FeCrAlOxidation

Computes the oxide mass gain and oxide scale thickness for the C35M FeCrAl alloy.

Description

The material FeCrAlOxidation models oxidation and corrosion of FeCrAl cladding.

The oxygen mass gain is calculated by: $var element = document.getElementById("moose-equation-79db8484-4644-493d-a0b2-0295aecc5da4");katex.render("w_1 = k_1 \\sqrt{t}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-a2770376-a3f7-4fe5-9d39-cc2dcc756388");katex.render("k_1", element, {displayMode:false,throwOnError:false});$ is the parabolic rate constant and t is the time. Once the mass gain is known in SI units the oxide thickness is calculated by: $var element = document.getElementById("moose-equation-a0559115-43b9-46a7-8aed-1a66a1b91b9c");katex.render("x = \\frac{w_1}{\\rho_{oxide}}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-d3a32fc4-4c64-40ef-9faf-263a69de6175");katex.render("\\rho_{oxide}", element, {displayMode:false,throwOnError:false});$ is the density of the oxygen in the oxide layer that is formed, and $var element = document.getElementById("moose-equation-176f4101-0df3-4cfe-9700-882d19dbe694");katex.render("x", element, {displayMode:false,throwOnError:false});$ is the oxide thickness in meters.

For the calculation of the parabolic rate constant, the model includes distinct correlations for normal operating temperature and high temperature. More details are given below.

Normal Operating Temperature Model

This component considers the growth of a chromium rich chromite (FeCr $var element = document.getElementById("moose-equation-3bde8b1f-0d0b-4cfb-88ab-1df4142f4136");katex.render("_2", element, {displayMode:false,throwOnError:false});$ O $var element = document.getElementById("moose-equation-b85258c9-cf3f-4fd3-92ef-0052d586cdc3");katex.render("_4", element, {displayMode:false,throwOnError:false});$ ) scale at normal reactor operating temperatures and is based on experimental tests of various FeCrAl alloys completed by Terrani et al. (2016) in PWR and BWR water conditions. Both hydrogenated BWR and normal BWR water chemistry was investigated. The parabolic rate constant depends upon whether the reactor is PWR or BWR. To make the BISON model as general as possible the average value of the rate constant for the both PWR and BWR-NRC is used. Specifically, for PWR, k $var element = document.getElementById("moose-equation-b9efd016-b729-44e2-a7ae-f087188afc3e");katex.render("_1", element, {displayMode:false,throwOnError:false});$ = 3.49 $var element = document.getElementById("moose-equation-82e1563d-c84c-478f-989f-b3ccf2e7866b");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-a201bc31-6793-453f-b576-78ebf48fd81e");katex.render("^{-3}", element, {displayMode:false,throwOnError:false});$ mg cm $var element = document.getElementById("moose-equation-866741c1-0c40-4c62-9d44-f2740e7ef51e");katex.render("^{-2}", element, {displayMode:false,throwOnError:false});$ h $var element = document.getElementById("moose-equation-ab814bbf-bf16-4b3b-a02c-76e2f3544659");katex.render("^{1/2}", element, {displayMode:false,throwOnError:false});$ and for BWR, k $var element = document.getElementById("moose-equation-7a83c9c3-7374-447d-9b48-c42f30b4431d");katex.render("_1", element, {displayMode:false,throwOnError:false});$ = 3.45 $var element = document.getElementById("moose-equation-a2f68de8-54da-455f-a891-0202f8ee87bc");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-cf3d11ea-749d-4499-8709-39650e49f26e");katex.render("^{-4}", element, {displayMode:false,throwOnError:false});$ mg cm $var element = document.getElementById("moose-equation-2ba85170-aa5c-42c8-8502-6f7b37a2f36d");katex.render("^{-2}", element, {displayMode:false,throwOnError:false});$ h $var element = document.getElementById("moose-equation-c2b7b3c8-83ab-4c65-b961-c3e4f0a065e0");katex.render("^{1/2}", element, {displayMode:false,throwOnError:false});$ . To be consistent with BISON's SI units the value of $var element = document.getElementById("moose-equation-ba961aad-9cc1-4fe6-b161-a57ed843559e");katex.render("k_1", element, {displayMode:false,throwOnError:false});$ is multiplied by a conversion factor to change the units to kg m $var element = document.getElementById("moose-equation-b5af94e6-b2a6-4e7b-bac4-cc11220627bc");katex.render("^{-2}", element, {displayMode:false,throwOnError:false});$ s $var element = document.getElementById("moose-equation-fd5721ec-6511-40e1-ad4b-40feccfb4205");katex.render("^{1/2}", element, {displayMode:false,throwOnError:false});$ . The density of oxygen in the chromite layer is taken as 1440kg m $var element = document.getElementById("moose-equation-c1ca3f21-6439-4e95-8057-9187a581951a");katex.render("^{-3}", element, {displayMode:false,throwOnError:false});$ (Terrani et al., 2016).

