
block = SiC
property_name = arrhenius_diffusion_coef_Cs_dT
coupled_variables = 'temperature'
material_property_names = 'time arrhenius_diffusion_coef_Cs_intact_dT'
constant_names = 'failure_time'
expression = 'if(time<=failure_time, arrhenius_diffusion_coef_Cs_intact_dT, 0)'
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Ag_generation
kind = Ag
[]
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[SiC_conc_Ag_intact]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag_intact
[]
[SiC_conc_Ag]
type = ParsedMaterial
block = SiC
property_name = arrhenius_diffusion_coef_Ag
material_property_names = 'time arrhenius_diffusion_coef_Ag_intact'
constant_names = 'failure_time'
expression = 'if(time<=failure_time, arrhenius_diffusion_coef_Ag_intact, 1e-6)'
[]
[SiC_conc_Ag_dT]
type = ParsedMaterial
block = SiC
property_name = arrhenius_diffusion_coef_Ag_dT
material_property_names = 'time arrhenius_diffusion_coef_Ag_intact_dT'
constant_names = 'failure_time'
expression = 'if(time<=failure_time, arrhenius_diffusion_coef_Ag_intact_dT, 0)'
[]
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[fuel_conc_Sr]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 2.2e-3 # m^2/s
q1 = 488e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[mass_source_Sr_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Sr_generation
kind = Sr
[]
[buffer_conc_Sr]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[IPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[SiC_conc_Sr_intact]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 1.2e-9 # m^2/s
q1 = 205e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr_intact
[]
[SiC_conc_Sr]
type = ParsedMaterial
block = SiC
property_name = arrhenius_diffusion_coef_Sr
material_property_names = 'time arrhenius_diffusion_coef_Sr_intact'
constant_names = 'failure_time'
expression = 'if(time<=failure_time, arrhenius_diffusion_coef_Sr_intact, 1e-6)'
[]
[SiC_conc_Sr_dT]
type = ParsedMaterial
block = SiC
property_name = arrhenius_diffusion_coef_Sr_dT
material_property_names = 'time arrhenius_diffusion_coef_Sr_intact_dT'
constant_names = 'failure_time'
expression = 'if(time<=failure_time, arrhenius_diffusion_coef_Sr_intact_dT, 0)'
[]
[OPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs conc_Ag'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 3e-19
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 31525200
num_steps = 1450
dt = 86400
dtmax = 86400
#dtmin = 86400
[TimeStepper]
type = FunctionDT
function = 'if(t<30326400,86400,
if(t<30430800,1800,
3600))'
[]
[]
[Postprocessors]
[_temp]
type = NodalExtremeValue
variable = temperature
[]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released_overall]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
start_time = 30326400
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial timestep_end'
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released_overall]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
start_time = 30326400
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
execute_on = 'initial timestep_end'
[]
[release_Sr_inc]
type = SideIntegralMassFlux
variable = conc_Sr
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
execute_on = 'initial timestep_end'
[]
[released_Sr]
type = TimeIntegratedPostprocessor
value = release_Sr_inc
execute_on = 'initial timestep_end'
[]
[total_Sr]
type = ElementIntegralMaterialProperty
mat_prop = Sr_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Sr_released_overall]
type = FractionalRelease
released = released_Sr
total = total_Sr
execute_on = 'initial timestep_end'
[]
[x_Sr_released]
type = FractionalRelease
released = released_Sr
total = total_Sr
execute_on = 'initial timestep_end'
start_time = 30326400
[]
[retained_Sr]
type = ElementIntegralVariablePostprocessor
variable = conc_Sr
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
[]
[out_final]
type = CSV
execute_on = final
[]
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_3/case_3_1D.i)
#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# See also Hales, et al., Multidimensional multiphysics simulation of TRISO
# particle fuel, JNM, 443, 2013. https://doi.org/10.1016/j.jnucmat.2013.07.070
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark. The best way to do this is to compare
# results with information in the JNM article.
#
[GlobalParams]
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
use_displaced_mesh = false
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.5e-4 2.5e-4 3.5e-4 3.9e-4 4.25e-4'
mesh_density = '1 0 1 128 128'
block_names = 'fuel buffer IPyC SiC'
[]
[]
[Variables]
[disp_x]
[]
[temp]
initial_condition = 1273.0
[]
[]
[AuxVariables]
[stress_xx]
order = CONSTANT
family = MONOMIAL
[]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[stress_zz]
order = CONSTANT
family = MONOMIAL
[]
[stress_xy]
order = CONSTANT
family = MONOMIAL
[]
[stress_yz]
order = CONSTANT
family = MONOMIAL
[]
[stress_xz]
order = CONSTANT
family = MONOMIAL
[]
[hydrostatic_stress]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
initial_condition = 0.0
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[all]
strain = small
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temp
[]
[heat]
type = HeatConduction
variable = temp
[]
[]
[AuxKernels]
[stress_xx]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xx
index_i = 0
index_j = 0
execute_on = timestep_end
[]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[stress_zz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_zz
index_i = 2
index_j = 2
execute_on = timestep_end
[]
[stress_xy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xy
index_i = 0
index_j = 1
execute_on = timestep_end
[]
[stress_yz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yz
index_i = 1
index_j = 2
execute_on = timestep_end
[]
[stress_xz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xz
index_i = 0
index_j = 2
execute_on = timestep_end
[]
[hydrostatic_stress]
type = RankTwoScalarAux
rank_two_tensor = stress
variable = hydrostatic_stress
scalar_type = hydrostatic
execute_on = timestep_end
[]
[]
[BCs]
# pin particle along symmetry planes
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
# fix temperature on free surface
[freesurf_temp]
type = DirichletBC
variable = temp
boundary = exterior
value = 1273.0
[]
# exterior and internal pressures
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[interior_pressure_x]
type = Pressure
variable = disp_x
boundary = IPyC_inner_boundary
factor = 25e6
[]
[]
[Materials]
[stress]
type = ComputeLinearElasticStress
block = 'fuel buffer IPyC SiC'
[]
[fuel_thermal] # temperature and burnup dependent thermal properties of UO2 (BISON kernel)
type = UO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temp
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 1
poissons_ratio = 0.345
[]
[fuel_den]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10800.0
[]
[buffer_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 1
poissons_ratio = 0.345
[]
[buffer_temp]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[buffer_den]
type = StrainAdjustedDensity
strain_free_density = 950 #kg/m^3
block = buffer
[]
[IPyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = IPyC
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[IPyC_temp]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[IPyC_den]
type = StrainAdjustedDensity
strain_free_density = 1900.0 # kg/m^3
block = IPyC
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_temp]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9 # J/m-s-K
specific_heat = 620.0 # J/kg-K
[]
[SiC_den]
type = StrainAdjustedDensity
strain_free_density = 3180.0 # kg/m^3
block = SiC
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temp
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 1.0
dt = 1.0
[]
[Postprocessors]
[max_xx_IPyC]
type = ElementExtremeValue
variable = stress_xx
block = IPyC
[]
[max_yy_IPyC]
type = ElementExtremeValue
variable = stress_yy
block = IPyC
[]
[max_zz_IPyC]
type = ElementExtremeValue
variable = stress_zz
block = IPyC
[]
[max_xx_SiC]
type = ElementExtremeValue
variable = stress_xx
block = SiC
[]
[max_yy_SiC]
type = ElementExtremeValue
variable = stress_yy
block = SiC
[]
[max_zz_SiC]
type = ElementExtremeValue
variable = stress_zz
block = SiC
[]
[]
[PerformanceMetricOutputs]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = true
csv = true
perf_graph = true
[]
(test/tests/triso_failure/triso_1d_kernel_migration.i)
kernel_radius = 213.35e-6
buffer_thickness = 98.9e-6
IPyC_thickness = 40.4e-6
SiC_thickness = 35.2e-6
OPyC_thickness = 43.4e-6
coordinates1 = '${fparse kernel_radius}'
coordinates2 = '${fparse coordinates1+buffer_thickness}'
coordinates3 = '${fparse coordinates2+IPyC_thickness}'
coordinates4 = '${fparse coordinates3+SiC_thickness}'
coordinates5 = '${fparse coordinates4+OPyC_thickness}'
[GlobalParams]
order = FIRST
family = LAGRANGE
displacements = 'disp_x'
initial_enrichment = 0.14029 # [wt-]
flux_conversion_factor = 1.0 # convert E>0.10 to E>0.18 MeV
stress_free_temperature = 1573 # used for thermal expansion
energy_per_fission = 3.204e-11 # [J/fission]
O_U = 1.428 # Initial Oxygen to Uranium atom ratio
C_U = 0.392 # Initial Carbon to Uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[mesh]
type = TRISO1DMeshGenerator
elem_type = EDGE2
coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} '
'${coordinates5}'
mesh_density = '20 8 0 4 4 4'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = OPyC_outer_boundary
outer_SiC = SiC_outer_boundary
outer_IPyC = IPyC_outer_boundary
inner_IPyC = IPyC_inner_boundary
outer_buffer = buffer_outer_boundary
outer_kernel = fuel_outer_boundary
include_particle = true
include_pebble = false
execute_on = 'INITIAL TIMESTEP_END'
[]
[]
[Variables]
[temperature]
initial_condition = 1573
[]
[]
[AuxVariables]
[fission_rate]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_flux]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[fission_rate]
type = ConstantFunction
value = 5.75e19
[]
[high_fidelity_strength_crackedIPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1000000 1000000'
[]
[high_fidelity_strength_crackedOPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1000000 1000000'
[]
[stress_correlation_crackedOPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[stress_correlation_crackedIPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '100 100'
[]
[]
[Physics/SolidMechanics/QuasiStatic]
generate_output = 'stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz '
'max_principal_stress'
add_variables = true
strain = FINITE
incremental = true
[fuel]
block = fuel
eigenstrain_names = 'UCO_swelling_eigenstrain UCO_TE_strain'
extra_vector_tags = 'ref'
[]
[buffer]
block = buffer
eigenstrain_names = 'Buffer_IIDC_strain Buffer_TE_strain'
extra_vector_tags = 'ref'
[]
[IPyC]
block = IPyC
eigenstrain_names = 'IPyC_IIDC_strain IPyC_TE_strain'
extra_vector_tags = 'ref'
[]
[SiC]
block = SiC
eigenstrain_names = 'SiC_thermal_eigenstrain'
extra_vector_tags = 'ref'
[]
[OPyC]
block = OPyC
eigenstrain_names = 'OPyC_IIDC_strain OPyC_TE_strain'
extra_vector_tags = 'ref'
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[fissionrate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = fuel
execute_on = timestep_begin
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = fuel
execute_on = timestep_begin
[]
[fast_neutron_flux]
type = MaterialRealAux
variable = fast_neutron_flux
property = fast_neutron_flux
execute_on = timestep_begin
[]
[fast_neutron_fluence]
type = MaterialRealAux
variable = fast_neutron_fluence
property = fast_neutron_fluence
execute_on = timestep_begin
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
initial_moles = initial_moles
gas_released = 'fis_gas_released'
released_gas_types = 'Kr Xe'
released_fractions = '0.185 0.815'
tangential_tolerance = 1e-6
quadrature = false
min_gap = 1e-7
max_gap = 50e-6
gap_geometry_type = sphere
[]
[]
[BCs]
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[freesurf_temp]
type = DirichletBC
variable = temperature
value = 1573
boundary = exterior
[]
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure]
[plenumPressure]
boundary = buffer_IPyC_boundary
startup_time = 1e4
initial_pressure = 0
output_initial_moles = initial_moles
temperature = ave_gas_temp
volume = 'gap_volume buffer_void_volume kernel_void_volume'
material_input = 'fis_gas_released'
output = gas_pressure
[]
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
block = fuel
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 6.2425e+17
[]
[UCO_burnup]
type = TRISOBurnup
initial_density = 10966
block = fuel
[]
[UCO_thermal]
type = UCOThermal
block = fuel
temperature = temperature
[]
[UCO_elasticity_tensor]
type = UCOElasticityTensor
block = fuel
temperature = temperature
[]
[UCO_stress]
type = ComputeFiniteStrainElasticStress
block = fuel
[]
[UCO_VolumetricSwellingEigenstrain]
type = UCOVolumetricSwellingEigenstrain
block = fuel
eigenstrain_name = UCO_swelling_eigenstrain
[]
[fuel_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10.0e-6
temperature = temperature
eigenstrain_name = UCO_TE_strain
[]
[UCO_density]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10966
[]
[fission_gas_release]
type = UCOFGR
block = fuel
average_grain_radius = 10e-6
temperature = temperature
triso_geometry = particle_geometry
cutoff_neutron_flux = 0.0
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'buffer IPyC OPyC'
[]
[BAF_IPyC]
type = BaconAnisotropyFactor
initial_BAF = 1.0465
block = IPyC
[]
[BAF_OPyC]
type = BaconAnisotropyFactor
initial_BAF = 1.0429
block = OPyC
[]
[buffer_elasticity_tensor]
type = BufferElasticityTensor
block = buffer
temperature = temperature
[]
[buffer_stress]
type = BufferCEGACreep
block = buffer
temperature = temperature
[]
[buffer_thermal]
type = BufferThermal
block = buffer
initial_density = 1050.0
[]
[buffer_density]
type = StrainAdjustedDensity
block = buffer
strain_free_density = 1050.0
[]
[buffer_TE]
type = BufferThermalExpansionEigenstrain
block = buffer
eigenstrain_name = Buffer_TE_strain
temperature = temperature
[]
[buffer_IIDC]
type = BufferCEGAIrradiationEigenstrain
block = buffer
eigenstrain_name = Buffer_IIDC_strain
temperature = temperature
[]
[IPyC_elasticity_tensor]
type = PyCElasticityTensor
block = IPyC
temperature = temperature
[]
[IPyC_stress]
type = PyCCEGACreep
block = IPyC
creep_rate_scale_factor = 1
temperature = temperature
[]
[IPyC_thermal]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_density]
type = GenericConstantMaterial
block = IPyC
prop_names = 'density'
prop_values = 1890
[]
[IPyC_IIDC]
type = PyCCEGAIrradiationEigenstrain
block = IPyC
eigenstrain_name = IPyC_IIDC_strain
temperature = temperature
irradiation_eigenstrain_scale_factor = 1
[]
[IPyC_TE]
type = PyCThermalExpansionEigenstrain
block = IPyC
eigenstrain_name = IPyC_TE_strain
temperature = temperature
[]
[SiC_elasticity_tensor]
type = MonolithicSiCElasticityTensor
block = SiC
temperature = temperature
elastic_modulus_model = miller
[]
[SiC_stress]
type = ComputeFiniteStrainElasticStress
block = SiC
[]
[SiC_thermal]
type = MonolithicSiCThermal
block = SiC
temperature = temperature
thermal_conductivity_model = miller
[]
[SiC_density]
type = StrainAdjustedDensity
block = SiC
strain_free_density = 3200.0
[]
[SiC_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
temperature = temperature
eigenstrain_name = SiC_thermal_eigenstrain
[]
[OPyC_elasticity_tensor]
type = PyCElasticityTensor
block = OPyC
temperature = temperature
initial_BAF = 1.0
[]
[OPyC_stress]
type = PyCCEGACreep
block = OPyC
creep_rate_scale_factor = 1
temperature = temperature
[]
[OPyC_thermal_conductivity]
type = HeatConductionMaterial
block = OPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[OPyC_density]
type = GenericConstantMaterial
block = OPyC
prop_names = 'density'
prop_values = 1900
[]
[OPyC_IIDC]
type = PyCCEGAIrradiationEigenstrain
block = OPyC
eigenstrain_name = OPyC_IIDC_strain
temperature = temperature
irradiation_eigenstrain_scale_factor = 1
[]
[OPyC_TE]
type = PyCThermalExpansionEigenstrain
block = OPyC
eigenstrain_name = OPyC_TE_strain
temperature = temperature
[]
[characteristic_strength_SiC]
type = GenericConstantMaterial
prop_values = '9640000'
block = SiC
prop_names = 'characteristic_strength'
[]
[characteristic_strength_PyC]
type = PyCCharacteristicStrength
temperature = temperature
X = 1.02
block = 'IPyC OPyC'
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temperature
max_increment = 100
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-8
nl_max_its = 20
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
num_steps = 10
dtmin = 1e-4
dt = 1e4
[]
[Postprocessors]
[ave_gas_temp]
type = ElementAverageValue
block = buffer
variable = temperature
execute_on = 'initial timestep_end'
[]
[fis_gas_released]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_released
block = fuel
use_displaced_mesh = false
execute_on = 'initial timestep_end'
[]
[gap_volume]
type = InternalVolume
boundary = buffer_IPyC_boundary
execute_on = 'initial linear'
use_displaced_mesh = true
[]
[buffer_void_volume]
type = VoidVolume
block = buffer
theoretical_density = 2250
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[kernel_th_density]
type = UCOTheoreticalDensity
execute_on = initial
[]
[kernel_void_volume]
type = VoidVolume
block = fuel
theoretical_density = kernel_th_density
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[particle_power]
type = ElementIntegralPower
variable = temperature
use_material_fission_rate = true
fission_rate_material = fission_rate
block = fuel
execute_on = 'initial timestep_end'
[]
[max_fluence]
type = ElementExtremeValue
variable = fast_neutron_fluence
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_burnup]
type = ElementExtremeValue
variable = burnup
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[SiC_stress_max]
type = ElementExtremeMaterialProperty
block = SiC
value_type = max
mat_prop = stress_yy
[]
[SiC_stress_min]
type = ElementExtremeMaterialProperty
block = SiC
value_type = min
mat_prop = stress_yy
[]
[strength_SiC]
type = WeibullEffectiveMeanStrength
block = SiC
weibull_modulus = 6
[]
[kernel_migration_distance]
type = KernelMigrationDistance
block = 'fuel buffer IPyC SiC OPyC'
variable = temperature
temperature_gradient = 15000
kernel_type = UO2
[]
[failure_indicator_kernel_migration]
type = KernelMigrationFailureIndicator
kernel_migration_distance = kernel_migration_distance
triso_geometry = particle_geometry
[]
[failure_indicator_SiC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_SiC
[]
[strength_IPyC]
type = WeibullEffectiveMeanStrength
block = IPyC
weibull_modulus = 6
[]
[failure_indicator_IPyC]
type = WeibullFailureOutputUsingCorrelation
block = IPyC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_IPyC
[]
[strength_OPyC]
type = WeibullEffectiveMeanStrength
block = OPyC
weibull_modulus = 6
[]
[failure_indicator_OPyC]
type = WeibullFailureOutputUsingCorrelation
block = OPyC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_OPyC
[]
[pd_penetration]
type = PdPenetration
boundary = SiC_inner_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
[failure_indicator_pd_penetration]
type = PdPenetrationFailureIndicator
triso_geometry = particle_geometry
pd_penetration = pd_penetration
[]
[failure_indicator_SiC_crackedIPyC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = max_principal_stress
high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
stress_correlation_function = 'stress_correlation_crackedIPyC'
[]
[failure_indicator_SiC_crackedOPyC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = max_principal_stress
high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
stress_correlation_function = 'stress_correlation_crackedOPyC'
[]
[triso_failure]
type = TRISOFailureEvaluation
IPyC_failure = failure_indicator_IPyC
OPyC_failure = failure_indicator_OPyC
SiC_failure = failure_indicator_SiC
SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
SiC_failure_crackedOPyC = failure_indicator_SiC_crackedOPyC
SiC_failure_pd_penetration = failure_indicator_pd_penetration
SiC_failure_kernel_migration = failure_indicator_kernel_migration
[]
[]
[Outputs]
show = 'kernel_migration_distance failure_indicator_kernel_migration triso_failure '
print_linear_residuals = false
time_step_interval = 1
csv = true
perf_graph = true
[]
(assessment/TRISO/validation/AGR-34/Compacts/AGR-34_dtf_base.i)
kernel_radius = 178.65e-6
PyC_thickness = 20e-6
coordinates1 = '${fparse kernel_radius}'
coordinates2 = '${fparse coordinates1+PyC_thickness}'
initial_fuel_density = 11100.0
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.19717 # [wt-]
energy_per_fission = 3.204e-11 # [J/fission]
O_U = 1.430 # Initial Oxygen to Uranium atom ratio
C_U = 0.361 # Initial Carbon to Uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 ${coordinates1} ${coordinates2}'
mesh_density = '18 14'
block_names = 'fuel PyC'
bias = '1 1.25'
dual_bias = '0.8 1'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = PyC_outer_boundary
outer_SiC = PyC_outer_boundary
outer_IPyC = PyC_outer_boundary
inner_IPyC = PyC_outer_boundary
outer_buffer = PyC_outer_boundary
outer_kernel = fuel_outer_boundary
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temperature]
