Nuclear Material UN

Reduces the Material block length for UN ceramic fuel within input files.

Description

This NuclearMaterialUN action reduces BISON input file length by internally generating the Materials required for simulating metallic nuclear fuel, specifically UN.

The user may elect to use the nuclear_material_UN_table action to generate the necessary material classes for common metallic fuel simulations. All of the material blocks, generated with the default parameter settings, are shown in Table 1.

Fission Operation

note

This required parameter describes the characteristic type of fission study that will occur. For metallic fuel type simulations, this is simply labeled as fission_operation = Normal. This must be placed under the NuclearMaterials block heading and cannot be placed under sub-blocks such as UN.

Table 1: Material classes created by the NuclearMaterialUN action

Created Classes	Pre-Set Parameters	Block Name
MNElasticityTensor		fuel_elasticity_tensor

ComputeMultipleInelasticStress	inelastic_models = fuel_zrycreep	fuel_stress

MNCreepUpdate		fuel_creep

MNThermalExpansionEigenstrain	burnup_function = burnup	fuel_thermal_expansion
	eigenstrain_name = fuel_thermal_strain
MNVolumetricSwellingEigenstrain	initial_porosity = 0.3	fuel_volumetric_swelling
	eigenstrain_name = fuel_volumetric_strain
StrainAdjustedDensity	strain_free_density = 13630.0	fuel_density
Burnup		fuel_burnup

Example Input Syntax

Expanded fuel Block

[Materials]
  [fission]
    type = ADGenericFunctionMaterial
    prop_names = fission_rate
    prop_values = fission_func
    outputs = all
  []

  [fuel_thermal]
    block = pellet
    type = ADMNThermal
    temperature = temp
    porosity = porosity
    outputs = all
  []
  [fuel_porosity]
    block = pellet
    type = ADGenericFunctionMaterial
    prop_names = porosity
    prop_values = porosity_ramp
    outputs = all
  []

Simplified fuel Block

[NuclearMaterials<<<{"href": "../index.html"}>>>]
  [UN<<<{"href": "index.html"}>>>]
    [fuel]
      block<<<{"description": "The list of ids of the blocks (subdomain) that the stress divergence kernels will be applied to"}>>> = pellet
      density<<<{"description": "Initial fuel density"}>>> = ${density}
      atoms_heavy_metal_per_volume<<<{"description": "Atoms of heavy metal atoms per volume of fuel."}>>> = ${atoms_heavy_metal_per_volume}
      fission_function<<<{"description": "Function that describes the fission as a function of time."}>>> = fission_func
      incremental<<<{"description": "Use incremental or total strain"}>>> = true
      strain<<<{"description": "Strain formulation"}>>> = SMALL
      un_models<<<{"description": "Type(s) of physics models used on this block.   The choices are: Burnup Elastic Creep Swelling ThermalExpansion"}>>> = 'Burnup Elastic Creep Swelling ThermalExpansion'
      properties_to_output<<<{"description": "List of material properties that are to outputed."}>>> = 'youngs_modulus poissons_ratio'
      initial_porosity<<<{"description": "Initial (as-fabricated) fuel porosity (dimensionless)"}>>> = 0.03
      porosity_function<<<{"description": "Function that describes the change in porosity."}>>> = porosity_ramp
      stress_free_temperature<<<{"description": "Reference temperature for thermal eigenstrain calculation"}>>> = 350
    []
  []
[]

The eigenstrains have been automatically parsed and included by wrapping the SolidMechanics QuasiStatic Action inside the NuclearMaterials following the naming convention created by this class.

Input Parameters

densityInitial fuel density
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial fuel density
un_modelsType(s) of physics models used on this block. The choices are: Burnup Elastic Creep Swelling ThermalExpansion
C++ Type:MultiMooseEnum
Options:Burnup, Elastic, Creep, Swelling, ThermalExpansion
Controllable:No
Description:Type(s) of physics models used on this block. The choices are: Burnup Elastic Creep Swelling ThermalExpansion

