AnisoHomogenizedHeatConduction

Kernel for asymptotic expansion homogenization for thermal conductivity when anisotropic thermal conductivities are used

commentnote:Einstein summation convention

Einstein summation convention is used in this documentation page.

Description

This Kernel computes the right hand side of the equation

where is the thermal conductivity tensor, is the coordinate in the unit cell, and is the -th characteristic function used for homogenizing the thermal conductivity. It is used in conjunction with the Anisotropic Heat Conduction Kernel and the Homogenized Thermal Conductivity Postprocessor to compute homogenized thermal conductivity values.

This homogenization is executed for a unit cell with periodic boundary conditions. For any vector on the boundary, the unit cell geometry must satisfy the condition:

where is the outward normal vector, and is the periodicity of the boundary where is located.

This kernel is the anisotropic version of HomogenizedHeatConduction. See Hales et al. (2015) and Song and Youn (2006) for more details.

Example Input File Syntax

[Kernels]
  [heat_rhs_x]
    type = AnisoHomogenizedHeatConduction
    variable = temp_x
    component = 0
  []
[]
(moose/modules/heat_transfer/test/tests/homogenization/heatConduction2D_tensor_tc.i)

Input Parameters

  • componentAn integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z)

    C++ Type:unsigned int

    Unit:(no unit assumed)

    Controllable:No

    Description:An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z)

  • 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>

    Unit:(no unit assumed)

    Controllable:No

    Description:The list of blocks (ids or names) that this object will be applied

  • diffusion_coefficientthermal_conductivityThe diffusion coefficient for the temperature gradient

    Default:thermal_conductivity

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:The diffusion coefficient for the temperature gradient

  • displacementsThe displacements

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The displacements

  • 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

    Unit:(no unit assumed)

    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.

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>

    Unit:(no unit assumed)

    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>

    Unit:(no unit assumed)

    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>

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    Options:nontime, time

    Controllable:No

    Description:The tag for the vectors this Kernel should fill

Tagging Parameters

  • control_tagsAdds user-defined labels for accessing object parameters via control logic.

    C++ Type:std::vector<std::string>

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    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

References

  1. J. D. Hales, M. R. Tonks, K. Chockalingam, D. M. Perez, S. R. Novascone, B. W. Spencer, and R. L. Williamson. Asymptotic expansion homogenization for multiscale nuclear fuel analysis. Computational Materials Science, 99:290–297, March 2015. URL: http://dx.doi.org/10.1016/j.commatsci.2014.12.039, doi:10.1016/j.commatsci.2014.12.039.[BibTeX]
  2. Young Seok Song and Jae Ryoun Youn. Evaluation of effective thermal conductivity for carbon nanotube/polymer composites using control volume finite element method. Carbon, 44(4):710–717, 2006. URL: https://www.sciencedirect.com/science/article/pii/S0008622305005609, doi:https://doi.org/10.1016/j.carbon.2005.09.034.[BibTeX]