- eigenstrain_nameMaterial property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
C++ Type:std::string
Controllable:No
Description:Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
PyCIrradiationEigenstrain
Computes irradiation-induced eigenstrains for pyrolytic carbon.
Description
pyrolytic carbon (PyC) experiences irradiation-induced strain which is a function of fluence. For low-density PyC, such as that used in the buffer layer of a TRISO fuel particle, the irradiation strain is given by Petti et al. (2004) as where is in units of and , the fluence, is in units of . Integrating to obtain the strain as a function of fluence,
For dense PyC, the irradiation strain differs in the radial and tangential directions (Petti et al., 2004) of a TRISO particle:
Example Input Syntax
[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
[PyC]
type = PyCIrradiationEigenstrain<<<{"description": "Computes irradiation-induced eigenstrains for pyrolytic carbon.", "href": "PyCIrradiationEigenstrain.html"}>>>
block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
pyc_type<<<{"description": "Type of PyC (buffer or dense)"}>>> = buffer
eigenstrain_name<<<{"description": "Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator."}>>> = irrad_strain
[]
[]Input Parameters
- base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
C++ Type:std::string
Controllable:No
Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
- blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
- boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
- computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
- constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
- declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
- disp_ppX0The reporting postprocessor for particle displacement x-axis
Default:0
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The reporting postprocessor for particle displacement x-axis
- disp_ppY0The reporting postprocessor for particle displacement y-axis
Default:0
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The reporting postprocessor for particle displacement y-axis
- disp_ppZ0The reporting postprocessor for particle displacement z-axis
Default:0
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The reporting postprocessor for particle displacement z-axis
- fast_neutron_fluencefast_neutron_fluenceFast neutron fluence
Default:fast_neutron_fluence
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Fast neutron fluence
- particle_center0 0 0Center of particle
Default:0 0 0
C++ Type:libMesh::Point
Controllable:No
Description:Center of particle
- pyc_typebufferType of PyC (buffer or dense)
Default:buffer
C++ Type:MooseEnum
Options:buffer, dense
Controllable:No
Description:Type of PyC (buffer or dense)
- radial_eigenstrain_functionRadial eigenstrain as a function of fluence (in place of time)
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Radial eigenstrain as a function of fluence (in place of time)
- tangential_eigenstrain_functionTangential eigenstrain a function of temperature (in place of time)
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Tangential eigenstrain a function of temperature (in place of time)
Optional Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
- enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
- implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
- seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
- use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Advanced Parameters
- output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
- outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object
Outputs Parameters
- prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
- use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Material Property Retrieval Parameters
Input Files
- (test/tests/triso_failure/triso_1d_failure_error.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_9/case_9_1D.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_13/case_13_1D.i)
- (test/tests/triso_failure/triso_ipyc_characteristic_strength.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_7/case_7_1D.i)
- (examples/TRISO/accident_simulation/triso2D_accident.i)
- (test/tests/triso/base_irradiation/triso1D_accident.i)
- (test/tests/triso_failure/ad_ipyc_characteristic_strength.i)
- (test/tests/triso_failure/triso_1d_ipyc_failure.i)
- (test/tests/triso_failure/triso_1d_layer_stress_strength.i)
- (examples/TRISO/full_particle/1D/full_particle_1D.i)
- (test/tests/triso/pyc_eigenstrains/irradiation_strain/ad_irradiation_strain_rz.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_12/case_12_1D.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_5/case_5_1D.i)
- (examples/TRISO/accident_simulation/triso2D_accident_mortar.i)
- (test/tests/triso_failure/triso_1d_pd_penetration.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_4c/case_4c_1D.i)
- (test/tests/triso_failure/ad_triso_1d_weibull_probability.i)
- (test/tests/triso_failure/sub.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_4d/case_4d_1D.i)
- (examples/TRISO/full_particle/2D/full_particle.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_6/case_6_1D.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_4a/case_4a_1D.i)
- (test/tests/triso/pyc_eigenstrains/irradiation_strain/irradiation_strain_rz.i)
- (test/tests/triso_failure/triso_1d_asphericity_failure.i)
- (test/tests/triso_failure/ad_triso_1d_failure.i)
- (test/tests/triso_failure/triso_1d_weibull_probability.i)
- (assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_11/case_11_1D.i)
- (test/tests/triso_failure/triso_1d_failure.i)
- (examples/TRISO/accident_simulation/triso1D_accident.i)
- (examples/TRISO/accident_simulation/triso2D_accident_ad.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)
References
- D. Petti, P. Martin, M. Phelip, and R. Ballinger.
Development of improved models and designs for coated-particle gas reactor fuels.
Technical Report INL/EXT-05-02615, Idaho National Laboratory, December 2004.[BibTeX]
@TECHREPORT{INLEXT-05-02615, author = "Petti, D. and Martin, P. and Phelip, M. and Ballinger, R.", title = "Development of Improved Models and Designs for Coated-Particle Gas Reactor Fuels", year = "2004", number = "INL/EXT-05-02615", month = "December", publisher = "INL Technical Report", institution = "Idaho National Laboratory" }
(test/tests/triso/pyc_eigenstrains/irradiation_strain/irradiation_strain_rz.i)
[GlobalParams]
displacements = 'disp_x disp_y'
[]
[Mesh]
coord_type = RZ
use_displaced_mesh = false
[mesh]
type = FileMeshGenerator
file = mesh.e
[]
[]
[Variables]
[disp_x]
order = FIRST
family = LAGRANGE
[]
[disp_y]
order = FIRST
family = LAGRANGE
[]
[]
[Functions]
[fluence]
type = PiecewiseLinear
x = '0 100'
y = '0e25 10e25'
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[all]
strain = small
incremental = true
eigenstrain_names = irrad_strain
[]
[]
[BCs]
[x]
type = DirichletBC
variable = disp_x
boundary = 1
value = 0.0
[]
[y]
type = DirichletBC
variable = disp_y
boundary = 2
value = 0.0
[]
[]
[Materials]
[fluence]
type = GenericFunctionMaterial
prop_values = fluence
prop_names = fast_neutron_fluence
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 1
[]
[PyC]
type = PyCIrradiationEigenstrain
block = 1
pyc_type = buffer
eigenstrain_name = irrad_strain
[]
[stress]
type = ComputeFiniteStrainElasticStress
block = 1
[]
[elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = 1
youngs_modulus = 1e6
poissons_ratio = 0.3
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options = '-snes_ksp '
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = none
l_max_its = 60
nl_rel_tol = 1e-8
nl_abs_tol = 1e-6
start_time = 0.0
dt = 1
end_time = 100
[]
[Outputs]
exodus = true
[]
(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/fuel_performance/case_9/case_9_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.
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark.
#
initial_fuel_density = 10840.0
[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 = TRISO1DFiveLayerMeshGenerator
elem_type = EDGE3
kernel_radius = 272e-6
buffer_thickness = 97e-6
IPyC_thickness = 33e-6
SiC_thickness = 34e-6
OPyC_thickness = 39e-6
kernel_mesh_density = 6
buffer_mesh_density = 6
IPyC_mesh_density = 6
SiC_mesh_density = 8
OPyC_mesh_density = 6
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Variables]
[disp_x]
[]
[temperature]
initial_condition = 1576.0
[]
[]
[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 = 1.5060805e20 # units of fissions/m**3/s
[]
[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_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 = 1576.0
[]
# 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 = 2.730961e18 # 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 = 1576.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[PyC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = 'buffer IPyC OPyC'
thermal_expansion_coeff = 5.5e-6
stress_free_temperature = 1576.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[SiC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
stress_free_temperature = 1576.0
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 = 1100 #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 = 1850.0 # 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
[]
[]
[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 = 7689600
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'
# ro = 369e-6
# ri = 272e-6
# vb = 4/3*pi*(ro^3-ri^3) = 1.26e-10
# buffer density = 1100
# PyC density = 1850
# fill ratio = 1100/1850
# vb*1100/1850 = 7.50e-11
# Must remove 7.50e-11 m^3 from the volume
addition = -7.50e-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_13/case_13_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.
