OxygenDiffusion

Computes diffusion of oxygen in hyper-stoichiometric UO2.

Description

Calculates oxygen diffusion according to Ramirez et al. (2006) and Newman et al. (2009) $var element = document.getElementById("moose-equation-e53a51b3-a45f-443f-acbd-a4ae3ca346a4");katex.render(" \\nabla \\cdot J = 0", element, {displayMode:true,throwOnError:false});$ and $var element = document.getElementById("moose-equation-eb066e78-87d6-4f30-836c-781aa7ea1fb2");katex.render(" J = -D\\left( \\nabla x - \\frac{xQ^*}{FRT^2} \\nabla T \\right)", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-50817eae-302e-45de-bda7-ef849c82ad3a");katex.render("D", element, {displayMode:false,throwOnError:false});$ is diffusivity, $var element = document.getElementById("moose-equation-19b2b4b8-8acf-4c41-8402-89c0a20f70fe");katex.render("F", element, {displayMode:false,throwOnError:false});$ is the thermodynamic factor of oxygen, $var element = document.getElementById("moose-equation-1b402407-fdae-4d51-aeb1-4a0910702fce");katex.render("Q^*", element, {displayMode:false,throwOnError:false});$ is the heat transport of oxygen, and R is the universal gas constant with x as non-stoichiometry. $var element = document.getElementById("moose-equation-1851b2e1-87a5-48f7-a65c-a981084d294f");katex.render("Q^* = -1380.8 - 134435.5 \\exp{\\left(-\\frac{x}{0.0261}\\right)}", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-61798006-6868-404d-9741-5c7f43544cfd");katex.render("D = \\log{\\left[ -9.386 - \\frac{4.26 \\times 10^{3}}{T} + 1.2 \\times 10^{-3} T x + 7.5 \\times 10^{-4} T \\mathrm{log}\\left(\\frac{2.0 + x}{x}\\right)\\right]}", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-d953e5e2-343a-4788-9296-928935a70d00");katex.render(" F = \\frac{2 + x}{2(1 - 3x) (1 - 2 x)}", element, {displayMode:true,throwOnError:false});$

Example Input Syntax

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [oxygen]
    type = OxygenDiffusion<<<{"description": "Computes diffusion of oxygen in hyper-stoichiometric UO2.", "href": "OxygenDiffusion.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = oxygen
    temperature<<<{"description": "Coupled temperature"}>>> = temp
  []
[]

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 residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on

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
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Contribution To Tagged Field Data 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.
diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
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
save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
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/thermo_mech_oxygen/thermo_mech_oxygen_test_constant.i)

References

C. Newman, G. Hansen, and D. Gaston. Three dimensional coupled simulation of thermomechanics, heat, and oxygen diffusion in uo2 nuclear fuel rods. Journal of Nuclear Materials, 392(1):6–15, 2009. doi:10.1016/j.jnucmat.2009.03.035.

@article{NEWMAN20096,
    author = "Newman, C. and Hansen, G. and Gaston, D.",
    title = "Three dimensional coupled simulation of thermomechanics, heat, and oxygen diffusion in UO2 nuclear fuel rods",
    journal = "Journal of Nuclear Materials",
    volume = "392",
    number = "1",
    pages = "6-15",
    year = "2009",
    issn = "0022-3115",
    doi = "10.1016/j.jnucmat.2009.03.035"
}

J. C. Ramirez, M. Stan, and P. Cristea. Simulations of heat and oxygen diffusion in $\mathrm UO_2$ nuclear fuel rods. Journal of Nuclear Materials, 359(3):174–184, 2006.

@ARTICLE{ramirez.ea06,
    author = "Ramirez, J. C. and Stan, M. and Cristea, P.",
    title = "Simulations of heat and oxygen diffusion in $\mathrm{UO}\_2$ nuclear fuel rods",
    journal = "Journal of Nuclear Materials",
    year = "2006",
    volume = "359",
    pages = "174-184",
    number = "3"
}

(test/tests/thermo_mech_oxygen/thermo_mech_oxygen_test_constant.i)

#Run with 4 procs

[GlobalParams]
  displacements = 'x_disp y_disp z_disp'
[]

[Mesh]
  use_displaced_mesh = false
  [mesh]
    type = FileMeshGenerator
    file = cube.e
  []
[]

[Variables]
  [x_disp]
    order = FIRST
    family = LAGRANGE
  []

  [y_disp]
    order = FIRST
    family = LAGRANGE
  []

