UO2PulverizationTransientFissionGasRelease

Computes the amount of fission gas release due to fuel pulverization.

Description

The UO2PulverizationTransientFissionGasRelease material computes the amount of fission gas released as a result of fuel pulverization. This is one of the mechanisms proposed to contribute to transient FGR. The amount of FGR is calculated using the approach developed in Aagesen et al. (2022).

During fuel pulverization, a fraction of the pores become exposed to free surfaces and release fission gas. The amount of fission gas released is therefore equal to $(1)var element = document.getElementById("moose-equation-4ff6eee4-e583-4c59-877b-6d54daa9bac7");katex.render(" n_{tFG}^{pul} = f^{pul}_V n_{FG} V^{pul}, ", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-c6dfad82-d8e1-44b1-af6e-d748be76c55c");katex.render("n_{FG}", element, {displayMode:false,throwOnError:false});$ is the density of fission gas release in the pulverized fuel in mol/m $var element = document.getElementById("moose-equation-02204ba4-a0a3-4eb3-813d-69c7a9b687eb");katex.render("^3", element, {displayMode:false,throwOnError:false});$ , derived as the product of the bubble density in bubble/m $var element = document.getElementById("moose-equation-2f59efc6-e3c2-4939-bd81-a2859f6c7710");katex.render("^3", element, {displayMode:false,throwOnError:false});$ and the average number of atoms in intragranular gas bubbles (atoms/bubble), and divided by the Avogadro constant. $var element = document.getElementById("moose-equation-10224449-fa87-405a-af3c-decf28e99069");katex.render("V^{pul}", element, {displayMode:false,throwOnError:false});$ is the volume of pulverized fuel in m $var element = document.getElementById("moose-equation-5222e2c6-5dd8-4d03-a88f-c6c78fe47aee");katex.render("^3", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-aed48bca-0480-410e-bb83-ea22711ccd01");katex.render("f^{pul}_V", element, {displayMode:false,throwOnError:false});$ is the volume fraction of bubbles opened during fuel pulverization, over the total bubble volume.

$var element = document.getElementById("moose-equation-33c7218a-fb0b-4767-948d-e118e95862ad");katex.render("f^{pul}_V", element, {displayMode:false,throwOnError:false});$ is expected to depend on pore structure, fragment size, and porosity. Its derivation based on a geometric criteria is detailed in Aagesen et al. (2022). Assuming cuboid fuel fragments of size $var element = document.getElementById("moose-equation-4809e005-efd0-41f0-a1f3-0c9d4c48b3ac");katex.render("l_f", element, {displayMode:false,throwOnError:false});$ and homogeneous bubble radius $var element = document.getElementById("moose-equation-06f2d6d3-3502-4739-8492-135cca7a6a77");katex.render("r_b", element, {displayMode:false,throwOnError:false});$ , it is defined as $var element = document.getElementById("moose-equation-28c91c38-d246-40f9-99f6-8e37290bbdfe");katex.render(" f^{pul}_V = \\frac{V_{b,open}^{pul}}{V_{b}^{pul}}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-8cb0e8a2-9542-4d14-a790-f86c5962b96e");katex.render("V_{b}^{pul}", element, {displayMode:false,throwOnError:false});$ is the total bubble volume in pulverized fuel, and $var element = document.getElementById("moose-equation-39d591b2-7597-46e4-ba56-cefd289caac1");katex.render("V_{b,open}^{pul}", element, {displayMode:false,throwOnError:false});$ is the volume of pores that become exposed during fragmentation. Performing calculations on a number of random bubble microstructures showed that $var element = document.getElementById("moose-equation-8e55fe22-86fe-44e3-91ea-81d7bf892b80");katex.render("f^{pul}_V", element, {displayMode:false,throwOnError:false});$ can be approximated as $var element = document.getElementById("moose-equation-8cedf3d7-90cb-42d6-9c66-973cb3d51cf3");katex.render(" f^{pul}_V = c_p p + c_r \\frac{r_b}{l_f} + c_0", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-f8d6d20f-83f4-45c3-b69e-d8c5f376ef82");katex.render("c_p = 0.03", element, {displayMode:false,throwOnError:false});$ (-) the coefficient for the porosity, $var element = document.getElementById("moose-equation-7dbbe892-e24a-4ee7-9cd9-741f54e9d3ec");katex.render("c_r = 5.17", element, {displayMode:false,throwOnError:false});$ (-) the coefficient for the bubble-radius-to-fragment-size ratio, and $var element = document.getElementById("moose-equation-b435fc25-a4ef-45b1-ba2b-91c9c3b74bc2");katex.render("c_0 = 0.02", element, {displayMode:false,throwOnError:false});$ (-) a constant (Aagesen et al., 2022). This correlation has been derived for a porosity ranging from 1 % to 13 % and a bubble-radius-to-fragment-size ratio $var element = document.getElementById("moose-equation-cb7ff3fc-e33b-4ff3-b6e1-6ab085e62653");katex.render("\\frac{r_b}{l_f}", element, {displayMode:false,throwOnError:false});$ ranging from 0.01 to 0.1.

