- k_functionK coefficient as a function of temperature (Kelvin)
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:K coefficient as a function of temperature (Kelvin)
- temperatureCoupled temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature
MonolithicSiCCreepUpdate
Computes irradiation creep for monolithic SiC. This class must be used in conjunction with ComputeMultipleInelasticStress.
Description
The model for irradiation creep of silicon carbide, MonolithicSiCCreepUpdate, is taken as (see Lewinsohn et al. (1998) ): where is the irradiation creep rate, is a temperature-dependent conversion factor (Pa-n/m), is the stress, and is the flux.
Lewinsohn et al. (1998) gives as (PaN/m) at C and (PaN/m) at C. However, a figure in that reference seems to indicate that typical values for are about one-tenth those mentioned in the text. Little creep data for monolithic SiC is available at lower temperatures.
Example Input Syntax
[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
[monolithic_sic_creep]
type = MonolithicSiCCreepUpdate<<<{"description": "Computes irradiation creep for monolithic SiC. This class must be used in conjunction with ComputeMultipleInelasticStress.", "href": "MonolithicSiCCreepUpdate.html"}>>>
block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
temperature<<<{"description": "Coupled temperature"}>>> = temp
k_function<<<{"description": "K coefficient as a function of temperature (Kelvin)"}>>> = k_function
[]
[]Input Parameters
- absolute_tolerance1e-11Absolute convergence tolerance for Newton iteration
Default:1e-11
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Absolute convergence tolerance for Newton iteration
- acceptable_multiplier10Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress
Default:10
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress
- adaptive_substeppingFalseUse adaptive substepping, where the number of substeps is successively doubled until the return mapping model successfully converges or the maximum number of substeps is reached.
Default:False
C++ Type:bool
Controllable:No
Description:Use adaptive substepping, where the number of substeps is successively doubled until the return mapping model successfully converges or the maximum number of substeps is reached.
- automatic_differentiation_return_mappingFalseWhether to use automatic differentiation to compute the derivative.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use automatic differentiation to compute the derivative.
- base_nameOptional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.
C++ Type:std::string
Controllable:No
Description:Optional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.
- 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
- 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.
- fast_neutron_fluxfast_neutron_fluxThe fast neutron flux
Default:fast_neutron_flux
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:The fast neutron flux
- max_inelastic_increment0.0001The maximum inelastic strain increment allowed in a time step
Default:0.0001
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The maximum inelastic strain increment allowed in a time step
- maximum_number_substeps25The maximum number of substeps allowed before cutting the time step.
Default:25
C++ Type:unsigned int
Controllable:No
Description:The maximum number of substeps allowed before cutting the time step.
- relative_tolerance1e-08Relative convergence tolerance for Newton iteration
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Relative convergence tolerance for Newton iteration
- use_substep_integration_errorFalseIf true, it establishes a substep size that will yield, at most,the creep numerical integration error given by substep_strain_tolerance.
Default:False
C++ Type:bool
Controllable:No
Description:If true, it establishes a substep size that will yield, at most,the creep numerical integration error given by substep_strain_tolerance.
- use_substeppingNONEWhether and how to use substepping
Default:NONE
C++ Type:MooseEnum
Options:NONE, ERROR_BASED, INCREMENT_BASED
Controllable:No
Description:Whether and how to use substepping
Optional Parameters
- apply_strainTrueFlag to apply strain. Used for testing.
Default:True
C++ Type:bool
Controllable:No
Description:Flag to apply strain. Used for testing.
- 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.
- effective_inelastic_strain_nameeffective_creep_strainName of the material property that stores the effective inelastic strain
Default:effective_creep_strain
C++ Type:std::string
Controllable:No
Description:Name of the material property that stores the effective inelastic strain
- 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
- substep_strain_tolerance0.1Maximum ratio of the initial elastic strain increment at start of the return mapping solve to the maximum inelastic strain allowable in a single substep. Reduce this value to increase the number of substeps
Default:0.1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Maximum ratio of the initial elastic strain increment at start of the return mapping solve to the maximum inelastic strain allowable in a single substep. Reduce this value to increase the number of substeps
- 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
- internal_solve_full_iteration_historyFalseSet true to output full internal Newton iteration history at times determined by `internal_solve_output_on`. If false, only a summary is output.