initial_condition = 888.5
[]
[]
[AuxVariables]
[fission_rate]
block = fuel
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = fuel
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_flux]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temp_bc]
type = PiecewiseLinear
x_index_in_file = 0
y_index_in_file = 1
xy_in_file_only = false
format = columns
[]
[power_history]
type = PiecewiseLinear
x = '0 76e6'
y = '1 1'
[]
[fission_rate]
type = LinearCombinationFunction
functions = power_history
w = 4.2602e+19
[]
[d1_function]
type = ParsedFunction
expression = 'exp(t/4.5e25)'
[]
[]
[Kernels]
[heat_dt]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[fissionrate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = 'fuel'
execute_on = timestep_begin
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = 'fuel'
execute_on = timestep_begin
[]
[fast_neutron_flux]
type = MaterialRealAux
variable = fast_neutron_flux
property = fast_neutron_flux
block = 'fuel PyC'
execute_on = timestep_begin
[]
[fast_neutron_fluence]
type = MaterialRealAux
variable = fast_neutron_fluence
property = fast_neutron_fluence
block = 'fuel PyC'
execute_on = timestep_begin
[]
[]
[BCs]
# fix temperature on free surface
[freesurf_temp]
type = FunctionDirichletBC
variable = temperature
function = temp_bc
boundary = exterior
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
flux_function = power_history
factor = 4.4440e+17
[]
### UCO fuel properties
[UCO_burnup]
type = TRISOBurnup
initial_density = ${initial_fuel_density}
[]
[UCO_thermal]
type = UCOThermal
block = 'fuel'
temperature = temperature
[]
[UCO_density]
type = ParsedMaterial
block = fuel
property_name = density
expression = ${initial_fuel_density}
[]
### IPyC properties
[PyC_thermal]
type = HeatConductionMaterial
block = PyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[PyC_density]
type = ParsedMaterial
block = PyC
property_name = density
expression = 1904.0
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Debug]
show_var_residual_norms = true
#show_var_residual = 'temperature conc_Ag conc_Cs conc_Sr'
show_var_residual = 'temperature'
[]
[Executioner]
type = Transient
solve_type = 'NEWTON'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 1e-6
nl_max_its = 20
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 3.189024e7
dt = 10000
[]
[Postprocessors]
[_dt]
type = TimestepSize
execute_on = timestep_end
[]
### Temperature
[temp_min]
type = NodalExtremeValue
variable = temperature
value_type = 'min'
execute_on = 'initial timestep_end'
[]
[temp_max]
type = NodalExtremeValue
variable = temperature
value_type = 'max'
execute_on = 'initial timestep_end'
[]
### Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
outputs = exodus
execute_on = 'initial timestep_end'
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
outputs = exodus
execute_on = 'initial timestep_end'
[]
##### irradiation conditions
[particle_power]
type = ElementIntegralPower
variable = temperature
use_material_fission_rate = true
fission_rate_material = fission_rate
block = fuel
execute_on = 'initial timestep_end'
[]
[max_fluence]
type = ElementExtremeValue
variable = fast_neutron_fluence
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_burnup]
type = ElementExtremeValue
variable = burnup
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
[console]
type = Console
time_step_interval = 1
#hide = 'release_Ag_inc release_Cs_inc release_Sr_inc'
[]
[exodus]
type = Exodus
file_base = COMPACT
[]
[release]
type = CSV
file_base = release_COMPACT
sort_columns = true
#show = 'release_Ag_inc released_Ag release_Cs_inc released_Cs release_Sr_inc released_Sr total_Ag total_Cs total_Sr x_Ag_released x_Cs_released x_Sr_released'
[]
[final_release]
type = CSV
file_base = final_release_COMPACT
sort_columns = true
#show = 'retained_Ag retained_Cs retained_Sr released_Ag released_Cs released_Sr total_Ag total_Cs total_Sr x_Ag_released x_Cs_released x_Sr_released'
execute_on = 'final'
[]
[]
(examples/TRISO/pebble/triso_1d_failed.i)
kernel_radius = 213.35e-6
buffer_thickness = 98.9e-6
IPyC_thickness = 40.4e-6
SiC_thickness = 35.2e-6
OPyC_thickness = 43.4e-6
coordinates1 = '${fparse kernel_radius}'
coordinates2 = '${fparse coordinates1+buffer_thickness}'
coordinates3 = '${fparse coordinates2+IPyC_thickness}'
coordinates4 = '${fparse coordinates3+SiC_thickness}'
coordinates5 = '${fparse coordinates4+OPyC_thickness}'
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.14029 # [wt-]
energy_per_fission = 3.204e-11 # [J/fission]
O_U = 1.428 # Initial Oxygen to Uranium atom ratio
C_U = 0.392 # Initial Carbon to Uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[mesh]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
mesh_density = '18 14 12 16 16'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = OPyC_outer_boundary
outer_SiC = SiC_outer_boundary
outer_IPyC = IPyC_outer_boundary
inner_IPyC = IPyC_inner_boundary
outer_buffer = buffer_outer_boundary
outer_kernel = fuel_outer_boundary
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temperature]
initial_condition = 773.15
[]
[conc_Cs]
initial_condition = 0.0
scaling = 1e18
[]
[]
[AuxVariables]
[fission_rate]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_flux]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
order = CONSTANT
family = MONOMIAL
[]
[fis_gas_produced]
order = CONSTANT
family = MONOMIAL
[]
[fis_gas_released]
order = CONSTANT
family = MONOMIAL
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[power_history]
type = PiecewiseLinear
x = '0 1e3 4.51008e7' #change time (s) for desired EFPD
y = '0 1 1'
[]
[fission_rate]
type = LinearCombinationFunction
functions = power_history
w = 2.927e18
[]
[temp_bc_func]
type = ParsedFunction
value = temp_bc
symbol_names = temp_bc
symbol_values = temp_bc
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[fissionrate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = fuel
execute_on = timestep_begin
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = fuel
execute_on = timestep_begin
[]
[fast_neutron_flux]
type = MaterialRealAux
variable = fast_neutron_flux
property = fast_neutron_flux
execute_on = timestep_begin
[]
[fast_neutron_fluence]
type = MaterialRealAux
variable = fast_neutron_fluence
property = fast_neutron_fluence
execute_on = timestep_begin
[]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[]
[BCs]
[freesurf_temp]
type = FunctionDirichletBC
variable = temperature
function = temp_bc_func
boundary = exterior
[]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
flux_function = power_history
factor = 1.109e18
[]
[UCO_burnup]
type = TRISOBurnup
initial_density = ${initial_fuel_density}
[]
[UCO_thermal]
type = UCOThermal
block = fuel
temperature = temperature
[]
[UCO_density]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10966.0
[]
[fission_gas_release]
type = UCOFGR
block = fuel
average_grain_radius = 10e-6
temperature = temperature
triso_geometry = particle_geometry
[]
# Arrhenius diffusion coefficients for kernel, PyC, and SiC
# come from IAEA TECDOC-978, French parameters.
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
property_name = Cs_generation
kind = Cs
block = fuel
[]
### Buffer Properties
[buffer_thermal]
type = BufferThermal
block = buffer
initial_density = 1050.0
[]
[Buffer_density]
type = StrainAdjustedDensity
block = buffer
strain_free_density = 1050.0
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0.0
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
### IPyC properties
[IPyC_thermal]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_density]
type = StrainAdjustedDensity
block = IPyC
strain_free_density = 1907.0
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
### SiC properties
[SiC_thermal]
type = MonolithicSiCThermal
block = SiC
temperature = temperature
thermal_conductivity_model = miller
[]
[SiC_density]
type = StrainAdjustedDensity
block = SiC
strain_free_density = 3200.0
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 1e-6 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
### OPyC properties
[OPyC_thermal_conductivity]
type = HeatConductionMaterial
block = OPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[OPyC_density]
type = StrainAdjustedDensity
block = OPyC
strain_free_density = 1907.0
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu'
line_search = 'none'
nl_rel_tol = 1e-8
nl_abs_tol = 1e-6
nl_max_its = 20
l_tol = 1e-4
l_max_its = 50
end_time = 4.831315e7
dt = 500000
num_steps = 10
[]
[Postprocessors]
[temp_bc]
type = Receiver
[]
[release_heat_inc]
type = SideIntegralMassFlux
variable = temperature
boundary = exterior
arrhenius_prpty_name = thermal_conductivity
execute_on = 'initial timestep_end'
[]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
[]
[fis_gas_produced]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_produced
block = fuel
execute_on = 'initial timestep_end'
[]
[fis_gas_released]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_released
block = fuel
execute_on = 'initial timestep_end'
[]
### Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
execute_on = 'initial timestep_end'
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
execute_on = 'initial timestep_end'
[]
##### irradiation conditions
[particle_power]
type = ElementIntegralPower
variable = temperature
use_material_fission_rate = true
fission_rate_material = fission_rate
block = fuel
execute_on = 'initial timestep_end'
[]
[max_fluence]
type = ElementExtremeValue
variable = fast_neutron_fluence
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_burnup]
type = ElementExtremeValue
variable = burnup
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[aver_temp_exterior]
type = SideAverageValue
variable = temperature
boundary = exterior
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
print_linear_converged_reason = false
print_nonlinear_converged_reason = false
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_10/case_10.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
initial_enrichment = 0.1676
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 250.5e-6 342.5e-6 380.5e-6 413.5e-6 454.5e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
bias = '1 1.25 1.25 1.25 1.25'
dual_bias = '0.8 0.8 0.8 0.8 1'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[conc_Ag]
[]
[conc_Sr]
[]
[temperature]
initial_condition = 1373.15
scaling = 1e-10
[]
[]
[AuxVariables]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Ag_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Sr_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[temperature]
type = PiecewiseLinear
data_file = temperature_history.dat
format = columns
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Cs]
type = SpeciesSourceRate
variable = conc_Cs
property_name = Cs_generation
block = fuel
[]
[mass_Ag_dt]
type = TimeDerivative
variable = conc_Ag
[]
[mass_Ag]
type = ArrheniusDiffusion
variable = conc_Ag
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Ag]
type = SpeciesSourceRate
variable = conc_Ag
property_name = Ag_generation
block = fuel
[]
[mass_Sr_dt]
type = TimeDerivative
variable = conc_Sr
[]
[mass_Sr]
type = ArrheniusDiffusion
variable = conc_Sr
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_source_Sr]
type = SpeciesSourceRate
variable = conc_Sr
property_name = Sr_generation
block = fuel
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = FissionRateHeatSource
variable = temperature
block = fuel
energy_per_fission = 3.2e-11 # units of J/fission
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Ag_diff_coef]
type = MaterialRealAux
variable = Ag_diff_coef
property = arrhenius_diffusion_coef_Ag
execute_on = timestep_end
[]
[Sr_diff_coef]
type = MaterialRealAux
variable = Sr_diff_coef
property = arrhenius_diffusion_coef_Sr
execute_on = timestep_end
[]
[burnup]
type = MaterialRealAux
block = fuel
variable = burnup
property = burnup
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Ag]
type = DirichletBC
variable = conc_Ag
boundary = exterior
value = 0.0
[]
[freesurf_conc_Sr]
type = DirichletBC
variable = conc_Sr
boundary = exterior
value = 0.0
[]
[temperature]
type = FunctionDirichletBC
variable = temperature
function = temperature
boundary = exterior
[]
[]
[Materials]
[burnup]
type = GenericFunctionMaterial
block = fuel
prop_names = 'burnup'
prop_values = 'if(t<21513600,0.093/21513600*t,0.093)'
[]
[fission_rate]
type = GenericFunctionMaterial
block = fuel
prop_names = 'fission_rate'
# 1.05e21 = 0.093/21513600*10850/.27*6.0221409e23
prop_values = 'if(t<=21513600,1.05e21,0)'
[]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[mass_source_Cs_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Cs_generation
kind = Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 5.5e-14 # m^2/s
d1_function = 'if(t<21513600,exp(3.0e25/21513600*t/5e25),exp(3.0e25/5e25))'
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Ag]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 6.7e-9 # m^2/s
q1 = 165e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[mass_source_Ag_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Ag_generation
kind = Ag
[]
[buffer_conc_Ag]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[IPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[SiC_conc_Ag]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 3.6e-9 # m^2/s
q1 = 215e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[OPyC_conc_Ag]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 5.3e-9 # m^2/s
q1 = 154e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
[]
[fuel_conc_Sr]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 2.2e-3 # m^2/s
q1 = 488e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[mass_source_Sr_property]
type = SpeciesSourceMaterial
block = fuel
property_name = Sr_generation
kind = Sr
[]
[buffer_conc_Sr]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[IPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[SiC_conc_Sr]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 1.2e-9 # m^2/s
q1 = 205e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[OPyC_conc_Sr]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 2.3e-6 # m^2/s
q1 = 197e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
[]
[fuel_thermal]
type = UO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temperature
burnup = burnup
[]
[fuel_den]
type = ParsedMaterial
block = fuel
property_name = density
expression = 10850.0
[]
[buffer_temperature]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5
specific_heat = 720.0
[]
[buffer_den]
type = ParsedMaterial
block = buffer
property_name = density
expression = 1000
[]
[PyC_temperature]
type = HeatConductionMaterial
block = 'IPyC OPyC'
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_den]
type = ParsedMaterial
block = IPyC
property_name = density
expression = 1900
[]
[OPyC_den]
type = ParsedMaterial
block = OPyC
property_name = density
expression = 1880
[]
[SiC_temperature]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9
specific_heat = 620.0
[]
[SiC_den]
type = ParsedMaterial
block = SiC
property_name = density
expression = 3200.0
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs conc_Ag'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 5e-19 #5e-21 #1e-22
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 24523200
num_steps = 2500
dt = 86400
dtmax = 86400
#dtmin = 86400
[TimeStepper]
type = FunctionDT
function = 'if(t<21513600,86400,3600)'
[]
[]
[Postprocessors]
[_temp]
type = NodalExtremeValue
variable = temperature
[]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralMaterialProperty
mat_prop = Cs_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Cs_released_overall]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
execute_on = 'initial timestep_end'
start_time = 21513600
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial timestep_end'
[]
[release_Ag_inc]
type = SideIntegralMassFlux
variable = conc_Ag
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
execute_on = 'initial timestep_end'
[]
[released_Ag]
type = TimeIntegratedPostprocessor
value = release_Ag_inc
execute_on = 'initial timestep_end'
[]
[total_Ag]
type = ElementIntegralMaterialProperty
mat_prop = Ag_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Ag_released_overall]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
[]
[x_Ag_released]
type = FractionalRelease
released = released_Ag
total = total_Ag
execute_on = 'initial timestep_end'
start_time = 21513600
[]
[retained_Ag]
type = ElementIntegralVariablePostprocessor
variable = conc_Ag
execute_on = 'initial timestep_end'
[]
[release_Sr_inc]
type = SideIntegralMassFlux
variable = conc_Sr
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
execute_on = 'initial timestep_end'
[]
[released_Sr]
type = TimeIntegratedPostprocessor
value = release_Sr_inc
execute_on = 'initial timestep_end'
[]
[total_Sr]
type = ElementIntegralMaterialProperty
mat_prop = Sr_generation_total
block = fuel
execute_on = 'initial timestep_end'
[]
[x_Sr_released_overall]
type = FractionalRelease
released = released_Sr
total = total_Sr
execute_on = 'initial timestep_end'
[]
[x_Sr_released]
type = FractionalRelease
released = released_Sr
total = total_Sr
execute_on = 'initial timestep_end'
start_time = 21513600
[]
[retained_Sr]
type = ElementIntegralVariablePostprocessor
variable = conc_Sr
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
[]
[out_final]
type = CSV
execute_on = final
[]
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_3e/case_3e.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 250e-6 350e-6 390e-6 425e-6 465e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc_Cs]
[]
[conc_Kr]
[]
[]
[ICs]
[conc_Cs]
type = ConstantIC
block = fuel
value = 1
variable = conc_Cs
[]
[conc_Kr]
type = ConstantIC
block = fuel
value = 1
variable = conc_Kr
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1873.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[Kr_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
extra_vector_tags = 'ref'
[]
[mass_Kr_dt]
type = TimeDerivative
variable = conc_Kr
[]
[mass_Kr]
type = ArrheniusDiffusion
variable = conc_Kr
arrhenius_prpty_name = arrhenius_diffusion_coef_Kr
temperature = temperature
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[Kr_diff_coef]
type = MaterialRealAux
variable = Kr_diff_coef
property = arrhenius_diffusion_coef_Kr
execute_on = timestep_end
[]
[temperature]
type = FunctionAux
function = 'if(t<720000,1873.15,2073.15)'
variable = temperature
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[freesurf_conc_Kr]
type = DirichletBC
variable = conc_Kr
boundary = exterior
value = 0.0
[]
[]
[Materials]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
# 6.2228e6 = 1e-6 / (6.3e-8*exp(-222e3/8.3145/2073.15))
d1_function = 'if(t<720000,1,6.2228e6)'
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 1e-6
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
# 6.2228e6 = 1e-6 / (6.3e-8*exp(-222e3/8.3145/2073.15))
d1_function = 'if(t<720000,1,6.2228e6)'
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[fuel_conc_Kr]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 8.8e-15 # m^2/s
q1 = 54e3 # J/mol
d2 = 6.0e-1
q2 = 480e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Kr
[]
[buffer_conc_Kr]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Kr
[]
[IPyC_conc_Kr]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 2.9e-8 # m^2/s
# 7.40285e8 = 1e-6 / (2.9e-8*exp(-291e3/8.3145/2073.15))
d1_function = 'if(t<720000,1,7.40285e8)'
q1 = 291e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Kr
[]
[SiC_conc_Kr]
type = ArrheniusDiffusionCoef
block = SiC
d1 = 1e-6
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Kr
[]
[OPyC_conc_Kr]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 2.9e-8 # m^2/s
# 7.40285e8 = 1e-6 / (2.9e-8*exp(-291e3/8.3145/2073.15))
d1_function = 'if(t<720000,1,7.40285e8)'
q1 = 291e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Kr
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs conc_Kr'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 1e-22
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 1440000
num_steps = 1000
dt = 3600
dtmax = 3600
#dtmin = 3600
[]
[Postprocessors]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
[]
[release_Kr_inc]
type = SideIntegralMassFlux
variable = conc_Kr
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Kr
execute_on = 'initial timestep_end'
[]
[released_Kr]
type = TimeIntegratedPostprocessor
value = release_Kr_inc
execute_on = 'initial timestep_end'
[]
[total_Kr]
type = ElementIntegralVariablePostprocessor
variable = conc_Kr
execute_on = 'initial'
[]
[x_Kr_released]
type = FractionalRelease
released = released_Kr
total = total_Kr
[]
[retained_Kr]
type = ElementIntegralVariablePostprocessor
variable = conc_Kr
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
execute_on = final
[]
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_5/case_5_1D.i)
#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# See also Hales, et al., Multidimensional multiphysics simulation of TRISO
# particle fuel, JNM, 443, 2013. https://doi.org/10.1016/j.jnucmat.2013.07.070
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark. The best way to do this is to compare