note:Use with pulverization model

Since it computes the FGR due to pulverization, this material block is meant to be used with UO2Sifgrs along with a high burnup structure formation model (HighBurnupStructureFormation) and a pulverization model (UO2PulverizationMesoscale). Sifgrs describes the fission gas behavior and provides the bubble size and pressure, the high burnup structure formation model provides the volume fraction of high burnup structure fuel, and the pulverization model provides the location of pulverized fuel, as well as $var element = document.getElementById("moose-equation-554bd267-2f7f-43de-92db-403f95a40423");katex.render("n_{FG}", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-ed7ad17a-1671-48b2-a857-d9bf5d1cba14");katex.render("r_b", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-b2f4ff30-98d7-447b-ba84-77aa93851364");katex.render("p", element, {displayMode:false,throwOnError:false});$ . However, for now, the size of fuel fragment is assumed to be 50 $var element = document.getElementById("moose-equation-af75c956-f174-4779-b39c-79251a01dd0e");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ m to correspond to experimental measurements.

note:Returning 0 for null porosity

The amount of fission gas released due to pulverization is set to $var element = document.getElementById("moose-equation-ed9c10c0-c454-40b8-8e49-84bff9ed5041");katex.render("n_{tFG}^{pul}=0", element, {displayMode:false,throwOnError:false});$ when the porosity is equal to 0.

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [UO2PulverizationTransientFissionGasRelease]
    # moles/m^3
    type = ADUO2PulverizationTransientFissionGasRelease<<<{"description": "Computes the amount of fission gas release due to fuel pulverization.", "href": "UO2PulverizationTransientFissionGasRelease.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = fuel
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = exodus
  []
[]

Input Parameters

atoms_per_bubble_HBSatom_per_bubble_GB_HBSAverage number of atoms in intragranular gas bubbles (atoms/bubble) material property name.
Default:atom_per_bubble_GB_HBS
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Average number of atoms in intragranular gas bubbles (atoms/bubble) material property name.
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
bubble_density_HBSbubble_GB_volume_density_HBSBubble density in fuel (bubble/m$^3$) material property name.
Default:bubble_GB_volume_density_HBS
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Bubble density in fuel (bubble/m$^3$) material property name.
bubble_radius_HBSbubble_radius_GB_HBSIntragranular bubble radius in HBU structure (m^3) material property name.
Default:bubble_radius_GB_HBS
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Intragranular bubble radius in HBU structure (m^3) material property name.
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
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.
fragment_size5e-05Size of the fragment resulting from pulverization assuming cubic shape (m)
Default:5e-05
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Size of the fragment resulting from pulverization assuming cubic shape (m)
porosityhbs_porosityPorosity (-) material property name.
Default:hbs_porosity
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Porosity (-) material property name.
pulverizedpulverizedBoolean material property name that describes the local state of the fuel (0:not pulverized, 1:pulverized) (-).
Default:pulverized
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Boolean material property name that describes the local state of the fuel (0:not pulverized, 1:pulverized) (-).
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.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(test/tests/uo2_transient_fission_gas_release/uo2_pulverization_phasefield2_transient_FGR.i)
(test/tests/uo2_transient_fission_gas_release/ad_uo2_pulverization_phasefield2_transient_FGR.i)
(test/tests/uo2_transient_fission_gas_release/uo2_pulverization_transient_FGR_1D.i)

References

Larry K Aagesen, Sudipta Biswas, Kyle Gamble, Wen Jiang, Pierre-Clément Simon, and Benjamin Spencer. Implementation and testing of physics-based pulverization model in BISON. Technical Report INL/RPT-22-67941 Rev. 0, Idaho National Laboratory, 2022.

@techreport{aagesen2022_67941,
    author = "Aagesen, Larry K and Biswas, Sudipta and Gamble, Kyle and Jiang, Wen and Simon, Pierre-Cl\'{e}ment and Spencer, Benjamin",
    institution = "Idaho National Laboratory",
    number = "INL/RPT-22-67941 Rev. 0",
    title = "Implementation and testing of physics-based pulverization model in {BISON}",
    year = "2022"
}

(test/tests/uo2_transient_fission_gas_release/ad_uo2_pulverization_phasefield2_transient_FGR.i)

# This file is to test the transient fission gas release model that accounts for
# the amount of fission gas released as a result of fuel pulverization. it is
# based on the input file called uo2_pulverization_mesoscale.i, which tests the
# pulverization criteria for UO2 fuel with evolve_bubble_pressure_hbs = true and
# using the 3D phase field criterion for pulverization.
# In the test 5 axial fuel slices are modeled without cladding with an outer fuel
# radius of 4.5 mm and slice height of 0.1 m. Ten radial finite elements are used.
# The burnup increases linearly from the fuel centerline to the fuel surface.
# Temperature is held at constant T = 673.15 K from t = 0 to t = 100, followed
# by a ramp in temperature from t = 100 to t = 125. Pulverization will occur
# during the ramp only, in the rim region where a significant amount of high burnup
# structure formation has begun. Local pulverization is tracked with the material
# property pulverized, which is 0 where pulverization has not occured and 1 where
# it has occurred. A material property uses the local pulverization to compute the
# amount of fission gas released as a results of fuel pulverization.
# This material property is output to the exodus file for this test.