Default:False
C++ Type:bool
Controllable:No
Description:Set true to output full internal Newton iteration history at times determined by `internal_solve_output_on`. If false, only a summary is output.
- internal_solve_output_onon_errorWhen to output internal Newton solve information
Default:on_error
C++ Type:MooseEnum
Options:never, on_error, always
Controllable:No
Description:When to output internal Newton solve information
Debug 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/solid_mechanics/sic_creep/ad_monolithic_sic_creep.i)
- (examples/TRISO/accident_simulation/triso1D_accident.i)
- (test/tests/solid_mechanics/sic_creep/monolithic_sic_creep.i)
- (examples/TRISO/accident_simulation/triso2D_accident_mortar.i)
- (examples/TRISO/accident_simulation/triso2D_accident_ad.i)
- (examples/accident_tolerant_fuel/u3si2_sic/u3si2_outer_monolith_1.5D.i)
- (examples/TRISO/accident_simulation/triso2D_accident.i)
- (test/tests/triso/base_irradiation/triso1D_accident.i)
References
- C. A. Lewinsohn, M. L. Hamilton, G. E. Youngblood, R. H. Jones, F. A. Garner, S. L. Hecht, and A. Kohyama.
Irradiation-enhanced creep in SiC: data summary and planned experiments.
Journal of Nuclear Materials, 253:36–46, 1998.[BibTeX]
@ARTICLE{lewinsohn98, author = "Lewinsohn, C. A. and Hamilton, M. L. and Youngblood, G. E. and Jones, R. H. and Garner, F. A. and Hecht, S. L. and Kohyama, A.", title = "Irradiation-enhanced creep in {SiC}: data summary and planned experiments", journal = "Journal of Nuclear Materials", year = "1998", volume = "253", pages = "36-46" }
(test/tests/solid_mechanics/sic_creep/monolithic_sic_creep.i)
# Tests material model MonolothicSiCCreepUpdate which computes
# irradiation creep for monolithic SiC.
#
# The test is a single element unit cube which is pulled in the y direction
# with a pressure of 5.0e7 Pa. The temperature and fission rate within the cube
# are uniform and constant at 600 K and 5e17 fissions/m**3-s. The total time is
# 200e6s.
#
# The anaytical solution for the creep strain is 0.001.
[GlobalParams]
displacements = 'disp_x disp_y disp_z'
[]
[Mesh]
use_displaced_mesh = false
[mesh]
type = FileMeshGenerator
file = 1x1x1_cube.e
[]
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[disp_z]
[]
[temp]
initial_condition = 600.0
[]
[]
[AuxVariables]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[creep_strain_yy]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[k_function]
type = PiecewiseLinear
x = '0 200e6'
y = '2e-37 2e-37'
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[all]
strain = small
incremental = true
[]
[]
[Kernels]
[heat]
type = HeatConduction
variable = temp
[]
[]
[AuxKernels]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
[]
[creep_strain_yy]
type = RankTwoAux
rank_two_tensor = creep_strain
variable = creep_strain_yy
index_i = 1
index_j = 1
[]
[]
[BCs]
[u_top_pull]
type = Pressure
variable = disp_y
boundary = 5
factor = -5e7
[]
[u_bottom_fix]
type = DirichletBC
variable = disp_y
boundary = 3
value = 0.0
[]
[u_yz_fix]
type = DirichletBC
variable = disp_x
boundary = 4
value = 0.0
[]
[u_xy_fix]
type = DirichletBC
variable = disp_z
boundary = 2
value = 0.0
[]
[temp_top_fix]
type = DirichletBC
variable = temp
boundary = 5
value = 600.0
[]
[temp_bottom_fix]
type = DirichletBC
variable = temp
boundary = 3
value = 600.0
[]
[]
[Materials]
[flux]
type = FastNeutronFlux
factor = 5e17
[]
[elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = 1
youngs_modulus = 462.22e9
poissons_ratio = 0.21
[]
[stress]
type = ComputeMultipleInelasticStress
inelastic_models = monolithic_sic_creep
block = 1
[]
[monolithic_sic_creep]
type = MonolithicSiCCreepUpdate
block = 1
temperature = temp
k_function = k_function
[]
[thermal]
type = HeatConductionMaterial
block = 1
specific_heat = 1.0
thermal_conductivity = 100.