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark.
#
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 = TRISO1DFiveLayerMeshGenerator
elem_type = EDGE3
kernel_radius = 251e-6
buffer_thickness = 95e-6
IPyC_thickness = 41e-6
SiC_thickness = 35e-6
OPyC_thickness = 40e-6
kernel_mesh_density = 6
buffer_mesh_density = 6
IPyC_mesh_density = 6
SiC_mesh_density = 8
OPyC_mesh_density = 6
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[Variables]
[disp_x]
[]
[temperature]
initial_condition = 1298.0
[]
[]
[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 = 9.30203234e19 # units of fissions/m**3/s
[]
[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_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 = 1298.0
[]
# 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 = 1.041666666667e18 # 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 = 1298.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[PyC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = 'buffer IPyC OPyC'
thermal_expansion_coeff = 5.5e-6
stress_free_temperature = 1298.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[SiC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
stress_free_temperature = 1298.0
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 = 1010 #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 = 1870.0 # 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
[]
[]
[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 = 51840000
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'
# ro = 346e-6
# ri = 251e-6
# vb = 4/3*pi*(ro^3-ri^3) = 1.07e-10
# buffer density = 1010
# PyC density = 1870
# fill ratio = 1010/1870
# vb*1010/1870 = 5.79e-11
# Must remove 5.79e-11 m^3 from the volume
addition = -5.79e-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/triso_failure/triso_ipyc_characteristic_strength.i)
[GlobalParams]
density = 10810.0
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DFiveLayerMeshGenerator
elem_type = EDGE3
kernel_radius = 2.485e-4
buffer_thickness = 9.4e-5
IPyC_thickness = 4.1e-5
SiC_thickness = 3.6e-5
OPyC_thickness = 4.0e-5
kernel_mesh_density = 6
buffer_mesh_density = 6
IPyC_mesh_density = 6
SiC_mesh_density = 8
OPyC_mesh_density = 6
[]
[]
[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 = '100 100'
[]
[]
[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
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
# 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]
# 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
[]
# apply gas pressure on buffer and IPyC boundaries
[PlenumPressure]
[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]
[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 = temp
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 = 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]
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
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_temp]
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_temp]
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'
block = SiC
prop_names = 'characteristic_strength'
[]
[characteristic_strength_PyC]
type = PyCCharacteristicStrength
temperature = temp
X = 1.02
flux_conversion_factor = 0.85
block = 'IPyC OPyC'
[]
[]
[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
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 = 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
[]
[characteristic_strength]
type = ElementExtremeMaterialProperty
mat_prop = characteristic_strength
block = IPyC
value_type = max
[]
[flence]
type = ElementExtremeMaterialProperty
mat_prop = fast_neutron_fluence
block = IPyC
value_type = max
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
csv = true
[]
(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
[]
(examples/TRISO/accident_simulation/triso2D_accident.i)
# This example is 2D-RZ 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.
initial_fuel_density = 11000.0
[GlobalParams]
order = SECOND
family = LAGRANGE
displacements = 'disp_x disp_y'
flux_conversion_factor = 0.85
[]
[Mesh]
coord_type = RZ
[mesh]
type = FileMeshGenerator
file = triso2Dmed.e
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[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_condSlave]
order = CONSTANT
family = MONOMIAL
[]
[creep_xx]
order = CONSTANT
family = MONOMIAL
[]
[creep_yy]
order = CONSTANT
family = MONOMIAL
[]
[creep_zz]
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)'
[]
[d_gap]
type = PiecewiseLinear
x = '1500 2100'
y = '1e-14 1e-12'
[]
[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'
[]
[]
[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
[]
[conductanceSlave]
type = MaterialRealAux
property = gap_conductance
variable = gap_condSlave
boundary = BufferGapBndry
execute_on = linear
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = 15
secondary = 17
penalty = 1e5
model = frictionless
formulation = penalty
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temp
primary = 15
secondary = 17
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 = CYLINDER
tangential_tolerance = 1e-6
roughness_coef = 0.0
quadrature = true
[]
[cesium_contact]
type = GapHeatTransfer
variable = conc
primary = 15
secondary = 17
tangential_tolerance = 1e-6
gap_conductivity_function = d_gap
gap_conductivity_function_variable = temp
appended_property_name = _conc
emissivity_primary = 0
emissivity_secondary = 0
quadrature = true
[]
[]
[BCs]
# pin particle along symmetry planes
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
extra_vector_tags = 'ref'
[]
[no_disp_y]
type = DirichletBC
variable = disp_y
boundary = yzero
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 = BufferGapVol
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
[]
[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
[]
[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
automatic_scaling = true
compute_scaling_once = false
scaling_group_variables = 'conc; disp_x disp_y; temp'
[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'
[]
[Quadrature]
order = THIRD
side_order = FIFTH
[]
[]
[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
execute_on = 'initial timestep_end'
[]
[volumeFuel]
type = InternalVolume
boundary = fuel
execute_on = 'initial timestep_end'
[]
[volumeGas]
type = InternalVolume
boundary = BufferGapVol
# 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 = BufferGapVol
execute_on = 'initial timestep_end'
[]
[ave_temp_interior]
type = SideAverageValue
boundary = BufferGapVol
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_avg_conc]
type = SideAverageValue
variable = conc
boundary = 17
[]
[IPyC_avg_conc]
type = SideAverageValue
variable = conc
boundary = 15
[]
[buffer_integral_flux]
type = SideIntegralMassFlux
variable = conc
boundary = 17
[]
[IPyC_integral_flux]
type = SideIntegralMassFlux
variable = conc
boundary = 15
[]
[integral_flux_error]
type = FunctionValuePostprocessor
function = integral_flux_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
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
[]
[]
(test/tests/triso/base_irradiation/triso1D_accident.i)
initial_fuel_density = 11000.0
[GlobalParams]
density = ${initial_fuel_density} # kg/m^3
order = SECOND
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[mesh]
type = FileMeshGenerator
file = triso1DFineTruss3.e
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Variables]
[disp_x]
[]
[temperature]
initial_condition = 1500.0
[]
[conc_Cs]
initial_condition = 0.0
scaling = 1e18
[]
[]
[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
[]
[gap_condSlave]
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 = false
strain = FINITE
eigenstrain_names = 'fuel_thermal_strain fuel_swelling'
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
extra_vector_tags = 'ref'
[]
[buffer]
block = buffer
add_variables = false
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 creep_strain_xx creep_strain_yy creep_strain_zz'
extra_vector_tags = 'ref'
[]
[IPyC]
block = IPyC
add_variables = false
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 creep_strain_xx creep_strain_yy creep_strain_zz'
extra_vector_tags = 'ref'
[]
[SiC]
block = SiC
add_variables = false
strain = FINITE
eigenstrain_names = 'SiC_thermal_strain'
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz creep_strain_xx creep_strain_yy creep_strain_zz'
extra_vector_tags = 'ref'
[]
[OPyC]
block = OPyC
add_variables = false
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 creep_strain_xx creep_strain_yy creep_strain_zz'
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
energy_per_fission = 3.2e-11 # units of J/fission
fission_rate = fission_rate
extra_vector_tags = 'ref'
[]
[mass_ie]
type = TimeDerivative
variable = conc_Cs
extra_vector_tags = 'ref'
[]
[mass]
type = ArrheniusDiffusion
variable = conc_Cs
extra_vector_tags = 'ref'
[]
[mass_source]
type = BodyForce
variable = conc_Cs
