MOXActinideRedistribution

Simulates actinide redistribution for MOX kernel.

Description

Actinide migration, or redistribution, is modeled by thermal diffusion and vapor transport. This kernel comes from Equation 6 in Di Marcello et al. (2014). This class [MOXActinideRedistribution], constructs the second term of that equation: $var element = document.getElementById("moose-equation-8ba99c46-aa6e-4ffe-80c2-b6dcab38d05a");katex.render(" \\frac{\\partial c}{\\partial t} - \\nabla \\cdot \\left\\{D\\left[ \\nabla c + c(1-c)\\frac{Q}{RT^{2}}\\nabla T\\right] - D\\left[ APc\\frac{l}{d} \\nabla T \\text{exp}\\left(-\\frac{D}{lv_p}\\right)\\right] \\right\\} = 0", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-a37312f3-97f6-4b31-a574-4cb4d5f03e48");katex.render("c", element, {displayMode:false,throwOnError:false});$ is the actinide concentration, $var element = document.getElementById("moose-equation-89bf00df-2acb-41e1-ba84-5935e7e0f7b7");katex.render("p", element, {displayMode:false,throwOnError:false});$ is the porosity, $var element = document.getElementById("moose-equation-1f8bf5ac-c333-4ed2-b3f0-3c074365ac16");katex.render("v_p", element, {displayMode:false,throwOnError:false});$ is the pore velocity, $var element = document.getElementById("moose-equation-a1aa3b75-9aca-426d-83d5-d30e805891cf");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature, $var element = document.getElementById("moose-equation-7853a4b7-8d51-4699-9809-416442efca12");katex.render("D", element, {displayMode:false,throwOnError:false});$ is the diffusion coefficient, $var element = document.getElementById("moose-equation-cd41b38f-708a-4df8-bd1e-e8afbfced4d2");katex.render("R", element, {displayMode:false,throwOnError:false});$ is the universal gas constant, $var element = document.getElementById("moose-equation-398084c7-c50a-485f-8d20-3a9581cd9e1c");katex.render("Q", element, {displayMode:false,throwOnError:false});$ is the effective molar heat of transport, $var element = document.getElementById("moose-equation-c0196813-0104-4166-bebb-72be7b3c0ba3");katex.render("l", element, {displayMode:false,throwOnError:false});$ is the pore thickness, $var element = document.getElementById("moose-equation-5590e46a-cc52-4f07-92ee-a0d6e1421c05");katex.render("d", element, {displayMode:false,throwOnError:false});$ is the pore diameter, and $var element = document.getElementById("moose-equation-4f5c8e8a-fb51-4018-a0e7-8e653123a903");katex.render("A", element, {displayMode:false,throwOnError:false});$ is a scaling parameter (default is 1.0). The pore speed, $var element = document.getElementById("moose-equation-8e44eb1b-0dc3-476e-91ce-608589dc6026");katex.render("v_p", element, {displayMode:false,throwOnError:false});$ , comes from a calculation performed in MOXPoreVelocity or MOXPoreVelocityVaporPressure. The diffusion coefficient, $var element = document.getElementById("moose-equation-8d64fb76-14cd-4db0-aed5-88efb9bf2998");katex.render("D", element, {displayMode:false,throwOnError:false});$ is defined by the following equation for Pu and Am: $var element = document.getElementById("moose-equation-3278d1fe-fb4e-4be0-b57b-6f7606346455");katex.render("D^{\\text{Pu}} = 3.4\\cdot 10^{-5}\\text{exp}\\left(-\\frac{55891}{T}\\right)", element, {displayMode:true,throwOnError:false});$

$var element = document.getElementById("moose-equation-fab82d8b-27ae-4cde-b64b-7bee8a73415c");katex.render("D^{\\text{Am}} = 2.0\\cdot 10^{-5}\\text{exp}\\left(-\\frac{46324}{T}\\right)", element, {displayMode:true,throwOnError:false});$

The last term in Equation (1) is defined by the class MOXActinideRedistributionEnhancement

construction

This class is still under development!

See bison/test/tests/mox_pore_velocity/ for examples of how this class should be used.

