FeCrAlOxideAux

Computes the oxidation and corrosion of FeCrAl cladding.

Description

The oxidation of FeCrAl cladding, FeCrAlOxideAux is calculated based upon a parabolic rate law to determine the mass gain of oxide. The mass gain is then converted into an oxide thickness. Currently, the oxidation model is not coupled to the Coolant Channel model to affect the heat transfer coefficient as the cladding becomes oxidized. The model presented here was developed for Kanthal APMT, which is one of the candidate ATF FeCrAl cladding alloys. The model was also developed for high temperature steam, resulting in low oxidation rates at normal operating temperatures.

It is expected that oxidation of FeCrAl alloys will be negligible during normal operation and the model can be applied to the normal operating regime. The parabolic rate constant was determined by Pint et al. (2015): $var element = document.getElementById("moose-equation-e1042f1f-4e24-4216-899b-202d9e636fed");katex.render(" k_p = k_o e^{-Q/T}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-333de075-d661-438e-89fd-1a69b3d0ddf8");katex.render("k_p", element, {displayMode:false,throwOnError:false});$ is the parabolic rate constant in units of g $var element = document.getElementById("moose-equation-7725d2c1-9b18-4f6b-8be4-6d32db314bc1");katex.render("^2", element, {displayMode:false,throwOnError:false});$ /cm $var element = document.getElementById("moose-equation-498be9ff-62f2-40da-9915-8158b8981884");katex.render("^4", element, {displayMode:false,throwOnError:false});$ -s, $var element = document.getElementById("moose-equation-0c991533-bf93-40a3-889e-56a0f0a6c92d");katex.render("k_o", element, {displayMode:false,throwOnError:false});$ is a constant equal to 7.84 g $var element = document.getElementById("moose-equation-b32149e2-e932-48ba-84bf-191fb5710797");katex.render("^2", element, {displayMode:false,throwOnError:false});$ /cm $var element = document.getElementById("moose-equation-6289947a-15b3-42a0-8a7a-faf8b78cb87e");katex.render("^4", element, {displayMode:false,throwOnError:false});$ -s, and $var element = document.getElementById("moose-equation-eed6c045-9642-493b-b731-5e044e23e2ca");katex.render("Q", element, {displayMode:false,throwOnError:false});$ is an activation energy in units of K with a value of 41373.7.

The mass gain due to the oxide formation is then calculated by $var element = document.getElementById("moose-equation-9dbb0a97-4b33-4c02-9d7f-96e63a38450e");katex.render(" w_g = k_p^{1/2} t^{1/2}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-197e0164-d27f-419f-9df0-10490e5b20d3");katex.render("w_g", element, {displayMode:false,throwOnError:false});$ is the mass gain due to oxidation in units of mg/cm $var element = document.getElementById("moose-equation-18c87c5d-edb4-4913-885c-42361d4b55bc");katex.render("^2", element, {displayMode:false,throwOnError:false});$ . Then the oxide thickness is determined by multiplying the mass gain by the conversion factor of 5.35 $var element = document.getElementById("moose-equation-d4253c46-bc65-4bb8-bd2b-3dc5a643db6e");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ m-(cm $var element = document.getElementById("moose-equation-bd74accf-4c23-4745-a817-e84ec6d4be6d");katex.render("^2", element, {displayMode:false,throwOnError:false});$ /mg) as proposed by Jönsson et al. (2013).

Example Input Syntax

[AuxKernels<<<{"href": "../../syntax/AuxKernels/index.html"}>>>]
  [oxide]
    type = FeCrAlOxideAux<<<{"description": "Computes the oxidation and corrosion of FeCrAl cladding.", "href": "FeCrAlOxideAux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = oxide_thickness
    temperature<<<{"description": "Cladding wall surface temperature (K)."}>>> = temp
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = 3
    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."}>>> = timestep_end
  []
[]

Input Parameters

temperatureCladding wall surface temperature (K).
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Cladding wall surface temperature (K).
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

activation_energy41373.7Activation energy in units of K (Q/R).
Default:41373.7
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Activation energy in units of K (Q/R).
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
end_timeinfWhen to turn off oxide growth.
Default:inf
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:When to turn off oxide growth.
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.
oxide_scale_factor1Oxide scale factor.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Oxide scale factor.
parabolic_rate_constant784Coefficient in parabolic rate equation (kg^2/m^4-s).
Default:784
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Coefficient in parabolic rate equation (kg^2/m^4-s).
start_time0When to turn on oxide growth.
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:When to turn on oxide growth.