Required Parameters

active__all__ If specified only the blocks named will be visited and made active
Default:__all__
C++ Type:std::vector<std::string>
Controllable:No
Description:If specified only the blocks named will be visited and made active
add_variablesFalseAdd the displacement variables
Default:False
C++ Type:bool
Controllable:No
Description:Add the displacement variables
additional_physicsType(s) of physics used on this block. The choices are: Mechanics Thermal
C++ Type:MultiMooseEnum
Options:Mechanics, Thermal
Controllable:No
Description:Type(s) of physics used on this block. The choices are: Mechanics Thermal
atoms_heavy_metal_per_volumeAtoms of heavy metal atoms per volume of fuel.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Atoms of heavy metal atoms per volume of fuel.
axial_power_profileName of the function describing axial power profile.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Name of the function describing axial power profile.
d1_functionFunction to be multiplied by d1
C++ Type:std::vector<FunctionName>
Unit:(no unit assumed)
Controllable:No
Description:Function to be multiplied by d1
d1_function_variableVariable to be used when evaluating d1_function. If not given, time will be used.
C++ Type:std::vector<std::string>
Controllable:No
Description:Variable to be used when evaluating d1_function. If not given, time will be used.
diffusion_1st_activation_energiesDiffusion activation energies.
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:Diffusion activation energies.
diffusion_1st_coefficients1st diffusion coefficient.
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:1st diffusion coefficient.
diffusion_2nd_activation_energiesSecond diffusion activation energy
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:Second diffusion activation energy
diffusion_2nd_coefficients2nd diffusion coefficient
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:2nd diffusion coefficient
element_decay_constantsRadioactive decay constant for elements tracked
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:Radioactive decay constant for elements tracked
element_scalingRelative scaling of element percentages
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:Relative scaling of element percentages
elements_initial_concentrationRelative ratio of element concentration
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:Relative ratio of element concentration
elements_trackedThe elements tracked within TRISO simulations.
C++ Type:MultiMooseEnum
Options:Ag, Cs, Sr
Controllable:No
Description:The elements tracked within TRISO simulations.
energy_deposited_in_fuel1Fraction of fission energy deposited in the fuel.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fraction of fission energy deposited in the fuel.
energy_per_fission3.28451e-11Energy released per fission
Default:3.28451e-11
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Energy released per fission
execute_onLINEARThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:LINEAR
C++ Type:ExecFlagEnum
Options:XFEM_MARK, NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
extra_vector_tagsThe tag names for extra vectors that residual data should be saved into
C++ Type:std::vector<TagName>
Controllable:No
Description:The tag names for extra vectors that residual data should be saved into
familyLAGRANGESpecifies the family of FE shape functions to use for this variable.
Default:LAGRANGE
C++ Type:MooseEnum
Options:LAGRANGE, MONOMIAL, SCALAR, LAGRANGE_VEC, MONOMIAL_VEC, L2_HIERARCHIC, L2_HIERARCHIC_VEC, L2_LAGRANGE, L2_LAGRANGE_VEC, L2_RAVIART_THOMAS
Controllable:No
Description:Specifies the family of FE shape functions to use for this variable.
fission_functionFunction that describes the fission as a function of time.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function that describes the fission as a function of time.
flux_factor1Constant multiplied against the function, rod average linear power, or q_variable.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Constant multiplied against the function, rod average linear power, or q_variable.
flux_functionThe function that describes the fast neutron flux
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The function that describes the fast neutron flux
fuel_pin_geometryName of the UserObject that reads the pin geometry from the mesh.
C++ Type:UserObjectName
Controllable:No
Description:Name of the UserObject that reads the pin geometry from the mesh.
generate_outputAdd scalar quantity output for stress and/or strain
C++ Type:MultiMooseEnum
Options:cauchy_stress_xx, cauchy_stress_xy, cauchy_stress_xz, cauchy_stress_yx, cauchy_stress_yy, cauchy_stress_yz, cauchy_stress_zx, cauchy_stress_zy, cauchy_stress_zz, creep_strain_xx, creep_strain_xy, creep_strain_xz, creep_strain_yx, creep_strain_yy, creep_strain_yz, creep_strain_zx, creep_strain_zy, creep_strain_zz, creep_stress_xx, creep_stress_xy, creep_stress_xz, creep_stress_yx, creep_stress_yy, creep_stress_yz, creep_stress_zx, creep_stress_zy, creep_stress_zz, deformation_gradient_xx, deformation_gradient_xy, deformation_gradient_xz, deformation_gradient_yx, deformation_gradient_yy, deformation_gradient_yz, deformation_gradient_zx, deformation_gradient_zy, deformation_gradient_zz, elastic_strain_xx, elastic_strain_xy, elastic_strain_xz, elastic_strain_yx, elastic_strain_yy, elastic_strain_yz, elastic_strain_zx, elastic_strain_zy, elastic_strain_zz, mechanical_strain_xx, mechanical_strain_xy, mechanical_strain_xz, mechanical_strain_yx, mechanical_strain_yy, mechanical_strain_yz, mechanical_strain_zx, mechanical_strain_zy, mechanical_strain_zz, pk1_stress_xx, pk1_stress_xy, pk1_stress_xz, pk1_stress_yx, pk1_stress_yy, pk1_stress_yz, pk1_stress_zx, pk1_stress_zy, pk1_stress_zz, pk2_stress_xx, pk2_stress_xy, pk2_stress_xz, pk2_stress_yx, pk2_stress_yy, pk2_stress_yz, pk2_stress_zx, pk2_stress_zy, pk