Input Parameters

temperatureTemperature.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Temperature.
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

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
debugFalseWhether or not to print debug information
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not to print debug information
diffusion_energy_barrier55891.0The diffusion energy barrier used in the kernel (J/mol)
Default:55891.0
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:The diffusion energy barrier used in the kernel (J/mol)
diffusion_prefactor3.4e-5The diffusivity pre-factor used in the kernel (m^2/s)
Default:3.4e-5
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:The diffusivity pre-factor used in the kernel (m^2/s)
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
heating_functionfunction for ralp
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:function for ralp
hmax1hmax
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:hmax
molar_heat_transport146500.0The effective molar heat of transport used in the kernel (J/mol)
Default:146500.0
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:The effective molar heat of transport used in the kernel (J/mol)
scale_factor1scale_factor
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:scale_factor
v_lower1v_lower
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:v_lower
v_upper1v_upper
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:v_upper

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Contribution To Tagged Field Data 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.
diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
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
save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
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

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/mox_pore_velocity/MOXActinide_simple.i)
(test/tests/mox_pore_velocity/MOXActinide.i)

References

Valentino Di Marcello, Vincenzo Rondinella, Arndt Schubert, and Jacques van de Larr. Modeling actinide redistribution in mixed oxide fuel for sodium fast reactors. Progress in Nuclear Energy, 72:83–90, 2014. doi:10.1016/j.pnucene.2013.10.008.

@ARTICLE{dimarcello_2014,
    author = "Di Marcello, Valentino and Rondinella, Vincenzo and Schubert, Arndt and van de Larr, Jacques",
    title = "Modeling actinide redistribution in mixed oxide fuel for sodium fast reactors",
    journal = "Progress in Nuclear Energy",
    year = "2014",
    volume = "72",
    pages = "83-90",
    doi = "10.1016/j.pnucene.2013.10.008"
}

(test/tests/mox_pore_velocity/MOXActinide_simple.i)

# This input files uses the actinide redistribution kernels

[UserObjects]
  [pin_geometry]
    type = Layered1DFuelPinGeometry
    include_clad = false
    mesh_generator = layered1D_mesh
  []
[]

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    fuel_height = 0.1
    pellet_outer_radius = 0.0041
    include_clad = false
    pellet_bottom_coor = 0.0
    pellet_mesh_density = customize
    nx_p = 200
    elem_type = EDGE2
    slices_per_block = 1
    include_plenum = false
  []
[]

[Variables]
  [temperature]
    initial_condition = 1400.0
  []
  [actinide]
    initial_condition = 20
    scaling = 1e8
  []
[]

[AuxVariables]
  [fission_rate_aux_variable_mox]
    order = first
    family = lagrange
  []
  [pore]
  []
[]

[Functions]
  [power_history1]
    type = PiecewiseLinear
    x = '0 10000'
    y = '0 50000'
  []
[]

[Kernels]

  [heat] # gradient term in heat conduction equation
    type = HeatConduction
    variable = temperature
  []
  [heat_ie] # time term in heat conduction equation
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat_source] # source term in heat conduction equation
    type = NeutronHeatSource
    variable = temperature
    block = fuel # fission rate applied to the fuel (block 2) only
    fission_rate = fission_rate_aux_variable_mox
  []
  [actinide_redistribution]
    type = MOXActinideRedistribution
    variable = actinide
    debug = 0
    temperature = temperature
    scale_factor = 0.5
    v_upper = 0
    v_lower = 0
    heating_function = power_history1
  []

  [actinide_redistribution_enhancement]
    type = MOXActinideRedistributionEnhancement
    variable = actinide
    debug = 0
    temperature = temperature
    pore = pore
    pore_diameter = 1e-10
    pore_thickness = 1e-11
    scaling_parameter_A = 0.35
    scale_factor = 0.5
    v_upper = 0
    v_lower = 0
    heating_function = power_history1
  []

  [actinide_time_derivative]
    type = CoefTimeDerivative
    variable = actinide
    Coefficient = 1
  []
[]

[AuxKernels]
  [fission_rate_aux_kernel_mox]
    type = FissionRateGeneral
    fission_rate_formulation = MOX
    variable = fission_rate_aux_variable_mox
    block = fuel
    porosity = pore
    initial_porosity = 0.12
    rod_ave_lin_pow = power_history1
    pellet_diameter = 0.0082
    pellet_inner_diameter = 0
    energy_per_fission = 3.2e-11
    execute_on = 'initial timestep_end'
  []
  [pore]
    type = ConstantAux
    value = 0.12
    variable = pore
  []
[]