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/fecral_oxidation/corrosion_test_fecral.i)

References

Bo Jönsson, Qin Lu, and Dilip Chandrasekaran. Oxidation and Creep Limited Lifetime of Kanthal APMT, a Dispersion Strengthened FeCrAlMo Alloy Designed for Strength and Oxidation Resistance at High Temperatures. Oxidation of Metals, 79:29–39, 2013.

@article{jonsson2013,
    author = {J{\"o}nsson, Bo and Lu, Qin and Chandrasekaran, Dilip},
    title = "{Oxidation and Creep Limited Lifetime of Kanthal APMT, a Dispersion Strengthened FeCrAlMo Alloy Designed for Strength and Oxidation Resistance at High Temperatures}",
    journal = "Oxidation of Metals",
    volume = "79",
    pages = "29-39",
    year = "2013"
}

B.A. Pint, K.A. Terrani, Y. Yamamoto, and L.L. Snead. Material Selection for Accident Tolerant Fuel Cladding. Metallurgical and Materials Transactions E, 2E:190–196, 2015.

@article{pint2015,
    author = "Pint, B.A. and Terrani, K.A. and Yamamoto, Y. and Snead, L.L.",
    title = "{Material Selection for Accident Tolerant Fuel Cladding}",
    journal = "Metallurgical and Materials Transactions E",
    volume = "2E",
    pages = "190-196",
    year = "2015"
}

(test/tests/fecral_oxidation/corrosion_test_fecral.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 = 1000 hours.
#
# The oxide thickness layer is analytically calculated to be 22.6162e-5
# (22.6162 um).BISON calculates an oxide thickness of 22.6162e-5 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
  []
[]

# Define dependent variables, element order and shape function family,
# and initial conditions
[AuxVariables]
  [oxide_thickness]
    order = CONSTANT
    family = MONOMIAL
  []
[]
[Variables]
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300 # K,  initial temperature
  []
[]

[AuxKernels]
  [oxide]
    type = FeCrAlOxideAux
    variable = oxide_thickness
    temperature = temp
    boundary = 3
    execute_on = timestep_end
  []
[]
[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []

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

# Define boundary conditions
[BCs]
  [clad_outer_surface]
    type = DirichletBC
    boundary = 3
    value = 1473 # K
    variable = temp
  []
[]

[Materials]
  [clad_thermal]
    type = FeCrAlThermal
    material = APMT
    block = 1
    temperature = temp
  []
  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 7250.0 # kg/m^3
  []
[]

[Executioner]
  type = Transient
  # PETSC options

  solve_type = 'PJFNK'

  # controls for linear iterations
  l_max_its = 200
  l_tol = 8e-3

  # controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-5
  nl_abs_tol = 1e-10

  # time control
  start_time = 0.0
  dt = 36000
  end_time = 3600000
[]

# Define output file(s)
[Outputs]
  exodus = true
  print_linear_residuals = true
[]

(test/tests/fecral_oxidation/corrosion_test_fecral.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 = 1000 hours.
#
# The oxide thickness layer is analytically calculated to be 22.6162e-5
# (22.6162 um).BISON calculates an oxide thickness of 22.6162e-5 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
  []
[]

# Define dependent variables, element order and shape function family,
# and initial conditions
[AuxVariables]
  [oxide_thickness]
    order = CONSTANT
    family = MONOMIAL
  []
[]
[Variables]
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300 # K,  initial temperature
  []
[]

[AuxKernels]
  [oxide]
    type = FeCrAlOxideAux
    variable = oxide_thickness
    temperature = temp
    boundary = 3
    execute_on = timestep_end
  []
[]
[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []

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

# Define boundary conditions
[BCs]
  [clad_outer_surface]
    type = DirichletBC
    boundary = 3
    value = 1473 # K
    variable = temp
  []
[]

[Materials]
  [clad_thermal]
    type = FeCrAlThermal
    material = APMT
    block = 1
    temperature = temp
  []
  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 7250.0 # kg/m^3
  []
[]

[Executioner]
  type = Transient
  # PETSC options

  solve_type = 'PJFNK'

  # controls for linear iterations
  l_max_its = 200
  l_tol = 8e-3

  # controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-5
  nl_abs_tol = 1e-10

  # time control
  start_time = 0.0
  dt = 36000
  end_time = 3600000
[]

# Define output file(s)
[Outputs]
  exodus = true
  print_linear_residuals = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References