2_stress_zz, plastic_strain_xx, plastic_strain_xy, plastic_strain_xz, plastic_strain_yx, plastic_strain_yy, plastic_strain_yz, plastic_strain_zx, plastic_strain_zy, plastic_strain_zz, small_stress_xx, small_stress_xy, small_stress_xz, small_stress_yx, small_stress_yy, small_stress_yz, small_stress_zx, small_stress_zy, small_stress_zz, strain_xx, strain_xy, strain_xz, strain_yx, strain_yy, strain_yz, strain_zx, strain_zy, strain_zz, stress_xx, stress_xy, stress_xz, stress_yx, stress_yy, stress_yz, stress_zx, stress_zy, stress_zz, effective_plastic_strain, effective_creep_strain, firstinv_stress, firstinv_cauchy_stress, firstinv_pk1_stress, firstinv_pk2_stress, firstinv_small_stress, firstinv_strain, hydrostatic_stress, hydrostatic_cauchy_stress, hydrostatic_pk1_stress, hydrostatic_pk2_stress, hydrostatic_small_stress, intensity_stress, intensity_cauchy_stress, intensity_pk1_stress, intensity_pk2_stress, intensity_small_stress, l2norm_mechanical_strain, l2norm_stress, l2norm_cauchy_stress, l2norm_pk1_stress, l2norm_strain, l2norm_elastic_strain, l2norm_plastic_strain, l2norm_creep_strain, max_principal_mechanical_strain, max_principal_stress, max_principal_cauchy_stress, max_principal_pk1_stress, max_principal_pk2_stress, max_principal_small_stress, max_principal_strain, maxshear_stress, maxshear_cauchy_stress, maxshear_pk1_stress, maxshear_pk2_stress, maxshear_small_stress, mid_principal_mechanical_strain, mid_principal_stress, mid_principal_cauchy_stress, mid_principal_pk1_stress, mid_principal_pk2_stress, mid_principal_small_stress, mid_principal_strain, min_principal_mechanical_strain, min_principal_stress, min_principal_cauchy_stress, min_principal_pk1_stress, min_principal_pk2_stress, min_principal_small_stress, min_principal_strain, secondinv_stress, secondinv_cauchy_stress, secondinv_pk1_stress, secondinv_pk2_stress, secondinv_small_stress, secondinv_strain, thirdinv_stress, thirdinv_cauchy_stress, thirdinv_pk1_stress, thirdinv_pk2_stress, thirdinv_small_stress, thirdinv_strain, triaxiality_stress, triaxiality_cauchy_stress, triaxiality_pk1_stress, triaxiality_pk2_stress, triaxiality_small_stress, volumetric_mechanical_strain, volumetric_strain, vonmises_stress, vonmises_cauchy_stress, vonmises_pk1_stress, vonmises_pk2_stress, directional_stress, directional_strain, axial_stress, axial_strain, axial_plastic_strain, axial_creep_strain, axial_elastic_strain, hoop_stress, hoop_strain, hoop_plastic_strain, hoop_creep_strain, hoop_elastic_strain, radial_stress, radial_strain, spherical_hoop_stress, spherical_hoop_strain, spherical_hoop_plastic_strain, spherical_hoop_creep_strain, spherical_hoop_elastic_strain, spherical_radial_stress, spherical_radial_strain
Controllable:No
Description:Add scalar quantity output for stress and/or strain
inactiveIf specified blocks matching these identifiers will be skipped.
C++ Type:std::vector<std::string>
Controllable:No
Description:If specified blocks matching these identifiers will be skipped.
incrementalFalseUse incremental or total strain
Default:False
C++ Type:bool
Controllable:No
Description:Use incremental or total strain
orderSECONDSpecifies the order of the FE shape function to use for this variable.
Default:SECOND
C++ Type:MooseEnum
Options:CONSTANT, FIRST, SECOND, THIRD, FOURTH, FIFTH, SIXTH, SEVENTH, EIGHTH, NINTH
Controllable:No
Description:Specifies the order of the FE shape function to use for this variable.
out_of_plane_pressure0Function used to prescribe pressure in the out-of-plane direction (y for 1D Axisymmetric or z for 2D Cartesian problems)
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function used to prescribe pressure in the out-of-plane direction (y for 1D Axisymmetric or z for 2D Cartesian problems)
pellet_radiusFuel slug radius.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fuel slug radius.
physicsType(s) of physics used on this block.
C++ Type:MultiMooseEnum
Options:Mechanics, Thermal
Controllable:No
Description:Type(s) of physics used on this block.
poissons_ratioPoisson's ratio for the material.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Poisson's ratio for the material.
porosity_functionFunction that describes the change in porosity.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function that describes the change in porosity.
properties_to_outputList of material properties that are to outputed.
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties that are to outputed.
rod_linear_powerName of the function describing rod linear power.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Name of the function describing rod linear power.
strainSMALLStrain formulation
Default:SMALL
C++ Type:MooseEnum
Options:SMALL, FINITE
Controllable:No
Description:Strain formulation
stress_free_temperatureReference temperature for thermal eigenstrain calculation
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Reference temperature for thermal eigenstrain calculation
system_pressure_functionThe function to use for the pressure on the exterior of the cladding.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The function to use for the pressure on the exterior of the cladding.
temperatureCoupled temperature: Used in multiple models
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature: Used in multiple models
use_automatic_differentiationFalseFlag to use automatic differentiation (AD) objects when possible
Default:False
C++ Type:bool
Controllable:No
Description:Flag to use automatic differentiation (AD) objects when possible
value_range_behaviorEXCEPTIONWhat to do if input value is outside the range of applicability.
Default:EXCEPTION
C++ Type:MooseEnum
Options:ERROR, WARN, IGNORE, EXCEPTION
Controllable:No
Description:What to do if input value is outside the range of applicability.
youngs_modulusYoung's modulus of the material.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Young's modulus of the material.

