FastMOXThermal

Computes the thermal conductivity for fast MOX fuel.

Description

The FastMOXThermal model computes the thermal conductivity for fast MOX fuel. Currently a single correlation is available from Inoue et al. (2004) and used by Karahan (2009).

Mixed oxide fuels for fast reactors contain higher concentrations of plutonium oxide than their LWR counterparts. The thermal model developed by Inoue et al. (2004) and used by Karahan (2009) is valid for for 25% PuO $var element = document.getElementById("moose-equation-2a208a19-4df5-4bd3-b8db-5d0907515953");katex.render("_2", element, {displayMode:false,throwOnError:false});$ . The thermal conductivity model for fast MOX is similar in form to the model proposed by Lucuta et al. (1996) for UO $var element = document.getElementById("moose-equation-bff8c42b-1dc2-4c78-8f15-bba38f52374d");katex.render("_2", element, {displayMode:false,throwOnError:false});$ . The model consists of an unirradiated thermal conductivity that is multiplied by corrective factors for dissolved solid fission products ( $var element = document.getElementById("moose-equation-3f0adb2f-a77a-445d-95c8-8bdc940b20c1");katex.render("F_1", element, {displayMode:false,throwOnError:false});$ ), precipitated solid fission products ( $var element = document.getElementById("moose-equation-c2c4cbf3-e641-4f7e-af6a-055c7a904233");katex.render("F_2", element, {displayMode:false,throwOnError:false});$ ), radiation damage ( $var element = document.getElementById("moose-equation-075c5739-d4f8-410e-9241-7555194079a5");katex.render("F_3", element, {displayMode:false,throwOnError:false});$ ), and porosity ( $var element = document.getElementById("moose-equation-91bd9e0b-6191-4147-8669-0f9d4af6d134");katex.render("F_4", element, {displayMode:false,throwOnError:false});$ ) as given by: $var element = document.getElementById("moose-equation-5ff4696e-b069-4bfb-b81f-8abf6b803df0");katex.render(" k = F_dF_pF_{por}F_rk_0", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-451de2a8-dc60-458c-8121-7084521241fd");katex.render("k", element, {displayMode:false,throwOnError:false});$ is the effective fuel thermal conductivity in W/m-K and $var element = document.getElementById("moose-equation-0230381f-e419-44f2-9f9e-2974b871c592");katex.render("k_0", element, {displayMode:false,throwOnError:false});$ is the fully dense fuel thermal conductivity in W/m-K. $var element = document.getElementById("moose-equation-b8e5b046-e4e7-4621-978f-83bbeec271bb");katex.render("F_1", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-caff0f0f-03c2-4a6a-897b-7238e427a144");katex.render("F_2", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-d94a90e0-9608-4cad-924b-49e32bf4779d");katex.render("F_3", element, {displayMode:false,throwOnError:false});$ are the same correlations as formulated by Lucuta et al.

The dissolved fission products correction is given as $(1)var element = document.getElementById("moose-equation-a31fe8a1-a6c0-44d5-aeb4-eb54ebacb6f1");katex.render(" f_{d} = \\left( \\dfrac{1.09}{{Bu}^{3.265}} + 0.0643 \\sqrt{ \\frac{T}{Bu}} \\right) arctan \\left( \\frac{1.0}{ \\frac{1.09}{Bu^{3.265}} + 0.0643 \\sqrt{\\frac{T}{Bu}}} \\right)", element, {displayMode:true,throwOnError:false});$ and the precipitated fission products correction is calculated as $(2)var element = document.getElementById("moose-equation-24aa667a-0a02-48bc-8387-390d6c3be9c2");katex.render(" f_{p} = 1.0 + \\left(\\frac{0.019 Bu}{3.0 - 0.019 Bu} \\right) \\left(\\frac{1.0}{1.0 + \\exp{\\left(\\frac{- \\left[T-1200 \\right]}{100} \\right)}} \\right)", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-27adbca4-7fea-41cc-af1c-3167a599ced4");katex.render("Bu", element, {displayMode:false,throwOnError:false});$ is the burnup in atomic percent and $var element = document.getElementById("moose-equation-7dfa4632-c8a6-4639-8063-491a26e534ac");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature in K. The porosity correction is determined with $(3)var element = document.getElementById("moose-equation-ef56d591-f97a-4d9d-8889-366b2899b7af");katex.render(" f_{por} = \\left(\\frac{1.0 - p}{1.0 + 0.5 p} \\right)", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-7cb027e7-a247-4c2a-8f89-ac166541a791");katex.render("p", element, {displayMode:false,throwOnError:false});$ is the porosity.