[BCs]
  [temp_outside] # pin pellets and clad along axis of symmetry (y)
    type = DirichletBC
    variable = temperature
    boundary = 10
    value = 1400
  []
[]

[Materials]
  [fuel_thermal]
    type = MAMOXThermal
    block = fuel
    temperature = temperature
    porosity = pore
  []
  [density_block]
    type = GenericConstantMaterial
    block = fuel
    prop_names = density
    prop_values = 10431.0
  []
  [pore_velocity]
    type = ParsedMaterial
    block = fuel
    expression = '1e-2'
    property_name = pore_velocity
  []
[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 100.0
    variable = temperature
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package' # -mat_superlu_dist_fact'
  petsc_options_value = 'lu superlu_dist' # SamePattern_SameRowPerm'

  line_search = 'none'

  l_max_its = 50
  l_tol = 8e-3
  nl_max_its = 25
  nl_rel_tol = 1e-5
  nl_abs_tol = 1e-8 #1e-10
  n_startup_steps = 1
  end_time = 8e4
  num_steps = 2
  dtmax = 1000
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    optimal_iterations = 8
    iteration_window = 2
    linear_iteration_ratio = 100
    growth_factor = 2
    cutback_factor = .5
    force_step_every_function_point = true
    timestep_limiting_function = power_history1
  []
[]

[Postprocessors]
  [_dt] # time step
    type = TimestepSize
  []
  [z_nonlinear_its] # number of nonlinear iterations at each timestep
    type = NumNonlinearIterations
  []
  [power_input]
    type = FunctionValuePostprocessor
    function = power_history1
    scale_factor = 0.1 # rod height
  []

  [rod_total_power_mox]
    type = LayeredElementIntegralPowerPostprocessor
    variable = temperature
    block = fuel
    fission_rate = fission_rate_aux_variable_mox
    fuel_pin_geometry = pin_geometry
  []

  [ave_fuel_temp]
    type = ElementAverageValue
    block = fuel
    variable = temperature
  []
  [max_fuel_temp]
    type = NodalExtremeValue
    block = fuel
    value_type = max
    variable = temperature
  []

  [ave_pore]
    type = ElementAverageValue
    block = fuel
    variable = pore
  []
  [max_pore]
    type = NodalExtremeValue
    block = fuel
    value_type = max
    variable = pore
  []
  [min_pore]
    type = NodalExtremeValue
    block = fuel
    value_type = min
    variable = pore
  []
  [max_actinide]
    type = NodalExtremeValue
    variable = actinide
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [min_actinide]
    type = NodalExtremeValue
    variable = actinide
    block = fuel
    value_type = min
    execute_on = 'initial timestep_end'
  []
  [average_actinide]
    type = AverageNodalVariableValue
    variable = actinide
    block = fuel
    execute_on = 'initial timestep_end'
  []
[]

# The MOX capabilities are under active development and the blocks below are useful for
# development and debugging by providing the profiles of the desired quantities.
# They are commented out for the tests, as it would unnecessarily increase computational costs
# and memory requirements.
# [VectorPostprocessors]
#   [line_value_vector_postprocessor_pore]
#     type = LineValueSampler
#     variable = pore
#     start_point = '0.0 0.05 0'
#     end_point = '0.0041 0.05 0'
#     num_points = 100
#     sort_by = x
#     execute_on = linear
#     outputs = stuff_v_rad
#     control_tags = a
#   []
#   [line_value_vector_postprocessor_pore_speed]
#     type = LineValueSampler
#     variable = pore_speed_aux
#     start_point = '0.0 0.05 0'
#     end_point = '0.0041 0.05 0'
#     num_points = 100
#     sort_by = x
#     execute_on = linear
#     outputs = stuff_v_rad
#   []
#   [line_value_vector_postprocessor_temperature]
#     type = LineValueSampler
#     variable = temperature
#     start_point = '0.0 0.05 0'
#     end_point = '0.0041 0.05 0'
#     num_points = 100
#     sort_by = x
#     execute_on = linear
#     outputs = stuff_v_rad
#   []
#   [line_value_vector_postprocessor_actinide]
#     type = LineValueSampler
#     variable = actinide
#     start_point = '0.0 0.05 0'
#     end_point = '0.0041 0.05 0'
#     num_points = 100
#     sort_by = x
#     execute_on = linear
#     outputs = stuff_v_rad
#   []
# []