[]
[density]
type = StrainAdjustedDensity
block = 1
strain_free_density = 1.0
[]
[]
[Executioner]
type = Transient
solve_type = PJFNK
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart'
petsc_options_value = '101'
line_search = 'none'
l_max_its = 30
nl_max_its = 10
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_tol = 1e-8
start_time = 0.0
end_time = 200e6
dt = 1e7
[]
[Outputs]
exodus = true
[]
(test/tests/solid_mechanics/sic_creep/ad_monolithic_sic_creep.i)
# Tests material model MonolothicSiCCreepUpdate which computes
# irradiation creep for monolithic SiC.
#
# The test is a single element unit cube which is pulled in the y direction
# with a pressure of 5.0e7 Pa. The temperature and fission rate within the cube
# are uniform and constant at 600 K and 5e17 fissions/m**3-s. The total time is
# 200e6s.
#
# The anaytical solution for the creep strain is 0.001.
[GlobalParams]
displacements = 'disp_x disp_y disp_z'
[]
[Mesh]
use_displaced_mesh = false
[mesh]
type = FileMeshGenerator
file = 1x1x1_cube.e
[]
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[disp_z]
[]
[temp]
initial_condition = 600.0
[]
[]
[AuxVariables]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[creep_strain_yy]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[k_function]
type = PiecewiseLinear
x = '0 200e6'
y = '2e-37 2e-37'
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[all]
strain = small
incremental = true
use_automatic_differentiation = true
[]
[]
[Kernels]
[heat]
type = ADHeatConduction
variable = temp
[]
[]
[AuxKernels]
[stress_yy]
type = ADRankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
[]
[creep_strain_yy]
type = ADRankTwoAux
rank_two_tensor = creep_strain
variable = creep_strain_yy
index_i = 1
index_j = 1
[]
[]
[BCs]
[u_top_pull]
type = ADPressure
variable = disp_y
boundary = 5
factor = -5e7
[]
[u_bottom_fix]
type = ADDirichletBC
variable = disp_y
boundary = 3
value = 0.0
[]
[u_yz_fix]
type = ADDirichletBC
variable = disp_x
boundary = 4
value = 0.0
[]
[u_xy_fix]
type = ADDirichletBC
variable = disp_z
boundary = 2
value = 0.0
[]
[temp_top_fix]
type = ADDirichletBC
variable = temp
boundary = 5
value = 600.0
[]
[temp_bottom_fix]
type = ADDirichletBC
variable = temp
boundary = 3
value = 600.0
[]
[]
[Materials]
[flux]
type = ADFastNeutronFlux
factor = 5e17
[]
[elasticity_tensor]
type = ADComputeIsotropicElasticityTensor
block = 1
youngs_modulus = 462.22e9
poissons_ratio = 0.21
[]
[stress]
type = ADComputeMultipleInelasticStress
inelastic_models = monolithic_sic_creep
block = 1
[]
[monolithic_sic_creep]
type = ADMonolithicSiCCreepUpdate
block = 1
temperature = temp
k_function = k_function
[]
[thermal]
type = ADHeatConductionMaterial
block = 1
specific_heat = 1.0
thermal_conductivity = 100.