# At each time step, the pulverized material property is computed, as well as
# the bubble radius and amount of fission gas in bubbles. These material property
# are then used to determine the amount of fission gas release due to pulverization.
# This amount predicted by the material block
# UO2PulverizationTransientFissionGasRelease is compared with analytical calculations
# made in the material block fission_gas_released_amount for verification.

# This input is the AD version.

hydrostatic_stress_constant = 1e7

[GlobalParams]
  value_range_behavior = WARN
[]

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 5
    pellet_outer_radius = 4.5e-3
    include_clad = false
    fuel_height = 0.5
    include_plenum = false
    nx_p = 10
    pellet_mesh_density = customize
    pellet_bottom_coor = 0.0
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 600
  []
[]

[AuxVariables]
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*1.6*t/4.275'
  []
  [temperature_function]
    type = ParsedFunction
    expression = 'if(t < 100, 900, 900+(t-100)*200)'
  []
  [Fiss_func]
    type = ParsedFunction
    expression = '1.e19'
  []
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temperature
  []
[]

[AuxKernels]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1
    fission_rate_function = Fiss_func
    execute_on = 'initial timestep_begin'
  []
  [pulverized]
    type = ADMaterialRealAux
    block = fuel
    variable = pulverized_aux
    property = pulverized
    execute_on = 'initial nonlinear'
  []
  [layered_pulverized_fuel_volume]
    type = SpatialUserObjectAux
    variable = layered_pulverized_fuel_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_pulverized_fuel_volume
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    boundary = '10 12'
    variable = temperature
    function = temperature_function
  []
[]

[Materials]
  [UO2PulverizationTransientFissionGasRelease] # moles/m^3
    type = ADUO2PulverizationTransientFissionGasRelease
    block = fuel
    outputs = exodus
  []
  [fission_gas_behavior]
    type = ADUO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    burnup = burnup
    skip_bdr_model = true
    ig_bubble_model = MECHANISTIC_AAGESEN
    hbs_model = true
    hbs_material = hbs_formation
    pulverization_model = true
    pulverization_transient_fission_gas_release_material = UO2PulverizationTransientFissionGasRelease
    ig_diff_algorithm = FORMAS
    hydrostatic_stress_const = ${hydrostatic_stress_constant}
    igdiffcoeff_scalef_HBS = 1e24 # Ensures that all the generated fission gases diffuse from the HBS matrix to the HBS bubbles
  []
  [uo2pulverizationmesoscale]
    type = ADUO2PulverizationMesoscale
    block = fuel
    temperature = temperature
    output_properties = pulverized
    pulverization_criterion_type = phase_field_3D
    outputs = exodus
  []
  [dummy_stress]
    type = ADGenericConstantRankTwoTensor
    tensor_name = 'stress'
    tensor_values = '-${hydrostatic_stress_constant} -${hydrostatic_stress_constant} -${hydrostatic_stress_constant} 0 0 0'
  []
  [fuel_thermal]
    type = ADUO2Thermal
    block = fuel
    thermal_conductivity_model = STAICU
    hbs_porosity_correction = KAMPF
    model_hbs_formation = true
    temperature = temperature
    burnup_function = burnup_function
    output_properties = hbs_porosity
    outputs = exodus
  []
  [hbs_formation]
    type = ADHighBurnupStructureFormation
    block = fuel
    temperature = temperature
    burnup = burnup
    threshold_temperature = 1273.15 # default
    output_properties = hbs_volume_fraction
    outputs = exodus
  []
  [fission_gas_density_bubble_HBS] # moles/m^3
    type = ADParsedMaterial
    block = fuel
    property_name = 'rho_FG_hbs'
    material_property_names = 'atom_per_bubble_GB_HBS bubble_GB_volume_density_HBS'
    constant_names = 'Na'
    constant_expressions = '6.02214076e23'
    expression = 'atom_per_bubble_GB_HBS * bubble_GB_volume_density_HBS / Na'
    outputs = exodus
  []
  [opened_pore_volume_fraction] # -
    type = ADParsedMaterial
    block = fuel
    property_name = 'f_V_pul'
    material_property_names = 'hbs_porosity bubble_radius_GB_HBS'
    constant_names = 'fragment_size c_p  c_r  c_0'
    constant_expressions = '5e-5    0.03 5.17 0.02'
    expression = 'c_p * hbs_porosity + c_r * bubble_radius_GB_HBS/fragment_size + c_0'
    outputs = exodus
  []
  [fission_gas_released_amount_analytical] # moles/m^3
    type = ADParsedMaterial
    block = fuel
    property_name = 'fis_gas_rel'
    material_property_names = 'f_V_pul rho_FG_hbs pulverized'
    expression = 'pulverized * f_V_pul * rho_FG_hbs'
    outputs = exodus
  []
[]

[UserObjects]
  [fuel_pin_geometry]
    type = Layered1DFuelPinGeometry
    include_clad = false
    mesh_generator = layered1D_mesh
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    variable = pulverized_aux
    fuel_pin_geometry = fuel_pin_geometry
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
[]