Optional Parameters

additional_generate_outputAdd scalar quantity output for stress and/or strain (will be appended to the list in `generate_output`)
C++ Type:MultiMooseEnum
Options:cauchy_stress_xx, cauchy_stress_xy, cauchy_stress_xz, cauchy_stress_yx, cauchy_stress_yy, cauchy_stress_yz, cauchy_stress_zx, cauchy_stress_zy, cauchy_stress_zz, creep_strain_xx, creep_strain_xy, creep_strain_xz, creep_strain_yx, creep_strain_yy, creep_strain_yz, creep_strain_zx, creep_strain_zy, creep_strain_zz, creep_stress_xx, creep_stress_xy, creep_stress_xz, creep_stress_yx, creep_stress_yy, creep_stress_yz, creep_stress_zx, creep_stress_zy, creep_stress_zz, deformation_gradient_xx, deformation_gradient_xy, deformation_gradient_xz, deformation_gradient_yx, deformation_gradient_yy, deformation_gradient_yz, deformation_gradient_zx, deformation_gradient_zy, deformation_gradient_zz, elastic_strain_xx, elastic_strain_xy, elastic_strain_xz, elastic_strain_yx, elastic_strain_yy, elastic_strain_yz, elastic_strain_zx, elastic_strain_zy, elastic_strain_zz, mechanical_strain_xx, mechanical_strain_xy, mechanical_strain_xz, mechanical_strain_yx, mechanical_strain_yy, mechanical_strain_yz, mechanical_strain_zx, mechanical_strain_zy, mechanical_strain_zz, pk1_stress_xx, pk1_stress_xy, pk1_stress_xz, pk1_stress_yx, pk1_stress_yy, pk1_stress_yz, pk1_stress_zx, pk1_stress_zy, pk1_stress_zz, pk2_stress_xx, pk2_stress_xy, pk2_stress_xz, pk2_stress_yx, pk2_stress_yy, pk2_stress_yz, pk2_stress_zx, pk2_stress_zy, pk2_stress_zz, plastic_strain_xx, plastic_strain_xy, plastic_strain_xz, plastic_strain_yx, plastic_strain_yy, plastic_strain_yz, plastic_strain_zx, plastic_strain_zy, plastic_strain_zz, small_stress_xx, small_stress_xy, small_stress_xz, small_stress_yx, small_stress_yy, small_stress_yz, small_stress_zx, small_stress_zy, small_stress_zz, strain_xx, strain_xy, strain_xz, strain_yx, strain_yy, strain_yz, strain_zx, strain_zy, strain_zz, stress_xx, stress_xy, stress_xz, stress_yx, stress_yy, stress_yz, stress_zx, stress_zy, stress_zz, effective_plastic_strain, effective_creep_strain, firstinv_stress, firstinv_cauchy_stress, firstinv_pk1_stress, firstinv_pk2_stress, firstinv_small_stress, firstinv_strain, hydrostatic_stress, hydrostatic_cauchy_stress, hydrostatic_pk1_stress, hydrostatic_pk2_stress, hydrostatic_small_stress, intensity_stress, intensity_cauchy_stress, intensity_pk1_stress, intensity_pk2_stress, intensity_small_stress, l2norm_mechanical_strain, l2norm_stress, l2norm_cauchy_stress, l2norm_pk1_stress, l2norm_strain, l2norm_elastic_strain, l2norm_plastic_strain, l2norm_creep_strain, max_principal_mechanical_strain, max_principal_stress, max_principal_cauchy_stress, max_principal_pk1_stress, max_principal_pk2_stress, max_principal_small_stress, max_principal_strain, maxshear_stress, maxshear_cauchy_stress, maxshear_pk1_stress, maxshear_pk2_stress, maxshear_small_stress, mid_principal_mechanical_strain, mid_principal_stress, mid_principal_cauchy_stress, mid_principal_pk1_stress, mid_principal_pk2_stress, mid_principal_small_stress, mid_principal_strain, min_principal_mechanical_strain, min_principal_stress, min_principal_cauchy_stress, min_principal_pk1_stress, min_principal_pk2_stress, min_principal_small_stress, min_principal_strain, secondinv_stress, secondinv_cauchy_stress, secondinv_pk1_stress, secondinv_pk2_stress, secondinv_small_stress, secondinv_strain, thirdinv_stress, thirdinv_cauchy_stress, thirdinv_pk1_stress, thirdinv_pk2_stress, thirdinv_small_stress, thirdinv_strain, triaxiality_stress, triaxiality_cauchy_stress, triaxiality_pk1_stress, triaxiality_pk2_stress, triaxiality_small_stress, volumetric_mechanical_strain, volumetric_strain, vonmises_stress, vonmises_cauchy_stress, vonmises_pk1_stress, vonmises_pk2_stress, directional_stress, directional_strain, axial_stress, axial_strain, axial_plastic_strain, axial_creep_strain, axial_elastic_strain, hoop_stress, hoop_strain, hoop_plastic_strain, hoop_creep_strain, hoop_elastic_strain, radial_stress, radial_strain, spherical_hoop_stress, spherical_hoop_strain, spherical_hoop_plastic_strain, spherical_hoop_creep_strain, spherical_hoop_elastic_strain, spherical_radial_stress, spherical_radial_strain
Controllable:No
Description:Add scalar quantity output for stress and/or strain (will be appended to the list in `generate_output`)
automatic_eigenstrain_namesTrueCollects all material eigenstrains and passes to required strain calculator within TMA internally.
Default:True
C++ Type:bool
Controllable:No
Description:Collects all material eigenstrains and passes to required strain calculator within TMA internally.
blockThe list of ids of the blocks (subdomain) that the stress divergence kernels will be applied to
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of ids of the blocks (subdomain) that the stress divergence kernels will be applied to
decomposition_methodEigenSolutionMethods to calculate the finite strain and rotation increments
Default:EigenSolution
C++ Type:MooseEnum
Options:TaylorExpansion, EigenSolution, HughesWinget
Controllable:No
Description:Methods to calculate the finite strain and rotation increments
displacementsThe displacements appropriate for the simulation geometry and coordinate system: Used in density and strain models
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements appropriate for the simulation geometry and coordinate system: Used in density and strain models
volumetric_locking_correctionFalseFlag to correct volumetric locking
Default:False
C++ Type:bool
Controllable:No
Description:Flag to correct volumetric locking