High-Temperature Model

This component considers the growth of an alumina (Al $var element = document.getElementById("moose-equation-de6df548-0283-451a-af07-a9d854e0d46c");katex.render("_2", element, {displayMode:false,throwOnError:false});$ O $var element = document.getElementById("moose-equation-b391e3cf-bccc-4578-9082-d7814a82c1ce");katex.render("_3", element, {displayMode:false,throwOnError:false});$ ) scale, which forms at temperatures above 1173 K Rybicki and Smialek (1989). This high-temperature model does not differentiate between PWR and BWR conditions. The correlation for the parabolic rate constant is based on the data reported in Field et al. (2018). These experiments indicated that for the FeCrAl alloys of interest (>10% Cr, 5-6% Al) the oxidation kinetics at high temperature is consistent with a multiplication factor of 2.3 for the square of the parabolic rate constant relative to the commercial alloy Kanthal APMT. Then, the model considers (in kg/m $var element = document.getElementById("moose-equation-02113187-a127-42f6-842a-a8009060f21a");katex.render("^2", element, {displayMode:false,throwOnError:false});$ -s $var element = document.getElementById("moose-equation-18d81a1e-99f1-4329-bc98-d53513dd530a");katex.render("^{1/2}", element, {displayMode:false,throwOnError:false});$ ):

$var element = document.getElementById("moose-equation-df61e6d8-68d2-40cf-baf1-45054227df7d");katex.render(" k_{1} = \\sqrt{1.803 \\times 10^3 \\exp(-3.440\\times10^5/\\left(RT\\right))}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-5b25850d-5610-4cfb-88bf-2727867d5d6d");katex.render("R", element, {displayMode:false,throwOnError:false});$ (J/mol-K) is the gas constant. The density of oxygen in the alumina layer is taken as 1888 kg m $var element = document.getElementById("moose-equation-809249d2-6810-4d76-8dc1-8322b14d823d");katex.render("^{-3}", element, {displayMode:false,throwOnError:false});$ . This high temperature model is based on the work (Sweet, 2018).

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [oxidation]
    type = FeCrAlOxidation<<<{"description": "Computes the oxide mass gain and oxide scale thickness for the C35M FeCrAl alloy.", "href": "FeCrAlOxidation.html"}>>>
    reactor_type<<<{"description": "The reactor type being simulated, either PWR or BWR.  Default is PWR."}>>> = BWR
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = 3
  []
[]

Input 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
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.
oxide_scale_factor1Scaling factor for oxide thickness
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scaling factor for oxide thickness
reactor_typePWRThe reactor type being simulated, either PWR or BWR. Default is PWR.
Default:PWR
C++ Type:MooseEnum
Options:PWR, BWR
Controllable:No
Description:The reactor type being simulated, either PWR or BWR. Default is PWR.
temperatureCladding outer surface temperature (K)
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Cladding outer surface temperature (K)

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/fecral_oxidation/corrosion_test_fecral_pwr.i)
(test/tests/fecral_oxidation/corrosion_test_fecral_high_temp.i)
(test/tests/fecral_oxidation/corrosion_test_fecral_bwr.i)
(examples/accident_tolerant_fuel/uo2_fecral/uo2_fecral.i)

References

K. G. Field, M. A. Snead, Y. Yamamoto, and K. A. Terrani. Handbook on the material properties of fecral alloys for nuclear power production applications. Technical Report ORNL/SPR-2018/905 Rev. 1, Oak Ridge National Laboratory, 2018.

@TECHREPORT{fecral_handbook,
    author = "Field, K. G. and Snead, M. A. and Yamamoto, Y. and Terrani, K. A.",
    title = "Handbook on the Material Properties of FeCrAl Alloys for Nuclear Power Production Applications",
    institution = "Oak Ridge National Laboratory",
    number = "ORNL/SPR-2018/905 Rev. 1",
    year = "2018"
}

G.C. Rybicki and J.L. Smialek. Effect of the θ-α-Al$_2$O$_3$ transformation on the oxidation behavior of β-NiAl + Zr. Oxidation of Metals, 31:275–304, 1989.