[Postprocessors]
  [FG_amount_bubble_HBS]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = rho_FG_hbs
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
  []
  [FGR_analytical]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = fis_gas_rel
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
  []
  [FGR]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = gas_concentration_release_pulverization
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
  []
  [FGR_pps_diff_bison_analytical]
    type = DifferencePostprocessor
    value1 = FGR_analytical
    value2 = FGR
  []
  [FG_pps_diff_total_released]
    type = DifferencePostprocessor
    value1 = FG_amount_bubble_HBS
    value2 = FGR
  []
  [volume_domain]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = 1
    block = fuel
    execute_on = TIMESTEP_END
    fuel_pin_geometry = fuel_pin_geometry
  []
  [hbs_volume]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = hbs_volume_fraction
    block = fuel
    execute_on = TIMESTEP_END
    fuel_pin_geometry = fuel_pin_geometry
  []
  [hbs_volume_fraction]
    type = ParsedPostprocessor
    pp_names = 'hbs_volume volume_domain'
    expression = 'hbs_volume / volume_domain'
    execute_on = TIMESTEP_END
  []
  [pulverized_volume]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = pulverized
    block = fuel
    execute_on = TIMESTEP_END
    fuel_pin_geometry = fuel_pin_geometry
  []
[]

[Executioner]
  type = Transient

  solve_type = Newton

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 125
  dt = 1
[]

[Outputs]
  exodus = true
  csv = true
  file_base = ad_uo2_pulverization_phasefield2_transient_FGR_out
[]

(test/tests/uo2_transient_fission_gas_release/uo2_pulverization_phasefield2_transient_FGR.i)

# This file is to test the transient fission gas release model that accounts for
# the amount of fission gas released as a result of fuel pulverization. it is
# based on the input file called uo2_pulverization_mesoscale.i, which tests the
# pulverization criteria for UO2 fuel with evolve_bubble_pressure_hbs = true and
# using the 3D phase field criterion for pulverization.
# In the test 5 axial fuel slices are modeled without cladding with an outer fuel
# radius of 4.5 mm and slice height of 0.1 m. Ten radial finite elements are used.
# The burnup increases linearly from the fuel centerline to the fuel surface.
# Temperature is held at constant T = 673.15 K from t = 0 to t = 100, followed
# by a ramp in temperature from t = 100 to t = 125. Pulverization will occur
# during the ramp only, in the rim region where a significant amount of high burnup
# structure formation has begun. Local pulverization is tracked with the material
# property pulverized, which is 0 where pulverization has not occured and 1 where
# it has occurred. A material property uses the local pulverization to compute the
# amount of fission gas released as a results of fuel pulverization.
# This material property is output to the exodus file for this test.

# At each time step, the pulverized material property is computed, as well as
# the bubble radius and amount of fission gas in bubbles. These material property
# are then used to determine the amount of fission gas release due to pulverization.
# This amount predicted by the material block
# UO2PulverizationTransientFissionGasRelease is compared with analytical calculations
# made in the material block fission_gas_released_amount for verification.

# This input is the non-AD version.

hydrostatic_stress_constant = 1e7

[GlobalParams]
  value_range_behavior = WARN
[]

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 5
    pellet_outer_radius = 4.5e-3
    include_clad = false
    fuel_height = 0.5
    include_plenum = false
    nx_p = 10
    pellet_mesh_density = customize
    pellet_bottom_coor = 0.0
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 600
  []
[]

[AuxVariables]
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*1.6*t/4.275'
  []
  [temperature_function]
    type = ParsedFunction
    expression = 'if(t < 100, 900, 900+(t-100)*200)'
  []
  [Fiss_func]
    type = ParsedFunction
    expression = '1.e19'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
  []
[]

[AuxKernels]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1
    fission_rate_function = Fiss_func
    execute_on = 'initial timestep_begin'
  []
  [pulverized]
    type = MaterialRealAux
    block = fuel
    variable = pulverized_aux
    property = pulverized
    execute_on = 'initial nonlinear'
  []
  [layered_pulverized_fuel_volume]
    type = SpatialUserObjectAux
    variable = layered_pulverized_fuel_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_pulverized_fuel_volume
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    boundary = '10 12'
    variable = temperature
    function = temperature_function
  []
[]