# results with information in the JNM article.
#
[GlobalParams]
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '2.75e-4 3.15e-4 3.5e-4 3.9e-4'
mesh_density = '4 4 4'
block_names = 'IPyC SiC OPyC'
[]
[]
[Variables]
[disp_x]
[]
[]
[Functions]
[radial_eigenstrain]
type = ParsedFunction
expression = 't*(1.36334e-3/4.0*t*t*t - 7.77024e-3/3.0*t*t + 2.00861e-2/2.0*t - 2.22642e-2)'
[]
[tangential_eigenstrain]
type = ParsedFunction
expression = 't*(-3.53804e-4/4.0*t*t*t + 1.69251e-3/3.0*t*t + 2.63307e-3/2.0*t - 1.91253e-2)'
[]
[pressure]
type = ParsedFunction
expression = '15.54e6/8e7*t'
[]
[k_function]
type = ParsedFunction
expression = '2.715e-29'
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1273.0
[]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[stress_zz]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
initial_condition = 0.0
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[IPyC_OPyC]
block = 'IPyC OPyC'
strain = finite
eigenstrain_names = pyc_eigenstrain
[]
[SiC]
block = SiC
strain = finite
[]
[]
[AuxKernels]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[stress_zz]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_zz
index_i = 2
index_j = 2
execute_on = timestep_end
[]
[]
[BCs]
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[interior_pressure_x]
type = Pressure
variable = disp_x
boundary = IPyC_inner_boundary
factor = 1.0
function = pressure
[]
[]
[Materials]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 3.75e17 # n/m^2-sec
[]
[stress]
type = ComputeFiniteStrainElasticStress
block = 'SiC'
[]
[PyC_stress]
type = PyCCreep
block = 'IPyC OPyC'
k = k_function
temperature = temperature
[]
[IPyC_den]
type = StrainAdjustedDensity
strain_free_density = 1900.0
block = 'IPyC OPyC'
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'IPyC OPyC'
[]
[PyC_eigenstrain]
type = PyCIrradiationEigenstrain
block = 'IPyC OPyC'
radial_eigenstrain_function = radial_eigenstrain
tangential_eigenstrain_function = tangential_eigenstrain
eigenstrain_name = pyc_eigenstrain
[]
[PyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = 'IPyC OPyC'
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 8e7
dt = 1.0
dtmax = 1e6
dtmin = 1.0e4
[TimeStepper]
type = IterationAdaptiveDT
dt = 1
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[max_yy_IPyC]
type = ElementExtremeValue
variable = stress_yy
block = IPyC
[]
[max_yy_SiC]
type = ElementExtremeValue
variable = stress_yy
block = SiC
[]
[]
[PerformanceMetricOutputs]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = true
csv = true
perf_graph = true
[]
(test/tests/triso/release_birth_ratio/exposed_kernel.i)
# Release rate to birth rate ratio (R/B) of short-lived Kr and Xe isotopes from exposed kernels.
# The geometry is a sphere with a diameter of 425 micrometers.
# The temperature is ramped from 673.15 to 2073.15 K.
#
# Bison results are checked against results computed in the *_exact Functions.
#
[GlobalParams]
U_contamination_fraction = 0.0
exposed_kernel_fraction = 1e-4
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.125e-4'
mesh_density = '6'
block_names = 'particle'
[]
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = '2'
outer_SiC = '2'
outer_IPyC = '2'
inner_IPyC = '2'
outer_buffer = '2'
outer_kernel = '2'
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temperature]
initial_condition = 673.15
[]
[]
[Functions]
[temp_function]
type = PiecewiseLinear
x = '0 3e6'
y = '673.15 2073.15'
[]
[D_1_Kr]
type = ParsedFunction
symbol_names = 'R temp'
symbol_values = '8.3145 temp_function'
expression = '3e-5*exp(-106e3/(R*temp))'
[]
[X_1_Kr85m]
type = ParsedFunction
symbol_names = 'decay D_1'
symbol_values = '4.298e-5 D_1_Kr'
expression = 'sqrt(decay / D_1)'
[]
[D_2]
type = ParsedFunction
symbol_names = 'radius temp'
symbol_values = '2.125e-4 temp_function'
expression = 'pow(500*1e-6/radius/2,2)*pow(10,if(temp<1173,-7.97-1920/temp,-2.6-8220/temp))'
[]
[X_2_Kr85m]
type = ParsedFunction
symbol_names = 'decay D_2'
symbol_values = '4.298e-5 D_2'
expression = 'sqrt(decay/D_2)'
[]
[Kr85m_exact]
type = ParsedFunction
symbol_names = 'expo X_2'
symbol_values = '1e-4 X_2_Kr85m'
expression = 'expo*3/X_2*(1/tanh(X_2)-1/X_2)'
[]
[X_2_Kr87]
type = ParsedFunction
symbol_names = 'decay D_2'
symbol_values = '1.514e-4 D_2'
expression = 'sqrt(decay/D_2)'
[]
[Kr87_exact]
type = ParsedFunction
symbol_names = 'expo X_2'
symbol_values = '1e-4 X_2_Kr87'
expression = 'expo*3/X_2*(1/tanh(X_2)-1/X_2)'
[]
[X_2_Kr88]
type = ParsedFunction
symbol_names = 'decay D_2'
symbol_values = '6.816e-5 D_2'
expression = 'sqrt(decay/D_2)'
[]
[Kr88_exact]
type = ParsedFunction
symbol_names = 'expo X_2'
symbol_values = '1e-4 X_2_Kr88'
expression = 'expo*3/X_2*(1/tanh(X_2)-1/X_2)'
[]
[X_2_Kr89]
type = ParsedFunction
symbol_names = 'decay D_2'
symbol_values = '3.667e-3 D_2'
expression = 'sqrt(decay/D_2)'
[]
[Kr89_exact]
type = ParsedFunction
symbol_names = 'expo X_2'
symbol_values = '1e-4 X_2_Kr89'
expression = 'expo*3/X_2*(1/tanh(X_2)-1/X_2)'
[]
[X_2_Kr90]
type = ParsedFunction
symbol_names = 'decay D_2'
symbol_values = '2.145e-2 D_2'
expression = 'sqrt(decay/D_2)'
[]
[Kr90_exact]
type = ParsedFunction
symbol_names = 'expo X_2'
symbol_values = '1e-4 X_2_Kr90'
expression = 'expo*3/X_2*(1/tanh(X_2)-1/X_2)'
[]
[X_2_Xe131m]
type = ParsedFunction
symbol_names = 'decay D_2'
symbol_values = '6.776e-7 D_2'
expression = 'sqrt(decay/D_2)'
[]
[Xe131m_exact]
type = ParsedFunction
symbol_names = 'expo X_2'
symbol_values = '1e-4 X_2_Xe131m'
expression = 'expo*3/X_2*(1/tanh(X_2)-1/X_2)'
[]
[X_2_Xe133]
type = ParsedFunction
symbol_names = 'decay D_2'
symbol_values = '1.529e-6 D_2'
expression = 'sqrt(decay/D_2)'
[]
[Xe133_exact]
type = ParsedFunction
symbol_names = 'expo X_2'
symbol_values = '1e-4 X_2_Xe133'
expression = 'expo*3/X_2*(1/tanh(X_2)-1/X_2)'
[]
[X_2_Xe135]
type = ParsedFunction
symbol_names = 'decay D_2'
symbol_values = '2.107e-5 D_2'
expression = 'sqrt(decay/D_2)'
[]
[Xe135_exact]
type = ParsedFunction
symbol_names = 'expo X_2'
symbol_values = '1e-4 X_2_Xe135'
expression = 'expo*3/X_2*(1/tanh(X_2)-1/X_2)'
[]
[X_2_Xe135m]
type = ParsedFunction
symbol_names = 'decay D_2'
symbol_values = '7.556e-4 D_2'
expression = 'sqrt(decay/D_2)'
[]
[Xe135m_exact]
type = ParsedFunction
symbol_names = 'expo X_2'
symbol_values = '1e-4 X_2_Xe135m'
expression = 'expo*3/X_2*(1/tanh(X_2)-1/X_2)'
[]
[X_2_Xe137]
type = ParsedFunction
symbol_names = 'decay D_2'
symbol_values = '3.026e-3 D_2'
expression = 'sqrt(decay/D_2)'
[]
[Xe137_exact]
type = ParsedFunction
symbol_names = 'expo X_2'
symbol_values = '1e-4 X_2_Xe137'
expression = 'expo*3/X_2*(1/tanh(X_2)-1/X_2)'
[]
[X_2_Xe138]
type = ParsedFunction
symbol_names = 'decay D_2'
symbol_values = '8.170e-4 D_2'
expression = 'sqrt(decay/D_2)'
[]
[Xe138_exact]
type = ParsedFunction
symbol_names = 'expo X_2'
symbol_values = '1e-4 X_2_Xe138'
expression = 'expo*3/X_2*(1/tanh(X_2)-1/X_2)'
[]
[X_2_Xe139]
type = ParsedFunction
symbol_names = 'decay D_2'
symbol_values = '1.747e-2 D_2'
expression = 'sqrt(decay/D_2)'
[]
[Xe139_exact]
type = ParsedFunction
symbol_names = 'expo X_2'
symbol_values = '1e-4 X_2_Xe139'
expression = 'expo*3/X_2*(1/tanh(X_2)-1/X_2)'
[]
# [Kr85m_exact]
# type = ParsedFunction
# symbol_names = 'cont X_1'
# symbol_values = '1e-6 X_1_Kr85m'
# expression = 'cont*3/X_1*(1/tanh(X_1)-1/X_1)'
# []
[]
[Kernels]
[heat] # gradient term in heat conduction equation
type = HeatConduction
variable = temperature
[]
[heat_ie] # time term in heat conduction equation
type = HeatConductionTimeDerivative
variable = temperature
[]
[]
[BCs]
[heat_removal]
type = FunctionDirichletBC
variable = temperature
boundary = '2'
function = temp_function
[]
[]
[Materials]
[thermal]
type = HeatConductionMaterial
block = '1'
thermal_conductivity = 1.0
specific_heat = 1.0
[]
[density]
type = ParsedMaterial
block = '1'
property_name = density
expression = 2570.0
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 51'
line_search = 'none'
l_max_its = 50
l_tol = 1e-2
nl_max_its = 150
nl_rel_tol = 1e-8
start_time = 0.0
end_time = 3e6
num_steps = 140
dtmax = 3e6
dtmin = 1.0
[TimeStepper]
type = IterationAdaptiveDT
dt = 1e5
time_t = '1e5'
time_dt = '1e5'
[]
[]
[Postprocessors]
[temperature]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = temperature
execute_on = 'initial timestep_end'
[]
[average_kernel_temperature]
type = ElementAverageValue
block = '1'
variable = temperature
execute_on = 'initial timestep_end'
[]
[average_matrix_temperature]
type = ElementAverageValue
block = '1'
variable = temperature
execute_on = 'initial timestep_end'
[]
[_dt]
type = TimestepSize
[]
[Kr85m_RB_ratio]
type = ReleaseBirthRatio
isotope = Kr85m
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr85m_exact]
type = FunctionValuePostprocessor
function = Kr85m_exact
execute_on = 'initial timestep_end'
[]
[Kr85m_check]
type = RelativeDifferencePostprocessor
value1 = Kr85m_RB_ratio
value2 = Kr85m_exact
[]
[Kr87_RB_ratio]
type = ReleaseBirthRatio
isotope = Kr87
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr87_exact]
type = FunctionValuePostprocessor
function = Kr87_exact
execute_on = 'initial timestep_end'
[]
[Kr87_check]
type = RelativeDifferencePostprocessor
value1 = Kr87_RB_ratio
value2 = Kr87_exact
[]
[Kr88_RB_ratio]
type = ReleaseBirthRatio
isotope = Kr88
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr88_exact]
type = FunctionValuePostprocessor
function = Kr88_exact
execute_on = 'initial timestep_end'
[]
[Kr88_check]
type = RelativeDifferencePostprocessor
value1 = Kr88_RB_ratio
value2 = Kr88_exact
[]
[Kr89_RB_ratio]
type = ReleaseBirthRatio
isotope = Kr89
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr89_exact]
type = FunctionValuePostprocessor
function = Kr89_exact
execute_on = 'initial timestep_end'
[]
[Kr89_check]
type = RelativeDifferencePostprocessor
value1 = Kr89_RB_ratio
value2 = Kr89_exact
[]
[Kr90_RB_ratio]
type = ReleaseBirthRatio
isotope = Kr90
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr90_exact]
type = FunctionValuePostprocessor
function = Kr90_exact
execute_on = 'initial timestep_end'
[]
[Kr90_check]
type = RelativeDifferencePostprocessor
value1 = Kr90_RB_ratio
value2 = Kr90_exact
[]
[Xe131m_RB_ratio]
type = ReleaseBirthRatio
isotope = Xe131m
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe131m_exact]
type = FunctionValuePostprocessor
function = Xe131m_exact
execute_on = 'initial timestep_end'
[]
[Xe131m_check]
type = RelativeDifferencePostprocessor
value1 = Xe131m_RB_ratio
value2 = Xe131m_exact
[]
[Xe133_RB_ratio]
type = ReleaseBirthRatio
isotope = Xe133
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe133_exact]
type = FunctionValuePostprocessor
function = Xe133_exact
execute_on = 'initial timestep_end'
[]
[Xe133_check]
type = RelativeDifferencePostprocessor
value1 = Xe133_RB_ratio
value2 = Xe133_exact
[]
[Xe135_RB_ratio]
type = ReleaseBirthRatio
isotope = Xe135
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe135_exact]
type = FunctionValuePostprocessor
function = Xe135_exact
execute_on = 'initial timestep_end'
[]
[Xe135_check]
type = RelativeDifferencePostprocessor
value1 = Xe135_RB_ratio
value2 = Xe135_exact
[]
[Xe135m_RB_ratio]
type = ReleaseBirthRatio
isotope = Xe135m
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe135m_exact]
type = FunctionValuePostprocessor
function = Xe135m_exact
execute_on = 'initial timestep_end'
[]
[Xe135m_check]
type = RelativeDifferencePostprocessor
value1 = Xe135m_RB_ratio
value2 = Xe135m_exact
[]
[Xe137_RB_ratio]
type = ReleaseBirthRatio
isotope = Xe137
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe137_exact]
type = FunctionValuePostprocessor
function = Xe137_exact
execute_on = 'initial timestep_end'
[]
[Xe137_check]
type = RelativeDifferencePostprocessor
value1 = Xe137_RB_ratio
value2 = Xe137_exact
[]
[Xe138_RB_ratio]
type = ReleaseBirthRatio
isotope = Xe138
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe138_exact]
type = FunctionValuePostprocessor
function = Xe138_exact
execute_on = 'initial timestep_end'
[]
[Xe138_check]
type = RelativeDifferencePostprocessor
value1 = Xe138_RB_ratio
value2 = Xe138_exact
[]
[Xe139_RB_ratio]
type = ReleaseBirthRatio
isotope = Xe139
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe139_exact]
type = FunctionValuePostprocessor
function = Xe139_exact
execute_on = 'initial timestep_end'
[]
[Xe139_check]
type = RelativeDifferencePostprocessor
value1 = Xe139_RB_ratio
value2 = Xe139_exact
[]
[]
[Outputs]
csv = true
exodus = false
[console]
type = Console
[]
[]
(test/tests/triso/release_birth_ratio/agr.i)