@article{rybicki1989,
    author = "Rybicki, G.C. and Smialek, J.L.",
    title = "Effect of the $\theta$-$\alpha$-{A}l$\_2${O}$\_3$ transformation on the oxidation behavior of $\beta$-{N}i{A}l + {Z}r",
    journal = "Oxidation of Metals",
    volume = "31",
    pages = "275-304",
    year = "1989"
}

R. T. Sweet. Thermo-mechanical analysis of iron-chromium-aluminum (FeCrAl) alloy cladding for light water reactor fuel elements. PhD thesis, The University of Tennessee, Knoxville, August 2018.

@phdthesis{sweet2018,
    author = "Sweet, R. T.",
    title = "{Thermo-mechanical analysis of iron-chromium-aluminum (FeCrAl) alloy cladding for light water reactor fuel elements}",
    school = "The University of Tennessee, Knoxville",
    year = "2018",
    month = "August"
}

K.A. Terrani, B.A. Pint, Y.-J. Kim, K.A. Unocic, Y. Yang, C.M. Silva, H.M. Meyer III, and R.B. Rebak. Uniform corrosion of fecral alloys in lwr coolant environments. Journal of Nuclear Materials, 479:36–47, 2016.

@article{terrani2016,
    author = "Terrani, K.A. and Pint, B.A. and Kim, Y.-J. and Unocic, K.A. and Yang, Y. and Silva, C.M. and Meyer III, H.M. and Rebak, R.B.",
    title = "Uniform corrosion of FeCrAl alloys in LWR coolant environments",
    journal = "Journal of Nuclear Materials",
    volume = "479",
    pages = "36-47",
    year = "2016"
}

(test/tests/fecral_oxidation/corrosion_test_fecral_bwr.i)

################################################################################
#
# The test case is a plate with an axial length of 0.01 meter and
# a thickness of 0.05cm; cladding OD temperature is 500 K;
# EOL time = 277.778 hours (1000000 seconds).
#
# The model calculates the oxide (oxygen) mass gain and oxide layer thickness
# based upon the latest data of Terrani et al.:
#
# [1] Terrani et al. "Uniform corrosion of FeCrAl alloys in LWR Coolant
#     environments, Journal of Nuclear Materials, p. 36-47, 2016"
#
# For normal water chemistry BWR environments the parabolic rate constant for
# the oxidation correlation is given by: k_1 = 3.45e-4 mg/cm^2-h^(1/2) for the
# alloy with a composition very close to C35M. (Fe-13Cr-4Al).  The analytical
# oxygen mass gain is then determined by:
#
# w = k_1 * sqrt(t)                                              (1)
#
# Where t is the time within the oxidizing environment.  Then the oxide
# thickness is determined from w and the oxygen density in the oxide, d:
#
# x = w / d                                                      (2)
#
# The oxygen mass gain calculated using equation (1) and converting to SI units
# gives w = 5.75e-5 kg/m^2.  BISON calculates an oxygen mass gain of
# 5.75e-5 kg/m^2 as well.
#
# Then in SI units of meters the oxide thickness layer is determined to be
# 3.99306e-8 m (0.0399306 um). BISON calculates an oxide thickness of
# 3.99306e-8 m.
#
# Mesh:
# Number of elements in radial direction = 5
# Number of elements in axial  direction = 1
#
################################################################################
[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = clad_rz_short_rev4.e
  []
[]

[AuxVariables]
   [oxide_thickness]
     order  = CONSTANT
     family = MONOMIAL
   []
   [mass_gain]
     order = CONSTANT
     family = MONOMIAL
   []
[]
[Variables]
   [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300
  []
[]

[AuxKernels]
  [oxide]
    type = MaterialRealAux
    variable = oxide_thickness
    property = scale_thickness
    boundary = 3
  []
  [mass_gain]
    type = MaterialRealAux
    variable = mass_gain
    property = oxide_mass_gain
    boundary = 3
  []
[]

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

 [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]

[BCs]
  [clad_outer_surface]
    type =  DirichletBC
    boundary =  3
    value =  500
    variable =  temp
  []
[]