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_Cs
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 = BurnupAux
variable = burnup
fission_rate = fission_rate
molecular_weight = 0.270 # units of kg/mol
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 = BufferGapBndry
execute_on = 'initial timestep_end'
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = 15
secondary = 17
penalty = 1e5
model = frictionless
formulation = kinematic
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = 15
secondary = 17
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
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_Cs
primary = 15
secondary = 17
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
boundary = exterior
function = temp_bc
[]
# fix concentration on free surface
[freesurf_conc]
type = DirichletBC
variable = conc_Cs
boundary = exterior
value = 0.0
[]
# exterior and internal pressures
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
# apply plenum pressure on clad inner walls and pellet surfaces
[PlenumPressure]
[plenumPressure]
boundary = BufferGapVol
initial_pressure = 100
startup_time = 0
R = 8.3145
output_initial_moles = initial_moles
temperature = ave_temp_interior
volume = volumeGas
material_input = 'fis_gas_released co_production'
output = plenum_pressure
[]
[]
[]
[Materials]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'IPyC OPyC buffer'
[]
[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
[]
[fuel_thermal]
type = UO2Thermal
block = fuel
thermal_conductivity_model = FINK_LUCUTA
initial_porosity = 0.0
temperature = temperature
burnup = burnup
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 2.2e11
poissons_ratio = 0.345
[]
[fuel_elastic_stress]
type = ComputeFiniteStrainElasticStress
block = fuel
[]
[fuel_swelling]
type = UO2VolumetricSwellingEigenstrain
gas_swelling_model_type = MATPRO
block = fuel
temperature = temperature
burnup = burnup
eigenstrain_name = fuel_swelling
initial_fuel_density = ${initial_fuel_density}
[]
[fuel_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10.0e-6
temperature = temperature
stress_free_temperature = 1500.0
eigenstrain_name = fuel_thermal_strain
[]
[fuel_den]
type = StrainAdjustedDensity
block = fuel
strain_free_density = ${initial_fuel_density}
[]
[fission_gas_release]
type = UO2Sifgrs
block = fuel
temperature = temperature
fission_rate = fission_rate
[]
[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 = temperature
[]
[buffer_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 2.0e10
poissons_ratio = 0.23
[]
[buffer_stress]
type = PyCCreep
block = buffer
flux_conversion_factor = 1.0
temperature = temperature
[]
[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_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = buffer
thermal_expansion_coeff = 5.65e-6
temperature = temperature
stress_free_temperature = 1500.0
eigenstrain_name = buffer_thermal_strain
[]
[buffer_irraditation]
type = PyCIrradiationEigenstrain
block = buffer
pyc_type = buffer
eigenstrain_name = buffer_eigenstrain
[]
[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_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = IPyC
youngs_modulus = 4.74e10
poissons_ratio = 0.23
[]
[IPyC_stress]
type = PyCCreep
block = IPyC
flux_conversion_factor = 1.0
temperature = temperature
[]
[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
[]
[IPyC_densification]
type = PyCIrradiationEigenstrain
block = IPyC
pyc_type = dense
eigenstrain_name = IPyC_eigenstrain
[]
[IPyC_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = IPyC
thermal_expansion_coeff = 5.65e-6
temperature = temperature
stress_free_temperature = 1500.0
eigenstrain_name = IPyC_thermal_strain
[]
[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_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.4e11
poissons_ratio = 0.13
[]
[monolithic_SiC_creep]
type = MonolithicSiCCreepUpdate
block = SiC
fast_neutron_flux = fast_neutron_flux
temperature = temperature
k_function = k_function
[]
[stress]
type = ComputeMultipleInelasticStress
inelastic_models = monolithic_SiC_creep
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
[]
[SiC_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
temperature = temperature
stress_free_temperature = 1500.0
eigenstrain_name = SiC_thermal_strain
[]
[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_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = OPyC
youngs_modulus = 4.74e10
poissons_ratio = 0.23
[]
[OPyC_stress]
type = PyCCreep
block = OPyC
flux_conversion_factor = 1.0
temperature = temperature
[]
[OPyC_temp]
type = HeatConductionMaterial
block = OPyC
thermal_conductivity = 4.0 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[OPyC_den]
type = StrainAdjustedDensity
strain_free_density = 1900.0 # kg/m^3
block = OPyC
[]
[OPyC_densification]
type = PyCIrradiationEigenstrain
block = OPyC
pyc_type = dense
eigenstrain_name = OPyC_eigenstrain
[]
[OPyC_thermal_expansion]
type = ComputeThermalExpansionEigenstrain
block = OPyC
thermal_expansion_coeff = 5.65e-6
temperature = temperature
stress_free_temperature = 1500.0
eigenstrain_name = OPyC_thermal_strain
[]
[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
[]
[]
[Debug]
show_var_residual_norms = 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-8
nl_abs_tol = 1e-7
nl_max_its = 15
l_tol = 1e-8
l_max_its = 50
start_time = 0.0
#end_time = 85.3682e6
end_time = 1e3
num_steps = 1000
dtmax = 2e6
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 20
time_t = '0 76e6 76.001e6 84.641e6 84.6482e6'
time_dt = '20 20 20 20 20'
growth_factor = 1.5
optimal_iterations = 8
linear_iteration_ratio = 100
[]
[Quadrature]
order = THIRD
[]
[]
[Postprocessors]
[release_Cs_inc]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = exterior
[]
[Int_Cs_release]
type = TimeIntegratedPostprocessor
value = release_Cs_inc
[]
[release_fuel_Cs]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = fuel
[]
[Int_Cs_release_fuel]
type = TimeIntegratedPostprocessor
value = release_fuel_Cs
[]
[release_PyCGapBndry_Cs]
type = SideIntegralMassFlux
variable = conc_Cs
boundary = PyCGapBndry
[]
[Int_Cs_release_PyCGapBndry]
type = TimeIntegratedPostprocessor
value = release_PyCGapBndry_Cs
[]
[fis_gas_produced]
type = ElementIntegralFisGasGeneratedSifgrs
block = fuel
execute_on = linear
[]
[fis_gas_released]
type = ElementIntegralFisGasReleasedSifgrs
block = fuel
execute_on = linear
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
execute_on = 'initial timestep_end'
[]
[volumeFuel]
type = InternalVolume
boundary = fuel
execute_on = 'initial timestep_end'
[]
[volumeGas]
type = InternalVolume
boundary = BufferGapVol
addition = -4.6e-11
execute_on = 'initial linear'
[]
[volumeBufferShell]
type = InternalVolume
boundary = BufferGapVol
execute_on = 'initial timestep_end'
[]
[ave_temp_interior]
type = SideAverageValue
boundary = BufferGapVol
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
outputs = exodus
execute_on = 'initial linear'
[]
[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'
[]
[co_production]
type = CarbonMonoxideProduction
total_fissions = total_fissions
time_integrated_triso_temperature = time_int_surf_temp
initial_enrichment = 0.14029
execute_on = 'initial nonlinear'
[]
[]
[Outputs]
print_linear_residuals = false
[console]
type = Console
max_rows = 5
outlier_variable_norms = false
[]
[exodus]
type = Exodus
file_base = triso1D_accident_out
[]
[]
(test/tests/triso_failure/ad_ipyc_characteristic_strength.i)
[GlobalParams]
density = 10810.0
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DFiveLayerMeshGenerator
elem_type = EDGE3
kernel_radius = 2.485e-4
buffer_thickness = 9.4e-5
IPyC_thickness = 4.1e-5
SiC_thickness = 3.6e-5
OPyC_thickness = 4.0e-5
kernel_mesh_density = 6
buffer_mesh_density = 6
IPyC_mesh_density = 6
SiC_mesh_density = 8
OPyC_mesh_density = 6
[]
[]
[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 = '100 100'
[]
[]
[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 = temp
[]
[heat]
type = ADHeatConduction
variable = temp
[]
[heat_source]
type = ADNeutronHeatSource
variable = temp
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 = 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
# 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]
# pin particle along symmetry planes
[no_disp_x]
type = ADDirichletBC
variable = disp_x
boundary = xzero
value = 0.0
[]
# fix temperature on free surface
[freesurf_temp]
type = ADDirichletBC
variable = temp
boundary = exterior
value = 1346.0
[]
# exterior and internal pressures
[exterior_pressure_x]
type = ADPressure
use_displaced_mesh = false
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
# apply gas pressure on buffer and IPyC boundaries
[PlenumPressure]
[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]
[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 = temp
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 = temp