[Outputs]
  exodus = true
  csv = false
  color = false
  [console]
    type = Console
    max_rows = 25
    all_variable_norms = true
  []
  # [stuff_v_rad]
  #   type = CSV
  #   execute_on = 'FINAL'
  # []
[]

[Debug]
  show_var_residual_norms = true
[]

(test/tests/mox_pore_velocity/MOXActinide.i)

# This input files uses the actinide redistribution kernels coupled with pore diffusion

[UserObjects]
  [pin_geometry]
    type = Layered1DFuelPinGeometry
    include_clad = false
    mesh_generator = layered1D_mesh
  []
[]

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    fuel_height = 0.1
    pellet_outer_radius = 0.0041
    include_clad = false
    pellet_bottom_coor = 0.0
    pellet_mesh_density = customize
    nx_p = 200
    elem_type = EDGE2
    slices_per_block = 1
    include_plenum = false
  []
[]

[Variables]
  [temperature]
    initial_condition = 1400.0
  []
  [pore]
    initial_condition = 0.12
    scaling = 1e14
  []
  [actinide]
    initial_condition = 20
    scaling = 1e8
  []
[]

[AuxVariables]
  [pore_speed_aux]
    order = constant
    family = monomial
  []
  [fission_rate_aux_variable_mox]
    order = first
    family = lagrange
  []
[]

[Functions]
  [power_history1]
    type = PiecewiseLinear
    x = '0 10000'
    y = '0 50000'
  []
[]

[Kernels]

  [heat] # gradient term in heat conduction equation
    type = HeatConduction
    variable = temperature
  []
  [heat_ie] # time term in heat conduction equation
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat_source] # source term in heat conduction equation
    type = NeutronHeatSource
    variable = temperature
    block = fuel # fission rate applied to the fuel (block 2) only
    fission_rate = fission_rate_aux_variable_mox
  []

  [pore_diffusion]
    type = MOXPoreDiffusion
    variable = pore
    debug = 0
    # nu = 3.25e-8 #seems to be THE value to use... result is super sensitive to this number
    # nu = 10e-10
    nu = 1e-12
    heating_function = power_history1
    v_upper = 1e-12
    v_lower = 1e-20
    # v_upper = 1
    # v_lower = 1
  []

  [pore_continuity]
    type = MOXPoreContinuity
    variable = pore
    temperature = temperature
    debug = 0
    alpha = 0.25
    beta = 1
    heating_function = power_history1
  []
  [poretimederivative]
    type = CoefTimeDerivative
    variable = pore
    Coefficient = 1
  []
  [actinide_redistribution]
    type = MOXActinideRedistribution
    variable = actinide
    debug = 0
    temperature = temperature
    scale_factor = 0.5
    v_upper = 0
    v_lower = 0
    heating_function = power_history1
  []

  [actinide_redistribution_enhancement]
    type = MOXActinideRedistributionEnhancement
    variable = actinide
    debug = 0
    temperature = temperature
    pore = pore
    pore_diameter = 1e-10
    pore_thickness = 1e-11
    scaling_parameter_A = 0.35
    scale_factor = 0.5
    v_upper = 0
    v_lower = 0
    heating_function = power_history1
  []

  [actinide_time_derivative]
    type = CoefTimeDerivative
    variable = actinide
    Coefficient = 1
  []
[]

[AuxKernels]
  [pore_speed_aux]
    type = MaterialRealAux
    variable = pore_speed_aux
    property = pore_velocity
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [fission_rate_aux_kernel_mox]
    type = FissionRateGeneral
    fission_rate_formulation = MOX
    variable = fission_rate_aux_variable_mox
    block = fuel
    porosity = pore
    initial_porosity = 0.12
    rod_ave_lin_pow = power_history1
    pellet_diameter = 0.0082
    pellet_inner_diameter = 0
    energy_per_fission = 3.2e-11
    execute_on = 'initial timestep_end'
  []
[]

[BCs]
  [temp_outside] # pin pellets and clad along axis of symmetry (y)
    type = DirichletBC
    variable = temperature
    boundary = 10
    value = 1400
  []
[]