[Materials]
  [clad_thermal]
    type = FeCrAlThermal
    material = APMT
    block = 1
    temperature = temp
  []
  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 7250.0
  []
  [oxidation]
    type = FeCrAlOxidation
    reactor_type = BWR
    boundary = 3
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  l_max_its = 200
  l_tol = 8e-3

  nl_max_its = 15
  nl_rel_tol = 1e-5
  nl_abs_tol = 1e-10

  start_time = 0.0
  dt = 10000
  end_time = 1000000
[]

[Outputs]
  exodus = true
  print_linear_residuals = true
[]

(test/tests/fecral_oxidation/corrosion_test_fecral_pwr.i)

################################################################################
#
# The test case is a plate with an axial length of 0.01 meter and
# a thickness of 0.05cm; cladding OD temperature is 500 K;
# EOL time = 277.778 hours (1000000 seconds).
#
# The model calculates the oxide (oxygen) mass gain and oxide layer thickness
# based upon the latest data of Terrani et al.:
#
# [1] Terrani et al. "Uniform corrosion of FeCrAl alloys in LWR Coolant
#     environments, Journal of Nuclear Materials, p. 36-47, 2016"
#
# For PWR environments the parabolic rate constant for the oxidation correlation
# is given by: k_1 = 3.49e-3 mg/cm^2-h^(1/2) which is the average of all alloys
# studied.  The analytical oxygen mass gain is then determined by:
#
# w = k_1 * sqrt(t)                                              (1)
#
# Where t is the time within the oxidizing environment.  Then the oxide
# thickness is determined from w and the oxygen density in the oxide, d:
#
# x = w / d                                                      (2)
#
# The oxygen mass gain calculated using equation (1) and converting to SI units
# gives w = 5.81667e-4 kg/m^2.  BISON calculates an oxygen mass gain of
# 5.81667e-4 kg/m^2 as well.
#
# Then in SI units of meters the oxide thickness layer is determined to be
# 4.03935e-7 m (0.403935 um). BISON calculates an oxide thickness of 4.03935e-7 m.
#
# Mesh:
# Number of elements in radial direction = 5
# Number of elements in axial  direction = 1
#
################################################################################
[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = clad_rz_short_rev4.e
  []
[]

[AuxVariables]
   [oxide_thickness]
     order  = CONSTANT
     family = MONOMIAL
   []
   [mass_gain]
     order = CONSTANT
     family = MONOMIAL
   []
[]
[Variables]
   [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300
  []
[]

[AuxKernels]
  [oxide]
    type = MaterialRealAux
    variable = oxide_thickness
    property = scale_thickness
    boundary = 3
  []
  [mass_gain]
    type = MaterialRealAux
    variable = mass_gain
    property = oxide_mass_gain
    boundary = 3
  []
[]

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

 [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]

[BCs]
  [clad_outer_surface]
    type =  DirichletBC
    boundary =  3
    value =  500
    variable =  temp
  []
[]

[Materials]
  [clad_thermal]
    type = FeCrAlThermal
    material = APMT
    block = 1
    temperature = temp
  []
  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 7250.0
  []
  [oxidation]
    type = FeCrAlOxidation
    reactor_type = PWR
    boundary = 3
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  l_max_its = 200
  l_tol = 8e-3

  nl_max_its = 15
  nl_rel_tol = 1e-5
  nl_abs_tol = 1e-10

  start_time = 0.0
  dt = 10000
  end_time = 1000000
[]

[Outputs]
  exodus = true
  print_linear_residuals = true
[]

(test/tests/fecral_oxidation/corrosion_test_fecral_high_temp.i)

################################################################################
#
# The test case is a plate with an axial length of 0.01 meter and
# a thickness of 0.05cm; cladding OD temperature is 1473 K;
# EOL time = 2.778 hours (10000 seconds).
#
# The model calculates the oxide (oxygen) mass gain and oxide layer thickness
# based upon the high-temperature data from:
#
# [2] K.G. Field, M.A. Snead, Y. Yamamoto, K.A. Terrani, Handbook on the Material
#     Properties of FeCrAl Alloys for Nuclear Power Production Applications,
#     ORNL/SPR-2018/905 (2018).
#
# The model considers the growth of a scale of alumina (Al2O3) above 1173 K.
# The parabolic rate constant for the oxidation correlation is given by:
# k_1 = sqrt(1.803e3*exp(-3.440e5/(RT))) kg^2/m^4-s, where the pre-factor
# 1.803e3 corresponds to 2.3 times that of the APMT alloy [2].
# The analytical oxygen mass gain is then determined by:
#
# w = k_1 * sqrt(t)                                              (1)
#
# where t is the time within the oxidizing environment.  Then the oxide
# thickness is determined from w and the oxygen density in the oxide, d:
#
# x = w / d                                                      (2)
#
# The oxygen mass gain calculated using equation (1) gives w = 3.38e-3 kg/m^2.
# BISON calculates an oxygen mass gain of 3.38e-3 kg/m^2 as well.
#
# Then the oxide thickness layer is determined by equation (2) to be 1.79e-6 m
# (1.79 um). BISON calculates an oxide thickness of 1.79e-6 m as well.
#
# Mesh:
# Number of elements in radial direction = 5
# Number of elements in axial  direction = 1
#
################################################################################
[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = clad_rz_short_rev4.e
  []
[]