[]
[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 = temp
[]
[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 = temp
[]
[SiC_thermal_strain]
type = ADComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
stress_free_temperature = 1346.0
eigenstrain_name = thermal_strain
temperature = temp
[]
[fuel_thermal]
type = ADUO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temp
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_temp]
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_temp]
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_temp]
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'
block = SiC
prop_names = 'characteristic_strength'
[]
[characteristic_strength_PyC]
type = ADPyCCharacteristicStrength
temperature = temp
X = 1.02
flux_conversion_factor = 0.85
block = 'IPyC OPyC'
[]
[]
[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-8
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 = 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 = 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
[]
[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
[]
[characteristic_strength]
type = ADElementExtremeMaterialProperty
mat_prop = characteristic_strength
block = IPyC
value_type = max
[]
[flence]
type = ADElementExtremeMaterialProperty
mat_prop = fast_neutron_fluence
block = IPyC
value_type = max
[]
[]
[Outputs]
file_base = triso_ipyc_characteristic_strength_out
print_linear_residuals = true
time_step_interval = 1
csv = true
[]
(test/tests/triso_failure/triso_1d_ipyc_failure.i)
[GlobalParams]
density = 10810.0
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DFiveLayerMeshGenerator
elem_type = EDGE3
kernel_radius = 2.485e-4
buffer_thickness = 9.4e-5
IPyC_thickness = 4.1e-5
SiC_thickness = 3.6e-5
OPyC_thickness = 4.0e-5
kernel_mesh_density = 6
buffer_mesh_density = 6
IPyC_mesh_density = 6
SiC_mesh_density = 8
OPyC_mesh_density = 6
[]
[]
[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 = '100 100'
[]
[]
[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
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
# 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]
# 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
[]
# apply gas pressure on buffer and IPyC boundaries
[PlenumPressure]
[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]
[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 = temp
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 = 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]
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
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_temp]
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_temp]
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]
[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
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 = 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
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
csv = true
perf_graph = true
[]
(test/tests/triso_failure/triso_1d_layer_stress_strength.i)
[GlobalParams]
density = 10810.0
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DFiveLayerMeshGenerator
elem_type = EDGE3
kernel_radius = 2.485e-4
buffer_thickness = 9.4e-5
IPyC_thickness = 4.1e-5
SiC_thickness = 3.6e-5
OPyC_thickness = 4.0e-5
kernel_mesh_density = 6
buffer_mesh_density = 6
IPyC_mesh_density = 6
SiC_mesh_density = 8
OPyC_mesh_density = 6
[]
[]
[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 = '100 100'
[]
[ipyc_stress_strength]
type = ParsedFunction
expression = 'a-b'
symbol_names = 'a b'
symbol_values = 'stress_IPyC actual_strength_IPyC'
[]
[opyc_stress_strength]
type = ParsedFunction
expression = 'a-b'
symbol_names = 'a b'
symbol_values = 'stress_OPyC actual_strength_OPyC'
[]
[sic_crackedipyc_stress_strength]
type = ParsedFunction
expression = 'a-b'
symbol_names = 'a b'
symbol_values = 'stress_SiC_crackedIPyC actual_strength_SiC_crackedIPyC'
[]
[sic_crackedopyc_stress_strength]
type = ParsedFunction
expression = 'a-b'
symbol_names = 'a b'
symbol_values = 'stress_SiC_crackedOPyC actual_strength_SiC_crackedOPyC'
[]
[]
[AuxVariables]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = fuel
initial_condition = 0.0
[]
[fission_rate]
block = fuel
[]
[]
[Physics/SolidMechanics/QuasiStatic]
strain = small
use_automatic_differentiation = true
[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
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
# 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]
# 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
[]
# apply gas pressure on buffer and IPyC boundaries
[PlenumPressure]
[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]
[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 = temp
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 = 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]
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
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_temp]
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_temp]
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]
[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
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 = 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
[]
[stress_SiC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_SiC
output_type = 'stress'
[]
[actual_strength_SiC]
type = WeibullFailureOutputUsingCorrelation
block = SiC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_SiC
output_type = 'strength'
[]
[strength_IPyC]
type = WeibullEffectiveMeanStrength
block = IPyC
weibull_modulus = 6
[]
[stress_IPyC]
type = WeibullFailureOutputUsingCorrelation
block = IPyC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_IPyC
output_type = 'stress'
[]
[actual_strength_IPyC]
type = WeibullFailureOutputUsingCorrelation
block = IPyC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_IPyC
output_type = 'strength'
[]
[IPyC_stressminusstrength]
type = FunctionValuePostprocessor
function = 'ipyc_stress_strength'
[]
[strength_OPyC]
type = WeibullEffectiveMeanStrength
block = OPyC
weibull_modulus = 6
[]
[stress_OPyC]
type = WeibullFailureOutputUsingCorrelation
block = OPyC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_OPyC
output_type = 'stress'
[]
[actual_strength_OPyC]
type = WeibullFailureOutputUsingCorrelation
block = OPyC
weibull_modulus = 6
stress_name = max_principal_stress
effective_mean_strength = strength_OPyC
output_type = 'strength'
[]
[OPyC_stressminusstrength]
type = FunctionValuePostprocessor
function = 'opyc_stress_strength'
[]
[stress_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'
output_type = 'stress'
[]
[actual_strength_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'
output_type = 'strength'
[]
[SiC_crackedIPyC_stressminusstrength]
type = FunctionValuePostprocessor
function = 'sic_crackedipyc_stress_strength'
[]
[stress_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'
output_type = 'stress'
[]
[actual_strength_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'
output_type = 'strength'
[]
[SiC_crackedOPyC_stressminusstrength]
type = FunctionValuePostprocessor
function = 'sic_crackedopyc_stress_strength'
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
csv = true
perf_graph = true
[]
(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/pyc_eigenstrains/irradiation_strain/ad_irradiation_strain_rz.i)
[GlobalParams]
displacements = 'disp_x disp_y'
[]
[Mesh]
coord_type = RZ
use_displaced_mesh = false
[mesh]
type = FileMeshGenerator
file = mesh.e
[]
[]
[Variables]
[disp_x]
order = FIRST
family = LAGRANGE
[]
[disp_y]
order = FIRST
family = LAGRANGE
[]
[]
[Functions]
[fluence]
type = PiecewiseLinear
x = '0 100'
y = '0e25 10e25'
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[all]
strain = small
incremental = true
use_automatic_differentiation = true
eigenstrain_names = irrad_strain
[]
[]
[BCs]
[x]
type = DirichletBC
variable = disp_x
boundary = 1
value = 0.0
[]
[y]
type = DirichletBC
variable = disp_y
boundary = 2
value = 0.0
[]
[]
[Materials]
[fluence]
type = ADGenericFunctionMaterial
prop_values = fluence
prop_names = fast_neutron_fluence
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 1
[]
[PyC]
type = ADPyCIrradiationEigenstrain
block = 1
pyc_type = buffer
eigenstrain_name = irrad_strain
[]
[stress]
type = ADComputeFiniteStrainElasticStress
block = 1
[]
[elasticity_tensor]
type = ADComputeIsotropicElasticityTensor
block = 1
youngs_modulus = 1e6
poissons_ratio = 0.3
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options = '-snes_ksp '
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = none
l_max_its = 60
nl_rel_tol = 1e-8
nl_abs_tol = 1e-6
start_time = 0.0
dt = 1
end_time = 100
automatic_scaling = true
[]
[Outputs]
exodus = true
[]
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_12/case_12_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.