[]
[density]
type = ADStrainAdjustedDensity
block = 1
strain_free_density = 1.0
[]
[]
[Executioner]
type = Transient
solve_type = PJFNK
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart'
petsc_options_value = '101'
line_search = 'none'
l_max_its = 30
nl_max_its = 10
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_tol = 1e-8
start_time = 0.0
end_time = 200e6
dt = 1e7
automatic_scaling = true
[]
[Outputs]
exodus = 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
[]
[]
(test/tests/solid_mechanics/sic_creep/monolithic_sic_creep.i)
# Tests material model MonolothicSiCCreepUpdate which computes
# irradiation creep for monolithic SiC.
#
# The test is a single element unit cube which is pulled in the y direction
# with a pressure of 5.0e7 Pa. The temperature and fission rate within the cube
# are uniform and constant at 600 K and 5e17 fissions/m**3-s. The total time is
# 200e6s.
#
# The anaytical solution for the creep strain is 0.001.
[GlobalParams]
displacements = 'disp_x disp_y disp_z'
[]
[Mesh]
use_displaced_mesh = false
[mesh]
type = FileMeshGenerator
file = 1x1x1_cube.e
[]
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[disp_z]
[]
[temp]
initial_condition = 600.0
[]
[]
[AuxVariables]
[stress_yy]
order = CONSTANT
family = MONOMIAL
[]
[creep_strain_yy]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[k_function]
type = PiecewiseLinear
x = '0 200e6'
y = '2e-37 2e-37'
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[all]
strain = small
incremental = true
[]
[]
[Kernels]
[heat]
type = HeatConduction
variable = temp
[]
[]
[AuxKernels]
[stress_yy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_yy
index_i = 1
index_j = 1
[]
[creep_strain_yy]
type = RankTwoAux
rank_two_tensor = creep_strain
variable = creep_strain_yy
index_i = 1
index_j = 1
[]
[]
[BCs]
[u_top_pull]
type = Pressure
variable = disp_y
boundary = 5
factor = -5e7
[]
[u_bottom_fix]
type = DirichletBC
variable = disp_y
boundary = 3
value = 0.0
[]
[u_yz_fix]
type = DirichletBC
variable = disp_x
boundary = 4
value = 0.0
[]
[u_xy_fix]
type = DirichletBC
variable = disp_z
boundary = 2
value = 0.0
[]
[temp_top_fix]
type = DirichletBC
variable = temp
boundary = 5
value = 600.0
[]
[temp_bottom_fix]
type = DirichletBC
variable = temp
boundary = 3
value = 600.0
[]
[]
[Materials]
[flux]
type = FastNeutronFlux
factor = 5e17
[]
[elasticity_tensor]
type = ComputeIsotropicElasticityTensor
block = 1
youngs_modulus = 462.22e9
poissons_ratio = 0.21
[]
[stress]
type = ComputeMultipleInelasticStress
inelastic_models = monolithic_sic_creep
block = 1
[]
[monolithic_sic_creep]
type = MonolithicSiCCreepUpdate
block = 1
temperature = temp
k_function = k_function
[]
[thermal]
type = HeatConductionMaterial
block = 1
specific_heat = 1.0
thermal_conductivity = 100.
[]
[density]
type = StrainAdjustedDensity
block = 1
strain_free_density = 1.0
[]
[]
[Executioner]
type = Transient
solve_type = PJFNK
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart'
petsc_options_value = '101'
line_search = 'none'
l_max_its = 30
nl_max_its = 10
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_tol = 1e-8
start_time = 0.0
end_time = 200e6
dt = 1e7
[]
[Outputs]
exodus = 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
[]
[]
(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
[]
[]
(examples/accident_tolerant_fuel/u3si2_sic/u3si2_outer_monolith_1.5D.i)