# Release rate to birth rate ratio (R/B) of short-lived Kr and Xe isotopes from exposed kernels.
# The geometry is a sphere with a diameter of 425 micrometers.
# The temperature is ramped from 673.15 to 2073.15 K.
#
# Bison results are checked against results computed in the *_exact Functions.
#
[GlobalParams]
U_contamination_fraction = 1e-6
exposed_kernel_fraction = 1e-4
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.125e-4'
mesh_density = '6'
block_names = 'particle'
[]
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = '2'
outer_SiC = '2'
outer_IPyC = '2'
inner_IPyC = '2'
outer_buffer = '2'
outer_kernel = '2'
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temperature]
initial_condition = 673.15
[]
[]
[Functions]
[temp_function]
type = PiecewiseLinear
x = '0 3e6'
y = '673.15 2073.15'
[]
[Kr85m_exact]
type = ParsedFunction
symbol_names = 'expo cont n B C decay factor'
symbol_values = '1e-4 1e-6 0.325 -8572 -1.41 4.298e-5 6.4'
expression = '(expo + cont * factor)*exp(n*log(1/decay)+B/(673.15 + 1400/3e6*t)+C)'
[]
[Kr87_exact]
type = ParsedFunction
symbol_names = 'expo cont n B C decay factor'
symbol_values = '1e-4 1e-6 0.325 -8572 -1.41 1.514e-4 6.3'
expression = '(expo + cont * factor)*exp(n*log(1/decay)+B/(673.15 + 1400/3e6*t)+C)'
[]
[Kr88_exact]
type = ParsedFunction
symbol_names = 'expo cont n B C decay factor'
symbol_values = '1e-4 1e-6 0.325 -8572 -1.41 6.816e-5 5.5'
expression = '(expo + cont * factor)*exp(n*log(1/decay)+B/(673.15 + 1400/3e6*t)+C)'
[]
[Xe135_exact]
type = ParsedFunction
symbol_names = 'expo cont n B C decay factor'
symbol_values = '1e-4 1e-6 0.302 -7793 -2.73 2.107e-5 2.3'
expression = '(expo + cont * factor)*exp(n*log(1/decay)+B/(673.15 + 1400/3e6*t)+C)'
[]
[Xe137_exact]
type = ParsedFunction
symbol_names = 'expo cont n B C decay factor'
symbol_values = '1e-4 1e-6 0.302 -7793 -2.73 3.026e-3 5.2'
expression = '(expo + cont * factor)*exp(n*log(1/decay)+B/(673.15 + 1400/3e6*t)+C)'
[]
[Xe138_exact]
type = ParsedFunction
symbol_names = 'expo cont n B C decay factor'
symbol_values = '1e-4 1e-6 0.302 -7793 -2.73 8.170e-4 4.6'
expression = '(expo + cont * factor)*exp(n*log(1/decay)+B/(673.15 + 1400/3e6*t)+C)'
[]
[]
[Kernels]
[heat] # gradient term in heat conduction equation
type = HeatConduction
variable = temperature
[]
[heat_ie] # time term in heat conduction equation
type = HeatConductionTimeDerivative
variable = temperature
[]
[]
[BCs]
[heat_removal]
type = FunctionDirichletBC
variable = temperature
boundary = '2'
function = temp_function
[]
[]
[Materials]
[thermal]
type = HeatConductionMaterial
block = '1'
thermal_conductivity = 1.0
specific_heat = 1.0
[]
[density]
type = ParsedMaterial
block = '1'
property_name = density
expression = 2570.0
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 51'
line_search = 'none'
l_max_its = 50
l_tol = 1e-2
nl_max_its = 150
nl_rel_tol = 1e-8
start_time = 0.0
end_time = 3e6
num_steps = 140
dtmax = 3e6
dtmin = 1.0
[TimeStepper]
type = IterationAdaptiveDT
dt = 1e5
time_t = '1e5'
time_dt = '1e5'
[]
[]
[Postprocessors]
[temperature]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = temperature
execute_on = 'initial timestep_end'
[]
[average_kernel_temperature]
type = ElementAverageValue
block = '1'
variable = temperature
execute_on = 'initial timestep_end'
[]
[average_matrix_temperature]
type = ElementAverageValue
block = '1'
variable = temperature
execute_on = 'initial timestep_end'
[]
[_dt]
type = TimestepSize
[]
[Kr85m_RB_ratio]
type = ReleaseBirthRatio
model = AGR
isotope = Kr85m
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr85m_exact]
type = FunctionValuePostprocessor
function = Kr85m_exact
execute_on = 'initial timestep_end'
[]
[Kr85m_check]
type = RelativeDifferencePostprocessor
value1 = Kr85m_RB_ratio
value2 = Kr85m_exact
[]
[Kr87_RB_ratio]
type = ReleaseBirthRatio
model = AGR
isotope = Kr87
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr87_exact]
type = FunctionValuePostprocessor
function = Kr87_exact
execute_on = 'initial timestep_end'
[]
[Kr87_check]
type = RelativeDifferencePostprocessor
value1 = Kr87_RB_ratio
value2 = Kr87_exact
[]
[Kr88_RB_ratio]
type = ReleaseBirthRatio
model = AGR
isotope = Kr88
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr88_exact]
type = FunctionValuePostprocessor
function = Kr88_exact
execute_on = 'initial timestep_end'
[]
[Kr88_check]
type = RelativeDifferencePostprocessor
value1 = Kr88_RB_ratio
value2 = Kr88_exact
[]
[Xe135_RB_ratio]
type = ReleaseBirthRatio
model = AGR
isotope = Xe135
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe135_exact]
type = FunctionValuePostprocessor
function = Xe135_exact
execute_on = 'initial timestep_end'
[]
[Xe135_check]
type = RelativeDifferencePostprocessor
value1 = Xe135_RB_ratio
value2 = Xe135_exact
[]
[Xe137_RB_ratio]
type = ReleaseBirthRatio
model = AGR
isotope = Xe137
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe137_exact]
type = FunctionValuePostprocessor
function = Xe137_exact
execute_on = 'initial timestep_end'
[]
[Xe137_check]
type = RelativeDifferencePostprocessor
value1 = Xe137_RB_ratio
value2 = Xe137_exact
[]
[Xe138_RB_ratio]
type = ReleaseBirthRatio
model = AGR
isotope = Xe138
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe138_exact]
type = FunctionValuePostprocessor
function = Xe138_exact
execute_on = 'initial timestep_end'
[]
[Xe138_check]
type = RelativeDifferencePostprocessor
value1 = Xe138_RB_ratio
value2 = Xe138_exact
[]
[]
[Outputs]
csv = true
exodus = false
[console]
type = Console
[]
[]
(test/tests/triso/release_birth_ratio/uranium_contamination.i)
# Release rate to birth rate ratio (R/B) of short-lived Kr and Xe isotopes from uranium contamination.
# The geometry is a sphere with a diameter of 425 micrometers.
# The temperature is ramped from 673.15 to 2073.15 K.
#
# Bison results are checked against results computed in the *_exact Functions.
#
[GlobalParams]
U_contamination_fraction = 3e-7
exposed_kernel_fraction = 0.0
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.125e-4'
mesh_density = '6'
block_names = 'particle'
[]
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = '2'
outer_SiC = '2'
outer_IPyC = '2'
inner_IPyC = '2'
outer_buffer = '2'
outer_kernel = '2'
include_particle = true
include_pebble = false
[]
[]
[Variables]
[temperature]
initial_condition = 673.15
[]
[]
[Functions]
[temp_function]
type = PiecewiseLinear
x = '0 3e6'
y = '673.15 2073.15'
[]
[D_1_Kr]
type = ParsedFunction
symbol_names = 'R temp'
symbol_values = '8.31446261815324 temp_function'
expression = '3e-5*exp(-106e3/(R*temp))'
[]
[D_1_Xe]
type = ParsedFunction
symbol_names = 'R temp'
symbol_values = '8.31446261815324 temp_function'
expression = '1.7e-7*exp(-78.6e3/(R*temp))'
[]
[X_1_Kr85m]
type = ParsedFunction
symbol_names = 'decay D_1'
symbol_values = '4.298e-5 D_1_Kr'
expression = 'sqrt(decay/D_1)'
[]
[Kr85m_exact]
type = ParsedFunction
symbol_names = 'cont X_1'
symbol_values = '3e-7 X_1_Kr85m'
expression = 'cont*3/X_1*(1/tanh(X_1)-1/X_1)'
[]
[X_1_Kr87]
type = ParsedFunction
symbol_names = 'decay D_1'
symbol_values = '1.514e-4 D_1_Kr'
expression = 'sqrt(decay/D_1)'
[]
[Kr87_exact]
type = ParsedFunction
symbol_names = 'cont X_1'
symbol_values = '3e-7 X_1_Kr87'
expression = 'cont*3/X_1*(1/tanh(X_1)-1/X_1)'
[]
[X_1_Kr88]
type = ParsedFunction
symbol_names = 'decay D_1'
symbol_values = '6.816e-5 D_1_Kr'
expression = 'sqrt(decay/D_1)'
[]
[Kr88_exact]
type = ParsedFunction
symbol_names = 'cont X_1'
symbol_values = '3e-7 X_1_Kr88'
expression = 'cont*3/X_1*(1/tanh(X_1)-1/X_1)'
[]
[X_1_Kr89]
type = ParsedFunction
symbol_names = 'decay D_1'
symbol_values = '3.667e-3 D_1_Kr'
expression = 'sqrt(decay/D_1)'
[]
[Kr89_exact]
type = ParsedFunction
symbol_names = 'cont X_1'
symbol_values = '3e-7 X_1_Kr89'
expression = 'cont*3/X_1*(1/tanh(X_1)-1/X_1)'
[]
[X_1_Kr90]
type = ParsedFunction
symbol_names = 'decay D_1'
symbol_values = '2.145e-2 D_1_Kr'
expression = 'sqrt(decay/D_1)'
[]
[Kr90_exact]
type = ParsedFunction
symbol_names = 'cont X_1'
symbol_values = '3e-7 X_1_Kr90'
expression = 'cont*3/X_1*(1/tanh(X_1)-1/X_1)'
[]
[X_1_Xe131m]
type = ParsedFunction
symbol_names = 'decay D_1'
symbol_values = '6.776e-7 D_1_Xe'
expression = 'sqrt(decay/D_1)'
[]
[Xe131m_exact]
type = ParsedFunction
symbol_names = 'cont X_1'
symbol_values = '3e-7 X_1_Xe131m'
expression = 'cont*3/X_1*(1/tanh(X_1)-1/X_1)'
[]
[X_1_Xe133]
type = ParsedFunction
symbol_names = 'decay D_1'
symbol_values = '1.529e-6 D_1_Xe'
expression = 'sqrt(decay/D_1)'
[]
[Xe133_exact]
type = ParsedFunction
symbol_names = 'cont X_1'
symbol_values = '3e-7 X_1_Xe133'
expression = 'cont*3/X_1*(1/tanh(X_1)-1/X_1)'
[]
[X_1_Xe135]
type = ParsedFunction
symbol_names = 'decay D_1'
symbol_values = '2.107e-5 D_1_Xe'
expression = 'sqrt(decay/D_1)'
[]
[Xe135_exact]
type = ParsedFunction
symbol_names = 'cont X_1'
symbol_values = '3e-7 X_1_Xe135'
expression = 'cont*3/X_1*(1/tanh(X_1)-1/X_1)'
[]
[X_1_Xe135m]
type = ParsedFunction
symbol_names = 'decay D_1'
symbol_values = '7.556e-4 D_1_Xe'
expression = 'sqrt(decay/D_1)'
[]
[Xe135m_exact]
type = ParsedFunction
symbol_names = 'cont X_1'
symbol_values = '3e-7 X_1_Xe135m'
expression = 'cont*3/X_1*(1/tanh(X_1)-1/X_1)'
[]
[X_1_Xe137]
type = ParsedFunction
symbol_names = 'decay D_1'
symbol_values = '3.026e-3 D_1_Xe'
expression = 'sqrt(decay/D_1)'
[]
[Xe137_exact]
type = ParsedFunction
symbol_names = 'cont X_1'
symbol_values = '3e-7 X_1_Xe137'
expression = 'cont*3/X_1*(1/tanh(X_1)-1/X_1)'
[]
[X_1_Xe138]
type = ParsedFunction
symbol_names = 'decay D_1'
symbol_values = '8.170e-4 D_1_Xe'
expression = 'sqrt(decay/D_1)'
[]
[Xe138_exact]
type = ParsedFunction
symbol_names = 'cont X_1'
symbol_values = '3e-7 X_1_Xe138'
expression = 'cont*3/X_1*(1/tanh(X_1)-1/X_1)'
[]
[X_1_Xe139]
type = ParsedFunction
symbol_names = 'decay D_1'
symbol_values = '1.747e-2 D_1_Xe'
expression = 'sqrt(decay/D_1)'
[]
[Xe139_exact]
type = ParsedFunction
symbol_names = 'cont X_1'
symbol_values = '3e-7 X_1_Xe139'
expression = 'cont*3/X_1*(1/tanh(X_1)-1/X_1)'
[]
[]
[Kernels]
[heat] # gradient term in heat conduction equation
type = HeatConduction
variable = temperature
[]
[heat_ie] # time term in heat conduction equation
type = HeatConductionTimeDerivative
variable = temperature
[]
[]
[BCs]
[heat_removal]
type = FunctionDirichletBC
variable = temperature
boundary = '2'
function = temp_function
[]
[]
[Materials]
[thermal]
type = HeatConductionMaterial
block = '1'
thermal_conductivity = 1.0
specific_heat = 1.0
[]
[density]
type = ParsedMaterial
block = '1'
property_name = density
expression = 2570.0
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 51'
line_search = 'none'
l_max_its = 50
l_tol = 1e-2
nl_max_its = 150
nl_rel_tol = 1e-8
start_time = 0.0
end_time = 3e6
num_steps = 140
dtmax = 3e6
dtmin = 1.0
[TimeStepper]
type = IterationAdaptiveDT
dt = 1e5
time_t = '1e5'
time_dt = '1e5'
[]
[]
[Postprocessors]
[temperature]
type = ElementExtremeValue
block = '1'
value_type = 'max'
variable = temperature
execute_on = 'initial timestep_end'
[]
[average_kernel_temperature]
type = ElementAverageValue
block = '1'
variable = temperature
execute_on = 'initial timestep_end'
[]
[average_matrix_temperature]
type = ElementAverageValue
block = '1'
variable = temperature
execute_on = 'initial timestep_end'
[]
[_dt]
type = TimestepSize
[]
[Kr85m_RB_ratio]
type = ReleaseBirthRatio
isotope = Kr85m
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr85m_exact]
type = FunctionValuePostprocessor
function = Kr85m_exact
[]
[Kr85m_check]
type = RelativeDifferencePostprocessor
value1 = Kr85m_RB_ratio
value2 = Kr85m_exact
[]
[Kr87_RB_ratio]
type = ReleaseBirthRatio
isotope = Kr87
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr87_exact]
type = FunctionValuePostprocessor
function = Kr87_exact
[]
[Kr87_check]
type = RelativeDifferencePostprocessor
value1 = Kr87_RB_ratio
value2 = Kr87_exact
[]
[Kr88_RB_ratio]
type = ReleaseBirthRatio
isotope = Kr88
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr88_exact]
type = FunctionValuePostprocessor
function = Kr88_exact
[]
[Kr88_check]
type = RelativeDifferencePostprocessor
value1 = Kr88_RB_ratio
value2 = Kr88_exact
[]
[Kr89_RB_ratio]
type = ReleaseBirthRatio
isotope = Kr89
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr89_exact]
type = FunctionValuePostprocessor
function = Kr89_exact
[]
[Kr89_check]
type = RelativeDifferencePostprocessor
value1 = Kr89_RB_ratio
value2 = Kr89_exact
[]
[Kr90_RB_ratio]
type = ReleaseBirthRatio
isotope = Kr90
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Kr90_exact]
type = FunctionValuePostprocessor
function = Kr90_exact
[]
[Kr90_check]
type = RelativeDifferencePostprocessor
value1 = Kr90_RB_ratio
value2 = Kr90_exact
[]
[Xe131m_RB_ratio]
type = ReleaseBirthRatio
isotope = Xe131m
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe131m_exact]
type = FunctionValuePostprocessor
function = Xe131m_exact
[]
[Xe131m_check]
type = RelativeDifferencePostprocessor
value1 = Xe131m_RB_ratio
value2 = Xe131m_exact
[]
[Xe133_RB_ratio]
type = ReleaseBirthRatio
isotope = Xe133
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe133_exact]
type = FunctionValuePostprocessor
function = Xe133_exact
[]
[Xe133_check]
type = RelativeDifferencePostprocessor
value1 = Xe133_RB_ratio
value2 = Xe133_exact
[]
[Xe135_RB_ratio]
type = ReleaseBirthRatio
isotope = Xe135
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe135_exact]
type = FunctionValuePostprocessor
function = Xe135_exact
[]
[Xe135_check]
type = RelativeDifferencePostprocessor
value1 = Xe135_RB_ratio
value2 = Xe135_exact
[]
[Xe135m_RB_ratio]
type = ReleaseBirthRatio
isotope = Xe135m
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe135m_exact]
type = FunctionValuePostprocessor
function = Xe135m_exact
[]
[Xe135m_check]
type = RelativeDifferencePostprocessor