The equation for $var element = document.getElementById("moose-equation-639c48d1-ebce-44cc-99d2-c26e98b62b4c");katex.render("F_r", element, {displayMode:false,throwOnError:false});$ is the modified Loeb correlation given by: $var element = document.getElementById("moose-equation-c42c9dbe-580e-4adf-a68e-6a2f8a8b3c53");katex.render(" F_r = 1- \\alpha p", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-45e8513a-706a-4a28-a003-77a8e0d26784");katex.render("p", element, {displayMode:false,throwOnError:false});$ is the volume fraction of porosity and $var element = document.getElementById("moose-equation-a7d52ee9-833d-4506-8f25-efe4d566b29a");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ is a coefficient. Karahan suggests a value of 2.5 for $var element = document.getElementById("moose-equation-9f19b344-7d86-4eef-a8ff-08ecb6cd2feb");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ for conservatism.

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [thermal_properties]
    type = FastMOXThermal<<<{"description": "Computes the thermal conductivity for fast MOX fuel.", "href": "FastMOXThermal.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
    temperature<<<{"description": "Coupled temperature"}>>> = T
    burnup<<<{"description": "Coupled Burnup Rate"}>>> = burnup
    initial_porosity<<<{"description": "Initial porosity"}>>> = 0.05
  []
[]

Input Parameters

temperatureCoupled temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature

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
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
burnupCoupled Burnup Rate
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled Burnup Rate
burnup_functionBurnup function
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Burnup function
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.
initial_porosity0.05Initial porosity
Default:0.05
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial porosity
oxy_to_metal_ratio2Deviation from stoichiometry
Default:2
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Deviation from stoichiometry
porosityCoupled Porosity
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled Porosity
thermal_conductivity_scale_factor1scaling factor for fuel thermal conductivity
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:scaling factor for fuel thermal conductivity

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/thermalFastMOX/test1.i)
(test/tests/thermalFastMOX/thermal_fastmox_negative_temperature_exception.i)
(test/tests/thermalFastMOX/test2.i)

References

M. Inoue, K. Maeda, K. Katsuyama, K. Tanaka, K. Mondo, and M. Hisada. Fuel-to-cladding gap evolution and its impact on thermal performance of high burnup fast reactor type uranium-plutonium oxide fuel pins. Journal of Nuclear Materials, 326(1):59–73, 2004.

@ARTICLE{inoue2004,
    author = "Inoue, M. and Maeda, K. and Katsuyama, K. and Tanaka, K. and Mondo, K. and Hisada, M.",
    title = "Fuel-to-cladding gap evolution and its impact on thermal performance of high burnup fast reactor type uranium-plutonium oxide fuel pins",
    journal = "Journal of Nuclear Materials",
    year = "2004",
    volume = "326",
    pages = "59-73",
    number = "1",
    publisher = "Elsevier"
}

Aydin Karahan. Modeling of thermo-mechanical and irradiation behavior of metallic and oxide fuels for sodium fast reactors. PhD thesis, Massachusetts Institute of Technology, Jun 2009. URL: https://tinyurl.com/y72vqvbn.

@phdthesis{karahan2009,
    author = "Karahan, Aydin",
    title = "Modeling of thermo-mechanical and irradiation behavior of metallic and oxide fuels for sodium fast reactors",
    school = "Massachusetts Institute of Technology",
    year = "2009",
    month = "Jun",
    url = "https://tinyurl.com/y72vqvbn"
}

P.G. Lucuta, Hj. Matzke, and I.J. Hastings. A pragmatic approach to modelling thermal conductivity of irradiated UO$_2$ fuel: review and recommendations. Journal of Nuclear Materials, 232(2-3):166–180, 1996. URL: http://www.sciencedirect.com/science/article/pii/S0022311596004047, doi:10.1016/S0022-3115(96)00404-7.

@ARTICLE{Lucuta1996,
    author = "Lucuta, P.G. and Matzke, Hj. and Hastings, I.J.",
    title = "A pragmatic approach to modelling thermal conductivity of irradiated {UO}$\_2$ fuel: Review and recommendations",
    journal = "Journal of Nuclear Materials",
    year = "1996",
    volume = "232",
    pages = "166-180",
    number = "2-3",
    bdsk-url-1 = "http://www.sciencedirect.com/science/article/pii/S0022311596004047",
    bdsk-url-2 = "http://dx.doi.org/10.1016/S0022-3115(96)00404-7",
    doi = "10.1016/S0022-3115(96)00404-7",
    issn = "0022-3115",
    url = "http://www.sciencedirect.com/science/article/pii/S0022311596004047"
}

(test/tests/thermalFastMOX/test1.i)

