BurnupMetalAux

Computes the burnup in FIMA from the fission rate and fuel constituents.

Description

BurnupMetalAux calculates the burnup as follows:

$var element = document.getElementById("moose-equation-11e9e5cf-5a6f-4e47-8997-13c90d636e26");katex.render("\\begin{array}{l} A = (1-X_{Pu}-X_{Zr})A_U + X_{Pu}A_{Pu} + X_{Zr}A_{Zr} \\\\ h = \\rho / A (1.0 - X_{Zr}) A_v \\\\ Bu = \\dot{F} t / h \\end{array}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-6de1cba5-5787-4abf-ad34-079b627e9119");katex.render("A", element, {displayMode:false,throwOnError:false});$ is atomic weight (kg/mol), $var element = document.getElementById("moose-equation-17b32920-d1c0-43b5-835a-615633446d97");katex.render("X_{Pu}", element, {displayMode:false,throwOnError:false});$ is the initial molar fraction of plutonium (dimensionless), $var element = document.getElementById("moose-equation-43064213-09a7-4aa8-8cc9-d73022cb8f52");katex.render("X_{Zr}", element, {displayMode:false,throwOnError:false});$ is the initial molar fraction of zirconium (dimensionless), $var element = document.getElementById("moose-equation-ab10bf03-d1d2-4a93-add7-00c9c8213c39");katex.render("A_U", element, {displayMode:false,throwOnError:false});$ is the atomic weight of uranium (kg/mol), $var element = document.getElementById("moose-equation-2ed364fb-ae5e-41df-883b-0cb48f691cd8");katex.render("A_{Pu}", element, {displayMode:false,throwOnError:false});$ is the atomic weight of plutonium (kg/mol), $var element = document.getElementById("moose-equation-bb04dc04-3d18-4e8e-951e-81fa5958089d");katex.render("A_{Zr}", element, {displayMode:false,throwOnError:false});$ is the atomic weight of zirconium (kg/mol), $var element = document.getElementById("moose-equation-b8dc3b09-25ab-43a2-a1a0-0e1ce660a46f");katex.render("h", element, {displayMode:false,throwOnError:false});$ is atoms of heavy metal (atoms/m $var element = document.getElementById("moose-equation-b1f1afa3-559a-4293-bcf1-a56aff9f2475");katex.render("^3", element, {displayMode:false,throwOnError:false});$ ), $var element = document.getElementById("moose-equation-f21ecb95-8947-4d5d-87b1-29b2bc5a7d04");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ is density (kg/m $var element = document.getElementById("moose-equation-02b55e39-97e3-49f6-9ceb-5fa282f5b59b");katex.render("^3", element, {displayMode:false,throwOnError:false});$ ), $var element = document.getElementById("moose-equation-cc0c95aa-d3e3-455e-bfb9-12b2ad9aced4");katex.render("A_v", element, {displayMode:false,throwOnError:false});$ is Avogadro's number (atoms/mol), $var element = document.getElementById("moose-equation-6a5f4da2-e8aa-4e30-84a3-f59c39bfeae5");katex.render("\\dot{F}", element, {displayMode:false,throwOnError:false});$ is the fission rate (fission/m $var element = document.getElementById("moose-equation-d87de741-c6b1-4c5d-8412-5fd78603fef1");katex.render("^3", element, {displayMode:false,throwOnError:false});$ /s), and $var element = document.getElementById("moose-equation-b4e84371-19a1-4ff7-89d2-40a4754f14a5");katex.render("t", element, {displayMode:false,throwOnError:false});$ is time (s).

Example Input Syntax

[AuxKernels<<<{"href": "../../syntax/AuxKernels/index.html"}>>>]
  [burnup]
    type = BurnupMetalAux<<<{"description": "Computes the burnup in FIMA from the fission rate and fuel constituents.", "href": "BurnupMetalAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = burnup
    density<<<{"description": "Initial fuel density."}>>> = ${initial_fuel_density}
    fission_rate<<<{"description": "Coupled fission rate."}>>> = fission_rate
    X_Pu<<<{"description": "Initial molar fraction of plutonium."}>>> = 0.10
    X_Zr<<<{"description": "Initial molar fraction of zirconium."}>>> = 0.225
    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_begin'
  []
[]

Input Parameters

densityInitial fuel density.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial fuel density.
fission_rateCoupled fission rate.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled fission rate.
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

A_Pu0.244Atomic weight of plutonium [kg/mol].
Default:0.244
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Atomic weight of plutonium [kg/mol].
A_U0.238029Atomic weight of uranium [kg/mol].
Default:0.238029
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Atomic weight of uranium [kg/mol].
A_Zr0.091224Atomic weight of zirconium [kg/mol].
Default:0.091224
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Atomic weight of zirconium [kg/mol].
X_Pu0Initial molar fraction of plutonium.
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial molar fraction of plutonium.
X_Zr0.225Initial molar fraction of zirconium.
Default:0.225
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial molar fraction of zirconium.
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
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.