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark.
#
initial_fuel_density = 10520.0
[GlobalParams]
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
O_U = 1.51
C_U = 0.36
initial_enrichment = 0.9315
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DFiveLayerMeshGenerator
elem_type = EDGE3
kernel_radius = 100e-6
buffer_thickness = 102e-6
IPyC_thickness = 53e-6
SiC_thickness = 35e-6
OPyC_thickness = 39e-6
kernel_mesh_density = 6
buffer_mesh_density = 6
IPyC_mesh_density = 6
SiC_mesh_density = 8
OPyC_mesh_density = 6
block_names = 'fuel buffer IPyC SiC OPyC'
[]
[]
[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]
[disp_x]
[]
[temperature]
initial_condition = 1533.0
[]
[]
[Functions]
[radial_eigenstrain]
type = ParsedFunction
expression = 't*(4.73765e-4/4.0*t*t*t - 3.80252e-3/3.0*t*t + 1.64999e-2/2.0*t - 2.13483e-2)'
[]
[tangential_eigenstrain]
type = ParsedFunction
expression = 't*(-1.03249e-3/4.0*t*t*t + 5.47396e-3/3.0*t*t - 3.29740e-3/2.0*t - 1.83549e-2)'
[]
[fission_rate]
type = ParsedFunction
expression = 1.29203e21 # units of fissions/m**3/s
[]
[k_function]
type = ParsedFunction
expression = '2.70e-29'
[]
[]
[AuxVariables]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[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
[]
[]
[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' # coupling to postprocessors which supply the fission gas addition
released_gas_types = 'Kr Xe'
released_fractions = '0.153 0.847'
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 = 1533.0
[]
# 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 = 8.3145
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' # coupling to post processor to get fission gas added
output = plenum_pressure # coupling to post processor to output plenum/gap pressure
[]
[]
[]
[Materials]
[fission_rate]
type = GenericFunctionMaterial
prop_names = fission_rate
prop_values = fission_rate
[]
[flux]
type = FastNeutronFlux
calculate_fluence = true
factor = 2.58714597e18 # n/m^2-sec
[]
[stress]
type = ComputeFiniteStrainElasticStress
block = 'fuel buffer SiC'
[]
[UCO_burnup]
type = TRISOBurnup
initial_density = ${initial_fuel_density}
[]
[UCO_thermal]
type = UCOThermal
block = fuel
temperature = temperature
[]
[fuel_elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 2e8
poissons_ratio = 0.345
[]
[UCO_VolumetricSwellingEigenstrain]
type = UCOVolumetricSwellingEigenstrain
block = fuel
eigenstrain_name = UCO_swelling_eigenstrain
[]
[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
[]
[PyC_stress]
type = PyCCreep
block = 'IPyC OPyC'
k = k_function
poissons_ratio = 0.5
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 = 1533.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[PyC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = 'buffer IPyC OPyC'
thermal_expansion_coeff = 5.5e-6
stress_free_temperature = 1533.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[SiC_thermal_strain]
type = ComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
stress_free_temperature = 1533.0
eigenstrain_name = thermal_strain
temperature = temperature
[]
[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 = 960 #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
[]
[IPyC_den]
type = StrainAdjustedDensity
strain_free_density = 1920.0 # kg/m^3
block = IPyC
[]
[OPyC_den]
type = StrainAdjustedDensity
strain_free_density = 1860.0 # kg/m^3
block = 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 = 3230.0 # kg/m^3
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 = 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 = 14688000
dtmax = 2e5
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 20
optimal_iterations = 6
iteration_window = 1
linear_iteration_ratio = 100
[]
[]
[Postprocessors]
[burnup]
type = ElementAverageMaterialProperty
block = fuel
mat_prop = burnup
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
[]
[volumeFuel]
type = InternalVolume
boundary = fuel_outer_boundary
[]
[volumeGas]
type = InternalVolume
boundary = 'fuel_outer_boundary IPyC_inner_boundary'
# ro = 202e-6
# ri = 100e-6
# vb = 4/3*pi*(ro^3-ri^3) = 3.03e-11
# buffer density = 960
# PyC density = 1890
# fill ratio = 960/1890
# vb*960/1890 = 1.54e-11
# Must remove 1.54e-11 m^3 from the volume
addition = -1.54e-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'
[]
[fis_gas_released]
type = ElementIntegralMaterialProperty
mat_prop = fis_gas_released
block = fuel
execute_on = 'initial timestep_end'
[]
[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_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
[]
(examples/TRISO/accident_simulation/triso2D_accident_mortar.i)