value1 = Xe135m_RB_ratio
value2 = Xe135m_exact
[]
[Xe137_RB_ratio]
type = ReleaseBirthRatio
isotope = Xe137
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe137_exact]
type = FunctionValuePostprocessor
function = Xe137_exact
[]
[Xe137_check]
type = RelativeDifferencePostprocessor
value1 = Xe137_RB_ratio
value2 = Xe137_exact
[]
[Xe138_RB_ratio]
type = ReleaseBirthRatio
isotope = Xe138
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe138_exact]
type = FunctionValuePostprocessor
function = Xe138_exact
[]
[Xe138_check]
type = RelativeDifferencePostprocessor
value1 = Xe138_RB_ratio
value2 = Xe138_exact
[]
[Xe139_RB_ratio]
type = ReleaseBirthRatio
isotope = Xe139
average_kernel_temperature = average_kernel_temperature
average_matrix_temperature = average_matrix_temperature
triso_geometry = particle_geometry
execute_on = 'initial timestep_end'
[]
[Xe139_exact]
type = FunctionValuePostprocessor
function = Xe139_exact
[]
[Xe139_check]
type = RelativeDifferencePostprocessor
value1 = Xe139_RB_ratio
value2 = Xe139_exact
[]
[]
[Outputs]
csv = true
exodus = false
[console]
type = Console
[]
[]
(examples/TRISO/two_layers/1D/two_layers_1D.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
volumetric_locking_correction = false
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '3.5e-4 3.9e-4 4.25e-4'
mesh_density = '8 8'
block_names = 'IPyC SiC'
[]
[]
[Variables]
[temp]
initial_condition = 1273.0
[]
[]
[AuxVariables]
[burnup]
initial_condition = 0
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[IPyC]
block = IPyC
add_variables = true
strain = FINITE
eigenstrain_names = ''
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz
strain_xy strain_yz strain_xz'
[]
[SiC]
block = SiC
add_variables = true
strain = FINITE
eigenstrain_names = ''
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz
strain_xy strain_yz strain_xz'
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temp
[]
[heat]
type = HeatConduction
variable = temp
[]
[]
[BCs]
# fix temperature on free surface
[freesurf_temp]
type = DirichletBC
variable = temp
boundary = exterior
value = 1273.0
[]
# exterior and internal pressures
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[interior_pressure_x]
type = Pressure
variable = disp_x
boundary = IPyC_inner_boundary
factor = 25e6
[]
[]
[Materials]
[IPyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = IPyC
youngs_modulus = 3.94e10
poissons_ratio = 0.33
[]
[IPyC_elastic_stress]
type = ComputeFiniteStrainElasticStress
block = IPyC
[]
[IPyC_temp]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[IPyC_den]
type = StrainAdjustedDensity
strain_free_density = 1900.0 # kg/m^3
block = IPyC
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_elastic_stress]
type = ComputeFiniteStrainElasticStress
block = SiC
[]
[SiC_temp]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9 # J/m-s-K
specific_heat = 620.0 # J/kg-K
[]
[SiC_den]
type = StrainAdjustedDensity
strain_free_density = 3180.0 # kg/m^3
block = SiC
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temp
max_increment = 50
[]
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 1.0
dt = 1.0
[]
[Postprocessors]
[dt]
type = TimestepSize
[]
[max_xx_IPyC]
type = ElementExtremeValue
variable = stress_xx
block = IPyC
[]
[max_yy_IPyC]
type = ElementExtremeValue
variable = stress_yy
block = IPyC
[]
[max_zz_IPyC]
type = ElementExtremeValue
variable = stress_zz
block = IPyC
[]
[max_xx_SiC]
type = ElementExtremeValue
variable = stress_xx
block = SiC
[]
[max_yy_SiC]
type = ElementExtremeValue
variable = stress_yy
block = SiC
[]
[max_zz_SiC]
type = ElementExtremeValue
variable = stress_zz
block = SiC
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = true
csv = true
perf_graph = true
[]
(test/tests/triso_failure/sub.i)
[GlobalParams]
density = 10810.0 # kg/m^3
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
mesh_density = '6 6 0 6 8 6'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Variables]
[disp_x]
[]
[temp]
initial_condition = 1346.0
[]
[]
[Functions]
[radial_eigenstrain]
type = ParsedFunction
expression = 't*(4.52013e-4/6.0*t*t*t*t*t - 8.36313e-3/5.0*t*t*t*t + 5.67549e-2/4.0*t*t*t - 1.74247e-1/3.0*t*t + 2.62692e-1/2.0*t - 1.43234e-1)'
[]
[tangential_eigenstrain]
type = ParsedFunction
expression = 't*(1.30457e-4/4.0*t*t*t - 2.10029e-3/3.0*t*t + 9.07826e-3/2.0*t - 3.24737e-2)'
[]
[fission_rate]
type = ParsedFunction
expression = 7.75e19 # units of fissions/m**3
[]
[k_function]
type = ParsedFunction
expression = '4.93e-29'
[]
[high_fidelity_strength_crackedIPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1000000 1000000'
[]
[high_fidelity_strength_crackedOPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1000000 1000000'
[]
[stress_correlation_crackedOPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[stress_correlation_crackedIPyC]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[]
[AuxVariables]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = fuel
initial_condition = 0.0
[]
[fission_rate]
block = fuel
[]
[]
[Physics/SolidMechanics/QuasiStatic]
strain = small
[fuel_buffer_sic]
block = 'fuel buffer SiC'
eigenstrain_names = thermal_strain
[]
[ipyc_opyc]
block = 'IPyC OPyC'
incremental = true
eigenstrain_names = 'thermal_strain pyc_eigenstrain'
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temp
[]
[heat]
type = HeatConduction
variable = temp
[]
[heat_source]
type = NeutronHeatSource
variable = temp
block = fuel
energy_per_fission = 3.2e-11 # units of J/fission
fission_rate = fission_rate
[]
[]
[AuxKernels]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[fission_rate]
type = FunctionAux
variable = fission_rate
block = fuel
function = fission_rate
[]
[burnup]
type = BurnupAux
variable = burnup
block = fuel
fission_rate = fission_rate
molecular_weight = 0.270 # units of kg/mole
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
penalty = 1e5
model = frictionless
formulation = kinematic
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temp
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
gas_released = 'fis_gas_released co_production' # coupling to postprocessors which supply the fission gas addition, co addition
released_gas_types = 'Kr Xe;
CO'
released_fractions = '0.153 0.847;
1'
tangential_tolerance = 1e-6
# contact_pressure_input = 10e6
# quadrature = true
[]
[]
[BCs]
# pin particle along symmetry planes
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
# fix temperature on free surface
[freesurf_temp]
type = DirichletBC
variable = temp
boundary = exterior
value = 1346.0
[]
# exterior and internal pressures
[exterior_pressure_x]
type = Pressure
use_displaced_mesh = false
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure] # apply gas pressure on buffer and IPyC boundaries
[plenumPressure]
use_displaced_mesh = false
boundary = buffer_IPyC_boundary
initial_pressure = 0
startup_time = 1.0e4
output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
volume = volumeGas # coupling to post processor to get gas volume
material_input = 'fis_gas_released co_production' # coupling to post processor to get fission gas added, co added
output = plenum_pressure # coupling to post processor to output plenum/gap pressure
[]
[]
[]
[Materials]
[max_principal_stress]
type = RankTwoInvariant
property_name = max_principal_stress
rank_two_tensor = stress
invariant = MaxPrincipal
[]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 1.708707e18 # n/m^2-sec
[]
[fission_gas_release] # Sifgr fission gas release mode
type = UO2Sifgrs
block = fuel
temperature = temp
fission_rate = fission_rate # coupling to fission_rate aux variable
grain_radius_const = 5.0e-6
[]
[stress]
type = ComputeLinearElasticStress
block = 'fuel buffer SiC'
[]
[PyC_stress]
type = PyCCreep
block = 'IPyC OPyC'
k = k_function
poissons_ratio = 0.4
temperature = temp
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'IPyC OPyC'
[]
[PyC_eigenstrain]
type = PyCIrradiationEigenstrain
block = 'IPyC OPyC'
radial_eigenstrain_function = radial_eigenstrain
tangential_eigenstrain_function = tangential_eigenstrain
eigenstrain_name = pyc_eigenstrain
[]
[fuel_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temp
[]
[PyC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = 'buffer IPyC OPyC'
thermal_expansion_coeff = 5.5e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temp
[]
[SiC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temp
[]
[fuel_thermal] # temperature and burnup dependent thermal properties of UO2 (bison kernel)
type = UO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temp
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[fuel_den]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10810.0
[]
[buffer_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[buffer_temp]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[buffer_den]
type = StrainAdjustedDensity
strain_free_density = 1000 #kg/m^3
block = buffer
[]
[PyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = 'IPyC OPyC'
youngs_modulus = 3.96e10 #47787559927.148 #3.96e10
poissons_ratio = 0.33
[]
[PyC_temp]
type = HeatConductionMaterial
block = 'IPyC OPyC'
thermal_conductivity = 4.0 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[PyC_den]
type = StrainAdjustedDensity
strain_free_density = 1880.0 # kg/m^3
block = 'IPyC OPyC'
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_temp]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9 # J/m-s-K
specific_heat = 620.0 # J/kg-K
[]
[SiC_den]
type = StrainAdjustedDensity
strain_free_density = 3200.0 # kg/m^3
block = SiC
[]
[characteristic_strength_SiC]
type = GenericConstantMaterial
prop_values = '9640000'
prop_names = 'characteristic_strength'
block = SiC
[]
[characteristic_strength_PyC]
type = GenericConstantMaterial
prop_values = '964000'
prop_names = 'characteristic_strength'
block = 'IPyC OPyC'
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temp
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Executioner]
type = Transient
# petsc_options = '-snes_mf_operator -snes_ksp_ew -ksp_monitor'
# petsc_options_iname = '-pc_type -pc_hypre_type'
# petsc_options_value = 'hypre boomeramg'
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
num_steps = 2
dtmax = 2e5
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 20
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[dt]
type = TimestepSize
[]
[burnup]
type = ElementExtremeValue
block = fuel
variable = burnup
[]
[fis_gas_produced] # fission gas produced (moles)
type = ElementIntegralFisGasGeneratedSifgrs
block = fuel
[]
[fis_gas_released] # fission gas released to plenum (moles)
type = ElementIntegralFisGasReleasedSifgrs
block = fuel
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
[]
[volumeFuel]
type = InternalVolume
boundary = fuel_outer_boundary
[]
[volumeGas]
type = InternalVolume
boundary = 'fuel_outer_boundary IPyC_inner_boundary'
addition = -5.53e-11
execute_on = 'initial timestep_end'
[]
[volumeBufferShell]
type = InternalVolume
boundary = buffer_IPyC_boundary
[]
[ave_temp_interior]
type = SideAverageValue
boundary = buffer_IPyC_boundary
variable = temp
execute_on = 'initial timestep_end'
[]
# Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temp
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
[]
[avg_surface_temp]
type = SideAverageValue
variable = temp
boundary = exterior
[]
[time_int_surf_temp]
type = TimeIntegratedPostprocessor
value = avg_surface_temp
[]
[co_production]
type = CarbonMonoxideProduction
total_fissions = total_fissions
time_integrated_triso_temperature = time_int_surf_temp
initial_enrichment = 0.14029
[]
[tang_SiC]
type = ElementalVariableValue
variable = stress_yy
elementid = 18
[]
[strength_SiC]
type = WeibullEffectiveMeanStrength
block = SiC
weibull_modulus = 6
[]
[failure_indicator_SiC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_SiC
[]
[strength_IPyC]
type = WeibullEffectiveMeanStrength
block = IPyC
weibull_modulus = 6
[]
[failure_indicator_IPyC]
type = WeibullFailureOutputUsingCorrelation
block = IPyC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_IPyC
[]
[strength_OPyC]
type = WeibullEffectiveMeanStrength
block = OPyC
weibull_modulus = 6
[]
[failure_indicator_OPyC]
type = WeibullFailureOutputUsingCorrelation
block = OPyC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_OPyC
[]
[failure_indicator_SiC_crackedIPyC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = max_principal_stress
high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
stress_correlation_function = 'stress_correlation_crackedIPyC'
[]
[failure_indicator_SiC_crackedOPyC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = max_principal_stress
high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
stress_correlation_function = 'stress_correlation_crackedOPyC'
[]
[triso_failure]
type = TRISOFailureEvaluation
IPyC_failure = failure_indicator_IPyC
OPyC_failure = failure_indicator_OPyC
SiC_failure = failure_indicator_SiC
SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
SiC_failure_crackedOPyC = failure_indicator_SiC_crackedOPyC
[]
[ipyc_cracking]
type = TRISOFailureEvaluation
IPyC_failure = failure_indicator_IPyC
OPyC_failure = failure_indicator_OPyC
SiC_failure = failure_indicator_SiC
SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
SiC_failure_crackedOPyC = failure_indicator_SiC_crackedOPyC
failure_type = IPYC_CRACKING
[]
[burnup_at_failure]
type = TRISOFailureOccurrenceStatus
failure_evaluation = ipyc_cracking
failure_information = burnup
[]
[left_bc]
type = NodalExtremeValue
boundary = xzero
variable = disp_x
[]
[]
[UserObjects]
[triso_failure_terminator]
type = Terminator
expression = 'triso_failure > 0'
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
csv = false
perf_graph = true
[]
[Controls]
[stochastic]
type = SamplerReceiver
[]
[]
(test/tests/void_volume/void_volume.i)