# Model is of a 10 pellet fuel rodlet modeled in 1.5D. The rodlet contains
# U3Si2 fuel and a multilayer silicon carbide cladding (an inner composite
# winding layer) and an outer monolithic layer. The inner composite layer is
# 0.75 mm thick and the outer monolithic layer is 0.25 mm thick. The internal
# layered1D mesh generator can model a clad an arbitrary number of additional blocks.
# Therefore, to create the multilayer SiC clad the composite layer is assigned to the
# clad block and the monolithic_layer is assigned to the monolithic_layer block
# as specified in the additional_block_names parameter in the Mesh block.
initial_fuel_density = 11590.0
[GlobalParams]
density = ${initial_fuel_density}
initial_porosity = 0.05
order = SECOND
family = LAGRANGE
energy_per_fission = 3.2e-11 # J/fission
displacements = disp_x
temperature = temperature
[]
[Problem]
type = ReferenceResidualProblem
reference_vector = 'ref'
extra_tag_vectors = 'ref'
[]
[Mesh]
coord_type = RZ
[layered1D_mesh]
type = Layered1DMeshGenerator
slices_per_block = 10
clad_gap_width = 8.0e-5
clad_mesh_density = customize
clad_thickness = 0.00075
nx_c = 5
additional_block_names = 'monolithic_layer'
additional_elements_per_ring = '3'
additional_ring_thicknesses = '0.00025'
fuel_height = 0.1186
plenum_height = 0.027
[]
patch_update_strategy = auto
partitioner = centroid
centroid_partitioner_direction = y
[]
[UserObjects]
[pin_geometry]
type = Layered1DFuelPinGeometry
mesh_generator = layered1D_mesh
[]
[]
[Variables]
[temperature]
initial_condition = 580.0 # set initial temperature to coolant inlet
[]
[]
[AuxVariables]
[disp_y] ## Required for easier visualization in Paraview
[]
[disp_z] ## Required for easier visualization in Paraview
[]
[fast_neutron_flux]
block = 'clad monolithic_layer'
order = CONSTANT
family = MONOMIAL
[]
[fast_neutron_fluence]
block = 'clad monolithic_layer'
order = CONSTANT
family = MONOMIAL
[]
[grain_radius]
block = fuel
initial_condition = 10e-6
[]
[solid_swell]
order = CONSTANT
family = MONOMIAL
block = fuel
[]
[gaseous_swelling]
order = CONSTANT
family = MONOMIAL
block = fuel
[]
[densification]
order = CONSTANT
family = MONOMIAL
block = fuel
[]
[volumetric_swelling_strain]
order = CONSTANT
family = MONOMIAL
block = fuel
[]
[relocation]
order = CONSTANT
family = MONOMIAL
block = fuel
[]
[]
[Functions]
[power_history]
type = PiecewiseLinear
x = '0 1e4 1e8'
y = '0 25000 25000'
scale_factor = 1
[]
[axial_peaking_factors]
type = ParsedFunction
expression = 1
[]
[pressure_ramp]
type = PiecewiseLinear
x = '-200 0 1e8'
y = '6.537e-3 1 1'
[]
[q]
type = CompositeFunction
functions = 'power_history axial_peaking_factors'
[]
[clad_axial_pressure]
type = CladdingAxialPressureFunction
plenum_pressure = plenum_pressure
coolant_pressure = pressure_ramp
coolant_pressure_scaling_factor = 15.5e6
fuel_pin_geometry = pin_geometry
[]
[fuel_axial_pressure]
type = ParsedFunction
expression = plenum_pressure
symbol_names = plenum_pressure
symbol_values = plenum_pressure
[]
[]
[Kernels]
[heat]
type = HeatConduction
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_ie]
type = HeatConductionTimeDerivative
variable = temperature
extra_vector_tags = 'ref'
[]
[heat_source]
type = NeutronHeatSource
variable = temperature
block = fuel
burnup_function = burnup
extra_vector_tags = 'ref'
[]
[]
[Physics]
[SolidMechanics]
[Layered1D]
[fuel]
block = fuel
add_variables = true
strain = SMALL
incremental = true
add_scalar_variables = true
out_of_plane_strain_name = strain_yy
fuel_pin_geometry = pin_geometry
out_of_plane_pressure_function = fuel_axial_pressure
eigenstrain_names = 'fuel_thermal_strain fuel_swelling_strain'