# This example is 2D-RZ 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 a thermomechanical mortar approach.
initial_fuel_density = 11000.0
[GlobalParams]
order = SECOND
family = LAGRANGE
displacements = 'disp_x disp_y'
flux_conversion_factor = 0.85
[]
[Mesh]
coord_type = RZ
[file]
type = FileMeshGenerator
file = triso2Dmed.e
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
converge_on = 'disp_x disp_y temp conc'
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[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
[]
[creep_xx]
order = CONSTANT
family = MONOMIAL
[]
[creep_yy]
order = CONSTANT
family = MONOMIAL
[]
[creep_zz]
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)'
[]
[d_gap]
type = PiecewiseLinear
x = '1500 2100'
y = '1e-14 1e-12'
[]
[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'
[]
[]
[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'
block = 'fuel buffer IPyC SiC OPyC'
[]
[heat]
type = HeatConduction
variable = temp
extra_vector_tags = 'ref'
block = 'fuel buffer IPyC SiC OPyC'
[]
[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'
block = 'fuel buffer IPyC SiC OPyC'
[]
[mass]
type = ArrheniusDiffusion
variable = conc
extra_vector_tags = 'ref'
block = 'fuel buffer IPyC SiC OPyC'
[]
[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
block = 'fuel buffer IPyC SiC OPyC'
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
[]
[]
[ThermalContactMortar]
[thermal]
secondary_variable = temp
primary_boundary = 15
secondary_boundary = 17
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 = CYLINDER
min_gap = 1e-7
max_gap = 50e-6
roughness_coef = 0.0
correct_edge_dropping = true
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = 15
secondary = 17
model = frictionless
formulation = mortar
c_normal = 1.0e8
correct_edge_dropping = true
[]
[]
[ThermalContact]
[cesium_contact]
type = GapHeatTransfer
variable = conc
primary = 15
secondary = 17
tangential_tolerance = 1e-6
gap_conductivity_function = d_gap
gap_conductivity_function_variable = temp
appended_property_name = _conc
emissivity_primary = 0
emissivity_secondary = 0
quadrature = true
[]
[]
[BCs]
# pin particle along symmetry planes
[no_disp_x]
type = DirichletBC
variable = disp_x
boundary = xzero
value = 0.0
extra_vector_tags = 'ref'
[]
[no_disp_y]
type = DirichletBC
variable = disp_y
boundary = yzero
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 = BufferGapVol
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
[]
[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 = 'NEWTON'
petsc_options = '-snes_converged_reason -ksp_converged_reason -snes_ksp_ew'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -mat_mffd_err -pc_factor_shift_type -pc_factor_shift_amount'
petsc_options_value = 'lu superlu_dist 1e-5 NONZERO 1e-14'
snesmf_reuse_base = false
line_search = 'none'
nl_rel_tol = 5e-4
nl_abs_tol = 1e-10
nl_max_its = 20
l_max_its = 8
start_time = 0.0
end_time = 85.3682e6
dt = 100
dtmax = 2e6
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 100
optimal_iterations = 10
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 = 0.5
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
execute_on = 'initial timestep_end'
[]
[volumeFuel]
type = InternalVolume
boundary = fuel
execute_on = 'initial timestep_end'
[]
[volumeGas]
type = InternalVolume
boundary = BufferGapVol
# 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 = BufferGapVol
execute_on = 'initial timestep_end'
[]
[ave_temp_interior]
type = SideAverageValue
boundary = BufferGapVol
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_avg_conc]
type = SideAverageValue
variable = conc
boundary = 17
[]
[IPyC_avg_conc]
type = SideAverageValue
variable = conc
boundary = 15
[]
[buffer_integral_flux]
type = SideIntegralMassFlux
variable = conc
boundary = 17
[]
[IPyC_integral_flux]
type = SideIntegralMassFlux
variable = conc
boundary = 15
[]
[integral_flux_error]
type = FunctionValuePostprocessor
function = integral_flux_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
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
[]
[]
(test/tests/triso_failure/triso_1d_pd_penetration.i)
[GlobalParams]
density = 10810.0
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x'
[]
[Mesh]
coord_type = RSPHERICAL
[gen]
type = TRISO1DFiveLayerMeshGenerator
elem_type = EDGE3
kernel_radius = 2.485e-4
buffer_thickness = 9.4e-5
IPyC_thickness = 4.1e-5
SiC_thickness = 3.6e-5
OPyC_thickness = 4.0e-5
kernel_mesh_density = 6
buffer_mesh_density = 6
IPyC_mesh_density = 6
SiC_mesh_density = 8
OPyC_mesh_density = 6
[]
[]
[Variables]
[disp_x]
[]
[temperature]
initial_condition = 1346.0
[]
[]
[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
[]
[]
[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 = '100 100'
[]
[]
[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 # 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
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]
# 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 = 1346.0
[]
# exterior and internal pressures
[exterior_pressure_x]
type = Pressure
use_displaced_mesh = false
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
# apply gas pressure on buffer and IPyC boundaries
[PlenumPressure]
[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_temp_interior
volume = volumeGas
material_input = 'fis_gas_released co_production'
output = plenum_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
[]
[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_temp]
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_temp]
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_temp]
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 = 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]
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
[]
[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
[]
[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
[]
[]
[Outputs]
print_linear_residuals = true
time_step_interval = 1
csv = true
perf_graph = 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_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
[]
(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
[]
[]
(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
[]
(examples/TRISO/full_particle/2D/full_particle.i)
initial_fuel_density = 10810.0
[GlobalParams]
density = ${initial_fuel_density}
flux_conversion_factor = 1.0
order = SECOND
family = LAGRANGE
displacements = 'disp_x disp_y'
volumetric_locking_correction = false
[]
[Mesh]
coord_type = RZ
[mesh]
type = FileMeshGenerator
file = full_particle.e
[]
[]
[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]
[fast_neutron_flux]
type = ParsedFunction
expression = 1.708707e18
[]
[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 = 15
secondary = 17
penalty = 1e5
model = frictionless
formulation = penalty
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = 15
secondary = 17
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
[]
[no_disp_y]
type = DirichletBC
variable = disp_y
boundary = yzero
value = 0.0
[]
[freesurf_temperature]
type = DirichletBC
variable = temperature
boundary = exterior
value = 1346
[]
[exterior_pressure_x]
type = Pressure
variable = disp_x
boundary = exterior
factor = 0.1e6
[]
[exterior_pressure_y]
type = Pressure
variable = disp_y
boundary = exterior
factor = 0.1e6
[]
[PlenumPressure]
[plenumPressure]
boundary = 'PyCGapBndry BufferGapBndry'
initial_pressure = 0
startup_time = 1.0e4
R = 8.3143
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 # 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_temperature]
type = HeatConductionMaterial
block = 'IPyC OPyC'
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IOPyC_density]
type = StrainAdjustedDensity
block = 'IPyC OPyC'
strain_free_density = 1880.0
[]
[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_den]
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 = 20
[]
[]
[Executioner]
type = Transient
petsc_options = '-snes_ksp_ew'