#
# This tests VoidVolume and UCOTheoreticalDensity.
#
# VoidVolume computes the integral of 1 - rho / rho_th
# where rho is density and rho_th is theoretical density.
#
# UCOTheoreticalDensity reports the theoretical density
# of UCO as computed by a utility function.
#
# In this test, the initial geometry has a volume of 0.1.
# Displacements are applied which change the volume to
# 0.2. This volume change must be void volume.
# Therefore, the final void volume should be 0.1 higher
# than the initial void volume. This is exactly what
# is computed.
#
[GlobalParams]
displacements = 'disp_x'
initial_enrichment = 0.1955 # [wt-]
O_U = 1.5 # Initial Oxygen to Uranium atom ratio
C_U = 0.4 # Initial Carbon to Uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE2
coordinates = '0 0.28794119114848615'
mesh_density = '4'
block_names = 'fuel'
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[fuel]
block = fuel
add_variables = true
strain = SMALL
[]
[]
[BCs]
[no_x]
type = DirichletBC
variable = disp_x
boundary = fuel_inner_boundary
value = 0.0
[]
[pull]
type = DirichletBC
variable = disp_x
boundary = fuel_outer_boundary
value = 0.07484197671129483
[]
[]
[Materials]
[elastic]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 1
poissons_ratio = 0.0
[]
[stress]
type = ComputeLinearElasticStress
block = fuel
[]
[fuel_density]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10400.0
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 51'
line_search = 'none'
l_tol = 1e-5
nl_rel_tol = 1e-10
nl_abs_tol = 1e-12
start_time = 0.0
end_time = 5.0e6
num_steps = 1
dt = 1
[]
[Postprocessors]
[volume]
type = InternalVolume
boundary = fuel_outer_boundary
scale_factor = -1
execute_on = 'initial timestep_end'
[]
[uco_theoretical_density]
type = UCOTheoreticalDensity
execute_on = initial
[]
[void_volume]
type = VoidVolume
block = fuel
theoretical_density = uco_theoretical_density
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[]
[Outputs]
csv = true
[]
(test/tests/triso_failure/triso_1d_asphericity_failure.i)
[GlobalParams]
density = 10810.0
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
mesh_density = '6 6 0 6 8 6'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Variables]
[disp_x]
[]
[temperature]
initial_condition = 1346.0
[]
[]
[Functions]
[radial_eigenstrain]
type = ParsedFunction
expression = 't*(4.52013e-4/6.0*t*t*t*t*t - 8.36313e-3/5.0*t*t*t*t + 5.67549e-2/4.0*t*t*t - 1.74247e-1/3.0*t*t + 2.62692e-1/2.0*t - 1.43234e-1)'
[]
[tangential_eigenstrain]
type = ParsedFunction
expression = 't*(1.30457e-4/4.0*t*t*t - 2.10029e-3/3.0*t*t + 9.07826e-3/2.0*t - 3.24737e-2)'
[]
[fission_rate]
type = ParsedFunction
expression = 7.75e19
[]
[k_function]
type = ParsedFunction
expression = '4.93e-29'
[]
[high_fidelity_strength_asphericity]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1000000 1000000'
[]
[stress_correlation_asphericity]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[stress_change_correlation_asphericity]
type = PiecewiseLinear
x = '0 1.0e11'
y = '1 1'
[]
[]
[AuxVariables]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = fuel
initial_condition = 0.0
[]
[fission_rate]
block = fuel
[]
[]
[Physics/SolidMechanics/QuasiStatic]
strain = small
[fuel_buffer_sic]
block = 'fuel buffer SiC'
eigenstrain_names = thermal_strain
[]
[ipyc_opyc]
block = 'IPyC OPyC'
incremental = true
eigenstrain_names = 'thermal_strain pyc_eigenstrain'
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
[]
[heat]
type = HeatConduction
variable = temperature
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
energy_per_fission = 3.2e-11
fission_rate = fission_rate
[]
[]
[AuxKernels]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[fission_rate]
type = FunctionAux
variable = fission_rate
block = fuel
function = fission_rate
[]
[burnup]
type = BurnupAux
variable = burnup
block = fuel
fission_rate = fission_rate
molecular_weight = 0.270
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
penalty = 1e5
model = frictionless
formulation = kinematic
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
# coupling to a postprocessor
initial_moles = initial_moles
gas_released = 'fis_gas_released co_production'
released_gas_types = 'Kr Xe;
CO'
released_fractions = '0.153 0.847;
1'
tangential_tolerance = 1e-6
# contact_pressure_input = 10e6
# quadrature = true
[]
[]
[BCs]
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[freesurf_temperature]
type = DirichletBC
variable = temperature
boundary = exterior
value = 1346.0
[]
[exterior_pressure_x]
type = Pressure
use_displaced_mesh = false
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure]
# apply gas pressure on buffer and IPyC boundaries
[plenumPressure]
use_displaced_mesh = false
boundary = buffer_IPyC_boundary
initial_pressure = 0
startup_time = 1.0e4
R = 8.3143
# coupling to post processor
output_initial_moles = initial_moles
temperature = ave_temp_interior
volume = volumeGas
material_input = 'fis_gas_released co_production'
output = plenum_pressure
[]
[]
[]
[Materials]
[stress_yy]
type = RankTwoCartesianComponent
rank_two_tensor = stress
property_name = stress_yy
index_i = 1
index_j = 1
[]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 1.708707e18
[]
[fission_gas_release]
type = UO2Sifgrs
block = fuel
temperature = temperature
fission_rate = fission_rate
grain_radius_const = 5.0e-6
[]
[stress]
type = ComputeLinearElasticStress
block = 'fuel buffer SiC'
[]
[PyC_stress]
type = PyCCreep
block = 'IPyC OPyC'
k = k_function
poissons_ratio = 0.4
temperature = temperature
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'IPyC OPyC'
[]
[PyC_eigenstrain]
type = PyCIrradiationEigenstrain
block = 'IPyC OPyC'
radial_eigenstrain_function = radial_eigenstrain
tangential_eigenstrain_function = tangential_eigenstrain
eigenstrain_name = pyc_eigenstrain
[]
[fuel_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[PyC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = 'buffer IPyC OPyC'
thermal_expansion_coeff = 5.5e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[SiC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[fuel_thermal]
type = UO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temperature
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[fuel_den]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10810.0
[]
[buffer_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[buffer_thermal]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5
specific_heat = 720.0
[]
[buffer_den]
type = StrainAdjustedDensity
strain_free_density = 1000
block = buffer
[]
[PyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = 'IPyC OPyC'
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[PyC_thermal]
type = HeatConductionMaterial
block = 'IPyC OPyC'
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[PyC_den]
type = StrainAdjustedDensity
strain_free_density = 1880.0
block = 'IPyC OPyC'
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_thermal]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9
specific_heat = 620.0
[]
[SiC_den]
type = StrainAdjustedDensity
strain_free_density = 3200.0
block = SiC
[]
[characteristic_strength]
type = GenericConstantMaterial
prop_values = '9640000'
prop_names = 'characteristic_strength'
block = SiC
[]
[]
[Dampers]
[temperature]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
num_steps = 10
dtmax = 2e5
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 20
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[dt]
type = TimestepSize
[]
[burnup]
type = ElementExtremeValue
block = fuel
variable = burnup
[]
[fis_gas_produced]
type = ElementIntegralFisGasGeneratedSifgrs
block = fuel
[]
[fis_gas_released]
type = ElementIntegralFisGasReleasedSifgrs
block = fuel
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
[]
[volumeFuel]
type = InternalVolume
boundary = fuel_outer_boundary
[]
[volumeGas]
type = InternalVolume
boundary = 'fuel_outer_boundary IPyC_inner_boundary'
addition = -5.53e-11
execute_on = 'initial timestep_end'
[]
[volumeBufferShell]
type = InternalVolume
boundary = buffer_IPyC_boundary
[]
[ave_temp_interior]
type = SideAverageValue
boundary = buffer_IPyC_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
# Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
[]
[avg_surface_temperature]
type = SideAverageValue
variable = temperature
boundary = exterior
[]
[time_int_surf_temperature]
type = TimeIntegratedPostprocessor
value = avg_surface_temperature
[]
[co_production]
type = CarbonMonoxideProduction
total_fissions = total_fissions
time_integrated_triso_temperature = time_int_surf_temperature
initial_enrichment = 0.14029
[]
[tang_SiC]
type = ElementalVariableValue
variable = stress_yy
elementid = 18
[]
[strength_SiC]
type = WeibullEffectiveMeanStrength
block = SiC
weibull_modulus = 6
[]
[failure_indicator_SiC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = stress_yy
high_fidelity_analysis_strength = 'high_fidelity_strength_asphericity'
stress_correlation_function = 'stress_correlation_asphericity'
stress_change_correlation_function = 'stress_change_correlation_asphericity'
[]
[triso_failure]
type = TRISOFailureEvaluation
SiC_failure = failure_indicator_SiC
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
csv = true
perf_graph = true
[]
(test/tests/triso_failure/triso_1d_ipyc_weibull_probability.i)
kernel_radius = 213.35e-6
buffer_thickness = 98.9e-6
IPyC_thickness = 40.4e-6
SiC_thickness = 35.2e-6
OPyC_thickness = 43.4e-6
coordinates1 = '${fparse kernel_radius}'
coordinates2 = '${fparse coordinates1+buffer_thickness}'
coordinates3 = '${fparse coordinates2+IPyC_thickness}'
coordinates4 = '${fparse coordinates3+SiC_thickness}'
coordinates5 = '${fparse coordinates4+OPyC_thickness}'
[GlobalParams]
order = FIRST
family = LAGRANGE
displacements = 'disp_x'
initial_enrichment = 0.14029 # [wt-]
flux_conversion_factor = 1.0 # convert E>0.10 to E>0.18 MeV
stress_free_temperature = 481 # used for thermal expansion
energy_per_fission = 3.204e-11 # [J/fission]
O_U = 1.428 # Initial Oxygen to Uranium atom ratio
C_U = 0.392 # Initial Carbon to Uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
mesh_density = '5 3 0 5 3 4'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = OPyC_outer_boundary
outer_SiC = SiC_outer_boundary
outer_IPyC = IPyC_outer_boundary
inner_IPyC = IPyC_inner_boundary
outer_buffer = buffer_outer_boundary
outer_kernel = fuel_outer_boundary
include_particle = true
include_pebble = false
IPyC_thickness_mean = 40.4e-6
SiC_thickness_mean = 35.2e-6
OPyC_thickness_mean = 43.4e-6
[]
[]
[Variables]
[temperature]
initial_condition = 900
[]
[]
[AuxVariables]
[fission_rate]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_flux]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[fission_rate]
type = ConstantFunction
value = 5.75e19
[]
[high_fidelity_strength_crackedIPyC]
type = ConstantFunction
value = '1363350801.3058'
[]
[stress_correlation_crackedIPyC]
type = TRISOStressCorrelationFunction
triso_geometry = particle_geometry
polynomial_coefficients_IPyC = '1 7017 -2.368e8'
polynomial_coefficients_SiC = '1 1.492e4 -3.802e7'
polynomial_coefficients_OPyC = '1 -1.273e4 1.849e8'
correlation_factor = -1.1824630660785265
[]
[high_fidelity_strength_asphericity]
type = ConstantFunction
value = '1086690814.283'
[]
[stress_correlation_asphericity]
type = TRISOStressCorrelationFunction
triso_geometry = particle_geometry
polynomial_coefficients_IPyC = '1 -2070 3.458e7'
polynomial_coefficients_SiC = '1 -868.9 -1.368e7'
polynomial_coefficients_OPyC = '1 1734 -1.988e7'
correlation_factor = 1.0626986695756293
[]
[stress_change_correlation_asphericity]
type = TRISOStressCorrelationFunction
triso_geometry = particle_geometry
polynomial_coefficients_IPyC = '1 -856 1.593e7'
polynomial_coefficients_SiC = '1 1774 -5.253e7'
polynomial_coefficients_OPyC = '1 456.4 -1.459e7'
correlation_factor = 1.0113764663823708
[]
[]
[Physics/SolidMechanics/QuasiStatic]
generate_output = 'stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz max_principal_stress'
add_variables = true
strain = FINITE
incremental = true
[fuel]
block = fuel
eigenstrain_names = 'UCO_swelling_eigenstrain UCO_TE_strain'
extra_vector_tags = 'ref'
[]
[buffer]
block = buffer
eigenstrain_names = 'Buffer_IIDC_strain Buffer_TE_strain'
extra_vector_tags = 'ref'
[]
[IPyC]
block = IPyC
eigenstrain_names = 'IPyC_IIDC_strain IPyC_TE_strain'
extra_vector_tags = 'ref'
[]
[SiC]
block = SiC
eigenstrain_names = 'SiC_thermal_eigenstrain'
extra_vector_tags = 'ref'
[]
[OPyC]
block = OPyC
eigenstrain_names = 'OPyC_IIDC_strain OPyC_TE_strain'
extra_vector_tags = 'ref'
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[fissionrate]
type = MaterialRealAux
variable = fission_rate
property = fission_rate
block = fuel
execute_on = timestep_begin
[]
[burnup]
type = MaterialRealAux
variable = burnup
property = burnup
block = fuel
execute_on = timestep_begin
[]
[fast_neutron_flux]
type = MaterialRealAux
variable = fast_neutron_flux
property = fast_neutron_flux
execute_on = timestep_begin
[]
[fast_neutron_fluence]
type = MaterialRealAux
variable = fast_neutron_fluence
property = fast_neutron_fluence
execute_on = timestep_begin
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
initial_moles = initial_moles
gas_released = 'fis_gas_released'
released_gas_types = 'Kr Xe'
released_fractions = '0.185 0.815'
tangential_tolerance = 1e-6
quadrature = false
min_gap = 1e-7
max_gap = 50e-6
gap_geometry_type = sphere
[]
[]
[BCs]
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[freesurf_temp]
type = DirichletBC
variable = temperature
value = 900
boundary = exterior
[]
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure]
[plenumPressure]
boundary = buffer_IPyC_boundary
startup_time = 1e4
initial_pressure = 0
output_initial_moles = initial_moles
temperature = ave_gas_temp
volume = 'gap_volume buffer_void_volume kernel_void_volume'
material_input = 'fis_gas_released'
output = gas_pressure
[]
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
block = fuel
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 6.2425e+17
[]
[UCO_burnup]
type = TRISOBurnup
initial_density = 10966
block = fuel
[]
[UCO_thermal]
type = UCOThermal
block = fuel
temperature = temperature
[]
[UCO_elasticity_tensor]
type = UCOElasticityTensor
block = fuel
temperature = temperature
[]
[UCO_stress]
type = ComputeFiniteStrainElasticStress
block = fuel
[]
[UCO_VolumetricSwellingEigenstrain]
type = UCOVolumetricSwellingEigenstrain
block = fuel
eigenstrain_name = UCO_swelling_eigenstrain
[]
[fuel_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10.0e-6
temperature = temperature
eigenstrain_name = UCO_TE_strain
[]
[UCO_density]
type = StrainAdjustedDensity
block = fuel
strain_free_density = 10966
[]
[fission_gas_release]
type = UCOFGR
block = fuel
average_grain_radius = 10e-6
temperature = temperature
triso_geometry = particle_geometry
cutoff_neutron_flux = 0.0
[]
[BAF_IPyC]
type = BaconAnisotropyFactor
initial_BAF = 1.0465
block = IPyC
[]
[BAF_OPyC]
type = BaconAnisotropyFactor
initial_BAF = 1.0429
block = OPyC
[]
[buffer_elasticity_tensor]
type = BufferElasticityTensor
block = buffer
temperature = temperature
[]
[buffer_stress]
type = BufferCEGACreep
block = buffer
temperature = temperature
[]
[buffer_thermal]
type = BufferThermal
block = buffer
initial_density = 1050.0
[]
[buffer_density]
type = StrainAdjustedDensity
block = buffer
strain_free_density = 1050.0
[]
[buffer_TE]
type = BufferThermalExpansionEigenstrain
block = buffer
eigenstrain_name = Buffer_TE_strain
temperature = temperature
[]
[buffer_IIDC]
type = BufferCEGAIrradiationEigenstrain
block = buffer
eigenstrain_name = Buffer_IIDC_strain
temperature = temperature
[]
[IPyC_elasticity_tensor]
type = PyCElasticityTensor
block = IPyC
temperature = temperature
[]
[IPyC_stress]
type = PyCCEGACreep
block = IPyC
creep_rate_scale_factor = 1
temperature = temperature
[]
[IPyC_thermal]
type = HeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_density]
type = GenericConstantMaterial
block = IPyC
prop_names = 'density'
prop_values = 1890
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'buffer IPyC OPyC'
[]
[IPyC_IIDC]
type = PyCCEGAIrradiationEigenstrain
block = IPyC
eigenstrain_name = IPyC_IIDC_strain
temperature = temperature
irradiation_eigenstrain_scale_factor = 1
[]
[IPyC_TE]
type = PyCThermalExpansionEigenstrain
block = IPyC
eigenstrain_name = IPyC_TE_strain
temperature = temperature
[]
[SiC_elasticity_tensor]
type = MonolithicSiCElasticityTensor
block = SiC
temperature = temperature
elastic_modulus_model = miller
[]
[SiC_stress]
type = ComputeFiniteStrainElasticStress
block = SiC
[]
[SiC_thermal]
type = MonolithicSiCThermal
block = SiC
temperature = temperature
thermal_conductivity_model = miller
[]
[SiC_density]
type = StrainAdjustedDensity
block = SiC
strain_free_density = 3200.0
[]
[SiC_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
temperature = temperature
eigenstrain_name = SiC_thermal_eigenstrain
[]
[OPyC_elasticity_tensor]
type = PyCElasticityTensor
block = OPyC
temperature = temperature
initial_BAF = 1.0
[]
[OPyC_stress]
type = PyCCEGACreep
block = OPyC
creep_rate_scale_factor = 1
temperature = temperature
[]
[OPyC_thermal_conductivity]
type = HeatConductionMaterial
block = OPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[OPyC_density]
type = GenericConstantMaterial
block = OPyC
prop_names = 'density'
prop_values = 1900
[]
[OPyC_IIDC]
type = PyCCEGAIrradiationEigenstrain
block = OPyC
eigenstrain_name = OPyC_IIDC_strain
temperature = temperature
irradiation_eigenstrain_scale_factor = 1
[]
[OPyC_TE]
type = PyCThermalExpansionEigenstrain
block = OPyC
eigenstrain_name = OPyC_TE_strain
temperature = temperature
[]
[characteristic_strength_SiC]
type = GenericConstantMaterial
prop_values = '9640000'
block = SiC
prop_names = 'characteristic_strength'
[]
[characteristic_strength_PyC]
type = PyCCharacteristicStrength
temperature = temperature
X = 1.02
block = 'IPyC OPyC'
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temperature
max_increment = 100
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-8
nl_max_its = 20
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 4.831315e7
dtmin = 1e-4
dt = 5e5
[]
[Postprocessors]
[ave_gas_temp]
type = ElementAverageValue
block = buffer
variable = temperature
execute_on = 'initial timestep_end'
[]
[fis_gas_released]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_released
block = fuel
use_displaced_mesh = false
execute_on = 'initial timestep_end'
[]
[gap_volume]
type = InternalVolume
boundary = buffer_IPyC_boundary
execute_on = 'initial linear'
use_displaced_mesh = true
[]
[buffer_void_volume]
type = VoidVolume
block = buffer
theoretical_density = 2250
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[kernel_th_density]
type = UCOTheoreticalDensity
execute_on = initial
[]
[kernel_void_volume]
type = VoidVolume
block = fuel
theoretical_density = kernel_th_density
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[particle_power]
type = ElementIntegralPower
variable = temperature
use_material_fission_rate = true
fission_rate_material = fission_rate
block = fuel
execute_on = 'initial timestep_end'
[]
[max_fluence]
type = ElementExtremeValue
variable = fast_neutron_fluence
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_burnup]
type = ElementExtremeValue
variable = burnup
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[SiC_stress]
type = ElementExtremeMaterialProperty
block = SiC
value_type = min
mat_prop = stress_yy
[]
[weibull_failure_probability_IPyC]
type = WeibullFailureProbability
block = IPyC
weibull_modulus = 9.5
characteristic_strength = characteristic_strength
[]
[weibull_failure_probability_SiC_crackedIPyC]
type = WeibullFailureProbabilityUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = stress_yy
high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
stress_correlation_function = 'stress_correlation_crackedIPyC'
[]
[weibull_failure_probability_SiC]
type = WeibullFailureProbabilityUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = stress_yy
high_fidelity_analysis_strength = 'high_fidelity_strength_asphericity'
stress_correlation_function = 'stress_correlation_asphericity'
stress_change_correlation_function = 'stress_change_correlation_asphericity'
[]
[]
[Outputs]
show = 'weibull_failure_probability_IPyC weibull_failure_probability_SiC weibull_failure_probability_SiC_crackedIPyC'
print_linear_residuals = false
time_step_interval = 1
csv = true
exodus = false
perf_graph = false
print_linear_converged_reason = false
print_nonlinear_converged_reason = false
[]
(assessment/verification/TRISO_diffusion/outofpile/outofpile.i)
#
# TRISO kernel in 1D spherical
#
# Out-of-pile, a decaying fission product
# -------------------------------
# Zero source, p=0
# Decaying fission product, decay_const/=0
# Non-zero initial concentration, C0/=0
#
timestep = 10
p = 0.0
C0 = 1.0
decay_const = 1e-5
Dprime = 1e-4
kernel_radius = 212.5e-6
[GlobalParams]
order = SECOND
family = LAGRANGE
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 ${kernel_radius}'
mesh_density = 100
block_names = 'fuel'
bias = 1
dual_bias = 0.8
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[conc]
initial_condition = '${C0}'
[]
[]
[Kernels]
[mass_dt]
type = TimeDerivative
variable = conc
[]
[mass]
type = MatDiffusion
variable = conc
diffusivity = diffusion_coef
extra_vector_tags = 'ref'
[]
[mass_source]
type = BodyForce
variable = conc
value = '${p}'
extra_vector_tags = 'ref'
[]
[decay]
type = Decay
variable = conc
radioactive_decay_constant = ${decay_const}
extra_vector_tags = 'ref'
[]
[]
[BCs]
[freesurf_conc]
type = DirichletBC
variable = conc
boundary = exterior
value = 0.0
[]
[]
[Materials]
[fuel_conc]
type = GenericConstantMaterial
block = fuel
prop_names = diffusion_coef
prop_values = '${fparse Dprime*kernel_radius^2}'
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-10
nl_abs_tol = 1e-20
nl_max_its = 20
l_tol = 1e-8
l_max_its = 30
start_time = 0.0
end_time = '${fparse 1/Dprime}'
num_steps = 100
dtmax = '${timestep}'
dtmin = '${timestep}'
[Predictor]
type = SimplePredictor
scale = 1.0
[]
[]
[Postprocessors]
[dt]
type = TimestepSize
execute_on = timestep_end
[]
# Release rate
[release_inc]
type = SideIntegralMassFlux
variable = conc
boundary = exterior
arrhenius_prpty_name = diffusion_coef
execute_on = 'initial timestep_end'
[]
[released]
type = TimeIntegratedPostprocessor
value = release_inc
execute_on = 'initial timestep_end'
[]
[total]
type = ElementIntegralVariablePostprocessor
variable = conc
execute_on = 'initial timestep_end'
[]
[x_released]
type = FractionalRelease
released = released
retained = retained
[]
[retained]
type = ElementIntegralVariablePostprocessor
variable = conc
[]
[conc_point_25]
type = PointValue
variable = conc
point = '${fparse 0.25*kernel_radius} 0 0'
execute_on = 'initial timestep_end'
[]
[conc_point_50]
type = PointValue
variable = conc
point = '${fparse 0.50*kernel_radius} 0 0'
execute_on = 'initial timestep_end'
[]
[conc_point_75]
type = PointValue
variable = conc
point = '${fparse 0.75*kernel_radius} 0 0'
execute_on = 'initial timestep_end'
[]
[conc_point_95]
type = PointValue
variable = conc
point = '${fparse 0.95*kernel_radius} 0 0'
execute_on = 'initial timestep_end'
[]
[bison_dimensionless_25]
type = ParsedPostprocessor
expression = 'conc_point_25 / C0'
pp_names = conc_point_25
constant_names = 'C0'
constant_expressions = '${C0}'
execute_on = 'initial timestep_end'
[]
[bison_dimensionless_50]
type = ParsedPostprocessor
expression = 'conc_point_50 / C0'
pp_names = conc_point_50
constant_names = 'C0'
constant_expressions = '${C0}'
execute_on = 'initial timestep_end'
[]
[bison_dimensionless_75]
type = ParsedPostprocessor
expression = 'conc_point_75 / C0'
pp_names = conc_point_75
constant_names = 'C0'
constant_expressions = '${C0}'
execute_on = 'initial timestep_end'
[]
[bison_dimensionless_95]
type = ParsedPostprocessor
expression = 'conc_point_95 / C0'
pp_names = conc_point_95
constant_names = 'C0'
constant_expressions = '${C0}'
execute_on = 'initial timestep_end'
[]
[analytic_dimensionless_25]
type = ParsedPostprocessor
# The analytic expression involves a sum we can't compute here
expression = '0.640190356'
pp_names = ''
execute_on = 'initial timestep_end'
[]
[analytic_dimensionless_50]
type = ParsedPostprocessor
# The analytic expression involves a sum we can't compute here
expression = '0.469766231'
pp_names = ''
execute_on = 'initial timestep_end'
[]
[analytic_dimensionless_75]
type = ParsedPostprocessor
# The analytic expression involves a sum we can't compute here
expression = '0.229613020'
pp_names = ''
execute_on = 'initial timestep_end'
[]
[analytic_dimensionless_95]
type = ParsedPostprocessor
# The analytic expression involves a sum we can't compute here
expression = '0.040674510'
pp_names = ''
execute_on = 'initial timestep_end'
[]
[error_25]
type = ParsedPostprocessor
pp_names = 'bison_dimensionless_25 analytic_dimensionless_25'
expression = '(bison_dimensionless_25 - analytic_dimensionless_25)/analytic_dimensionless_25*100'
execute_on = 'initial timestep_end'
[]
[error_50]
type = ParsedPostprocessor
pp_names = 'bison_dimensionless_50 analytic_dimensionless_50'
expression = '(bison_dimensionless_50 - analytic_dimensionless_50)/analytic_dimensionless_50*100'
execute_on = 'initial timestep_end'
[]
[error_75]
type = ParsedPostprocessor
pp_names = 'bison_dimensionless_75 analytic_dimensionless_75'
expression = '(bison_dimensionless_75 - analytic_dimensionless_75)/analytic_dimensionless_75*100'
execute_on = 'initial timestep_end'
[]
[error_95]
type = ParsedPostprocessor
pp_names = 'bison_dimensionless_95 analytic_dimensionless_95'
expression = '(bison_dimensionless_95 - analytic_dimensionless_95)/analytic_dimensionless_95*100'
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
time_step_interval = 1
exodus = false
print_linear_converged_reason = false
print_linear_residuals = false
print_nonlinear_converged_reason = false
[console]
type = Console
show = 'analytic_dimensionless_25 analytic_dimensionless_50 analytic_dimensionless_75 analytic_dimensionless_95
bison_dimensionless_25 bison_dimensionless_50 bison_dimensionless_75 bison_dimensionless_95
error_25 error_50 error_75 error_95 released x_released'
[]
[out]
type = CSV
execute_on = final
[]
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_11/case_11_1D.i)
#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# See also Hales, et al., Multidimensional multiphysics simulation of TRISO
# particle fuel, JNM, 443, 2013. https://doi.org/10.1016/j.jnucmat.2013.07.070
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark. The best way to do this is to compare
