Al2O3Aux

Computes the Aluminum oxide thickness with either the Griess model or a user-defined function.

Description

Using either a user defined function or the Griess model, Al2O3Aux finds the thickness of the aluminum oxide layer. The Griess model calculates the thickness, $var element = document.getElementById("moose-equation-db9763ad-935a-4f82-a361-f0adae138a73");katex.render("h_{oxide}", element, {displayMode:false,throwOnError:false});$ , as $var element = document.getElementById("moose-equation-740fd258-66c3-4129-bd28-327b0b468209");katex.render("h_{oxide} = 7.87654\\times 10^{-3} h^{0.778} \\exp{\\left( -\\frac{4600}{T} \\right)}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-0ea379b4-4c70-4ffa-99ea-2f0a66fb6599");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature in Kelvin and $var element = document.getElementById("moose-equation-b9ada706-be38-4a78-aed0-f433d44b2d89");katex.render("h", element, {displayMode:false,throwOnError:false});$ is given by $var element = document.getElementById("moose-equation-63187572-cc35-475f-b99e-b1acbfc27477");katex.render(" h = \\frac{\\Delta t}{3600} + \\left[ \\frac{1.0\\times 10^6}{7876.54 \\exp{ \\left( -\\dfrac{4600}{T} \\right)} } \\right]^{1.285347}", element, {displayMode:true,throwOnError:false});$ in which $var element = document.getElementById("moose-equation-5c1749f8-e7ce-404b-bcfb-59c30952d75b");katex.render("t", element, {displayMode:false,throwOnError:false});$ is the simulation time (s), $var element = document.getElementById("moose-equation-f0327b3d-6ec8-4e7c-bd08-efa64074b233");katex.render("x", element, {displayMode:false,throwOnError:false});$ is the position (m), and $var element = document.getElementById("moose-equation-2916f745-4ddf-4a2d-ab76-ed487e96806c");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature (K).

Example Input Syntax

[AuxKernels<<<{"href": "../../syntax/AuxKernels/index.html"}>>>]
  [fred]
    type = Al2O3Aux<<<{"description": "Computes the Aluminum oxide thickness with either the Griess model or a user-defined function.", "href": "Al2O3Aux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = al2o3
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = 2
    temperature<<<{"description": "Coupled temperature"}>>> = temp
    function<<<{"description": "Function describing oxide thickness."}>>> = al2o3
  []
  [bill]
    type = Al2O3Aux<<<{"description": "Computes the Aluminum oxide thickness with either the Griess model or a user-defined function.", "href": "Al2O3Aux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = al2o3
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = 3
    temperature<<<{"description": "Coupled temperature"}>>> = temp
    model<<<{"description": "Oxide model: function griess."}>>> = function
    function<<<{"description": "Function describing oxide thickness."}>>> = al2o3
  []
  [jack]
    type = Al2O3Aux<<<{"description": "Computes the Aluminum oxide thickness with either the Griess model or a user-defined function.", "href": "Al2O3Aux.html"}>>>
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = al2o3
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = 4
    temperature<<<{"description": "Coupled temperature"}>>> = temp
    model<<<{"description": "Oxide model: function griess."}>>> = griess
  []
[]

Input Parameters

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

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.
functionFunction describing oxide thickness.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function describing oxide thickness.
modelfunctionOxide model: function griess.
Default:function
C++ Type:MooseEnum
Options:function, griess
Controllable:No
Description:Oxide model: function griess.
oxide_scale_factor1Oxide scale factor.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Oxide scale factor.