generate_output = 'stress_xx stress_yy stress_zz vonmises_stress strain_xx'
extra_vector_tags = 'ref'
group_scalar_vars_in_reference_residual = true
mesh_generator = layered1D_mesh
[]
[composite]
block = clad
add_variables = true
strain = SMALL
incremental = true
add_scalar_variables = true
out_of_plane_strain_name = strain_yy
fuel_pin_geometry = pin_geometry
out_of_plane_pressure_function = clad_axial_pressure
eigenstrain_names = 'composite_thermal_strain composite_swelling_strain'
generate_output = 'stress_xx stress_yy stress_zz vonmises_stress strain_xx'
extra_vector_tags = 'ref'
group_scalar_vars_in_reference_residual = true
mesh_generator = layered1D_mesh
[]
[monolith]
block = monolithic_layer
add_variables = true
strain = SMALL
incremental = true
add_scalar_variables = true
out_of_plane_strain_name = strain_yy
fuel_pin_geometry = pin_geometry
out_of_plane_pressure_function = clad_axial_pressure
eigenstrain_names = 'monolith_thermal_strain monolith_swelling_strain'
generate_output = 'stress_xx stress_yy stress_zz vonmises_stress strain_xx'
extra_vector_tags = 'ref'
group_scalar_vars_in_reference_residual = true
mesh_generator = layered1D_mesh
[]
[]
[]
[]
[Burnup]
[burnup]
block = fuel
rod_ave_lin_pow = power_history
axial_power_profile = axial_peaking_factors
num_radial = 80
num_axial = 11
order = CONSTANT
family = MONOMIAL
fuel_pin_geometry = pin_geometry
fuel_volume_ratio = 1.0
RPF = RPF
fuel_type = U3Si2
[]
[]
[AuxKernels]
[fast_neutron_flux]
type = MaterialRealAux
variable = fast_neutron_flux
property = fast_neutron_flux
block = 'clad monolithic_layer'
execute_on = timestep_begin
[]
[fast_neutron_fluence]
type = MaterialRealAux
variable = fast_neutron_fluence
property = fast_neutron_fluence
block = 'clad monolithic_layer'
execute_on = timestep_begin
[]
[grain_radius]
type = GrainRadiusAux
block = fuel
variable = grain_radius
temperature = temperature
execute_on = linear
[]
[solid_swell]
type = MaterialRealAux
variable = solid_swell
property = solid_swelling
execute_on = timestep_end
block = fuel
[]
[gas_swell]
type = MaterialRealAux
variable = gaseous_swelling
property = gaseous_swelling
execute_on = timestep_end
block = fuel
[]
[densification]
type = MaterialRealAux
variable = densification
property = densification
execute_on = timestep_end
block = fuel
[]
[volumetric_swelling_strain]
type = MaterialRealAux
variable = volumetric_swelling_strain
property = volumetric_swelling_strain
execute_on = timestep_end
block = fuel
[]
[]
[Contact]
[pellet_clad_mechanical]
primary = 5
secondary = 10
formulation = kinematic
model = frictionless
penalty = 1e7
[]
[]
[ThermalContact]
[thermal_contact]
type = GasGapHeatTransfer
variable = temperature
primary = 5
secondary = 10
initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
gas_released = fis_gas_released # coupling to a postprocessor which supplies the fission gas addition
contact_pressure = contact_pressure
[]
[]
[BCs]
[no_x_all] # pin pellets and clad along axis of symmetry (y)
type = DirichletBC
variable = disp_x
boundary = 12
value = 0.0
[]
[Pressure] # apply coolant pressure on clad outer walls
[coolantPressure]
use_displaced_mesh = false
boundary = 2
function = pressure_ramp # use the pressure_ramp function defined above
factor = 15.5e6
[]
[]
[PlenumPressure] # apply plenum pressure on clad inner walls and pellet surfaces
[plenumPressure]
use_displaced_mesh = false
boundary = 9
initial_pressure = 2.0e6
startup_time = 0
R = 8.314
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 = gas_volume # 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
[]