# results with information in the JNM article.
#
initial_fuel_density = 10810.0
[GlobalParams]
density = ${initial_fuel_density} # kg/m^3
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
mesh_density = '6 6 0 6 8 6'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Variables]
[disp_x]
[]
[temperature]
initial_condition = 1608.0
[]
[]
[Functions]
[radial_eigenstrain]
type = ParsedFunction
expression = 't*(4.52013e-4/6.0*t*t*t*t*t - 8.36313e-3/5.0*t*t*t*t + 5.67549e-2/4.0*t*t*t - 1.74247e-1/3.0*t*t + 2.62692e-1/2.0*t - 1.43234e-1)'
[]
[tangential_eigenstrain]
type = ParsedFunction
expression = 't*(1.30457e-4/4.0*t*t*t - 2.10029e-3/3.0*t*t + 9.07826e-3/2.0*t - 3.24737e-2)'
[]
[fission_rate]
type = ParsedFunction
expression = 1.1135e20 # units of fissions/m**3
[]
[k_function]
type = ParsedFunction
expression = '4.93e-29'
[]
[]
[AuxVariables]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = fuel
initial_condition = 0.0
[]
[fission_rate]
block = fuel
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[IPyC_OPyC]
block = 'IPyC OPyC'
strain = finite
eigenstrain_names = 'thermal_strain pyc_eigenstrain'
[]
[rest]
block = 'fuel buffer SiC'
strain = finite
eigenstrain_names = thermal_strain
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
[]
[heat]
type = HeatConduction
variable = temperature
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
energy_per_fission = 3.2e-11 # units of J/fission
fission_rate = fission_rate
[]
[]
[AuxKernels]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
execute_on = timestep_end
[]
[fission_rate]
type = FunctionAux
variable = fission_rate
block = fuel
function = fission_rate
[]
[burnup]
type = BurnupAux
variable = burnup
block = fuel
fission_rate = fission_rate
molecular_weight = 0.270 # units of kg/mole
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
penalty = 1e5
model = frictionless
formulation = kinematic
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
gas_released = 'fis_gas_released co_production' # coupling to postprocessors which supply the fission gas addition, co addition
released_fractions = '0.153 0.847;
1'
released_gas_types = 'Kr Xe;
CO'
tangential_tolerance = 1e-6
# contact_pressure_input = 10e6
# quadrature = true
[]
[]
[BCs]
# pin particle along symmetry planes
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
# fix temperature on free surface
[freesurf_temp]
type = DirichletBC
variable = temperature
boundary = exterior
value = 1608.0
[]
# exterior and internal pressures
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure] # apply gas pressure on buffer and IPyC boundaries
[plenumPressure]
boundary = buffer_IPyC_boundary
initial_pressure = 0
startup_time = 1.0e4
R = 8.3143
output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
volume = volumeGas # coupling to post processor to get gas volume
material_input = 'fis_gas_released co_production' # coupling to post processor to get fission gas added, co added
output = plenum_pressure # coupling to post processor to output plenum/gap pressure
[]
[]
[]
[Materials]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 2.37417e18 # n/m^2-sec
[]
[fission_gas_release]
type = UO2Sifgrs
block = fuel
temperature = temperature
fission_rate = fission_rate
grain_radius_const = 5.0e-6
[]
[stress]
type = ComputeFiniteStrainElasticStress
block = 'fuel buffer SiC'
[]
[PyC_stress]
type = PyCCreep
block = 'IPyC OPyC'
k = k_function
poissons_ratio = 0.4
temperature = temperature
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'IPyC OPyC'
[]
[PyC_eigenstrain]
type = PyCIrradiationEigenstrain
block = 'IPyC OPyC'
radial_eigenstrain_function = radial_eigenstrain
tangential_eigenstrain_function = tangential_eigenstrain
eigenstrain_name = pyc_eigenstrain
[]
[fuel_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10e-6
stress_free_temperature = 1608.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[PyC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = 'buffer IPyC OPyC'
thermal_expansion_coeff = 5.5e-6
stress_free_temperature = 1608.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[SiC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
stress_free_temperature = 1608.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[fuel_thermal]
type = UO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temperature
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[fuel_den]
type = StrainAdjustedDensity
block = fuel
strain_free_density = ${initial_fuel_density}
[]
[buffer_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[buffer_temperature]
type = HeatConductionMaterial
block = buffer
thermal_conductivity = 0.5 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[buffer_den]
type = StrainAdjustedDensity
strain_free_density = 1000 #kg/m^3
block = buffer
[]
[PyC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = 'IPyC OPyC'
youngs_modulus = 3.96e10
poissons_ratio = 0.33
[]
[PyC_temperature]
type = HeatConductionMaterial
block = 'IPyC OPyC'
thermal_conductivity = 4.0 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[PyC_den]
type = StrainAdjustedDensity
strain_free_density = 1880.0 # kg/m^3
block = 'IPyC OPyC'
[]
[SiC_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.7e11
poissons_ratio = 0.13
[]
[SiC_temperature]
type = HeatConductionMaterial
block = SiC
thermal_conductivity = 13.9 # J/m-s-K
specific_heat = 620.0 # J/kg-K
[]
[SiC_den]
type = StrainAdjustedDensity
strain_free_density = 3200.0 # kg/m^3
block = SiC
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Dampers]
[temperature]
type = MaxIncrement
variable = temperature
max_increment = 50
[]
[]
[Debug]
show_var_residual_norms = true
[]
[Executioner]
type = Transient
petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
petsc_options_value = '201 hypre boomeramg 4'
line_search = 'none'
solve_type = 'PJFNK'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-10
nl_max_its = 15
l_tol = 1e-3
l_max_its = 50
start_time = 0.0
end_time = 3.032e7
dtmax = 2e5
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 20
optimal_iterations = 6
iteration_window = 2
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[burnup]
type = ElementExtremeValue
block = fuel
variable = burnup
[]
[fis_gas_produced]
type = ElementIntegralFisGasGeneratedSifgrs
block = fuel
[]
[fis_gas_released]
type = ElementIntegralFisGasReleasedSifgrs
block = fuel
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
[]
[volumeFuel]
type = InternalVolume
boundary = fuel_outer_boundary
[]
[volumeGas]
type = InternalVolume
boundary = 'fuel_outer_boundary IPyC_inner_boundary'
addition = -5.53e-11
execute_on = 'initial timestep_end'
[]
[volumeBufferShell]
type = InternalVolume
boundary = buffer_IPyC_boundary
[]
[ave_temp_interior]
type = SideAverageValue
boundary = buffer_IPyC_boundary
variable = temperature
execute_on = 'initial timestep_end'
[]
# Postprocessors for CO production
[total_fission_rate]
type = ElementIntegralPower
variable = temperature
fission_rate = fission_rate
block = fuel
energy_per_fission = 1.0
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
[]
[avg_surface_temp]
type = SideAverageValue
variable = temperature
boundary = exterior
[]
[time_int_surf_temp]
type = TimeIntegratedPostprocessor
value = avg_surface_temp
[]
[co_production]
type = CarbonMonoxideProduction
total_fissions = total_fissions
time_integrated_triso_temperature = time_int_surf_temp
initial_enrichment = 0.14029
[]
[tang_SiC]
type = ElementalVariableValue
variable = stress_yy
elementid = 18
[]
[]
[PerformanceMetricOutputs]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
exodus = true
csv = true
perf_graph = true
[]
(test/tests/void_volume/ad_void_volume.i)
# This tests VoidVolume and UCOTheoreticalDensity.
#
# VoidVolume computes the integral of 1 - rho / rho_th
# where rho is density and rho_th is theoretical density.
#
# UCOTheoreticalDensity reports the theoretical density
# of UCO as computed by a utility function.
#
# In this test, the initial geometry has a volume of 0.1.
# Displacements are applied which change the volume to
# 0.2. This volume change must be void volume.
# Therefore, the final void volume should be 0.1 higher
# than the initial void volume. This is exactly what
# is computed.
[GlobalParams]
displacements = 'disp_x'
initial_enrichment = 0.1955 # [wt-]
O_U = 1.5 # Initial Oxygen to Uranium atom ratio
C_U = 0.4 # Initial Carbon to Uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE2
coordinates = '0 0.28794119114848615'
mesh_density = '4'
block_names = 'fuel'
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[fuel]
block = fuel
add_variables = true
strain = SMALL
use_automatic_differentiation = true
[]
[]
[BCs]
[no_x]
type = ADDirichletBC
variable = disp_x
boundary = fuel_inner_boundary
value = 0.0
[]
[pull]
type = ADDirichletBC
variable = disp_x
boundary = fuel_outer_boundary
value = 0.07484197671129483
[]
[]
[Materials]
[elastic]
type = ADComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 1
poissons_ratio = 0.0
[]
[stress]
type = ADComputeLinearElasticStress
block = fuel
[]
[fuel_density]
type = ADStrainAdjustedDensity
block = fuel
strain_free_density = 10400.0
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
petsc_options_value = 'lu superlu_dist 51'
line_search = 'none'
l_tol = 1e-5
nl_rel_tol = 1e-10
nl_abs_tol = 1e-12
start_time = 0.0
end_time = 5.0e6
num_steps = 1
dt = 1
[]
[Postprocessors]
[volume]
type = InternalVolume
boundary = fuel_outer_boundary
scale_factor = -1
execute_on = 'initial timestep_end'
[]
[uco_theoretical_density]
type = UCOTheoreticalDensity
execute_on = initial
[]
[void_volume]
type = ADVoidVolume
block = fuel
theoretical_density = uco_theoretical_density
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[]
[Outputs]
csv = true
[]
(test/tests/triso_failure/ad_triso_1d_ipyc_weibull_probability.i)
kernel_radius = 213.35e-6
buffer_thickness = 98.9e-6
IPyC_thickness = 40.4e-6
SiC_thickness = 35.2e-6
OPyC_thickness = 43.4e-6
coordinates1 = '${fparse kernel_radius}'
coordinates2 = '${fparse coordinates1+buffer_thickness}'
coordinates3 = '${fparse coordinates2+IPyC_thickness}'
coordinates4 = '${fparse coordinates3+SiC_thickness}'
coordinates5 = '${fparse coordinates4+OPyC_thickness}'
[GlobalParams]
order = FIRST
family = LAGRANGE
displacements = 'disp_x'
initial_enrichment = 0.14029 # [wt-]
flux_conversion_factor = 1.0 # convert E>0.10 to E>0.18 MeV
stress_free_temperature = 481 # used for thermal expansion
energy_per_fission = 3.204e-11 # [J/fission]
O_U = 1.428 # Initial Oxygen to Uranium atom ratio
C_U = 0.392 # Initial Carbon to Uranium atom ratio
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
mesh_density = '5 3 0 5 3 4'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_OPyC = OPyC_outer_boundary
outer_SiC = SiC_outer_boundary
outer_IPyC = IPyC_outer_boundary
inner_IPyC = IPyC_inner_boundary
outer_buffer = buffer_outer_boundary
outer_kernel = fuel_outer_boundary
include_particle = true
include_pebble = false
IPyC_thickness_mean = 40.4e-6
SiC_thickness_mean = 35.2e-6
OPyC_thickness_mean = 43.4e-6
[]
[]
[Variables]
[temperature]
initial_condition = 900
[]
[]
[AuxVariables]
[fission_rate]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_flux]
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[fission_rate]
type = ConstantFunction
value = 5.75e19
[]
[high_fidelity_strength_crackedIPyC]
type = ConstantFunction
value = '1363350801.3058'
[]
[stress_correlation_crackedIPyC]
type = TRISOStressCorrelationFunction
triso_geometry = particle_geometry
polynomial_coefficients_IPyC = '1 7017 -2.368e8'
polynomial_coefficients_SiC = '1 1.492e4 -3.802e7'
polynomial_coefficients_OPyC = '1 -1.273e4 1.849e8'
correlation_factor = -1.1824630660785265
[]
[high_fidelity_strength_asphericity]
type = ConstantFunction
value = '1086690814.283'
[]
[stress_correlation_asphericity]
type = TRISOStressCorrelationFunction
triso_geometry = particle_geometry
polynomial_coefficients_IPyC = '1 -2070 3.458e7'
polynomial_coefficients_SiC = '1 -868.9 -1.368e7'
polynomial_coefficients_OPyC = '1 1734 -1.988e7'
correlation_factor = 1.0626986695756293
[]
[stress_change_correlation_asphericity]
type = TRISOStressCorrelationFunction
triso_geometry = particle_geometry
polynomial_coefficients_IPyC = '1 -856 1.593e7'
polynomial_coefficients_SiC = '1 1774 -5.253e7'
polynomial_coefficients_OPyC = '1 456.4 -1.459e7'
correlation_factor = 1.0113764663823708
[]
[]
[Physics/SolidMechanics/QuasiStatic]
generate_output = 'stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz max_principal_stress'
add_variables = true
strain = FINITE
incremental = true
[fuel]
block = fuel
eigenstrain_names = 'UCO_swelling_eigenstrain UCO_TE_strain'
extra_vector_tags = 'ref'
use_automatic_differentiation = true
[]
[buffer]
block = buffer
eigenstrain_names = 'Buffer_IIDC_strain Buffer_TE_strain'
extra_vector_tags = 'ref'
use_automatic_differentiation = true
[]
[IPyC]
block = IPyC
eigenstrain_names = 'IPyC_IIDC_strain IPyC_TE_strain'
extra_vector_tags = 'ref'
use_automatic_differentiation = true
[]
[SiC]
block = SiC
eigenstrain_names = 'SiC_thermal_eigenstrain'
extra_vector_tags = 'ref'
use_automatic_differentiation = true
[]
[OPyC]
block = OPyC
eigenstrain_names = 'OPyC_IIDC_strain OPyC_TE_strain'
extra_vector_tags = 'ref'
use_automatic_differentiation = true
[]
[]
[Kernels]
[heat_ie]
type = ADHeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = ADHeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = ADNeutronHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[fissionrate]
type = ADMaterialRealAux
variable = fission_rate
property = fission_rate
block = fuel
execute_on = timestep_begin
[]
[burnup]
type = ADMaterialRealAux
variable = burnup
property = burnup
block = fuel
execute_on = timestep_begin
[]
[fast_neutron_flux]
type = ADMaterialRealAux
variable = fast_neutron_flux
property = fast_neutron_flux
execute_on = timestep_begin
[]
[fast_neutron_fluence]
type = ADMaterialRealAux
variable = fast_neutron_fluence
property = fast_neutron_fluence
execute_on = timestep_begin
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = IPyC_inner_boundary
secondary = buffer_outer_boundary
initial_moles = initial_moles
gas_released = 'fis_gas_released'
released_gas_types = 'Kr Xe'
released_fractions = '0.185 0.815'
tangential_tolerance = 1e-6
quadrature = false
min_gap = 1e-7
max_gap = 50e-6
gap_geometry_type = sphere
use_automatic_differentiation = true
[]
[]
[BCs]
[no_disp_x]
type = ADDirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
[freesurf_temp]
type = ADDirichletBC
variable = temperature
value = 900
boundary = exterior
[]
[exterior_pressure_x]
type = ADPressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure]
[plenumPressure]
boundary = buffer_IPyC_boundary
startup_time = 1e4
initial_pressure = 0
output_initial_moles = initial_moles
temperature = ave_gas_temp
volume = 'gap_volume buffer_void_volume kernel_void_volume'
material_input = 'fis_gas_released'
output = gas_pressure
use_automatic_differentiation = true
[]
[]
[]
[Materials]
[fission_rate]
type = ADGenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
block = fuel
[]
[fast_neutron_flux]
type = ADFastNeutronFlux
calculate_fluence = true
factor = 6.2425e+17
[]
[UCO_burnup]
type = ADTRISOBurnup
initial_density = 10966
block = fuel
[]
[UCO_thermal]
type = ADUCOThermal
block = fuel