[Materials]
  [fission_gas_behavior]
    type = UO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    burnup = burnup
    skip_bdr_model = true
    ig_bubble_model = MECHANISTIC_AAGESEN
    hbs_model = true
    hbs_material = hbs_formation
    pulverization_model = true
    pulverization_transient_fission_gas_release_material = UO2PulverizationTransientFissionGasRelease
    ig_diff_algorithm = FORMAS
    hydrostatic_stress_const = ${hydrostatic_stress_constant}
    igdiffcoeff_scalef_HBS = 1e24 # Ensures that all the generated fission gases diffuse from the HBS matrix to the HBS bubbles
  []
  [uo2pulverizationmesoscale]
    type = UO2PulverizationMesoscale
    block = fuel
    temperature = temperature
    output_properties = pulverized
    pulverization_criterion_type = phase_field_3D
    outputs = exodus
  []
  [dummy_stress]
    type = GenericConstantRankTwoTensor
    tensor_name = 'stress'
    tensor_values = '-${hydrostatic_stress_constant} -${hydrostatic_stress_constant} -${hydrostatic_stress_constant} 0 0 0'
  []
  [fuel_thermal]
    type = UO2Thermal
    block = fuel
    thermal_conductivity_model = STAICU
    hbs_porosity_correction = KAMPF
    model_hbs_formation = true
    temperature = temperature
    burnup_function = burnup_function
    output_properties = hbs_porosity
    outputs = exodus
  []
  [hbs_formation]
    type = HighBurnupStructureFormation
    block = fuel
    temperature = temperature
    burnup = burnup
    threshold_temperature = 1273.15 # default
    output_properties = hbs_volume_fraction
    outputs = exodus
  []
  [fission_gas_density_bubble_HBS] # moles/m^3
    type = ParsedMaterial
    block = fuel
    property_name = 'rho_FG_hbs'
    material_property_names = 'atom_per_bubble_GB_HBS bubble_GB_volume_density_HBS'
    constant_names = 'Na'
    constant_expressions = '6.02214076e23'
    expression = 'atom_per_bubble_GB_HBS * bubble_GB_volume_density_HBS / Na'
    outputs = exodus
  []
  [opened_pore_volume_fraction] # -
    type = ParsedMaterial
    block = fuel
    property_name = 'f_V_pul'
    material_property_names = 'hbs_porosity bubble_radius_GB_HBS'
    constant_names = 'fragment_size c_p  c_r  c_0'
    constant_expressions = '5e-5    0.03 5.17 0.02'
    expression = 'c_p * hbs_porosity + c_r * bubble_radius_GB_HBS/fragment_size + c_0'
    outputs = exodus
  []
  [fission_gas_released_amount_analytical] # moles/m^3
    type = ParsedMaterial
    block = fuel
    property_name = 'fis_gas_rel'
    material_property_names = 'f_V_pul rho_FG_hbs pulverized'
    expression = 'pulverized * f_V_pul * rho_FG_hbs'
    outputs = exodus
  []
  [UO2PulverizationTransientFissionGasRelease] # moles/m^3
    type = UO2PulverizationTransientFissionGasRelease
    block = fuel
    outputs = exodus
  []
[]

[UserObjects]
  [fuel_pin_geometry]
    type = Layered1DFuelPinGeometry
    include_clad = false
    mesh_generator = layered1D_mesh
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    variable = pulverized_aux
    fuel_pin_geometry = fuel_pin_geometry
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
[]

[Postprocessors]
  [FG_amount_bubble_HBS]
    type = LayeredElementIntegralMaterialProperty
    mat_prop = rho_FG_hbs
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
  []
  [FGR_analytical]
    type = LayeredElementIntegralMaterialProperty
    mat_prop = fis_gas_rel
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
  []
  [FGR]
    type = LayeredElementIntegralMaterialProperty
    mat_prop = gas_concentration_release_pulverization
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
  []
  [FGR_pps_diff_bison_analytical]
    type = DifferencePostprocessor
    value1 = FGR_analytical
    value2 = FGR
  []
  [FG_pps_diff_total_released]
    type = DifferencePostprocessor
    value1 = FG_amount_bubble_HBS
    value2 = FGR
  []
  [volume_domain]
    type = LayeredElementIntegralMaterialProperty
    mat_prop = 1
    block = fuel
    execute_on = TIMESTEP_END
    fuel_pin_geometry = fuel_pin_geometry
  []
  [hbs_volume]
    type = LayeredElementIntegralMaterialProperty
    mat_prop = hbs_volume_fraction
    block = fuel
    execute_on = TIMESTEP_END
    fuel_pin_geometry = fuel_pin_geometry
  []
  [hbs_volume_fraction]
    type = ParsedPostprocessor
    pp_names = 'hbs_volume volume_domain'
    expression = 'hbs_volume / volume_domain'
    execute_on = TIMESTEP_END
  []
  [pulverized_volume]
    type = LayeredElementIntegralMaterialProperty
    mat_prop = pulverized
    block = fuel
    execute_on = TIMESTEP_END
    fuel_pin_geometry = fuel_pin_geometry
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 125
  dt = 1
[]

[Outputs]
  exodus = true
  csv = true
  file_base = uo2_pulverization_phasefield2_transient_FGR_out
[]

(test/tests/uo2_transient_fission_gas_release/ad_uo2_pulverization_phasefield2_transient_FGR.i)

# This file is to test the transient fission gas release model that accounts for
# the amount of fission gas released as a result of fuel pulverization. it is
# based on the input file called uo2_pulverization_mesoscale.i, which tests the
# pulverization criteria for UO2 fuel with evolve_bubble_pressure_hbs = true and
# using the 3D phase field criterion for pulverization.
# In the test 5 axial fuel slices are modeled without cladding with an outer fuel
# radius of 4.5 mm and slice height of 0.1 m. Ten radial finite elements are used.
# The burnup increases linearly from the fuel centerline to the fuel surface.
# Temperature is held at constant T = 673.15 K from t = 0 to t = 100, followed
# by a ramp in temperature from t = 100 to t = 125. Pulverization will occur
# during the ramp only, in the rim region where a significant amount of high burnup
# structure formation has begun. Local pulverization is tracked with the material
# property pulverized, which is 0 where pulverization has not occured and 1 where
# it has occurred. A material property uses the local pulverization to compute the
# amount of fission gas released as a results of fuel pulverization.
# This material property is output to the exodus file for this test.