[]
[]
[CoolantChannel]
[convective_clad_surface] # apply convective boundary to clad outer surface
variable = temperature
boundary = 2
inlet_temperature = 580 # K
inlet_pressure = 15.5e6 # Pa
inlet_massflux = 3800 # kg/m^2-sec
rod_diameter = 10.368e-3 # m
rod_pitch = 1.26e-2 # m
linear_heat_rate = power_history
axial_power_profile = axial_peaking_factors
[]
[]
[Materials]
[flux]
type = FastNeutronFlux
calculate_fluence = true
block = 'clad monolithic_layer'
rod_ave_lin_pow = power_history
axial_power_profile = axial_peaking_factors
factor = 3e13
[]
### U3Si2 Fuel
[fuel_thermal]
type = SilicideFuelThermal
block = fuel
thermal_conductivity_model = WHITE
temperature = temperature
[]
[fuel_elasticity_tensor]
type = U3Si2ElasticityTensor
block = fuel
[]
[fuel_stress]
type = ComputeMultipleInelasticStress
block = fuel
tangent_operator = elastic
inelastic_models = 'fuel_creep'
[]
[fuel_creep]
type = U3Si2CreepUpdate
block = fuel
temperature = temperature
[]
[fuel_thermal_expansion]
type = U3Si2ThermalExpansionEigenstrain
block = fuel
temperature = temperature
stress_free_temperature = 295.0
eigenstrain_name = fuel_thermal_strain
[]
[fuel_volumetric_swelling]
type = U3Si2VolumetricSwellingEigenstrain
block = fuel
gaseous_swelling_type = FINLAY
temperature = temperature
burnup_function = burnup
eigenstrain_name = fuel_swelling_strain
[]
[fission_gas_release]
type = U3Si2Sifgrs
block = fuel
temperature = temperature
burnup_function = burnup
grain_radius_const = 2.5e-05
[]
[fuel_density]
type = StrainAdjustedDensity
block = fuel
strain_free_density = ${initial_fuel_density}
[]
### Composite SiC
[composite_thermal]
type = CompositeSiCThermal
thermal_conductivity_model = STONE
temperature = temperature
block = clad
[]
[composite_density]
type = StrainAdjustedDensity
block = clad
strain_free_density = 2700.0
[]
[composite_elasticity_tensor]
type = CompositeSiCElasticityTensor
block = clad
[]
[composite_stress]
type = ComputeStrainIncrementBasedStress
block = clad
[]
[composite_thermal_expansion]
type = CompositeSiCThermalExpansionEigenstrain
block = clad
stress_free_temperature = 295.0
temperature = temperature
eigenstrain_name = composite_thermal_strain
[]
[composite_irradiation_swelling]
type = CompositeSiCVolumetricSwellingEigenstrain
block = clad
temperature = temperature
fast_neutron_fluence = fast_neutron_fluence
swelling_model = KATOH
number_of_substeps = 1000
eigenstrain_name = composite_swelling_strain
[]
### Monolithic SiC
[monolith_thermal]
type = MonolithicSiCThermal
temperature = temperature
thermal_conductivity_model = STONE
block = monolithic_layer
[]
[monolith_density]
type = StrainAdjustedDensity
block = monolithic_layer
strain_free_density = 3120.0
[]
[monolith_elasticity_tensor]
type = MonolithicSiCElasticityTensor
block = monolithic_layer
[]
[monolith_stress]
type = ComputeMultipleInelasticStress
block = monolithic_layer
tangent_operator = elastic
inelastic_models = 'monolith_creep'
[]
[monolith_creep]
type = MonolithicSiCCreepUpdate
block = monolithic_layer
fast_neutron_flux = fast_neutron_flux
temperature = temperature
k_function = 2e-37
[]
[monolith_thermal_expansion]
type = MonolithicSiCThermalExpansionEigenstrain
block = monolithic_layer
stress_free_temperature = 295.0
temperature = temperature
eigenstrain_name = monolith_thermal_strain
[]
[monolith_irradiation_swelling]
type = CompositeSiCVolumetricSwellingEigenstrain
block = monolithic_layer
temperature = temperature
fast_neutron_fluence = fast_neutron_fluence
swelling_model = KATOH
number_of_substeps = 1000
eigenstrain_name = monolith_swelling_strain
[]
[]
[Dampers]
[limitT]