Mechanics Parameters

burnupCoupled Burnup: Used in fuel creep, fission gas, relocation, swelling, and thermal models
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled Burnup: Used in fuel creep, fission gas, relocation, swelling, and thermal models
fission_rateCoupled Fission rate: Used in fuel burnup, creep, densification, fission gas, relocation, swelling, and thermal models
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled Fission rate: Used in fuel burnup, creep, densification, fission gas, relocation, swelling, and thermal models

Fission Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.

Advanced Parameters

initial_porosity0.05Initial (as-fabricated) fuel porosity (dimensionless)
Default:0.05
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial (as-fabricated) fuel porosity (dimensionless)

Swelling Parameters

(assessment/nitride/EBRII/K4/analysis/base.i)

density = 13630.0
A_U = 0.238
A_Pu = 0.239
A_N = 0.014
X_Pu = 0.1
X_N = 0.5
avo = 6.0221408e23
M_avg = '${fparse X_N * A_N + X_Pu * A_Pu + (1.0 - X_N - X_Pu) * A_U}'
atoms = '${fparse density / M_avg * (1.0 - X_N) * avo}'

[GlobalParams]
  density = ${density}
  order = SECOND
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
  volumetric_locking_correction = false
  displacements = 'disp_x disp_y'

[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
  group_variables = 'disp_x disp_y'
[]

[Mesh]
  coord_type = RZ
  use_displaced_mesh = false
  [smeared_pellet_mesh]
    type = FuelPinMeshGenerator
    clad_thickness = 0.51e-3
    pellet_outer_radius = 3.1e-3
    pellet_height = 343e-3
    clad_top_gap_height = 43.5e-3
    clad_gap_width = 0.325e-3
    bottom_clad_height = 8e-3
    top_clad_height = 8e-3
    clad_bot_gap_height = 0.2e-3 # unknown
    clad_mesh_density = customize
    pellet_mesh_density = customize
    nx_p = 6
    ny_p = 260
    nx_c = 4
    ny_c = 260
    ny_cu = 3
    ny_cl = 3
    pellet_quantity = 1
    elem_type = QUAD8
  []
  patch_size = 30
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 350
  []
[]

[AuxVariables]
  [pellet_wall_temp]
    order = CONSTANT
    family = MONOMIAL
  []
  [radial_heat_flux]
    order = CONSTANT
    family = MONOMIAL
  []
  [clad_inner_wall_temp]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1e5   35e6 35100000' # unknown, final burnup was 9.6 %
    y = '0 1     1    0'
  []
  [axial_peaking_factors]
    type = PiecewiseLinear
    axis = y
    x = '0    46e-3 111e-3 200e-3 248e-3 313e-3 352e-3'
    y = '73e3 73e3  82e3   85e3   82e3   74e3   74e3'
  []
  [fission_func]
    type = ParsedFunction
    symbol_names = 'axial_peaking_factors power_history'
    symbol_values = 'axial_peaking_factors power_history'
    expression = 'linear_heating_rate := axial_peaking_factors * power_history;
             pellet_cross_sectional_area := 3.14159 * pow( 3.1e-3, 2 );
             volumetric_power := linear_heating_rate / pellet_cross_sectional_area;
             energy_per_fission := 3.2e-11;
             volumetric_power / energy_per_fission'
  []