[AuxVariables]
   [oxide_thickness]
     order  = CONSTANT
     family = MONOMIAL
   []
   [mass_gain]
     order = CONSTANT
     family = MONOMIAL
   []
[]
[Variables]
   [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1473
  []
[]

[AuxKernels]
  [oxide]
    type = MaterialRealAux
    variable = oxide_thickness
    property = scale_thickness
    boundary = 3
  []
  [mass_gain]
    type = MaterialRealAux
    variable = mass_gain
    property = oxide_mass_gain
    boundary = 3
  []
[]

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

 [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]

[BCs]
  [clad_outer_surface]
    type =  DirichletBC
    boundary =  3
    value =  1473
    variable =  temp
  []
[]

[Materials]
  [clad_thermal]
    type = FeCrAlThermal
    material = APMT
    block = 1
    temperature = temp
  []
  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 7250.0
  []
  [oxidation]
    type = FeCrAlOxidation
    reactor_type = PWR
    temperature = temp
    boundary = 3
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  l_max_its = 200
  l_tol = 8e-3

  nl_max_its = 15
  nl_rel_tol = 1e-5
  nl_abs_tol = 1e-10

  start_time = 0.0
  dt = 20
  end_time = 10000
[]

[Outputs]
  exodus = true
  print_linear_residuals = true
[]

(test/tests/fecral_oxidation/corrosion_test_fecral_bwr.i)

################################################################################
#
# The test case is a plate with an axial length of 0.01 meter and
# a thickness of 0.05cm; cladding OD temperature is 500 K;
# EOL time = 277.778 hours (1000000 seconds).
#
# The model calculates the oxide (oxygen) mass gain and oxide layer thickness
# based upon the latest data of Terrani et al.:
#
# [1] Terrani et al. "Uniform corrosion of FeCrAl alloys in LWR Coolant
#     environments, Journal of Nuclear Materials, p. 36-47, 2016"
#
# For normal water chemistry BWR environments the parabolic rate constant for
# the oxidation correlation is given by: k_1 = 3.45e-4 mg/cm^2-h^(1/2) for the
# alloy with a composition very close to C35M. (Fe-13Cr-4Al).  The analytical
# oxygen mass gain is then determined by:
#
# w = k_1 * sqrt(t)                                              (1)
#
# Where t is the time within the oxidizing environment.  Then the oxide
# thickness is determined from w and the oxygen density in the oxide, d:
#
# x = w / d                                                      (2)
#
# The oxygen mass gain calculated using equation (1) and converting to SI units
# gives w = 5.75e-5 kg/m^2.  BISON calculates an oxygen mass gain of
# 5.75e-5 kg/m^2 as well.
#
# Then in SI units of meters the oxide thickness layer is determined to be
# 3.99306e-8 m (0.0399306 um). BISON calculates an oxide thickness of
# 3.99306e-8 m.
#
# Mesh:
# Number of elements in radial direction = 5
# Number of elements in axial  direction = 1
#
################################################################################
[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = clad_rz_short_rev4.e
  []
[]

[AuxVariables]
   [oxide_thickness]
     order  = CONSTANT
     family = MONOMIAL
   []
   [mass_gain]
     order = CONSTANT
     family = MONOMIAL
   []
[]
[Variables]
   [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300
  []
[]

[AuxKernels]
  [oxide]
    type = MaterialRealAux
    variable = oxide_thickness
    property = scale_thickness
    boundary = 3
  []
  [mass_gain]
    type = MaterialRealAux
    variable = mass_gain
    property = oxide_mass_gain
    boundary = 3
  []
[]

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

 [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]