  [z_disp]
    order = FIRST
    family = LAGRANGE
  []

  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 750
  []

  [oxygen]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.01
    scaling = 1e16
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = small
    eigenstrain_names = eigenstrain
  []
[]

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

  [oxygen]
    type = OxygenDiffusion
    variable = oxygen
    temperature = temp
  []
[]

[BCs]
  [bottom_x]
    type = DirichletBC
    variable = x_disp
    boundary = 1
    value = 0.0
  []

  [bottom_y]
    type = DirichletBC
    variable = y_disp
    boundary = 1
    value = 0.0
  []

  [bottom_z]
    type = DirichletBC
    variable = z_disp
    boundary = 1
    value = 0.0
  []

  [top_temp]
    type = DirichletBC
    variable = temp
    boundary = 2
    value = 1200.0
  []

  [bottom_temp]
    type = DirichletBC
    variable = temp
    boundary = 1
    value = 750.0
  []

  [bottom_oxygen]
    type = DirichletBC
    variable = oxygen
    boundary = 1
    value = 0.01
  []
[]

[Materials]
  [constantHeat]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 1.0
    specific_heat = 1.0
  []
  [density]
    type = StrainAdjustedDensity
    block = 1
    strain_free_density = 1
  []
  [elasticity]
    type = ComputeIsotropicElasticityTensor
    block = 1
    youngs_modulus = 1.0
    poissons_ratio = .3
  []
  [ComputeSmallStrainElasticStress]
    type = ComputeLinearElasticStress
    block = 1
  []
  [ComputeThermalExpansionEigenstrain]
    type = ComputeThermalExpansionEigenstrain
    temperature = temp
    stress_free_temperature = 300.0
    thermal_expansion_coeff = 1.0e-5
    block = 1
    eigenstrain_name = eigenstrain
  []
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'



  nl_rel_tol = 1e-14
[]

[Outputs]
  file_base = constant_out
  exodus = true
[]

(test/tests/thermo_mech_oxygen/thermo_mech_oxygen_test_constant.i)

#Run with 4 procs

[GlobalParams]
  displacements = 'x_disp y_disp z_disp'
[]

[Mesh]
  use_displaced_mesh = false
  [mesh]
    type = FileMeshGenerator
    file = cube.e
  []
[]

[Variables]
  [x_disp]
    order = FIRST
    family = LAGRANGE
  []

  [y_disp]
    order = FIRST
    family = LAGRANGE
  []

  [z_disp]
    order = FIRST
    family = LAGRANGE
  []

  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 750
  []

  [oxygen]
    order = FIRST
    family = LAGRANGE
    initial_condition = 0.01
    scaling = 1e16
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = small
    eigenstrain_names = eigenstrain
  []
[]

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

  [oxygen]
    type = OxygenDiffusion
    variable = oxygen
    temperature = temp
  []
[]

[BCs]
  [bottom_x]
    type = DirichletBC
    variable = x_disp
    boundary = 1
    value = 0.0
  []

  [bottom_y]
    type = DirichletBC
    variable = y_disp
    boundary = 1
    value = 0.0
  []

  [bottom_z]
    type = DirichletBC
    variable = z_disp
    boundary = 1
    value = 0.0
  []

  [top_temp]
    type = DirichletBC
    variable = temp
    boundary = 2
    value = 1200.0
  []

  [bottom_temp]
    type = DirichletBC
    variable = temp
    boundary = 1
    value = 750.0
  []

  [bottom_oxygen]
    type = DirichletBC
    variable = oxygen
    boundary = 1
    value = 0.01
  []
[]

[Materials]
  [constantHeat]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 1.0
    specific_heat = 1.0
  []
  [density]
    type = StrainAdjustedDensity
    block = 1
    strain_free_density = 1
  []
  [elasticity]
    type = ComputeIsotropicElasticityTensor
    block = 1
    youngs_modulus = 1.0
    poissons_ratio = .3
  []
  [ComputeSmallStrainElasticStress]
    type = ComputeLinearElasticStress
    block = 1
  []
  [ComputeThermalExpansionEigenstrain]
    type = ComputeThermalExpansionEigenstrain
    temperature = temp
    stress_free_temperature = 300.0
    thermal_expansion_coeff = 1.0e-5
    block = 1
    eigenstrain_name = eigenstrain
  []
[]

[Executioner]
  type = Steady

  solve_type = 'PJFNK'



  nl_rel_tol = 1e-14
[]

[Outputs]
  file_base = constant_out
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References