HomogenizedThermalConductivity

Postprocessor for asymptotic expansion homogenization for thermal conductivity

commentnote:Einstein summation convention

Einstein summation convention is used in this documentation page.

Description

This PostProcessor computes

(1)

where is the -th element of the homogenized thermal conductivity tensor, is the -th element of the thermal conductivity tensor in the heterogeneous problem, is the j-th characteristic function defined as:

(2)

This PostProcessor is used in conjunction with the Heat Conduction Kernel and the Homogenized Heat Conduction Kernel. An application can be found in Hales et al. (2015).

commentnote:Notation

First, compared to standard notation for homogenization theory applied to thermal conductivity (e.g. Song and Youn (2006)), MOOSE computes . This is achieved by inverting the sign of the right hand side of Eq. (2). This leads to an inversion of the sign in the parenthesis in Eq. (1). Second, Eq. (2) is the weak form of the equation typically provided in literature and integration by parts on the right hand side leads to another sign flip. Third, in contrast to Hales et al. (2015) some notational inconsistencies are resolved in this document.

Example Input File Syntax

[Postprocessors]
  [k_xx]
    type = HomogenizedThermalConductivity
    chi = 'temp_x temp_y'
    row = 0
    col = 0
    execute_on = 'initial timestep_end'
  []
[]
(moose/modules/heat_transfer/test/tests/homogenization/heatConduction2D.i)

Input Parameters

  • chiThe characteristic functions used for homogenization of the thermal conductivity.

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

    Unit:(no unit assumed)

    Controllable:No

    Description:The characteristic functions used for homogenization of the thermal conductivity.

  • colThe column index of the homogenized thermal conductivity tensor entry computed by this postprocessor.

    C++ Type:unsigned int

    Unit:(no unit assumed)

    Controllable:No

    Description:The column index of the homogenized thermal conductivity tensor entry computed by this postprocessor.

  • rowThe row index of the homogenized thermal conductivity tensor entry computed by this postprocessor.

    C++ Type:unsigned int

    Unit:(no unit assumed)

    Controllable:No

    Description:The row index of the homogenized thermal conductivity tensor entry computed by this postprocessor.

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_conductivityProperty name of the diffusivity

    Default:thermal_conductivity

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:Property name of the diffusivity

  • execute_onTIMESTEP_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:TIMESTEP_END

    C++ Type:ExecFlagEnum

    Unit:(no unit assumed)

    Options:NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, TRANSFER

    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.

  • is_tensorFalseTrue if the material property in diffusion_coefficient is a tensor

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:True if the material property in diffusion_coefficient is a tensor

  • 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.

  • scale_factor1Scale factor

    Default:1

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Scale factor

  • 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

  • allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).

  • 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.

  • 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.

  • execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.

    Default:0

    C++ Type:int

    Unit:(no unit assumed)

    Controllable:No

    Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.

  • force_postauxFalseForces the UserObject to be executed in POSTAUX

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Forces the UserObject to be executed in POSTAUX

  • force_preauxFalseForces the UserObject to be executed in PREAUX

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Forces the UserObject to be executed in PREAUX

  • force_preicFalseForces the UserObject to be executed in PREIC during initial setup

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Forces the UserObject to be executed in PREIC during initial setup

  • 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

  • outputsVector of output names where you would like to restrict the output of variables(s) associated with this object

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

    Unit:(no unit assumed)

    Controllable:No

    Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

  • 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]