temperature = temperature
[]
[UCO_elasticity_tensor]
type = ADUCOElasticityTensor
block = fuel
temperature = temperature
[]
[UCO_stress]
type = ADComputeFiniteStrainElasticStress
block = fuel
[]
[UCO_VolumetricSwellingEigenstrain]
type = ADUCOVolumetricSwellingEigenstrain
block = fuel
eigenstrain_name = UCO_swelling_eigenstrain
[]
[fuel_thermal_expansion]
type = ADComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10.0e-6
temperature = temperature
eigenstrain_name = UCO_TE_strain
[]
[UCO_density]
type = ADStrainAdjustedDensity
block = fuel
strain_free_density = 10966
[]
[fission_gas_release]
type = ADUCOFGR
block = fuel
average_grain_radius = 10e-6
temperature = temperature
triso_geometry = particle_geometry
cutoff_neutron_flux = 0.0
[]
[BAF_IPyC]
type = ADBaconAnisotropyFactor
initial_BAF = 1.0465
block = IPyC
[]
[BAF_OPyC]
type = ADBaconAnisotropyFactor
initial_BAF = 1.0429
block = OPyC
[]
[buffer_elasticity_tensor]
type = ADBufferElasticityTensor
block = buffer
temperature = temperature
[]
[buffer_stress]
type = ADBufferCEGACreep
block = buffer
temperature = temperature
[]
[buffer_thermal]
type = ADBufferThermal
block = buffer
initial_density = 1050.0
[]
[buffer_density]
type = ADStrainAdjustedDensity
block = buffer
strain_free_density = 1050.0
[]
[buffer_TE]
type = ADBufferThermalExpansionEigenstrain
block = buffer
eigenstrain_name = Buffer_TE_strain
temperature = temperature
[]
[buffer_IIDC]
type = ADBufferCEGAIrradiationEigenstrain
block = buffer
eigenstrain_name = Buffer_IIDC_strain
temperature = temperature
[]
[IPyC_elasticity_tensor]
type = ADPyCElasticityTensor
block = IPyC
temperature = temperature
[]
[IPyC_stress]
type = ADPyCCEGACreep
block = IPyC
creep_rate_scale_factor = 1
temperature = temperature
[]
[IPyC_thermal]
type = ADHeatConductionMaterial
block = IPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_density]
type = ADGenericConstantMaterial
block = IPyC
prop_names = 'density'
prop_values = 1890
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'buffer IPyC OPyC'
[]
[IPyC_IIDC]
type = ADPyCCEGAIrradiationEigenstrain
block = IPyC
eigenstrain_name = IPyC_IIDC_strain
temperature = temperature
irradiation_eigenstrain_scale_factor = 1
[]
[IPyC_TE]
type = ADPyCThermalExpansionEigenstrain
block = IPyC
eigenstrain_name = IPyC_TE_strain
temperature = temperature
[]
[SiC_elasticity_tensor]
type = ADMonolithicSiCElasticityTensor
block = SiC
temperature = temperature
elastic_modulus_model = miller
[]
[SiC_stress]
type = ADComputeFiniteStrainElasticStress
block = SiC
[]
[SiC_thermal]
type = ADMonolithicSiCThermal
block = SiC
temperature = temperature
thermal_conductivity_model = miller
[]
[SiC_density]
type = ADStrainAdjustedDensity
block = SiC
strain_free_density = 3200.0
[]
[SiC_thermal_expansion]
type = ADComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
temperature = temperature
eigenstrain_name = SiC_thermal_eigenstrain
[]
[OPyC_elasticity_tensor]
type = ADPyCElasticityTensor
block = OPyC
temperature = temperature
initial_BAF = 1.0
[]
[OPyC_stress]
type = ADPyCCEGACreep
block = OPyC
creep_rate_scale_factor = 1
temperature = temperature
[]
[OPyC_thermal_conductivity]
type = ADHeatConductionMaterial
block = OPyC
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[OPyC_density]
type = ADGenericConstantMaterial
block = OPyC
prop_names = 'density'
prop_values = 1900
[]
[OPyC_IIDC]
type = ADPyCCEGAIrradiationEigenstrain
block = OPyC
eigenstrain_name = OPyC_IIDC_strain
temperature = temperature
irradiation_eigenstrain_scale_factor = 1
[]
[OPyC_TE]
type = ADPyCThermalExpansionEigenstrain
block = OPyC
eigenstrain_name = OPyC_TE_strain
temperature = temperature
[]
[characteristic_strength_SiC]
type = ADGenericConstantMaterial
prop_values = '9640000'
block = SiC
prop_names = 'characteristic_strength'
[]
[characteristic_strength_PyC]
type = ADPyCCharacteristicStrength
temperature = temperature
X = 1.02
block = 'IPyC OPyC'
[]
[]
[Dampers]
[temp]
type = MaxIncrement
variable = temperature
max_increment = 100
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 5e-6
nl_abs_tol = 1e-8
nl_max_its = 20
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 4.831315e7
dtmin = 1e-4
dt = 5e5
[]
[Postprocessors]
[ave_gas_temp]
type = ElementAverageValue
block = buffer
variable = temperature
execute_on = 'initial timestep_end'
[]
[fis_gas_released]
type = ADElementIntegralMaterialProperty
mat_prop = fis_gas_released
block = fuel
use_displaced_mesh = false
execute_on = 'initial timestep_end'
[]
[gap_volume]
type = InternalVolume
boundary = buffer_IPyC_boundary
execute_on = 'initial linear'
use_displaced_mesh = true
[]
[buffer_void_volume]
type = ADVoidVolume
block = buffer
theoretical_density = 2250
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[kernel_th_density]
type = UCOTheoreticalDensity
execute_on = initial
[]
[kernel_void_volume]
type = ADVoidVolume
block = fuel
theoretical_density = kernel_th_density
execute_on = 'initial timestep_end'
use_displaced_mesh = true
[]
[particle_power]
type = ADElementIntegralPower
variable = temperature
use_material_fission_rate = true
fission_rate_material = fission_rate
block = fuel
execute_on = 'initial timestep_end'
[]
[max_fluence]
type = ElementExtremeValue
variable = fast_neutron_fluence
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[max_burnup]
type = ElementExtremeValue
variable = burnup
block = fuel
value_type = 'max'
execute_on = 'initial timestep_end'
[]
[SiC_stress]
type = ADElementExtremeMaterialProperty
block = SiC
value_type = min
mat_prop = stress_yy
[]
[weibull_failure_probability_IPyC]
type = ADWeibullFailureProbability
block = IPyC
weibull_modulus = 9.5
characteristic_strength = characteristic_strength
[]
[weibull_failure_probability_SiC_crackedIPyC]
type = ADWeibullFailureProbabilityUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = stress_yy
high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
stress_correlation_function = 'stress_correlation_crackedIPyC'
[]
[weibull_failure_probability_SiC]
type = ADWeibullFailureProbabilityUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = stress_yy
high_fidelity_analysis_strength = 'high_fidelity_strength_asphericity'
stress_correlation_function = 'stress_correlation_asphericity'
stress_change_correlation_function = 'stress_change_correlation_asphericity'
[]
[]
[Outputs]
show = 'weibull_failure_probability_IPyC weibull_failure_probability_SiC weibull_failure_probability_SiC_crackedIPyC'
print_linear_residuals = false
time_step_interval = 1
csv = true
exodus = false
perf_graph = false
print_linear_converged_reason = false
print_nonlinear_converged_reason = false
[]
(test/tests/triso_pebble/1D_pebble.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
flux_conversion_factor = 0.85
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 0.0138 0.018 0.02'
mesh_density = '5 10 10'
block_names = 'core fuel shell'
[]
[]
[Distributions]
[normal_kernel_r]
type = TruncatedNormal
mean = 213.35e-6
standard_deviation = 4.4e-6
lower_bound = 1.9575e-04
upper_bound = 2.3095e-04
[]
[normal_buffer_t]
type = TruncatedNormal
mean = 98.9e-6
standard_deviation = 8.4e-6
lower_bound = 6.53e-05
upper_bound = 1.325e-04
[]
[normal_ipyc_t]
type = TruncatedNormal
mean = 40.4e-6
standard_deviation = 2.5e-6
lower_bound = 3.0400e-05
upper_bound = 5.0400e-05
[]
[normal_sic_t]
type = TruncatedNormal
mean = 35.2e-6
standard_deviation = 1.2e-6
lower_bound = 3.0400e-05
upper_bound = 4.0000e-05
[]
[normal_opyc_t]
type = TruncatedNormal
mean = 43.4e-6
standard_deviation = 2.9e-6
lower_bound = 3.1800e-05
upper_bound = 5.5000e-05
[]
[]
[Samplers]
[sample]
type = MonteCarlo
num_rows = 10
distributions = 'normal_kernel_r normal_buffer_t normal_ipyc_t normal_sic_t normal_opyc_t'
execute_on = 'PRE_MULTIAPP_SETUP'
[]
[]
[MultiApps]
[sub]
type = SamplerTransientMultiApp
input_files = triso_1d.i
sampler = sample
execute_on = 'TIMESTEP_BEGIN'
mode = normal
[]
[]
[DiracKernels]
[vpp_point_source]
type = TRISOMonteCarloPointSource
variable = temperature
point_source_values = released_heat_inc
value_name = released_heat_inc:released_heat_inc
point_source_location = point_source_location
[]
[]
[UserObjects]
[point_source_location]
type = TRISOMonteCarloPointSourceLocation
min_radius = 0.0138
max_radius = 0.018
geometry = SPHERE
sampler = sample
fuel_element_blocks = fuel
execute_on = 'INITIAL'
[]
[]
[Transfers]
[released_heat_inc]
type = SamplerPostprocessorTransfer
from_multi_app = sub
sampler = sample
to_vector_postprocessor = released_heat_inc
from_postprocessor = released_heat_inc
[]
[sub_temp_bc]
type = SamplerPostprocessorTransfer
from_multi_app = sub
sampler = sample
to_vector_postprocessor = temp_bc
from_postprocessor = aver_temp_exterior
[]
[temp_bc]
type = MultiAppVectorPostprocessorTransfer
to_multi_app = sub
vector_postprocessor = sample_points
postprocessor = temp_bc
vector_name = temperature
[]
[]
[Controls]
[cmdline]
type = MultiAppSamplerControl
multi_app = sub
sampler = sample
param_names = 'kernel_radius buffer_thickness IPyC_thickness SiC_thickness OPyC_thickness'
[]
[]
[VectorPostprocessors]
[sample_points]
type = TRISOMonteCarloPointValueSampler
variable = temperature
execute_on = 'INITIAL TIMESTEP_BEGIN'
point_source_location = point_source_location
[]
[sampler_data]
type = SamplerData
execute_on = 'TIMESTEP_BEGIN'
sampler = sample
[]
[released_heat_inc]
type = StochasticResults
execute_on = 'TIMESTEP_BEGIN'
[]
[temp_bc]
type = StochasticResults
execute_on = 'INITIAL TIMESTEP_BEGIN'
[]
[point_source_output]
type = TRISOMonteCarloPointSourceOutput
vector_postprocessor = released_heat_inc
value_name = released_heat_inc:released_heat_inc
point_source_location = point_source_location
[]
[temp_bc_output]
type = TRISOMonteCarloPointSourceOutput
vector_postprocessor = temp_bc
value_name = sub_temp_bc:aver_temp_exterior
point_source_location = point_source_location
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[temperature]
initial_condition = 773.15
[]
[]
[AuxVariables]
[density]
order = CONSTANT
family = MONOMIAL
[]
[thermal_conductivity]
order = CONSTANT
family = MONOMIAL
[]
[specific_heat]
order = CONSTANT
family = MONOMIAL
[]
[]
[Kernels]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = FissionRateHeatSource
variable = temperature
block = fuel
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[]
[AuxKernels]
[density]
type = MaterialRealAux
variable = density
property = density
block = 'core fuel shell'
execute_on = 'initial linear'
[]
[thermal_conductivity]
type = MaterialRealAux
variable = thermal_conductivity
property = thermal_conductivity
block = 'core fuel shell'
execute_on = timestep_end
[]
[specific_heat]
type = MaterialRealAux
variable = specific_heat
property = specific_heat
block = 'core fuel shell'
execute_on = timestep_end
[]
[]
[BCs]
[coolant_temp]
type = DirichletBC
variable = temperature
boundary = exterior
value = 773.15
[]
[]
[Functions]
[power_history]
type = PiecewiseLinear
x = '0 76e6'
y = '1 1'
[]
[fission_rate]
type = LinearCombinationFunction
functions = power_history
w = 5.75e19
[]
[]
[UserObjects]
[particle_geometry]
type = TRISOGeometry
outer_core = core_outer_boundary
outer_fueled_region = fuel_outer_boundary
outer_shell = shell_outer_boundary
include_particle = false
include_pebble = true
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[fast_neutron_flux]
type = FastNeutronFlux
calculate_fluence = true
flux_function = power_history
factor = 6.28e17
[]
[fueled_region_thermal]
type = GraphiteMatrixThermal
block = fuel
graphite_grade = A3_27_1800
packing_fraction = 0.22
temperature = temperature
initial_matrix_density = 1750.0
[]
[fuel_region_density]
type = ParsedMaterial
block = fuel
property_name = density
expression = 1750.0
[]
[shell_region_thermal]
type = GraphiteMatrixThermal
block = shell
graphite_grade = A3_27_1800
packing_fraction = 0.0
temperature = temperature
initial_matrix_density = 1750.0
[]
[shell_region_density]
type = ParsedMaterial
block = shell
property_name = density
expression = 1750.0
[]
[core_region_thermal]
type = GraphiteMatrixThermal
block = core
graphite_grade = A3_27_1800
packing_fraction = 0.0
temperature = temperature
initial_matrix_density = 1400.0
[]
[core_region_density]
type = ParsedMaterial
block = core
property_name = density
expression = 1400.0
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'temperature'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-12
nl_abs_tol = 1e-12
nl_max_its = 15
l_tol = 1e-5
l_max_its = 30
start_time = 0.0
dt = 20000
num_steps = 2
[]
[Outputs]
exodus = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/diffusion/case_3a/case_3a.i)
[GlobalParams]
order = SECOND
family = LAGRANGE
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DMeshGenerator
elem_type = EDGE3
coordinates = '0 250e-6 350e-6 390e-6 425e-6 465e-6'
mesh_density = '50 30 15 15 15'
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Problem]
[]
[Variables]
[conc_Cs]
[]
[]
[ICs]
[conc_Cs]
type = ConstantIC
block = fuel
value = 1
variable = conc_Cs
[]
[]
[AuxVariables]
[temperature]
initial_condition = 1873.15
[]
[Cs_diff_coef]
order = CONSTANT
family = MONOMIAL
[]
[]
[Kernels]
[mass_Cs_dt]
type = TimeDerivative
variable = conc_Cs
[]
[mass_Cs]
type = ArrheniusDiffusion
variable = conc_Cs
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
temperature = temperature
[]
[]
[AuxKernels]
[Cs_diff_coef]
type = MaterialRealAux
variable = Cs_diff_coef
property = arrhenius_diffusion_coef_Cs
execute_on = timestep_end
[]
[]
[BCs]
[freesurf_conc_Cs]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
[]
[Materials]
[fuel_conc_Cs]
type = ArrheniusDiffusionCoef
block = fuel
d1 = 5.6e-8 # m^2/s
q1 = 209e3 # J/mol
d2 = 5.2e-4
q2 = 362e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[buffer_conc_Cs]
type = ArrheniusDiffusionCoef
block = buffer
d1 = 1e-8 # m^2/s
q1 = 0 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[IPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = IPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[SiC_conc_Cs]
type = ArrheniusDiffusionCoef
block = SiC
# 5.5e-14*exp(2/5) = 8.2e-14
d1 = 8.2e-14 # m^2/s
q1 = 125e3 # J/mol
d2 = 1.6e-2
q2 = 514e3
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[OPyC_conc_Cs]
type = ArrheniusDiffusionCoef
block = OPyC
d1 = 6.3e-8 # m^2/s
q1 = 222e3 # J/mol
temperature = temperature
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
[]
[]
[Debug]
show_var_residual_norms = true
show_var_residual = 'conc_Cs'
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
nl_rel_tol = 1e-6
nl_abs_tol = 1e-20
nl_max_its = 50
l_tol = 1e-4
l_max_its = 50
start_time = 0.0
end_time = 720000
num_steps = 700
dt = 1800
dtmax = 1800
dtmin = 1800
[]
[Postprocessors]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
execute_on = 'initial timestep_end'
[]
[released_Cs]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
execute_on = 'initial timestep_end'
[]
[total_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
execute_on = 'initial'
[]
[x_Cs_released]
type = FractionalRelease
released = released_Cs
total = total_Cs
[]
[retained_Cs]
type = ElementIntegralVariablePostprocessor
variable = conc_Cs
[]
[]
[Outputs]
perf_graph = true
print_linear_residuals = false
exodus = true
[console]
type = Console
time_step_interval = 1
[]
[out]
type = CSV
execute_on = final
[]
[]