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/Al2O3/input.i)

(test/tests/Al2O3/input.i)

################################################################################
#
# The alumina thickness (al2o3) should be
#   1e-5 for the first two blocks (2 and 3)
#   9.321e-6 for the bottom node of block 4
#

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = 3sections.e
  []
[]

[Functions]
  [al2o3]
    type = PiecewiseLinear
    x = '0 1'
    y = '0 1e-5'
  []
[]

[AuxVariables]
  [al2o3]
    order = SECOND
    family = LAGRANGE
  []
[]

[AuxKernels]
  [fred]
    type = Al2O3Aux
    variable = al2o3
    boundary = 2
    temperature = temp
    function = al2o3
  []
  [bill]
    type = Al2O3Aux
    variable = al2o3
    boundary = 3
    temperature = temp
    model = function
    function = al2o3
  []
  [jack]
    type = Al2O3Aux
    variable = al2o3
    boundary = 4
    temperature = temp
    model = griess
  []
[]

# Define dependent variables, element order and shape function family,
# and initial conditions

[Variables]
  [temp]
    order = SECOND
    family = LAGRANGE
    initial_condition = 300 # K,  initial temperature
  []
[]

[Kernels]
  [heat] # gradient term in heat conduction equation
    type = HeatConduction
    variable = temp
  []

  [heat_ie] # time term in heat conduction equation
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]

# Define boundary conditions
[BCs]
  [clad_inner_surface]
    type = NeumannBC
    boundary = 1
    value = 636619.77 # heat flux from fuel
    variable = temp
  []
[]

# convective boundary condition at clad outer surface
[CoolantChannel]
  [clad_outer_surface2]
    boundary = 2
    variable = temp
    inlet_temperature = 553 # K
    inlet_pressure = 15.5E6 # Pa
    inlet_massflux = 1000 # kg/m^2-sec
    rod_diameter = 1.10e-2 # m
    rod_pitch = 1.26e-2 # m
    heat_flux = 578745.25 # W/m^2
    heat_transfer_coefficient = 10000 # W/m^2-K
    oxide_thickness = al2o3
    oxide_model = alumina
  []
  [clad_outer_surface3]
    boundary = 3
    variable = temp
    inlet_temperature = 553 # K
    inlet_pressure = 15.5E6 # Pa
    inlet_massflux = 1000 # kg/m^2-sec
    rod_diameter = 1.10e-2 # m
    rod_pitch = 1.26e-2 # m
    heat_flux = 578745.25 # W/m^2
    heat_transfer_coefficient = 10000 # W/m^2-K
    oxide_thickness = al2o3
    oxide_model = user
    cond_metal = 175
    cond_oxide = 2.25
    pbr = 1.28
  []
  [clad_outer_surface4]
    boundary = 4
    variable = temp
    inlet_temperature = 553 # K
    inlet_pressure = 15.5E6 # Pa
    inlet_massflux = 1000 # kg/m^2-sec
    rod_diameter = 1.10e-2 # m
    rod_pitch = 1.26e-2 # m
    heat_flux = 578745.25 # W/m^2
    heat_transfer_coefficient = 10000 # W/m^2-K
    oxide_thickness = al2o3
    oxide_model = alumina
  []
[]

[Materials]
  [clad_thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 16.0 # W/m-K
    specific_heat = 330.0 # J/kg-K
    block = '2 3 4'
  []
  [density]
    type = ParsedMaterial
    property_name = density
    expression = 6551.0 # kg/m^3
    block = '2 3 4'
  []
[]

[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 = 1e4
  end_time = 1e4
[]

[Postprocessors]
  [clad_inner_surface_flux] # area integrated heat flux at clad inner surface
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = '1'
    diffusivity = thermal_conductivity
  []

  [clad_outer_surface_flux2] # area integrated heat flux at clad outer  surface
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = '2'
    diffusivity = thermal_conductivity
  []
  [clad_outer_surface_flux3] # area integrated heat flux at clad outer  surface
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = '3'
    diffusivity = thermal_conductivity
  []
  [clad_outer_surface_flux4] # area integrated heat flux at clad outer  surface
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = '4'
    diffusivity = thermal_conductivity
  []

[]

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

(test/tests/Al2O3/input.i)

################################################################################
#
# The alumina thickness (al2o3) should be
#   1e-5 for the first two blocks (2 and 3)
#   9.321e-6 for the bottom node of block 4
#

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = 3sections.e
  []
[]