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-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 = 10
optimal_iterations = 8
iteration_window = 2
linear_iteration_ratio = 100
[]
[Quadrature]
order = FIFTH
side_order = SEVENTH
[]
[]
[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
[]
[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
[]
[fis_gas_produced]
type = ElementIntegralFisGasGeneratedSifgrs
block = fuel
execute_on = 'initial linear'
[]
[fis_gas_released]
type = ElementIntegralFisGasReleasedSifgrs
block = fuel
execute_on = 'initial linear'
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
execute_on = 'initial TIMESTEP_END'
[]
[volumeFuel]
type = InternalVolume
boundary = fuel
execute_on = 'initial TIMESTEP_END'
[]
[volumeGas]
type = InternalVolume
boundary = BufferGapVol
addition = -5.53e-11
execute_on = 'initial TIMESTEP_END'
[]
[volumeBufferShell]
type = InternalVolume
boundary = BufferGapVol
execute_on = 'initial TIMESTEP_END'
[]
[ave_temp_interior]
type = SideAverageValue
boundary = BufferGapVol
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
execute_on = 'INITIAL TIMESTEP_END'
[]
[total_fissions]
type = TimeIntegratedPostprocessor
value = total_fission_rate
execute_on = 'INITIAL TIMESTEP_END'
[]
[avg_surface_temperature]
type = SideAverageValue
variable = temperature
boundary = exterior
execute_on = 'INITIAL TIMESTEP_END'
[]
[time_int_surf_temperature]
type = TimeIntegratedPostprocessor
value = avg_surface_temperature
execute_on = 'INITIAL TIMESTEP_END'
[]
[co_production]
type = CarbonMonoxideProduction
total_fissions = total_fissions
time_integrated_triso_temperature = time_int_surf_temperature
initial_enrichment = 0.14029
execute_on = 'INITIAL TIMESTEP_END'
[]
[]
[PerformanceMetricOutputs]
[]
[Outputs]
perf_graph = true
exodus = true
csv = 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 co_production fis_gas_released avg_surface_temperature'
[]
[]
(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
[]
(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
[]
(test/tests/triso/pyc_eigenstrains/irradiation_strain/irradiation_strain_rz.i)
[GlobalParams]
displacements = 'disp_x disp_y'
[]
[Mesh]
coord_type = RZ
use_displaced_mesh = false
[mesh]
type = FileMeshGenerator
file = mesh.e
[]
[]
[Variables]
[disp_x]
order = FIRST
family = LAGRANGE
[]
[disp_y]
order = FIRST
family = LAGRANGE
[]
[]
[Functions]
[fluence]
type = PiecewiseLinear
x = '0 100'
y = '0e25 10e25'
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[all]
strain = small
incremental = true
eigenstrain_names = irrad_strain
[]
[]
[BCs]
[x]
type = DirichletBC
variable = disp_x
boundary = 1
value = 0.0
[]
[y]
type = DirichletBC
variable = disp_y
boundary = 2
value = 0.0
[]
[]
[Materials]
[fluence]
type = GenericFunctionMaterial
prop_values = fluence
prop_names = fast_neutron_fluence
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 1
[]
[PyC]
type = PyCIrradiationEigenstrain
block = 1
pyc_type = buffer
eigenstrain_name = irrad_strain
[]
[stress]
type = ComputeFiniteStrainElasticStress
block = 1
[]
[elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = 1
youngs_modulus = 1e6
poissons_ratio = 0.3
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options = '-snes_ksp '
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = none
l_max_its = 60
nl_rel_tol = 1e-8
nl_abs_tol = 1e-6
start_time = 0.0
dt = 1
end_time = 100
[]
[Outputs]
exodus = 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/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_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
[]
(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/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
[]
[]
(examples/TRISO/accident_simulation/triso2D_accident_ad.i)
# This example is 2D-RZ 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 a thermomechanical mortar approach. It uses
# Automatic Differentiation classes and models gap mass transfer using
# flux preserving and sorption mortar constraints. 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 = 11000.0
[GlobalParams]
order = SECOND
family = LAGRANGE
displacements = 'disp_x disp_y'
flux_conversion_factor = 0.85
use_automatic_differentiation = true
[]
[Mesh]
coord_type = RZ
[file]
type = FileMeshGenerator
file = triso2Dmed.e
[]
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
converge_on = 'disp_x disp_y temp conc'
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[temp]
initial_condition = 1500.0
[]
[conc]
initial_condition = 0.0
[]
[conc_lm]
block = pellet_clad_mechanical_secondary_subdomain
[]
[conc_dx_lm]
block = pellet_clad_mechanical_secondary_subdomain
[]
[conc_dy_lm]
block = pellet_clad_mechanical_secondary_subdomain
[]
[]
[AuxVariables]
[fission_rate]
block = fuel
order = CONSTANT
family = MONOMIAL
[]
[fluence]
order = CONSTANT
family = MONOMIAL
[]
[burnup]
block = fuel
order = CONSTANT
family = MONOMIAL
[]
[creep_xx]
order = CONSTANT
family = MONOMIAL
[]
[creep_yy]
order = CONSTANT
family = MONOMIAL
[]
[creep_zz]
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 = ADHeatConductionTimeDerivative
variable = temp
extra_vector_tags = 'ref'
block = 'fuel buffer IPyC SiC OPyC'
[]
[heat]
type = ADHeatConduction
variable = temp
extra_vector_tags = 'ref'
block = 'fuel buffer IPyC SiC OPyC'
[]
[heat_source]
type = ADNeutronHeatSource
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 = ADTimeDerivative
variable = conc
extra_vector_tags = 'ref'
block = 'fuel buffer IPyC SiC OPyC'
[]
[mass]
type = ADArrheniusDiffusion
variable = conc
extra_vector_tags = 'ref'
block = 'fuel buffer IPyC SiC OPyC'
[]
[mass_source]
type = ADBodyForce
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
block = 'fuel buffer IPyC SiC OPyC'
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 = ADMaterialRealAux
property = fast_neutron_fluence
variable = fluence
[]
[burnup]
type = ADBurnupAux
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 = ADRankTwoAux
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 = ADRankTwoAux
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 = ADRankTwoAux
rank_two_tensor = creep_strain
variable = creep_zz
index_i = 2
index_j = 2
block = 'buffer IPyC SiC OPyC'
execute_on = timestep_end
[]
[]
[ThermalContactMortar]
[thermal]
secondary_variable = temp
primary_boundary = 15
secondary_boundary = 17
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 = CYLINDER
min_gap = 1e-7
max_gap = 50e-6
roughness_coef = 0.0
correct_edge_dropping = true
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = 15
secondary = 17
model = frictionless
formulation = mortar
c_normal = 1.0e8
correct_edge_dropping = true
[]
[]
[Constraints]
[cesium_gap_value]
type = MassSorptionConstraint
variable = conc_lm
primary_variable = conc
primary_boundary = 15
primary_subdomain = pellet_clad_mechanical_primary_subdomain
secondary_variable = conc
secondary_boundary = 17
secondary_subdomain = pellet_clad_mechanical_secondary_subdomain
partial_pressure_name = partial_pressure
epsilon = 1e-4
correct_edge_dropping = true
[]
[cesium_gap_flux_x]
type = MassFluxConstraint
variable = conc_dx_lm
primary_variable = conc
diffusivity_primary = arrhenius_diffusion_coef
primary_boundary = 15
primary_subdomain = pellet_clad_mechanical_primary_subdomain
secondary_variable = conc
diffusivity_secondary = arrhenius_diffusion_coef
secondary_boundary = 17
secondary_subdomain = pellet_clad_mechanical_secondary_subdomain
component = 0
epsilon = 1e-5
correct_edge_dropping = true
[]
[cesium_gap_flux_y]
type = MassFluxConstraint
variable = conc_dy_lm
primary_variable = conc
diffusivity_primary = arrhenius_diffusion_coef
primary_boundary = 15
primary_subdomain = pellet_clad_mechanical_primary_subdomain
secondary_variable = conc
diffusivity_secondary = arrhenius_diffusion_coef
secondary_boundary = 17
secondary_subdomain = pellet_clad_mechanical_secondary_subdomain
component = 1
epsilon = 1e-5
correct_edge_dropping = true
[]
[]
[BCs]
# pin particle along symmetry planes
[no_disp_x]