  [coolant_press_ramp]
    type = PiecewiseLinear
    x = '0       35100000'
    y = '0.151e6 0.151e6' # unknown, Na coolant
  []
  [coolant_inlet_temp]
    type = PiecewiseLinear
    x = '0   1e5 35e6 35100000'
    y = '350 644 644  350'
  []
  [coolant_outlet_temp]
    type = PiecewiseLinear
    x = '0   1e5 35e6 35100000'
    y = '350 746 746  350'
  []
  [coolant_wall_temp]
    type = ParsedFunction
    symbol_values = 'coolant_inlet_temp coolant_outlet_temp'
    symbol_names = 'coolant_inlet_temp coolant_outlet_temp'
    expression = 'rod_length := 343e-3 + 43.5e-3 + 2 * 8e-3;
             delta_temp := coolant_outlet_temp - coolant_inlet_temp;
             interpolated_temp := coolant_inlet_temp + y * delta_temp / rod_length;
             max( min( interpolated_temp, coolant_outlet_temp ), coolant_inlet_temp )'
  []
  [radial_heat_flux]
    type = ParsedFunction
    symbol_values = 'coolant_wall_temp power_history axial_peaking_factors'
    symbol_names = 'coolant_wall_temp power_history axial_peaking_factors'
    expression = 'linear_heating_rate := axial_peaking_factors * power_history;
             pellet_radius := 3.1e-3;
             pellet_circumference := 3.14159 * pellet_radius * 2;
             linear_heating_rate / pellet_circumference'
  []
  [clad_inner_wall_temp]
    type = ParsedFunction
    symbol_values = 'radial_heat_flux coolant_wall_temp'
    symbol_names = 'radial_heat_flux coolant_wall_temp'
    expression = 'conductivity_316ss := 22;
             clad_thickness := 0.51e-3;
             coolant_wall_temp + radial_heat_flux / conductivity_316ss * clad_thickness'
  []
  [pellet_wall_temp]
    type = ParsedFunction
    symbol_values = 'radial_heat_flux coolant_wall_temp clad_inner_wall_temp'
    symbol_names = 'radial_heat_flux coolant_wall_temp clad_inner_wall_temp'
    expression = 'conductivity_gap := 100;
             gap_thickness := 0.325e-3;
             clad_inner_wall_temp + radial_heat_flux / conductivity_gap * gap_thickness'
  []

  [plenum_pressure]
    type = ConstantFunction
    value = 12.4e6 # initial fill
  []

  [porosity_ramp]
    type = PiecewiseLinear
    x = '0   1e5 35e6 35100000'
    y = '0.03 0.03 0.05  0.05' # Pellets start at 96.8% TD, but no data on final porosity.
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [fuel]
    block = pellet
    strain = SMALL
    incremental = true
    extra_vector_tags = 'ref'
    eigenstrain_names = 'fuel_thermal_expansion fuel_swelling'
    use_automatic_differentiation = true
  []
  [clad]
    block = clad
    strain = SMALL
    incremental = true
    extra_vector_tags = 'ref'
    use_automatic_differentiation = true
  []
[]

[Kernels]
  [gravity]
    type = ADGravity
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []
  [heat]
    type = ADHeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = ADFissionRateHeatSource
    variable = temp
    block = pellet
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [pellet_wall_temp]
    type = FunctionAux
    variable = pellet_wall_temp
    function = pellet_wall_temp
  []
  [radial_heat_flux]
    type = FunctionAux
    variable = radial_heat_flux
    function = radial_heat_flux
  []
  [clad_inner_wall_temp]
    type = FunctionAux
    variable = clad_inner_wall_temp
    function = clad_inner_wall_temp
  []
[]

[BCs]
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [no_y_fuel]
    type = DirichletBC
    variable = disp_y
    boundary = 20
    value = 0.0
  []
  [no_y_clad]
    type = DirichletBC
    variable = disp_y
    boundary = 1
    value = 0.0
  []
  [Pressure]
    [coolantPressure]
      boundary = '1 2 3'
      function = coolant_press_ramp
    []
    [plenumPressure]
      boundary = 9
      function = plenum_pressure
    []
  []
  [clad_outer_temp]
    type = FunctionDirichletBC
    boundary = '1 2 3'
    function = coolant_wall_temp
    variable = temp
  []
  [pellet_to_clad_cooling]
    type = FunctionDirichletBC
    boundary = 10
    function = pellet_wall_temp
    variable = temp
  []
[]

[Materials]
  [fission]
    type = ADGenericFunctionMaterial
    prop_names = fission_rate
    prop_values = fission_func
    outputs = all
  []

  [fuel_thermal]
    block = pellet
    type = ADMNThermal
    temperature = temp
    porosity = porosity
    outputs = all
  []
  [fuel_porosity]
    block = pellet
    type = ADGenericFunctionMaterial
    prop_names = porosity
    prop_values = porosity_ramp
    outputs = all
  []
  [fuel_elasticity_tensor]
    block = pellet
    type = ADMNElasticityTensor
    temperature = temp
    porosity = porosity
    output_properties = 'youngs_modulus poissons_ratio'
    outputs = all
  []
  [fuel_thermal_expansion]
    block = pellet
    type = ADMNThermalExpansionEigenstrain
    eigenstrain_name = fuel_thermal_expansion
    stress_free_temperature = 350
    temperature = temp

  []
  [fuel_creep]
    block = pellet
    type = ADMNCreepUpdate
    temperature = temp
    porosity = porosity
    fission_rate = fission_rate
    outputs = all
  []
  [burnup]
    type = ADBurnup
    block = pellet
    atoms_heavy_metal_per_volume = ${atoms}
    outputs = all
  []
  [fuel_swelling]
    block = pellet
    type = ADMNVolumetricSwellingEigenstrain
    eigenstrain_name = fuel_swelling
    temperature = temp
    initial_porosity = 0.03
    burnup = burnup
    outputs = all
  []
  [fuel_radial_return_stress]
    block = pellet
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'fuel_creep'
  []
  [fuel_density]
    block = pellet
    type = ADStrainAdjustedDensity
    strain_free_density = ${density}
  []