[Materials]
  [fuel_thermal]
    type = MAMOXThermal
    block = fuel
    temperature = temperature
    porosity = pore
  []
  [density_block]
    type = GenericConstantMaterial
    block = fuel
    prop_names = density
    prop_values = 10431.0
  []
  [pore_velocity]
    type = MOXPoreVelocity
    block = fuel
    temperature = temperature
    limit = 1e-3
    # scale_factor = 0.05 # go back to this if necessary
    scale_factor = 0.1
  []
[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 100.0
    variable = temperature
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package' # -mat_superlu_dist_fact'
  petsc_options_value = 'lu superlu_dist' # SamePattern_SameRowPerm'

  line_search = 'none'

  l_max_its = 50
  l_tol = 8e-3
  nl_max_its = 25
  nl_rel_tol = 1e-5
  nl_abs_tol = 1e-8 #1e-10
  n_startup_steps = 1
  end_time = 8e4
  num_steps = 2
  dtmax = 1000
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    optimal_iterations = 8
    iteration_window = 2
    linear_iteration_ratio = 100
    growth_factor = 2
    cutback_factor = .5
    force_step_every_function_point = true
    timestep_limiting_function = power_history1
  []
[]

[Postprocessors]
  [_dt] # time step
    type = TimestepSize
  []
  [z_nonlinear_its] # number of nonlinear iterations at each timestep
    type = NumNonlinearIterations
  []
  [power_input]
    type = FunctionValuePostprocessor
    function = power_history1
    scale_factor = 0.1 # rod height
  []

  [rod_total_power_mox]
    type = LayeredElementIntegralPowerPostprocessor
    variable = temperature
    block = fuel
    fission_rate = fission_rate_aux_variable_mox
    fuel_pin_geometry = pin_geometry
  []

  [ave_fuel_temp]
    type = ElementAverageValue
    block = fuel
    variable = temperature
  []
  [max_fuel_temp]
    type = NodalExtremeValue
    block = fuel
    value_type = max
    variable = temperature
  []

  [ave_pore]
    type = ElementAverageValue
    block = fuel
    variable = pore
  []
  [max_pore]
    type = NodalExtremeValue
    block = fuel
    value_type = max
    variable = pore
  []
  [min_pore]
    type = NodalExtremeValue
    block = fuel
    value_type = min
    variable = pore
  []
  [max_pore_speed]
    type = ElementExtremeValue
    block = fuel
    value_type = max
    variable = pore_speed_aux
  []
  [max_actinide]
    type = NodalExtremeValue
    variable = actinide
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [min_actinide]
    type = NodalExtremeValue
    variable = actinide
    block = fuel
    value_type = min
    execute_on = 'initial timestep_end'
  []
  [average_actinide]
    type = AverageNodalVariableValue
    variable = actinide
    block = fuel
    execute_on = 'initial timestep_end'
  []
[]

# The MOX capabilities are under active development and the blocks below are useful for
# development and debugging by providing the profiles of the desired quantities.
# They are commented out for the tests, as it would unnecessarily increase computational costs
# and memory requirements.
# [VectorPostprocessors]
#   [line_value_vector_postprocessor_pore]
#     type = LineValueSampler
#     variable = pore
#     start_point = '0.0 0.05 0'
#     end_point = '0.0041 0.05 0'
#     num_points = 100
#     sort_by = x
#     execute_on = linear
#     outputs = stuff_v_rad
#     control_tags = a
#   []
#   [line_value_vector_postprocessor_pore_speed]
#     type = LineValueSampler
#     variable = pore_speed_aux
#     start_point = '0.0 0.05 0'
#     end_point = '0.0041 0.05 0'
#     num_points = 100
#     sort_by = x
#     execute_on = linear
#     outputs = stuff_v_rad
#   []
#   [line_value_vector_postprocessor_temperature]
#     type = LineValueSampler
#     variable = temperature
#     start_point = '0.0 0.05 0'
#     end_point = '0.0041 0.05 0'
#     num_points = 100
#     sort_by = x
#     execute_on = linear
#     outputs = stuff_v_rad
#   []
#   [line_value_vector_postprocessor_actinide]
#     type = LineValueSampler
#     variable = actinide
#     start_point = '0.0 0.05 0'
#     end_point = '0.0041 0.05 0'
#     num_points = 100
#     sort_by = x
#     execute_on = linear
#     outputs = stuff_v_rad
#   []
# []

[Outputs]
  exodus = true
  csv = false
  color = false
  [console]
    type = Console
    max_rows = 25
    all_variable_norms = true
  []
  # [stuff_v_rad]
  #   type = CSV
  #   execute_on = 'FINAL'
  # []
[]

[Debug]
  show_var_residual_norms = true
[]

Description
Input Parameters
Input Files
References