[BCs]
  [clad_outer_surface]
    type =  DirichletBC
    boundary =  3
    value =  500
    variable =  temp
  []
[]

[Materials]
  [clad_thermal]
    type = FeCrAlThermal
    material = APMT
    block = 1
    temperature = temp
  []
  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 7250.0
  []
  [oxidation]
    type = FeCrAlOxidation
    reactor_type = BWR
    boundary = 3
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  l_max_its = 200
  l_tol = 8e-3

  nl_max_its = 15
  nl_rel_tol = 1e-5
  nl_abs_tol = 1e-10

  start_time = 0.0
  dt = 10000
  end_time = 1000000
[]

[Outputs]
  exodus = true
  print_linear_residuals = true
[]

(examples/accident_tolerant_fuel/uo2_fecral/uo2_fecral.i)


initial_fuel_density = 10431.0

[GlobalParams]
  # Set initial fuel density, other global parameters
  density = ${initial_fuel_density}
  order = SECOND
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
  displacements = 'disp_x disp_y'
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[Mesh]
  coord_type = RZ
  displacements = 'disp_x disp_y'
  patch_size = 10 # For contact algorithm
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
  [mesh]
    type = FileMeshGenerator
    file = uo2_fecral_smeared.e
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 293.0
  []
[]

[UserObjects]
  [pin_geometry]
    type = FuelPinGeometry
    clad_inner_wall = 5
    clad_outer_wall = 2
    clad_top = 3
    clad_bottom = 1
    pellet_exteriors = 8
  []
[]

[AuxVariables]
  [fast_neutron_flux]
    block = clad
  []
  [fast_neutron_fluence]
    block = clad
  []
  [grain_radius]
    block = pellet_type_1
    initial_condition = 10e-6
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
  []
  [oxide_thickness]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_hoop_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_hoop]
    order = CONSTANT
    family = MONOMIAL
  []
  [hoop_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_rate]
    order = CONSTANT
    family = MONOMIAL
  []
  [mass_gain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1e4 1e8'
    y = '0 2.5e4 2.5e4'
    scale_factor = 1
  []

  [axial_peaking_factors]
    type = ParsedFunction
    expression = 1
  []

  [pressure_ramp]
    type = PiecewiseLinear
    x = '-200 0 1e8'
    y = '6.537e-3 1 1'
    scale_factor = 15.5e6
  []

  [mass_flux_func]
    type = PiecewiseLinear
    x = '-200 0  1e8'
    y = '3800. 3800. 3800.'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [pellets]
    block = pellet_type_1
    strain = FINITE
    eigenstrain_names = 'fuel_relocation_strain fuel_thermal_strain fuel_volumetric_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
    temperature = temp
  []
  [clad]
    block = clad
    strain = FINITE
    eigenstrain_names = 'clad_thermal_eigenstrain clad_volumetric_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
    temperature = temp
  []
[]

[Kernels]
  [gravity]
    type = Gravity
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []

  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []

  [heat_source]
    type = NeutronHeatSource
    variable = temp
    block = pellet_type_1
    burnup_function = burnup
    extra_vector_tags = 'ref'
  []
[]

[Burnup]
  [burnup]
    block = pellet_type_1
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    num_radial = 81
    num_axial = 11
    fuel_pin_geometry = pin_geometry
    fuel_volume_ratio = 1.0
    RPF = RPF
  []
[]

[AuxKernels]
  [fast_neutron_flux]
    type = FastNeutronFluxAux
    variable = fast_neutron_flux
    block = clad
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    factor = 3e13
    execute_on = timestep_begin
  []
  [fast_neutron_fluence]
    type = FastNeutronFluenceAux
    variable = fast_neutron_fluence
    block = clad
    fast_neutron_flux = fast_neutron_flux
    execute_on = timestep_begin
  []
  [grain_radius]
    type = GrainRadiusAux
    block = pellet_type_1
    variable = grain_radius
    temperature = temp
    execute_on = linear
  []
  [hoop_stress]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = hoop_stress
    scalar_type = HoopStress
    execute_on = timestep_end
  []
  [total_hoop_strain]
    type = RankTwoScalarAux
    rank_two_tensor = total_strain
    variable = total_hoop_strain
    scalar_type = HoopStress
    execute_on = timestep_end
  []
  [creep_strain_hoop]
    type = RankTwoScalarAux
    rank_two_tensor = creep_strain
    variable = creep_strain_hoop
    scalar_type = HoopStress
    block = clad
    execute_on = timestep_end
  []
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 10
  []
  [coolant_htc]
    type = MaterialRealAux
    property = coolant_channel_htc
    variable = coolant_htc
    boundary = 2
  []
  [creep_rate]
    type = MaterialRealAux
    variable = creep_rate
    property = creep_rate
    execute_on = timestep_end
    block = clad
  []
  [oxide]
    type = MaterialRealAux
    variable = oxide_thickness
    property = scale_thickness
    boundary = 2
  []
  [mass_gain]
    type = MaterialRealAux
    variable = mass_gain
    property = oxide_mass_gain
    boundary = 2
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 5
    secondary = 10
    normal_smoothing_distance = 0.1
    penalty = 1e7
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temp
    primary = 5
    secondary = 10
    initial_moles = initial_moles
    gas_released = fis_gas_released
    contact_pressure = contact_pressure
    quadrature = true
  []
[]

