NSFVHeatFluxBC

Constant heat flux boundary condition with phase splitting for fluid and solid energy equations

Description

Boundary condition splitting a constant heat flux among a two-phase fluid and solid domain based on a number of different models. There is no general consensus on the best boundary condition for all flows, and virtually all models for splitting a constant heat flux among multiple phases are quite crude (Alazmi and Vafai, 2002).

By setting phase = fluid, this boundary condition specifies the heat flux in the fluid energy conservation equation as

ΓκfTfn^dΓ ,-\int_\Gamma\kappa_f\cdot\nabla T_f\cdot\hat{n}d\Gamma\ ,

where

κfTfn^=ζfζs+ζfq~ ,-\kappa_f\cdot\nabla T_f\cdot\hat{n}=\frac{\zeta_f}{\zeta_s+\zeta_f}\tilde{q}\ ,

where q~\tilde{q} is the total heat flux specified by the value parameter, ζf\zeta_f is the fluid-phase value of ζ\zeta and ζs\zeta_s is the solid-phase value of ζ\zeta. ζ\zeta is a placeholder to be discussed shortly.

By setting phase = solid, this boundary condition specifies the heat flux in the solid energy conservation equation as

ΓκsTsn^dΓ ,-\int_\Gamma\kappa_s\cdot\nabla T_s\cdot\hat{n}d\Gamma\ ,

where

κsTsn^=ζsζs+ζfq~ .-\kappa_s\cdot\nabla T_s\cdot\hat{n}=\frac{\zeta_s}{\zeta_s+\zeta_f}\tilde{q}\ .

The splitting parameter determines the form of ζ\zeta; the heat flux split can be assigned based on

  • porosity, in which case ζf=ϵ\zeta_f=\epsilon and ζs=1ϵ\zeta_s=1-\epsilon

  • effective thermal conductivity, in which case ζf=κf\zeta_f=\kappa_f and ζs=κs\zeta_s=\kappa_s

  • thermal conductivity, in which case ζf=kf\zeta_f=k_f and ζs=ks\zeta_s=k_s

ζ\zeta may also be calculated either from the local value at the wall by setting locality = local or from a domain-averaging postprocessor by setting locality = global. For instance, it is well known that the porosity at the wall is unity due to point contacts between pebbles and the wall; if splitting the heat flux based on the porosity, the unity porosity would result in the entire heat flux depositing in the fluid phase, when in reality the combined conduction, convection, and radiation processes always result in heat deposition into both phases. The locality parameter attempts to capture some of this phasic behavior independent of the closures precisely at the wall.

This boundary condition does not specify the interpretation of what constitutes the domain, so you may choose for the global values to represent averages over the entire geometry, or possibly a finite-width region near the wall.

For the following combinations of splitting method and locality, the following parameters must be provided: - splitting = porosity, locality = local: porosity coupled variable - splitting = porosity, locality = global: average_porosity postprocessor - splitting = thermal_conductivity, locality = local: nothing, material property grabs don't require user input - splitting = thermal_conductivity, locality = global: average_k_fluid and average_k_solid postprocessors - splitting = effective_thermal_conductivity, locality = local: porosity coupled variable due to internal representation of κf\kappa_f as ϵκ~f\epsilon\tilde{\kappa}_f, where κf~κfϵ\tilde{\kappa_f}\equiv\frac{\kappa_f}{\epsilon}. - splitting = effective_thermal_conductivity, locality = global: average_kappa and average_kappa_solid postprocessors, as well as average_eps postprocessor due to internal representation of κf\kappa_f as ϵκ~f\epsilon\tilde{\kappa}_f.

! alert note To protect against cases where at the first time step the thermal conductivity or effective thermal conductivity might not have yet been initialized, or cases where the coupled postprocessors have not yet been evaluated, we use an equal flux splitting.

Input Parameters

  • boundaryThe list of boundary IDs from the mesh where this object applies

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

    Unit:(no unit assumed)

    Controllable:No

    Description:The list of boundary IDs from the mesh where this object applies

  • localitywhether to use local (at the boundary) or global (domain-averaged) parameter values

    C++ Type:MooseEnum

    Unit:(no unit assumed)

    Options:local, global

    Controllable:No

    Description:whether to use local (at the boundary) or global (domain-averaged) parameter values

  • phase'fluid' or 'solid' phase to which this BC is applied.

    C++ Type:MooseEnum

    Unit:(no unit assumed)

    Options:fluid, solid

    Controllable:No

    Description:'fluid' or 'solid' phase to which this BC is applied.

  • splittingtype of splitting

    C++ Type:MooseEnum

    Unit:(no unit assumed)

    Options:porosity, thermal_conductivity, effective_thermal_conductivity

    Controllable:No

    Description:type of splitting

  • valuetotal heat flux

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:total heat flux

  • variableThe name of the variable that this boundary condition applies to

    C++ Type:NonlinearVariableName

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of the variable that this boundary condition applies to

Required Parameters

  • average_k_fluidpostprocessor that provides domain-averaged fluid thermal conductivity

    C++ Type:PostprocessorName

    Unit:(no unit assumed)

    Controllable:No

    Description:postprocessor that provides domain-averaged fluid thermal conductivity

  • average_k_solidpostprocessor that provides domain-averaged solid thermal conductivity

    C++ Type:PostprocessorName

    Unit:(no unit assumed)

    Controllable:No

    Description:postprocessor that provides domain-averaged solid thermal conductivity

  • average_kappapostprocessor that provides domain-averaged fluid thermal dispersion

    C++ Type:PostprocessorName

    Unit:(no unit assumed)

    Controllable:No

    Description:postprocessor that provides domain-averaged fluid thermal dispersion

  • average_kappa_solidpostprocessor that provides domain-averaged solid effective thermal conductivity

    C++ Type:PostprocessorName

    Unit:(no unit assumed)

    Controllable:No

    Description:postprocessor that provides domain-averaged solid effective thermal conductivity

  • average_porositypostprocessor that provides domain-averaged porosity

    C++ Type:PostprocessorName

    Unit:(no unit assumed)

    Controllable:No

    Description:postprocessor that provides domain-averaged porosity

  • displacementsThe displacements

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

    Unit:(no unit assumed)

    Controllable:No

    Description:The displacements

  • porosityporosity

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

    Unit:(no unit assumed)

    Controllable:No

    Description:porosity

  • 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.

  • 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

  • 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. B. Alazmi and K. Vafai. Constant Wall Heat Flux Boundary Conditions in Porous Media Under Local Thermal Non-Equilibrium Conditions. International Journal of Heat and Mass Transfer, 45:3071–3087, 2002. doi:10.1016/S0017-9310(02)00044-3.[BibTeX]