type = ADDirichletBC
variable = disp_x
boundary = xzero
value = 0.0
extra_vector_tags = 'ref'
[]
[no_disp_y]
type = ADDirichletBC
variable = disp_y
boundary = yzero
value = 0.0
extra_vector_tags = 'ref'
[]
# fix temperature on free surface
[freesurf_temp]
type = ADFunctionDirichletBC
variable = temp
boundary = exterior
function = temp_bc
extra_vector_tags = 'ref'
[]
# fix concentration on free surface
[freesurf_conc]
type = ADDirichletBC
variable = conc
boundary = exterior
value = 0.0
extra_vector_tags = 'ref'
[]
[PlenumPressure] # apply plenum pressure on clad inner walls and pellet surfaces
[plenumPressure]
boundary = BufferGapVol
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 = ADFastNeutronFlux
calculate_fluence = true
factor = 5e17
[]
[fission_gas_release] # Sifgrs fission gas release mode
type = ADUO2Sifgrs
block = fuel
temperature = temp
fission_rate = fission_rate # coupling to fission_rate aux variable
grain_radius_const = 5.0e-6
[]
[fuel_thermal]
type = ADUO2Thermal
thermal_conductivity_model = FINK_LUCUTA
block = fuel
temperature = temp
burnup = burnup
initial_porosity = 0.0
[]
[fuel_swelling]
type = ADUO2VolumetricSwellingEigenstrain
gas_swelling_model_type = MATPRO
block = fuel
temperature = temp
burnup = burnup
eigenstrain_name = 'swelling_strain'
initial_fuel_density = ${initial_fuel_density}
[]
[fuel_stress]
type = ADComputeFiniteStrainElasticStress
block = 'fuel'
[]
[fuel_elasticity]
type = ADComputeIsotropicElasticityTensor
block = fuel
youngs_modulus = 2.2e11
poissons_ratio = .345
[]
[fuel_thermal_strain]
type = ADComputeThermalExpansionEigenstrain
block = fuel
thermal_expansion_coeff = 10e-6
stress_free_temperature = 1500.0
eigenstrain_name = thermal_strain
temperature = temp
[]
[fuel_den]
type = ADStrainAdjustedDensity
block = fuel
strain_free_density = ${initial_fuel_density} # kg/m^3
[]
[fuel_conc]
type = ADArrheniusDiffusionCoef
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 = ADPyCIrradiationEigenstrain
block = buffer
pyc_type = buffer
eigenstrain_name = 'swelling_strain'
[]
[buffer_thermal_strain]
type = ADComputeThermalExpansionEigenstrain
block = buffer
thermal_expansion_coeff = 5.65e-6
stress_free_temperature = 1500.0
eigenstrain_name = thermal_strain
temperature = temp
[]
[buffer_elasticity]
type = ADComputeIsotropicElasticityTensor
block = buffer
youngs_modulus = 2e10
poissons_ratio = .23
[]
[buffer_stress]
type = ADPyCCreep
block = buffer
temperature = temp
[]
[buffer_temp]
type = ADHeatConductionMaterial
block = buffer
thermal_conductivity = 0.5 # J/m-s-K
specific_heat = 720.0 # J/kg-K
[]
[buffer_den]
type = ADStrainAdjustedDensity
strain_free_density = 1000.0 #kg/m^3
block = buffer
[]
[buffer_conc]
type = ADArrheniusDiffusionCoef
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 = ADSorptionPartialPressure
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 = 1000 # convert from mmol/m^3 to mmol/kg, using constant for compatibility with default AD derivative container size
concentration = conc
temperature = temp
block = buffer
outputs = 'all'
output_properties = partial_pressure
[]
[normal_vectors_triso]
type = NormalVectorsTRISO
block = 'IPyC OPyC buffer'
[]
[IPyC_eigenstrain]
type = ADPyCIrradiationEigenstrain
block = IPyC
pyc_type = dense
eigenstrain_name = 'swelling_strain'
[]
[IPyC_thermal_strain]
type = ADComputeThermalExpansionEigenstrain
block = IPyC
thermal_expansion_coeff = 5.65e-6
stress_free_temperature = 1500.0
eigenstrain_name = thermal_strain
temperature = temp
[]
[IPyC_elasticity]
type = ADComputeIsotropicElasticityTensor
block = IPyC
youngs_modulus = 4.74e10
poissons_ratio = .23
[]
[IPyC_disp]
type = ADPyCCreep
block = 'IPyC OPyC'
temperature = temp
[]
[IPyC_temp]
type = ADHeatConductionMaterial
block = 'IPyC OPyC'
thermal_conductivity = 4.0
specific_heat = 720.0
[]
[IPyC_den]
type = ADStrainAdjustedDensity
block = 'IPyC OPyC'
strain_free_density = 1900.0
[]
[IPyC_conc]
type = ADArrheniusDiffusionCoef
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
[]
[IPyC_partial_pressure]
type = ADSorptionPartialPressure
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 = 1900 # convert from mmol/m^3 to mmol/kg, using constant for compatibility with default AD derivative container size
concentration = conc
temperature = temp
block = IPyC
outputs = 'all'
output_properties = partial_pressure
[]
[SiC_thermal_strain]
type = ADComputeThermalExpansionEigenstrain
block = SiC
thermal_expansion_coeff = 4.9e-6
stress_free_temperature = 1500.0
eigenstrain_name = thermal_strain
temperature = temp
[]
[SiC_elasticity]
type = ADComputeIsotropicElasticityTensor
block = SiC
youngs_modulus = 3.4e11
poissons_ratio = .13
[]
[SiC_creep]
type = ADMonolithicSiCCreepUpdate
block = SiC
temperature = temp
k_function = k_function
[]
[SiC_stress]
type = ADComputeMultipleInelasticStress
block = SiC
inelastic_models = 'SiC_creep'
[]
[SiC_temp]
type = ADHeatConductionMaterial
block = SiC
thermal_conductivity = 13.9 # J/m-s-K
specific_heat = 620.0 # J/kg-K
[]
[SiC_den]
type = ADStrainAdjustedDensity
strain_free_density = 3180.0 # kg/m^3
block = SiC
[]
[SiC_conc]
type = ADArrheniusDiffusionCoef
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 = ADPyCIrradiationEigenstrain
block = OPyC
pyc_type = dense
eigenstrain_name = 'swelling_strain'
[]
[OPyC_thermal_strain]
type = ADComputeThermalExpansionEigenstrain
block = OPyC
thermal_expansion_coeff = 5.65e-6
stress_free_temperature = 1500.0
eigenstrain_name = thermal_strain
temperature = temp
[]
[OPyC_elasticity]
type = ADComputeIsotropicElasticityTensor
block = OPyC
youngs_modulus = 4.74e10
poissons_ratio = .23
[]
[OPyC_conc]
type = ADArrheniusDiffusionCoef
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 = 'NEWTON'
petsc_options = '-snes_converged_reason -ksp_converged_reason -snes_ksp_ew'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -mat_mffd_err -pc_factor_shift_type -pc_factor_shift_amount'
petsc_options_value = 'lu superlu_dist 1e-5 NONZERO 1e-14'
snesmf_reuse_base = false
line_search = 'none'
nl_rel_tol = 5e-4
nl_abs_tol = 1e-10
nl_max_its = 20
l_max_its = 8
start_time = 0.0
end_time = 85.3682e6
dt = 100
dtmax = 2e6
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 100
optimal_iterations = 10
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 = 0.5
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 = ADSideDiffusiveFluxIntegral
variable = conc
diffusivity = arrhenius_diffusion_coef
boundary = exterior
execute_on = timestep_end
[]
[dt]
type = TimestepSize
execute_on = timestep_end
[]
[fis_gas_produced] # fission gas produced (moles)
type = ADElementIntegralFisGasGeneratedSifgrs
block = fuel
execute_on = 'initial linear nonlinear timestep_begin timestep_end'
[]
[fis_gas_released] # fission gas released to plenum (moles)
type = ADElementIntegralFisGasReleasedSifgrs
block = fuel
execute_on = 'initial linear nonlinear timestep_begin timestep_end'
[]
[volumeTotal]
type = InternalVolume
boundary = exterior
execute_on = 'initial timestep_end'
[]
[volumeFuel]
type = InternalVolume
boundary = fuel
execute_on = 'initial timestep_end'
[]
[volumeGas]
type = InternalVolume
boundary = BufferGapVol
# 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 = BufferGapVol
execute_on = 'initial timestep_end'
[]
[ave_temp_interior]
type = SideAverageValue
boundary = BufferGapVol
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 = ADSideDiffusiveFluxIntegral
variable = conc
boundary = 17
diffusivity = arrhenius_diffusion_coef
[]
[IPyC_integral_flux]
type = ADSideDiffusiveFluxIntegral
variable = conc
boundary = 15
diffusivity = arrhenius_diffusion_coef
[]
[buffer_partial_pressure]
type = ADSideAverageMaterialProperty
property = partial_pressure
boundary = 17
[]
[IPyC_partial_pressure]
type = ADSideAverageMaterialProperty
property = partial_pressure
boundary = 15
[]
[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
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/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
[]