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/fgr_fraction/fgr_fraction_test_3D.i)
(test/tests/fgr_fraction/fgr_fraction_test_RZ.i)

References

No citations exist within this document.

(test/tests/fgr_fraction/fgr_fraction_test_RZ.i)

# This test is for verificication of BurnupMetalAux and FgrFraction in 2D-RZ
#
# BurnupMetalAux calculates the burnup in FIMA from the fission rate, and fuel
# constituents:
#
# atomic_weight = (1-X_Pu-X_Zr)*A_U + X_Pu*A_Pu + X_Zr*A_Zr;
# atoms_heavy_metal = density / atomic_weight * (1.0 - X_Zr) * avo;
# Bu = fission_rate *  time / atoms_heavy_metal;
#
# For the current test, the burnup at 1e7 seconds should be 1.468380e-02
#
#
# FgrFraction calculates the molar fission gas produced as a function of time
# and fission rate. In addition, FgrFraction calculates the fission gas release
# as a function of burnup.
#
# For the current test, the produced fission gas is:
#
#     fg_prod = yield / avo * time * fission_rate * volume = 7.869449E+02
#
# Also, gas release should occur above the threshold of 0.01 burnup, and should
# be 80% of gas produced = 6.295559E+02

initial_fuel_density = 15000

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
  []
[]

[Variables]
  [temp]
  []
[]

[AuxVariables]
  [fission_rate]
  []
  [burnup]
  []
[]

[Functions]
  [constant_fission_rate]
    type = ParsedFunction
    expression = 5.0e19
  []
[]

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

[AuxKernels]
  [fission_rate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    fission_rate_function = constant_fission_rate
    execute_on = initial
  []
  [burnup]
    type = BurnupMetalAux
    variable = burnup
    density = ${initial_fuel_density}
    fission_rate = fission_rate
    X_Pu = 0.10
    X_Zr = 0.225
    execute_on = 'initial timestep_begin'
  []
[]

[BCs]
  [fix_surf_temp]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 298.0
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 1.0
    specific_heat = 1.0
  []
  [density]
    type = ParsedMaterial
    property_name = density
    expression = ${initial_fuel_density}
  []
  [fission_gas_release]
    type = FgrFraction
    fission_rate = fission_rate
    burnup = burnup
    fraction_fission_gas_release = 0.8
    burnup_fgr = 0.01
  []
[]

[Executioner]
  type = Transient

  nl_abs_tol = 1e-10
  num_steps = 5
  dt = 2e6
[]

[Postprocessors]
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
    execute_on = 'initial timestep_end'
  []
  [burnup]
    type = ElementAverageValue
    variable = burnup
    execute_on = 'initial timestep_end'
  []
  [fis_gas_produced]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_prod
  []
  [fis_gas_released]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_rel
  []
  [volume]
    type = InternalVolume
    boundary = 'left right top bottom'
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/fgr_fraction/fgr_fraction_test_3D.i)

# This test is for verificication of BurnupMetalAux and FgrFraction in 3D
#
# BurnupMetalAux calculates the burnup in FIMA from the fission rate, and fuel
# constituents:
#
# atomic_weight = (1-X_Pu-X_Zr)*A_U + X_Pu*A_Pu + X_Zr*A_Zr;
# atoms_heavy_metal = density / atomic_weight * (1.0 - X_Zr) * avo;
# Bu = fission_rate *  time / atoms_heavy_metal;
#
# For the current test, the burnup at 1e7 seconds should be 1.468380e-02
#
#
# FgrFraction calculates the molar fission gas produced as a function of time
# and fission rate. In addition, FgrFraction calculates the fission gas release
# as a function of burnup.
#
# For the current test, the produced fission gas is:
#
#     fg_prod = yield / avo * time * fission_rate * volume = 2.504923E+02
#
# Also, gas release should occur above the threshold of 0.01 burup, and should
# be 80% of gas produced = 2.003939E+02

initial_fuel_density = 15000

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 3
  []
[]