# At each time step, the pulverized material property is computed, as well as
# the bubble radius and amount of fission gas in bubbles. These material property
# are then used to determine the amount of fission gas release due to pulverization.
# This amount predicted by the material block
# UO2PulverizationTransientFissionGasRelease is compared with analytical calculations
# made in the material block fission_gas_released_amount for verification.

# This input is the AD version.

hydrostatic_stress_constant = 1e7

[GlobalParams]
  value_range_behavior = WARN
[]

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 5
    pellet_outer_radius = 4.5e-3
    include_clad = false
    fuel_height = 0.5
    include_plenum = false
    nx_p = 10
    pellet_mesh_density = customize
    pellet_bottom_coor = 0.0
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 600
  []
[]

[AuxVariables]
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*1.6*t/4.275'
  []
  [temperature_function]
    type = ParsedFunction
    expression = 'if(t < 100, 900, 900+(t-100)*200)'
  []
  [Fiss_func]
    type = ParsedFunction
    expression = '1.e19'
  []
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temperature
  []
[]

[AuxKernels]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1
    fission_rate_function = Fiss_func
    execute_on = 'initial timestep_begin'
  []
  [pulverized]
    type = ADMaterialRealAux
    block = fuel
    variable = pulverized_aux
    property = pulverized
    execute_on = 'initial nonlinear'
  []
  [layered_pulverized_fuel_volume]
    type = SpatialUserObjectAux
    variable = layered_pulverized_fuel_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_pulverized_fuel_volume
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    boundary = '10 12'
    variable = temperature
    function = temperature_function
  []
[]

[Materials]
  [UO2PulverizationTransientFissionGasRelease] # moles/m^3
    type = ADUO2PulverizationTransientFissionGasRelease
    block = fuel
    outputs = exodus
  []
  [fission_gas_behavior]
    type = ADUO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    burnup = burnup
    skip_bdr_model = true
    ig_bubble_model = MECHANISTIC_AAGESEN
    hbs_model = true
    hbs_material = hbs_formation
    pulverization_model = true
    pulverization_transient_fission_gas_release_material = UO2PulverizationTransientFissionGasRelease
    ig_diff_algorithm = FORMAS
    hydrostatic_stress_const = ${hydrostatic_stress_constant}
    igdiffcoeff_scalef_HBS = 1e24 # Ensures that all the generated fission gases diffuse from the HBS matrix to the HBS bubbles
  []
  [uo2pulverizationmesoscale]
    type = ADUO2PulverizationMesoscale
    block = fuel
    temperature = temperature
    output_properties = pulverized
    pulverization_criterion_type = phase_field_3D
    outputs = exodus
  []
  [dummy_stress]
    type = ADGenericConstantRankTwoTensor
    tensor_name = 'stress'
    tensor_values = '-${hydrostatic_stress_constant} -${hydrostatic_stress_constant} -${hydrostatic_stress_constant} 0 0 0'
  []
  [fuel_thermal]
    type = ADUO2Thermal
    block = fuel
    thermal_conductivity_model = STAICU
    hbs_porosity_correction = KAMPF
    model_hbs_formation = true
    temperature = temperature
    burnup_function = burnup_function
    output_properties = hbs_porosity
    outputs = exodus
  []
  [hbs_formation]
    type = ADHighBurnupStructureFormation
    block = fuel
    temperature = temperature
    burnup = burnup
    threshold_temperature = 1273.15 # default
    output_properties = hbs_volume_fraction
    outputs = exodus
  []
  [fission_gas_density_bubble_HBS] # moles/m^3
    type = ADParsedMaterial
    block = fuel
    property_name = 'rho_FG_hbs'
    material_property_names = 'atom_per_bubble_GB_HBS bubble_GB_volume_density_HBS'
    constant_names = 'Na'
    constant_expressions = '6.02214076e23'
    expression = 'atom_per_bubble_GB_HBS * bubble_GB_volume_density_HBS / Na'
    outputs = exodus
  []
  [opened_pore_volume_fraction] # -
    type = ADParsedMaterial
    block = fuel
    property_name = 'f_V_pul'
    material_property_names = 'hbs_porosity bubble_radius_GB_HBS'
    constant_names = 'fragment_size c_p  c_r  c_0'
    constant_expressions = '5e-5    0.03 5.17 0.02'
    expression = 'c_p * hbs_porosity + c_r * bubble_radius_GB_HBS/fragment_size + c_0'
    outputs = exodus
  []
  [fission_gas_released_amount_analytical] # moles/m^3
    type = ADParsedMaterial
    block = fuel
    property_name = 'fis_gas_rel'
    material_property_names = 'f_V_pul rho_FG_hbs pulverized'
    expression = 'pulverized * f_V_pul * rho_FG_hbs'
    outputs = exodus
  []
[]