[BCs]
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []

  [no_y_clad_bottom]
    type = DirichletBC
    variable = disp_y
    boundary = 1
    value = 0.0
  []

  [no_y_fuel_bottom]
    type = DirichletBC
    variable = disp_y
    boundary = 1020
    value = 0.0
  []

  [Pressure]
    [coolantPressure]
      boundary = '1 2 3'
      function = pressure_ramp
    []
  []

  [PlenumPressure]
    [plenumPressure]
      boundary = 9
      initial_pressure = 2.0e6
      startup_time = 0
      R = 8.3143
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = gas_volume
      material_input = fis_gas_released
      output = plenum_pressure
    []
  []

[]

[CoolantChannel]
  [convective_clad_surface]
    boundary = '1 2 3'
    variable = temp
    inlet_temperature = 580 # K
    inlet_pressure = pressure_ramp # Pa
    inlet_massflux = mass_flux_func # kg/m^2-sec
    rod_diameter = 9.5e-3 # m
    rod_pitch = 1.26e-2 # m
    linear_heat_rate = power_history
    axial_power_profile = axial_peaking_factors
    oxide_thickness = oxide_thickness
  []
[]

[Materials]
  [fuel_thermal]
    type = UO2Thermal
    block = pellet_type_1
    thermal_conductivity_model = NFIR
    temperature = temp
    burnup_function = burnup
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = pellet_type_1
    youngs_modulus = 2.0e11
    poissons_ratio = 0.345
  []
  [elastic_stress]
    type = ComputeSmearedCrackingStress
    block = pellet_type_1
    cracking_stress = 1.68e8
    inelastic_models = 'fuel_creep'
    softening_models = exponential_softening
    shear_retention_factor = 0.1
    max_stress_correction = 0
    cracked_elasticity_type = DIAGONAL
    output_properties = crack_damage
    outputs = exodus
  []
  [exponential_softening]
    type = ExponentialSoftening
  []
  [fuel_creep]
    type = UO2CreepUpdate
    block = pellet_type_1
    burnup_function = burnup
    temperature = temp
  []
  [fuel_relocation]
    type = UO2RelocationEigenstrain
    block = pellet_type_1
    burnup_function = burnup
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    fuel_pin_geometry = 'pin_geometry'
    relocation_activation1 = 5000
    relocation_model = ESCORE_modified
    eigenstrain_name = fuel_relocation_strain
  []
  [fuel_thermal_expansion]
    type = UO2ThermalExpansionMATPROEigenstrain
    block = pellet_type_1
    temperature = temp
    stress_free_temperature = 295.0
    eigenstrain_name = fuel_thermal_strain
  []
  [fuel_volumetric_swelling]
    type = UO2VolumetricSwellingEigenstrain
    gas_swelling_model_type = SIFGRS
    block = pellet_type_1
    temperature = temp
    burnup_function = burnup
    initial_fuel_density = 10431.0
    eigenstrain_name = fuel_volumetric_strain
  []
  [clad_thermal]
    type = FeCrAlThermal
    material = C35M
    block = clad
    temperature = temp
  []
  [clad_elasticity_tensor] # isotropic elasticity tensor for Zry cladding
    type = FeCrAlElasticityTensor
    temperature = temp
    fecral_material_type = C35M
    block = clad
  []
  [clad_stress] # stress update class to govern the return mapping algorithm for creep
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'clad_creep clad_plasticity'
    block = clad
  []
  [clad_creep]
    type = FeCrAlCreepUpdate
    block = clad
    temperature = temp
    fecral_material_type = C35M
    fast_neutron_flux = fast_neutron_flux
    model_irradiation_creep = true
    model_thermal_creep = true
    max_inelastic_increment = 1e-4
  []
  [thermal_expansion]
    type = FeCrAlThermalExpansionEigenstrain
    block = clad
    temperature = temp
    fecral_material_type = C35M
    stress_free_temperature = 295.0
    eigenstrain_name = clad_thermal_eigenstrain
  []
  [irradiation_swelling]
    type = FeCrAlVolumetricSwellingEigenstrain
    block = clad
    temperature = temp
    fast_neutron_fluence = fast_neutron_fluence
    eigenstrain_name = clad_volumetric_strain
  []
  [clad_plasticity]
    type = FeCrAlPlasticityUpdate
    block = clad
    hardening_constant = 2.5e9
    temperature = temp
    yield_stress = 500.0
  []
  [fission_gas_release]
    type = UO2Sifgrs
    block = pellet_type_1
    temperature = temp
    burnup_function = burnup
    grain_radius = grain_radius
    gbs_model = true
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = clad
    strain_free_density = 7250.0
  []
  [fuel_density]
    type = StrainAdjustedDensity
    block = pellet_type_1
    strain_free_density = ${initial_fuel_density}
  []