  [clad_elasticity_tensor]
    block = clad
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 190e9
    poissons_ratio = 0.265
  []
  [clad_stress]
    block = clad
    type = ADComputeLinearElasticStress
  []
  [clad_thermal]
    block = clad
    type = ADSS316Thermal
    temperature = temp
  []
  [clad_density]
    block = clad
    type = ADStrainAdjustedDensity
    strain_free_density = 8000
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
  []
[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 100.0
    variable = temp
  []
  [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 -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'
  line_search = 'none'

  l_max_its = 50
  l_tol = 8e-3
  nl_max_its = 15
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-10

  start_time = -200
  n_startup_steps = 1
  end_time = 35100000
  dtmin = 1
  dtmax = 2e6

  [Quadrature]
    order = fifth
    side_order = seventh
  []

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    time_t = ' 0   1e5 35e6 35100000'
    time_dt = '1e2 1e2 1e2  1e2'
    optimal_iterations = 10
    growth_factor = 2
    cutback_factor = 0.5
    iteration_window = 1
    linear_iteration_ratio = 100
  []
[]

[Postprocessors]
  [peak_burnup]
    type = ElementExtremeValue
    block = pellet
    value_type = max
    variable = burnup
  []

  [_dt]
    type = TimestepSize
  []
  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []
[]

[PerformanceMetricOutputs]
  outputs = performance_metrics
[]

[Outputs]
  color = true
  exodus = true
  perf_graph = true
  [console]
    type = Console
    max_rows = 25
    time_step_interval =  1
    output_linear = true
  []
  [out]
    type = CSV
    show = 'peak_burnup'
  []
  [performance_metrics]
    type = CSV
    show = 'peak_burnup num_lin_it num_nonlin_it alive_time'
  []
[]

(assessment/nitride/EBRII/K4/analysis/base_action.i)

  density = 13630.0
  A_U = 0.238
  A_Pu = 0.239
  A_N = 0.014
  X_Pu = 0.1
  X_N = 0.5
  avo = 6.0221408e23
  M_avg = '${fparse X_N * A_N + X_Pu * A_Pu + (1.0 - X_N - X_Pu) * A_U}'
  atoms_heavy_metal_per_volume = '${fparse density / M_avg * (1.0 - X_N) * avo}'

[GlobalParams]
  order = SECOND
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
  volumetric_locking_correction = false
  displacements = 'disp_x disp_y'
  temperature = temperature
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
  group_variables = 'disp_x disp_y'
[]

[Mesh]
  coord_type = RZ
  use_displaced_mesh = false
  [smeared_pellet_mesh]
    type = FuelPinMeshGenerator
    clad_thickness = 0.51e-3
    pellet_outer_radius = 3.1e-3
    pellet_height = 343e-3
    clad_top_gap_height = 43.5e-3
    clad_gap_width = 0.325e-3
    bottom_clad_height = 8e-3
    top_clad_height = 8e-3
    clad_bot_gap_height = 0.2e-3 # unknown
    clad_mesh_density = customize
    pellet_mesh_density = customize
    nx_p = 6
    ny_p = 260
    nx_c = 4
    ny_c = 260
    ny_cu = 3
    ny_cl = 3
    pellet_quantity = 1
    elem_type = QUAD8
  []
  patch_size = 30
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[AuxVariables]
  [pellet_wall_temp]
    order = CONSTANT
    family = MONOMIAL
  []
  [radial_heat_flux]
    order = CONSTANT
    family = MONOMIAL
  []
  [clad_inner_wall_temp]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1e5   35e6 35100000' # unknown, final burnup was 9.6 %
    y = '0 1     1    0'
  []
  [axial_peaking_factors]
    type = PiecewiseLinear
    axis = y
    x = '0    46e-3 111e-3 200e-3 248e-3 313e-3 352e-3'
    y = '73e3 73e3  82e3   85e3   82e3   74e3   74e3'
  []
  [fission_func]
    type = ParsedFunction
    symbol_names = 'axial_peaking_factors power_history'
    symbol_values = 'axial_peaking_factors power_history'
    expression = 'linear_heating_rate := axial_peaking_factors * power_history;
             pellet_cross_sectional_area := 3.14159 * pow( 3.1e-3, 2 );
             volumetric_power := linear_heating_rate / pellet_cross_sectional_area;
             energy_per_fission := 3.2e-11;
             volumetric_power / energy_per_fission'
  []