# The mesh is a 1x1x1 cube (single element).
# The temperature is ramped on all faces of each cube from 500 K to 1500K.
# The fission rate is from 2e19 n/m3/s, so that the burnup is from 5 at.%
# at the end of the simulation.
# Thermal conductivity is computed using FastMOXThermal material model
# with a oxygen to metal ratio of 2.0
#
#
# The thermal conductivity computed by BISON was picked up each 10 time
# steps for each block, and compared with analytical solution
# The results are the following:
#
# Temp (k)   Bu (at. %)    BISON k (W/m/K)  analytical k (W/m/K)
# 700.172     0.999619         3.40129           3.40129
# 900.344     1.99924          2.86762           2.86762
# 1100.52     2.99886          2.59972           2.59971
# 1300.69     3.99848          2.29508           2.29508
# 1500.00     4.99810          2.06107           2.06107

initial_fuel_density = 10431.0

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 1x1x1cube.e
  []
[]

[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 500     # set initial T to 500 K
  []
[]

[AuxVariables]
  [fission_rate]
    order = FIRST
    family = LAGRANGE
    block = 1
  []
  [burnup]
    order = FIRST
    family = LAGRANGE
    block = 1
  []
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = T
  []
  [heat_source]
     type = NeutronHeatSource
     variable = T
     block = 1
     energy_per_fission = 3.2e-11
     fission_rate = fission_rate
  []
[]

[AuxKernels]
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable= fission_rate
    block = 1
    value = 2e19             # Standard fission_rate
    execute_on = 'initial timestep_begin'
  []
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    block = 1
  []
  [burnup]
    type = BurnupAux
    block = 1
    variable = burnup
    density = ${initial_fuel_density}
    fission_rate = fission_rate
    execute_on = timestep_begin
  []
[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0.0 5.81e7'
    y = '500 1500'
  []
[]

[BCs]
   [VariableT]
     type = FunctionDirichletBC
     boundary = 2      # All cube faces
     variable = T
     function = temp_ramp
   []
[]

[Materials]
  [thermal_properties]
    type = FastMOXThermal
    block = 1
    temperature = T
    burnup = burnup
    initial_porosity = 0.05
  []
  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = ${initial_fuel_density}
  []
[]

[Executioner]

   type = Transient

   solve_type = PJFNK

   petsc_options = '-snes_ksp_ew'
   petsc_options_iname = '-ksp_gmres_restart'
   petsc_options_value = '101'

   line_search = 'none'

   l_max_its = 100
   nl_max_its = 100
   nl_rel_tol = 1e-4
   nl_abs_tol = 1e-6
   l_tol = 1e-5
   start_time = 0.0
   num_steps = 50
   dt = 1.163e6
[]

[Outputs]
  file_base = out
  [exodus]
    type = Exodus
  []
[]

(test/tests/thermalFastMOX/test1.i)

# The mesh is a 1x1x1 cube (single element).
# The temperature is ramped on all faces of each cube from 500 K to 1500K.
# The fission rate is from 2e19 n/m3/s, so that the burnup is from 5 at.%
# at the end of the simulation.
# Thermal conductivity is computed using FastMOXThermal material model
# with a oxygen to metal ratio of 2.0
#
#
# The thermal conductivity computed by BISON was picked up each 10 time
# steps for each block, and compared with analytical solution
# The results are the following:
#
# Temp (k)   Bu (at. %)    BISON k (W/m/K)  analytical k (W/m/K)
# 700.172     0.999619         3.40129           3.40129
# 900.344     1.99924          2.86762           2.86762
# 1100.52     2.99886          2.59972           2.59971
# 1300.69     3.99848          2.29508           2.29508
# 1500.00     4.99810          2.06107           2.06107

initial_fuel_density = 10431.0

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 1x1x1cube.e
  []
[]

[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 500     # set initial T to 500 K
  []
[]

[AuxVariables]
  [fission_rate]
    order = FIRST
    family = LAGRANGE
    block = 1
  []
  [burnup]
    order = FIRST
    family = LAGRANGE
    block = 1
  []
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = T
  []
  [heat_source]
     type = NeutronHeatSource
     variable = T
     block = 1
     energy_per_fission = 3.2e-11
     fission_rate = fission_rate
  []
[]

[AuxKernels]
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable= fission_rate
    block = 1
    value = 2e19             # Standard fission_rate
    execute_on = 'initial timestep_begin'
  []
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    block = 1
  []
  [burnup]
    type = BurnupAux
    block = 1
    variable = burnup
    density = ${initial_fuel_density}
    fission_rate = fission_rate
    execute_on = timestep_begin
  []
[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0.0 5.81e7'
    y = '500 1500'
  []
[]

[BCs]
   [VariableT]
     type = FunctionDirichletBC
     boundary = 2      # All cube faces
     variable = T
     function = temp_ramp
   []
[]

[Materials]
  [thermal_properties]
    type = FastMOXThermal
    block = 1
    temperature = T
    burnup = burnup
    initial_porosity = 0.05
  []
  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = ${initial_fuel_density}
  []
[]