[UserObjects]
  [fuel_pin_geometry]
    type = Layered1DFuelPinGeometry
    include_clad = false
    mesh_generator = layered1D_mesh
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    variable = pulverized_aux
    fuel_pin_geometry = fuel_pin_geometry
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
[]

[Postprocessors]
  [FG_amount_bubble_HBS]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = rho_FG_hbs
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
  []
  [FGR_analytical]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = fis_gas_rel
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
  []
  [FGR]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = gas_concentration_release_pulverization
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
  []
  [FGR_pps_diff_bison_analytical]
    type = DifferencePostprocessor
    value1 = FGR_analytical
    value2 = FGR
  []
  [FG_pps_diff_total_released]
    type = DifferencePostprocessor
    value1 = FG_amount_bubble_HBS
    value2 = FGR
  []
  [volume_domain]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = 1
    block = fuel
    execute_on = TIMESTEP_END
    fuel_pin_geometry = fuel_pin_geometry
  []
  [hbs_volume]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = hbs_volume_fraction
    block = fuel
    execute_on = TIMESTEP_END
    fuel_pin_geometry = fuel_pin_geometry
  []
  [hbs_volume_fraction]
    type = ParsedPostprocessor
    pp_names = 'hbs_volume volume_domain'
    expression = 'hbs_volume / volume_domain'
    execute_on = TIMESTEP_END
  []
  [pulverized_volume]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = pulverized
    block = fuel
    execute_on = TIMESTEP_END
    fuel_pin_geometry = fuel_pin_geometry
  []
[]

[Executioner]
  type = Transient

  solve_type = Newton

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 125
  dt = 1
[]

[Outputs]
  exodus = true
  csv = true
  file_base = ad_uo2_pulverization_phasefield2_transient_FGR_out
[]

(test/tests/uo2_transient_fission_gas_release/uo2_pulverization_transient_FGR_1D.i)

# This file is to test the transient fission gas release model that accounts for
# the amount of fission gas released as a result of fuel pulverization.
# It uses evolve_bubble_pressure_hbs = true and the 3D phase field criterion for
# pulverization.
# Local pulverization is tracked with the material property pulverized, which is
# 0 where pulverization has not occured and 1 where it has occurred.
# A material property uses the local pulverization to compute the
# amount of fission gas released as a results of fuel pulverization.
# This material property is output to the exodus file for this test.

# At each time step, the pulverized material property is computed, as well as
# the bubble radius and amount of fission gas in bubbles. These material property
# are then used to determine the amount of fission gas release due to pulverization.
# This amount predicted by the material block
# UO2PulverizationTransientFissionGasRelease is compared with analytical calculations
# made in the material block fission_gas_released_amount for verification.

# This input is the non-AD version.

hydrostatic_stress_constant = 1e7

[GlobalParams]
  value_range_behavior = WARN
[]

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmax = 4.5e-3 # m pellet outer radius
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 600
  []
[]

[AuxVariables]
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized_aux]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*1.6*t/4.275'
  []
  [temperature_function]
    type = ParsedFunction
    expression = 'if(t < 100, 900, 900+(t-100)*200)'
  []
  [Fiss_func]
    type = ParsedFunction
    expression = '1.e19'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
  []
[]

[AuxKernels]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1
    fission_rate_function = Fiss_func
    execute_on = 'initial timestep_begin'
  []
  [pulverized]
    type = MaterialRealAux
    variable = pulverized_aux
    property = pulverized
    execute_on = 'initial nonlinear'
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    boundary = 'left right'
    variable = temperature
    function = temperature_function
  []
[]