[Variables]
  [temp]
  []
[]

[AuxVariables]
  [fission_rate]
  []
  [burnup]
  []
[]

[Functions]
  [constant_fission_rate]
    type = ParsedFunction
    expression = 5.0e19
  []
[]

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

[AuxKernels]
  [fission_rate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    fission_rate_function = constant_fission_rate
    execute_on = initial
  []
  [burnup]
    type = BurnupMetalAux
    variable = burnup
    density = ${initial_fuel_density}
    fission_rate = fission_rate
    X_Pu = 0.10
    X_Zr = 0.225
    execute_on = 'initial timestep_begin'
  []
[]

[BCs]
  [fix_surf_temp]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 298.0
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 1.0
    specific_heat = 1.0
  []
  [density]
    type = ParsedMaterial
    property_name = density
    expression = ${initial_fuel_density}
  []
  [fission_gas_release]
    type = FgrFraction
    fission_rate = fission_rate
    burnup = burnup
    fraction_fission_gas_release = 0.8
    burnup_fgr = 0.01
  []
[]

[Executioner]
  type = Transient

  nl_abs_tol = 1e-10
  num_steps = 5
  dt = 2e6
[]

[Postprocessors]
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
    execute_on = 'initial timestep_end'
  []
  [burnup]
    type = ElementAverageValue
    variable = burnup
  []
  [fis_gas_produced]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_prod
  []
  [fis_gas_released]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_rel
  []
  [volume]
    type = InternalVolume
    boundary = 'left right top bottom front back'
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/fgr_fraction/fgr_fraction_test_RZ.i)

# This test is for verificication of BurnupMetalAux and FgrFraction in 2D-RZ
#
# BurnupMetalAux calculates the burnup in FIMA from the fission rate, and fuel
# constituents:
#
# atomic_weight = (1-X_Pu-X_Zr)*A_U + X_Pu*A_Pu + X_Zr*A_Zr;
# atoms_heavy_metal = density / atomic_weight * (1.0 - X_Zr) * avo;
# Bu = fission_rate *  time / atoms_heavy_metal;
#
# For the current test, the burnup at 1e7 seconds should be 1.468380e-02
#
#
# FgrFraction calculates the molar fission gas produced as a function of time
# and fission rate. In addition, FgrFraction calculates the fission gas release
# as a function of burnup.
#
# For the current test, the produced fission gas is:
#
#     fg_prod = yield / avo * time * fission_rate * volume = 7.869449E+02
#
# Also, gas release should occur above the threshold of 0.01 burnup, and should
# be 80% of gas produced = 6.295559E+02

initial_fuel_density = 15000

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
  []
[]

[Variables]
  [temp]
  []
[]

[AuxVariables]
  [fission_rate]
  []
  [burnup]
  []
[]

[Functions]
  [constant_fission_rate]
    type = ParsedFunction
    expression = 5.0e19
  []
[]

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

[AuxKernels]
  [fission_rate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    fission_rate_function = constant_fission_rate
    execute_on = initial
  []
  [burnup]
    type = BurnupMetalAux
    variable = burnup
    density = ${initial_fuel_density}
    fission_rate = fission_rate
    X_Pu = 0.10
    X_Zr = 0.225
    execute_on = 'initial timestep_begin'
  []
[]

[BCs]
  [fix_surf_temp]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 298.0
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 1.0
    specific_heat = 1.0
  []
  [density]
    type = ParsedMaterial
    property_name = density
    expression = ${initial_fuel_density}
  []
  [fission_gas_release]
    type = FgrFraction
    fission_rate = fission_rate
    burnup = burnup
    fraction_fission_gas_release = 0.8
    burnup_fgr = 0.01
  []
[]

[Executioner]
  type = Transient

  nl_abs_tol = 1e-10
  num_steps = 5
  dt = 2e6
[]

[Postprocessors]
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
    execute_on = 'initial timestep_end'
  []
  [burnup]
    type = ElementAverageValue
    variable = burnup
    execute_on = 'initial timestep_end'
  []
  [fis_gas_produced]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_prod
  []
  [fis_gas_released]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_rel
  []
  [volume]
    type = InternalVolume
    boundary = 'left right top bottom'
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References