[Executioner]

   type = Transient

   solve_type = PJFNK

   petsc_options = '-snes_ksp_ew'
   petsc_options_iname = '-ksp_gmres_restart'
   petsc_options_value = '101'

   line_search = 'none'

   l_max_its = 100
   nl_max_its = 100
   nl_rel_tol = 1e-4
   nl_abs_tol = 1e-6
   l_tol = 1e-5
   start_time = 0.0
   num_steps = 50
   dt = 1.163e6
[]

[Outputs]
  file_base = out
  [exodus]
    type = Exodus
  []
[]

(test/tests/thermalFastMOX/thermal_fastmox_negative_temperature_exception.i)

# This tests ensures that the moose exception to cut the timestep when a
# negative temperature is detected in FastMOXThermal is properly executed.

[Mesh]
  [line]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Functions]
  [temperature_func]
    type = PiecewiseLinear
    x = '0 2'
    y = '300 -100.0'
  []
[]

[Variables]
  [temp]
    initial_condition = 300
  []
[]

[AuxVariables]
  [burnup]
    order = CONSTANT
    family = MONOMIAL
  []
[]

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

[AuxKernels]
  [burnup]
    type = ConstantAux
    variable = burnup
    value = 0
  []
[]

[BCs]
  [fixed_temp]
    type = FunctionDirichletBC
    variable = temp
    boundary = 'left right'
    function = temperature_func
  []
[]

[Materials]
  [thermal]
    type = FastMOXThermal
    temperature = temp
    burnup = burnup
  []
[]

[Executioner]
  type = Transient
  num_steps = 2
  dt = 2
[]

[Postprocessors]
  [dt]
   type = TimestepSize
  []
[]

[UserObjects]
  [terminator]
    type = Terminator
    expression = 'dt = 1'
    execute_on = timestep_end
  []
[]

[Outputs]
  csv = true
[]

(test/tests/thermalFastMOX/test2.i)

# The mesh is a 1x1x1 cube (single element).
# The temperature is ramped on all faces of each cube from 500 K to 1500K.
# The fission rate is from 2e19 n/m3/s, so that the burnup is from 5 at.%
# at the end of the simulation.
# Thermal conductivity is computed using FastMOXThermal material model
# with a oxygen to metal ratio of 1.98
#
#
# The thermal conductivity computed by BISON was picked up each 10 time
# steps for each block, and compared with analytical solution
# The results are the following:
#
# Temp (k)   Bu (at. %)    BISON k (W/m/K)  analytical k (W/m/K)
# 700.172     0.999619        2.85011            2.85011
# 900.344     1.99924         2.46959            2.46959
# 1100.52     2.99886         2.28426            2.28426
# 1300.69     3.99848         2.04831            2.04830
# 1500.00     4.99810         1.86372            1.86372

initial_fuel_density = 10431.0

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 1x1x1cube.e
  []
[]

[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 500     # set initial T to 500 K
  []
[]

[AuxVariables]
  [fission_rate]
    order = FIRST
    family = LAGRANGE
    block = 1
  []
  [burnup]
    order = FIRST
    family = LAGRANGE
    block = 1
  []
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = T
  []
  [heat_source]
     type = NeutronHeatSource
     variable = T
     block = 1
     energy_per_fission = 3.2e-11
     fission_rate = fission_rate
  []
[]

[AuxKernels]
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable= fission_rate
    block = 1
    value = 2e19             # Standard fission_rate
    execute_on = 'initial timestep_begin'
  []
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    block = 1
  []
  [burnup]
    type = BurnupAux
    block = 1
    variable = burnup
    density = ${initial_fuel_density}
    fission_rate = fission_rate
    execute_on = timestep_begin
  []
[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0.0 5.81e7'
    y = '500 1500'
  []
[]

[BCs]
   [VariableT]
     type = FunctionDirichletBC
     boundary = 2      # All cube faces
     variable = T
     function = temp_ramp
   []
[]


[Materials]
  [fuel_thermalFastMOX]
    type = FastMOXThermal
    block = 1
    temperature = T
    burnup = burnup
    initial_porosity = 0.05
    oxy_to_metal_ratio = 1.98
  []
  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = ${initial_fuel_density}
  []
[]

[Executioner]

   type = Transient

   solve_type = PJFNK

   petsc_options = '-snes_ksp_ew'
   petsc_options_iname = '-ksp_gmres_restart'
   petsc_options_value = '101'

   line_search = 'none'

   l_max_its = 100
   nl_max_its = 100
   nl_rel_tol = 1e-4
   nl_abs_tol = 1e-6
   l_tol = 1e-5
   start_time = 0.0
   num_steps = 50
   dt = 1.163e6
[]

[Outputs]
  file_base = out2
  [exodus]
    type = Exodus
  []
[]

Description
Example Input Syntax
Input Parameters
Input Files
References