[Functions]
  [al2o3]
    type = PiecewiseLinear
    x = '0 1'
    y = '0 1e-5'
  []
[]

[AuxVariables]
  [al2o3]
    order = SECOND
    family = LAGRANGE
  []
[]

[AuxKernels]
  [fred]
    type = Al2O3Aux
    variable = al2o3
    boundary = 2
    temperature = temp
    function = al2o3
  []
  [bill]
    type = Al2O3Aux
    variable = al2o3
    boundary = 3
    temperature = temp
    model = function
    function = al2o3
  []
  [jack]
    type = Al2O3Aux
    variable = al2o3
    boundary = 4
    temperature = temp
    model = griess
  []
[]

# Define dependent variables, element order and shape function family,
# and initial conditions

[Variables]
  [temp]
    order = SECOND
    family = LAGRANGE
    initial_condition = 300 # K,  initial temperature
  []
[]

[Kernels]
  [heat] # gradient term in heat conduction equation
    type = HeatConduction
    variable = temp
  []

  [heat_ie] # time term in heat conduction equation
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]

# Define boundary conditions
[BCs]
  [clad_inner_surface]
    type = NeumannBC
    boundary = 1
    value = 636619.77 # heat flux from fuel
    variable = temp
  []
[]

# convective boundary condition at clad outer surface
[CoolantChannel]
  [clad_outer_surface2]
    boundary = 2
    variable = temp
    inlet_temperature = 553 # K
    inlet_pressure = 15.5E6 # Pa
    inlet_massflux = 1000 # kg/m^2-sec
    rod_diameter = 1.10e-2 # m
    rod_pitch = 1.26e-2 # m
    heat_flux = 578745.25 # W/m^2
    heat_transfer_coefficient = 10000 # W/m^2-K
    oxide_thickness = al2o3
    oxide_model = alumina
  []
  [clad_outer_surface3]
    boundary = 3
    variable = temp
    inlet_temperature = 553 # K
    inlet_pressure = 15.5E6 # Pa
    inlet_massflux = 1000 # kg/m^2-sec
    rod_diameter = 1.10e-2 # m
    rod_pitch = 1.26e-2 # m
    heat_flux = 578745.25 # W/m^2
    heat_transfer_coefficient = 10000 # W/m^2-K
    oxide_thickness = al2o3
    oxide_model = user
    cond_metal = 175
    cond_oxide = 2.25
    pbr = 1.28
  []
  [clad_outer_surface4]
    boundary = 4
    variable = temp
    inlet_temperature = 553 # K
    inlet_pressure = 15.5E6 # Pa
    inlet_massflux = 1000 # kg/m^2-sec
    rod_diameter = 1.10e-2 # m
    rod_pitch = 1.26e-2 # m
    heat_flux = 578745.25 # W/m^2
    heat_transfer_coefficient = 10000 # W/m^2-K
    oxide_thickness = al2o3
    oxide_model = alumina
  []
[]

[Materials]
  [clad_thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 16.0 # W/m-K
    specific_heat = 330.0 # J/kg-K
    block = '2 3 4'
  []
  [density]
    type = ParsedMaterial
    property_name = density
    expression = 6551.0 # kg/m^3
    block = '2 3 4'
  []
[]

[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 = 1e4
  end_time = 1e4
[]

[Postprocessors]
  [clad_inner_surface_flux] # area integrated heat flux at clad inner surface
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = '1'
    diffusivity = thermal_conductivity
  []

  [clad_outer_surface_flux2] # area integrated heat flux at clad outer  surface
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = '2'
    diffusivity = thermal_conductivity
  []
  [clad_outer_surface_flux3] # area integrated heat flux at clad outer  surface
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = '3'
    diffusivity = thermal_conductivity
  []
  [clad_outer_surface_flux4] # area integrated heat flux at clad outer  surface
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = '4'
    diffusivity = thermal_conductivity
  []

[]

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

Description
Example Input Syntax
Input Parameters
Input Files