  [coolant_press_ramp]
    type = PiecewiseLinear
    x = '0       35100000'
    y = '0.151e6 0.151e6' # unknown, Na coolant
  []
  [coolant_inlet_temp]
    type = PiecewiseLinear
    x = '0   1e5 35e6 35100000'
    y = '350 644 644  350'
  []
  [coolant_outlet_temp]
    type = PiecewiseLinear
    x = '0   1e5 35e6 35100000'
    y = '350 746 746  350'
  []
  [coolant_wall_temp]
    type = ParsedFunction
    symbol_values = 'coolant_inlet_temp coolant_outlet_temp'
    symbol_names = 'coolant_inlet_temp coolant_outlet_temp'
    expression = 'rod_length := 343e-3 + 43.5e-3 + 2 * 8e-3;
             delta_temp := coolant_outlet_temp - coolant_inlet_temp;
             interpolated_temp := coolant_inlet_temp + y * delta_temp / rod_length;
             max( min( interpolated_temp, coolant_outlet_temp ), coolant_inlet_temp )'
  []
  [radial_heat_flux]
    type = ParsedFunction
    symbol_values = 'coolant_wall_temp power_history axial_peaking_factors'
    symbol_names = 'coolant_wall_temp power_history axial_peaking_factors'
    expression = 'linear_heating_rate := axial_peaking_factors * power_history;
             pellet_radius := 3.1e-3;
             pellet_circumference := 3.14159 * pellet_radius * 2;
             linear_heating_rate / pellet_circumference'
  []
  [clad_inner_wall_temp]
    type = ParsedFunction
    symbol_values = 'radial_heat_flux coolant_wall_temp'
    symbol_names = 'radial_heat_flux coolant_wall_temp'
    expression = 'conductivity_316ss := 22;
             clad_thickness := 0.51e-3;
             coolant_wall_temp + radial_heat_flux / conductivity_316ss * clad_thickness'
  []
  [pellet_wall_temp]
    type = ParsedFunction
    symbol_values = 'radial_heat_flux coolant_wall_temp clad_inner_wall_temp'
    symbol_names = 'radial_heat_flux coolant_wall_temp clad_inner_wall_temp'
    expression = 'conductivity_gap := 100;
             gap_thickness := 0.325e-3;
             clad_inner_wall_temp + radial_heat_flux / conductivity_gap * gap_thickness'
  []

  [plenum_pressure]
    type = ConstantFunction
    value = 12.4e6 # initial fill
  []

  [porosity_ramp]
    type = PiecewiseLinear
    x = '0   1e5 35e6 35100000'
    y = '0.03 0.03 0.05  0.05' # Pellets start at 96.8% TD, but no data on final porosity.
  []
[]

[Kernels]
  [gravity]
    type = ADGravity
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [pellet_wall_temp]
    type = FunctionAux
    variable = pellet_wall_temp
    function = pellet_wall_temp
  []
  [radial_heat_flux]
    type = FunctionAux
    variable = radial_heat_flux
    function = radial_heat_flux
  []
  [clad_inner_wall_temp]
    type = FunctionAux
    variable = clad_inner_wall_temp
    function = clad_inner_wall_temp
  []
[]

[BCs]
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [no_y_fuel]
    type = DirichletBC
    variable = disp_y
    boundary = 20
    value = 0.0
  []
  [no_y_clad]
    type = DirichletBC
    variable = disp_y
    boundary = 1
    value = 0.0
  []
  [Pressure]
    [coolantPressure]
      boundary = '1 2 3'
      function = coolant_press_ramp
    []
    [plenumPressure]
      boundary = 9
      function = plenum_pressure
    []
  []
  [clad_outer_temp]
    type = FunctionDirichletBC
    boundary = '1 2 3'
    function = coolant_wall_temp
    variable = temperature
  []
  [pellet_to_clad_cooling]
    type = FunctionDirichletBC
    boundary = 10
    function = pellet_wall_temp
    variable = temperature
  []
[]

[NuclearMaterials]
  stress_free_temperature = 350
  initial_temperature = 350
  fission_operation = 'HighBurnup'
  add_variables = true
  physics = 'Mechanics Thermal'
  extra_vector_tags = 'ref'
  automatic_eigenstrain_names = true
  use_automatic_differentiation = true
  decomposition_method = TaylorExpansion
  [UN]
    [fuel]
      block = pellet
      density = ${density}
      atoms_heavy_metal_per_volume = ${atoms_heavy_metal_per_volume}
      fission_function = fission_func
      incremental = true
      strain = SMALL
      un_models = 'Burnup Elastic Creep Swelling ThermalExpansion'
      properties_to_output = 'youngs_modulus poissons_ratio'
      initial_porosity = 0.03
      porosity_function = porosity_ramp
      stress_free_temperature = 350
    []
  []
  [SS316]
    [clad]
      block = clad
      incremental = true
      strain = SMALL
      ss316_models = 'Elastic'
    []
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
  []
[]

[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 -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'
  line_search = 'none'

  l_max_its = 50
  l_tol = 8e-3
  nl_max_its = 15
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-10

  start_time = -200
  n_startup_steps = 1
  end_time = 35100000
  dtmin = 1
  dtmax = 2e6

  [Quadrature]
    order = fifth
    side_order = seventh
  []

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    time_t = ' 0   1e5 35e6 35100000'
    time_dt = '1e2 1e2 1e2  1e2'
    optimal_iterations = 10
    growth_factor = 2
    cutback_factor = 0.5
    iteration_window = 1
    linear_iteration_ratio = 100
  []
[]

[Postprocessors]
  [peak_burnup]
    type = ElementExtremeValue
    block = pellet
    value_type = max
    variable = burnup
  []

  [_dt]
    type = TimestepSize
  []
  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []
[]

[PerformanceMetricOutputs]
  outputs = performance_metrics
[]

[Outputs]
  color = true
  exodus = true
  perf_graph = true
  [console]
    type = Console
    max_rows = 25
    time_step_interval =  1
    output_linear = true
  []
  [out]
    type = CSV
    show = 'peak_burnup'
  []
  [performance_metrics]
    type = CSV
    show = 'peak_burnup num_lin_it num_nonlin_it alive_time'
  []
[]

Description
Example Input Syntax
Input Parameters