[Materials]
  [fission_gas_behavior]
    type = UO2Sifgrs
    temperature = temperature
    fission_rate = fission_rate
    burnup = burnup
    skip_bdr_model = true
    ig_bubble_model = MECHANISTIC_AAGESEN
    hbs_model = true
    hbs_material = hbs_formation
    pulverization_model = true
    pulverization_transient_fission_gas_release_material = UO2PulverizationTransientFissionGasRelease
    ig_diff_algorithm = FORMAS
    hydrostatic_stress_const = ${hydrostatic_stress_constant}
    igdiffcoeff_scalef_HBS = 1e24 # Ensures that all the generated fission gases diffuse from the HBS matrix to the HBS bubbles
    output_properties = 'bubble_concentration_intra_non_restructured bubble_radius_intra_non_restructured gas_concentration_bubble_intra_non_restructured gas_concentration_matrix_intra_non_restructured bubble_GB_volume_density_non_restructured bubble_radius_GB_non_restructured gas_concentration_GB_bubble_volume_non_restructured deltav_v0_intra_total bubble_concentration_intra_HBS bubble_radius_intra_HBS gas_concentration_bubble_intra_HBS gas_concentration_matrix_intra_HBS bubble_GB_volume_density_HBS bubble_radius_GB_HBS gas_concentration_GB_bubble_volume_HBS atom_per_bubble_GB_HBS gas_concentration_release_total'
    outputs = 'exodus'
  []
  [uo2pulverizationmesoscale]
    type = UO2PulverizationMesoscale
    temperature = temperature
    output_properties = pulverized
    pulverization_criterion_type = phase_field_3D
    outputs = exodus
  []
  [dummy_stress]
    type = GenericConstantRankTwoTensor
    tensor_name = 'stress'
    tensor_values = '-${hydrostatic_stress_constant} -${hydrostatic_stress_constant} -${hydrostatic_stress_constant} 0 0 0'
  []
  [fuel_thermal]
    type = UO2Thermal
    thermal_conductivity_model = STAICU
    hbs_porosity_correction = KAMPF
    model_hbs_formation = true
    temperature = temperature
    burnup_function = burnup_function
    output_properties = hbs_porosity
    outputs = exodus
  []
  [hbs_formation]
    type = HighBurnupStructureFormation
    temperature = temperature
    burnup = burnup
    threshold_temperature = 1273.15 # default
    output_properties = hbs_volume_fraction
    outputs = exodus
  []
  [fission_gas_density_bubble_HBS] # moles/m^3
    type = ParsedMaterial
    property_name = 'rho_FG_hbs'
    material_property_names = 'atom_per_bubble_GB_HBS bubble_GB_volume_density_HBS'
    constant_names = 'Na'
    constant_expressions = '6.02214076e23'
    expression = 'atom_per_bubble_GB_HBS * bubble_GB_volume_density_HBS / Na'
    outputs = exodus
  []
  [opened_pore_volume_fraction] # -
    type = ParsedMaterial
    property_name = 'f_V_pul'
    material_property_names = 'hbs_porosity bubble_radius_GB_HBS'
    constant_names = 'fragment_size c_p  c_r  c_0'
    constant_expressions = '5e-5    0.03 5.17 0.02'
    expression = 'c_p * hbs_porosity + c_r * bubble_radius_GB_HBS/fragment_size + c_0'
    outputs = exodus
  []
  [fission_gas_released_amount_analytical] # moles/m^3
    type = ParsedMaterial
    property_name = 'fis_gas_rel'
    material_property_names = 'f_V_pul rho_FG_hbs pulverized'
    expression = 'pulverized * f_V_pul * rho_FG_hbs'
    outputs = exodus
  []
  [UO2PulverizationTransientFissionGasRelease] # moles/m^3
    type = UO2PulverizationTransientFissionGasRelease
    output_properties = 'gas_concentration_release_pulverization'
    outputs = exodus
  []
[]

[Postprocessors]
  [FG_amount_bubble_HBS]
    type = ElementIntegralMaterialProperty
    mat_prop = rho_FG_hbs
  []
  [FGR_transient_pulverization_analytical]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_rel
  []
  [FGR_transient_pulverization]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_release_pulverization
  []
  [FGR_pps_diff_bison_analytical]
    type = DifferencePostprocessor
    value1 = FGR_transient_pulverization_analytical
    value2 = FGR_transient_pulverization
  []
  [FG_pps_diff_total_released]
    type = DifferencePostprocessor
    value1 = FG_amount_bubble_HBS
    value2 = FGR_transient_pulverization
  []
  [fis_gas_generated]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_generated_total
  []
  [fis_gas_released_total]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_release_total
  []
  [fgr_percent]
    type = FGRPercent
    fission_gas_released = fis_gas_released_total
    fission_gas_generated = fis_gas_generated
  []
  [gas_amount_bubble_intra_non_restructured]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_bubble_intra_non_restructured
  []
  [gas_amount_matrix_intra_non_restructured]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_matrix_intra_non_restructured
  []
  [bubble_amount_intra_non_restructured]
    type = ElementIntegralMaterialProperty
    mat_prop = bubble_concentration_intra_non_restructured
  []
  [bubble_radius_intra_average_non_restructured]
    type = ElementAverageMaterialProperty
    mat_prop = bubble_radius_intra_non_restructured
  []
  [temperature]
    type = ElementAverageValue
    variable = temperature
  []
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
  []
  [gas_amount_hbs_GB_bubbles]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_GB_bubble_volume_HBS
  []
  [gas_amount_hbs_matrix]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_matrix_intra_HBS
  []
  [gas_amount_hbs_intra_bubbles]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_bubble_intra_HBS
  []
  [gas_amount_hbs_intra_total]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_intra_total_HBS
  []
  [bubble_amount_GB_hbs]
    type = ElementIntegralMaterialProperty
    mat_prop = bubble_GB_volume_density_HBS
  []
  [bubble_radius_GB_average_hbs]
    type = ElementAverageMaterialProperty
    mat_prop = bubble_radius_GB_HBS
  []
  [volume_domain]
    type = ElementIntegralMaterialProperty
    mat_prop = 1
    execute_on = TIMESTEP_END
  []
  [hbs_volume]
    type = ElementIntegralMaterialProperty
    mat_prop = hbs_volume_fraction
    execute_on = TIMESTEP_END
  []
  [hbs_volume_fraction]
    type = ParsedPostprocessor
    pp_names = 'hbs_volume volume_domain'
    expression = 'hbs_volume / volume_domain'
    execute_on = TIMESTEP_END
  []
  [pulverized_volume]
    type = ElementIntegralMaterialProperty
    mat_prop = pulverized
    execute_on = TIMESTEP_END
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 125
  dt = 1
[]

[Outputs]
  exodus = true
  csv = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References