type = MaxIncrement
max_increment = 100.0
variable = temperature
[]
[limitX]
type = MaxIncrement
max_increment = 1e-5
variable = disp_x
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
line_search = 'none'
l_max_its = 50
l_tol = 8e-3
nl_max_its = 50
nl_rel_tol = 1e-4
nl_abs_tol = 1e-7
start_time = -200
n_startup_steps = 1
end_time = 8.0e7
dtmax = 1e6
dtmin = 1
[TimeStepper]
type = IterationAdaptiveDT
dt = 2e2
optimal_iterations = 25
iteration_window = 5
growth_factor = 2
cutback_factor = .5
[]
[]
[Postprocessors]
[ave_temp_interior] # average temperature of the cladding interior and all pellet exteriors
type = LayeredSideAverageValuePostprocessor
boundary = 9
variable = temperature
execute_on = 'initial linear'
fuel_pin_geometry = pin_geometry
[]
[clad_inner_vol] # volume inside of cladding
type = LayeredInternalVolumePostprocessor
boundary = 7
component = 0
fuel_pin_geometry = pin_geometry
out_of_plane_strain = strain_yy
execute_on = 'initial linear'
[]
[pellet_volume] # fuel pellet total volume
type = LayeredInternalVolumePostprocessor
boundary = 8
component = 0
fuel_pin_geometry = pin_geometry
out_of_plane_strain = strain_yy
execute_on = 'initial linear'
[]
[avg_clad_temp] # average temperature of cladding interior
type = LayeredSideAverageValuePostprocessor
boundary = 7
variable = temperature
fuel_pin_geometry = pin_geometry
execute_on = 'initial linear'
[]
[fis_gas_produced] # fission gas produced (moles)
type = LayeredElementIntegralFisGasGeneratedSifgrsPostprocessor
block = fuel
fuel_pin_geometry = pin_geometry
[]
[fis_gas_released] # fission gas released to plenum (moles)
type = LayeredElementIntegralFisGasReleasedSifgrsPostprocessor
block = fuel
fuel_pin_geometry = pin_geometry
[]
[fis_gas_grain]
type = LayeredElementIntegralFisGasGrainSifgrsPostprocessor
block = fuel
outputs = exodus
fuel_pin_geometry = pin_geometry
[]
[fis_gas_boundary]
type = LayeredElementIntegralFisGasBoundarySifgrsPostprocessor
block = fuel
outputs = exodus
fuel_pin_geometry = pin_geometry
[]
[fission_gas_release]
type = FGRPercent
fission_gas_released = fis_gas_released
fission_gas_generated = fis_gas_produced
[]
[gas_volume]
type = LayeredInternalVolumePostprocessor
boundary = 9
execute_on = 'initial linear'
component = 0
out_of_plane_strain = strain_yy
fuel_pin_geometry = pin_geometry
[]
[flux_from_clad] # area integrated heat flux from the cladding
type = LayeredSideFluxIntegralPostprocessor
variable = temperature
boundary = 5
diffusivity = thermal_conductivity
fuel_pin_geometry = pin_geometry
[]
[flux_from_fuel] # area integrated heat flux from the fuel
type = LayeredSideFluxIntegralPostprocessor
variable = temperature
boundary = 10
diffusivity = thermal_conductivity
fuel_pin_geometry = pin_geometry
[]
[_dt] # time step
type = TimestepSize
[]
[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
[]
[rod_total_power]
type = LayeredElementIntegralPowerPostprocessor
variable = temperature
burnup_function = burnup
block = fuel
fuel_pin_geometry = pin_geometry
[]
[rod_input_power]
type = FunctionValuePostprocessor
function = power_history
scale_factor = 0.1186 # rod height
[]
[solid_swelling]
type = ElementAverageValue
variable = solid_swell
block = fuel
[]
[gaseous_swelling]
type = ElementAverageValue
variable = gaseous_swelling
block = fuel
[]
[densification]
type = ElementAverageValue
variable = densification
block = fuel
[]
[volumetric_swelling]
type = ElementAverageValue
variable = volumetric_swelling_strain
block = fuel
[]
[]
[Outputs]
perf_graph = true
exodus = true
csv = true
color = false
[]
(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
[]
[]