FissionRateMOX

Computes fission rate for right circular cylinder fast MOX fuel taking porosity into account.

Description

FissionRateMOX is designed to calculate fission rate given rod averaged linear power and pellet dimensions and porosity as a coupled variable. The fission rate is scaled by the following term: $var element = document.getElementById("moose-equation-eec75bba-bd8d-4d01-ac9b-d86a9e5e2ff0");katex.render("\\frac{1 - porosity_{current}}{1 - porosity_{initial}}", element, {displayMode:true,throwOnError:false});$

Example Input Syntax

[AuxKernels<<<{"href": "../../syntax/AuxKernels/index.html"}>>>]
  [pore_speed_aux]
    type = MaterialRealAux<<<{"description": "Outputs element volume-averaged material properties", "href": "MaterialRealAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = pore_speed_aux
    property<<<{"description": "The material property name."}>>> = pore_velocity
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = fuel
    execute_on<<<{"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."}>>> = 'initial timestep_end'
  []
  [fission_rate_aux_kernel_mox]
    type = FissionRateGeneral<<<{"description": "Provides various implementations which allow the user to set the fission rate.", "href": "FissionRateGeneral.html"}>>>
    fission_rate_formulation<<<{"description": "The active fission rate formulation."}>>> = MOX
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = fission_rate_aux_variable_mox
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = fuel
    porosity<<<{"description": "Coupled porosity"}>>> = pore
    initial_porosity<<<{"description": "Initial porosity. Must be the same as the initial condition in the variable block."}>>> = 0.12
    rod_ave_lin_pow<<<{"description": "The rod power history function."}>>> = power_history1
    pellet_diameter<<<{"description": "Fuel pellet diameter in meters."}>>> = 0.0082
    pellet_inner_diameter<<<{"description": "Pellet inner diameter in meters for an annular pellet."}>>> = 0
    energy_per_fission<<<{"description": "Energy in Joules per fission."}>>> = 3.2e-11
    execute_on<<<{"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."}>>> = 'initial timestep_end'
  []
[]

Input Parameters

pellet_diameterFuel pellet diameter in meters.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fuel pellet diameter in meters.
variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this object applies to

Required Parameters

axial_power_profileThe axial power profile function.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The axial power profile function.
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
check_boundary_restrictedTrueWhether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
Default:True
C++ Type:bool
Controllable:No
Description:Whether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
energy_per_fission3.28451e-11Energy per fission in J/fission.
Default:3.28451e-11
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Energy per fission in J/fission.
execute_onLINEAR TIMESTEP_ENDThe 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 TIMESTEP_END
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, PRE_DISPLACE
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.
fuel_volume_ratio1Reduction factor for deviation from right circular cylinder fuel. The ratio of actual volume to right circular cylinder volume.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Reduction factor for deviation from right circular cylinder fuel. The ratio of actual volume to right circular cylinder volume.
initial_porosity0Initial porosity. Must be the same as the initial condition in the variable block.
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial porosity. Must be the same as the initial condition in the variable block.
pellet_inner_diameter0Pellet inner diameter in meters for an annular pellet.
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Pellet inner diameter in meters for an annular pellet.
porosityCoupled porosity
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled porosity
radial_power_profileThe radial power profile function.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The radial power profile function.
rod_ave_lin_powThe rod power history function.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The rod power history function.
value1
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No

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.
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/fission_rate_MOX/deprecated.i)

(test/tests/mox_pore_velocity/MOXPoreVelocity.i)

# This input files uses the pore difusion 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
  []
  [pore]
    initial_condition = 0.12
    scaling = 1e14
  []
[]

[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
  []
[]

[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
    porosity_limit = 0.9
  []
  [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 = 1.5e5
  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
  []
[]

# 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
#   []
# []

[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/fission_rate_MOX/deprecated.i)

#The reason for this test is to determine if the fission rate is calculated correctly.  The fission rate is a function of
#rod average linear power (function named power here) in W/m - calculated via function PiecewiseLinear and  LinearInerpolation,
#the 2D axial power profile function (power factors as a function of axial position and time - calculated using the deprecated auxkernel FissionRateMOX via the
#function PiecewiseBilinear and BilinearInterpolation, function named axial_power_factors here), pellet diameter (m), inner pellet diameter (m) if fuel is annular, f_fuel (fraction of total power),
#and fuel_volume_ratio (volume reduction factor due to pellet dishing i.e. if the pellet is not a right circular cylinder), and energy per fission.
#
#The mesh consists of 5 1x1x1 brick elements "stacked" in the y-direction.  The y-coordinate of nodes is 0, 1, 2, 3, 4, or 5.
#The power is 1 for the duration...after a ramp from 0 to 1 during the first time step.
#The power factors for this test are in the file powerfactors.csv, which as the following format
#
#0.25,1.25,2.25,3.5,4.25,4.75
#0,0,0,0,0,0,0
#1,1,1,1,1,1,1
#2,.5,.75,2.5,2.5,.75,.5
#3,.5,.7,.3,.1,1,.1
#4,.2,.9,.8,.7,1,.9
#5,.2,.9,.8,.7,1,.25
#
#Where the first row is a list of the axial positions where the power factors are defined.
#After the first row, the first column is a list of the times where the power factors are defined.
#All the other numbers are the power factors defined at the given axial position and time.
#For a given power, pellet diameter, and reduction factors (all described previously) the fission rate is calculated for every node at every time.
#The file powerfactors.csv is used/read by PiecewiseBilinear, which sends a vector (x) of the axial position values,
#a vector (y) of the times, a ColumnMajorMatrix (z) of the powerfactors to BilinearInterpolation, and a sample point (position,time).  The value returned
#is used in the fission rate calculation.
#
#An example:
#
#At time 2.25 and axial position z = 1 (node 20)...sample point = (1, 2.25), the value returned is 0.847656.  You can check this value by hand using the data provided.
#
#For this test, the fission rate has the same value as the power factor divided by 1-initial_porosity (for this example 0.678125/(1-0.2)).
#This is by design to make it easy to determine if the fission rate is being calculated correctly.
#Look at the output file for this test and plot the fission rate at node 20 (z-coordinate = 1).  At time = 2.25, the value should be 0.847656.
#

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 1x5x1.e
  []
[]

[Variables]
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1373.15
  []
[]

[AuxVariables]
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
[]

[Functions]
  [power]
    type = PiecewiseLinear
    x = '0 1'
    y = '1 1'
  []

  [axial_power_factor]
    type = PiecewiseBilinear
    data_file = powerfactors.csv
    axis = 1
  []
[]

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

[AuxKernels]
  [fissionrate]
    type = FissionRateMOX
    variable = fission_rate
    rod_ave_lin_pow = power
    axial_power_profile = axial_power_factor
    initial_porosity = 0.2
    pellet_diameter = 1.1283791671 #fake pellet diameter to give a value of 1 for Power/area
    pellet_inner_diameter = 0
    energy_per_fission = 1 #J/fission
  []
[]

[BCs]
  [bottom_temp]
    type = DirichletBC
    variable = temp
    boundary = 3
    value = 1373.15
  []

  [top_temp]
    type = DirichletBC
    variable = temp
    boundary = 5
    value = 1373.15
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 1.e4
    specific_heat = 1.
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew '
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type'
  petsc_options_value = '70 hypre boomeramg'
  l_max_its = 60
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5
  start_time = 0.0
  dt = 0.25
  num_steps = 21
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files