  [failure_criterion]
    type = FeCrAlCladdingFailure
    boundary = '2 5'
    hoop_stress = hoop_stress
    failure_criterion = UTS
    temperature = temp
  []
  [oxidation]
    type = FeCrAlOxidation
    reactor_type = PWR
    boundary = 2
  []
[]

[Dampers]
  [limitT]
    type = BoundingValueNodalDamper
    max_value = 3200.0
    min_value = 293.0
    variable = temp
  []
  [limitX]
    type = MaxIncrement
    max_increment = 1e-5
    variable = disp_x
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  l_max_its = 100
  l_tol = 8e-3

  nl_max_its = 25
  nl_rel_tol = 1e-5
  nl_abs_tol = 1e-10

  start_time = -200
  n_startup_steps = 1
  end_time = 1e8

  dtmax = 1e5
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2.0e2
    force_step_every_function_point = true
    timestep_limiting_function = power_history
    max_function_change = 5e5
    optimal_iterations = 10
    iteration_window = 2
    linear_iteration_ratio = 100
    growth_factor = 2.0
    timestep_limiting_postprocessor = material_timestep
  []

  [Quadrature]
    order = FIFTH
    side_order = SEVENTH
  []
[]

[Postprocessors]
  [ave_temp_interior]
    type = SideAverageValue
    boundary = 9
    variable = temp
    execute_on = 'initial linear'
  []

  [avg_clad_temp]
    type = SideAverageValue
    boundary = 7
    variable = temp
  []

  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = pellet_type_1
  []

  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = pellet_type_1
  []
  [fis_gas_grain]
    type = ElementIntegralFisGasGrainSifgrs
    block = pellet_type_1
  []
  [fis_gas_boundary]
    type = ElementIntegralFisGasBoundarySifgrs
    block = pellet_type_1
  []

  [gas_volume]
    type = InternalVolume
    boundary = 9
    execute_on = 'initial linear'
  []

  [_dt]
    type = TimestepSize
  []

  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []

  [rod_total_power]
    type = ElementIntegralPower
    variable = temp
    burnup_function = burnup
    block = pellet_type_1
  []

  [alhr_input]
    type = FunctionValuePostprocessor
    function = power_history
  []
  [average_burnup]
    type = ElementAverageValue
    block = pellet_type_1
    variable = burnup
  []
  [oxide_thickness]
    type = ElementExtremeValue
    block = clad
    variable = oxide_thickness
  []
  [mass_gain]
    type = ElementExtremeValue
    block = clad
    variable = mass_gain
  []
  [fis_gas_percent]
    type = FGRPercent
    fission_gas_released = fis_gas_released
    fission_gas_generated = fis_gas_produced
  []
  [material_timestep]
    type = MaterialTimeStepPostprocessor
    block = clad
  []
[]

[Outputs]
  perf_graph = true
  time_step_interval =  1
  exodus = true
  csv = true
  print_linear_residuals = true
  color = false

  [console]
    type = Console
    max_rows = 25
  []
[]

Description
Example Input Syntax
Input Parameters
Input Files
References