INSFVTurbulentTemperatureWallFunction

The function sets up the equivalent heat flux of the near-wall boundary layer when the wall temperature is set by the T_w parameter.

The boundary conditions are different depending on whether the centroid of the cell near the identified boundary lies in the wall function profile. Taking the non-dimensional wall distance as $var element = document.getElementById("moose-equation-f64b4d57-f72f-4e23-87ba-f0392c776487");katex.render("y^+", element, {displayMode:false,throwOnError:false});$ , the three regions of the boundary layer are identified as follows:

Sub-laminar region: $var element = document.getElementById("moose-equation-25a9b3db-de2c-4e86-a23e-3ba08b8c045a");katex.render("y^+ \\le 5", element, {displayMode:false,throwOnError:false});$
Buffer region: $var element = document.getElementById("moose-equation-9b4f0fdc-d68d-4827-b0aa-3f157e72e66d");katex.render("y^+ \\in (5, 30)", element, {displayMode:false,throwOnError:false});$
Logarithmic region: $var element = document.getElementById("moose-equation-46017c29-b108-483d-81bc-8f000ed2f0b3");katex.render("y^+ \\ge 30", element, {displayMode:false,throwOnError:false});$

For the procedure of determining the non-dimensional wall distance as $var element = document.getElementById("moose-equation-5ab202db-3c88-4c5d-9bbf-1bdba2dfc88a");katex.render("y^+", element, {displayMode:false,throwOnError:false});$ and the friction velocity $var element = document.getElementById("moose-equation-2337f6a7-8f7d-4e46-9450-7025d58bb082");katex.render("u_{\\tau}", element, {displayMode:false,throwOnError:false});$ please see INSFVTurbulentViscosityWallFunction.

For the sub-laminar and logarithmic layer, the thermal diffusivity is defined as follows:

$var element = document.getElementById("moose-equation-b871d95e-34af-4864-85f0-4a4327ff7c81");katex.render(" \\alpha = \\begin{cases} \\alpha_l = \\frac{k}{\\rho c_p} & \\text{if } y^+ \\le 5 \\\\ \\alpha_t = \\frac{u_{\\tau} y_p}{Pr_t w_s} & \\text{if } y^+ \\ge 30 \\end{cases}", element, {displayMode:true,throwOnError:false});$

where:

$var element = document.getElementById("moose-equation-88dfbea1-ec97-47c6-bd74-b6d02c785d25");katex.render("k", element, {displayMode:false,throwOnError:false});$ is the thermal conductivity
$var element = document.getElementById("moose-equation-8f884ed1-39b7-4670-9825-9a81b2a34b33");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ is the density
$var element = document.getElementById("moose-equation-4d983e32-baf5-462f-b15e-261ebec0f477");katex.render("c_p", element, {displayMode:false,throwOnError:false});$ is the specific heat at constant pressure
$var element = document.getElementById("moose-equation-32b725e6-2ee9-4ca4-8ac0-a0ce5ab3242c");katex.render("u_{\\tau}", element, {displayMode:false,throwOnError:false});$ is the friction velocity defined by law of the wall
$var element = document.getElementById("moose-equation-c865c60f-bf83-4509-89a6-87191f07a472");katex.render("y_p", element, {displayMode:false,throwOnError:false});$ is the distance from the boundary to the centroid of the near-wall cell
$var element = document.getElementById("moose-equation-4d5e7c3a-260c-4a61-93e8-66b9dcc3303b");katex.render("Pr_t", element, {displayMode:false,throwOnError:false});$ is the turbulent Prandtl number, which typically ranges between 0.3 and 0.9
$var element = document.getElementById("moose-equation-5e86355a-e8a8-4838-b1e3-ef2f8921d761");katex.render("w_s", element, {displayMode:false,throwOnError:false});$ is a near-wall scaling factor that is defined as follows:

$var element = document.getElementById("moose-equation-987b6a8c-f189-4e68-85a2-55dafa376a3b");katex.render(" w_s = \\frac{1}{\\kappa} \\operatorname{ln}(E y^+) + J_k \\,,", element, {displayMode:true,throwOnError:false});$

where:

$var element = document.getElementById("moose-equation-14851de9-834b-43d2-89a7-4c6c84d81526");katex.render("\\kappa = 0.4187", element, {displayMode:false,throwOnError:false});$ is the von Kármán constant
$var element = document.getElementById("moose-equation-49a06b3b-3459-4688-a107-b6f3cae289bd");katex.render("E = 9.793", element, {displayMode:false,throwOnError:false});$ is a closure parameter
$var element = document.getElementById("moose-equation-a94445ce-4c42-436d-926b-07d42585c65f");katex.render("J_k", element, {displayMode:false,throwOnError:false});$ is the Jayatilleke wall functions defined as follows:

$var element = document.getElementById("moose-equation-ba92abc5-192a-447c-ba9b-93519f1d9b95");katex.render(" J_k = 9.24 \\left[ \\left( \\frac{Pr}{Pr_t} \\right)^{0.75} - 1 \\right] \\left( 1 + 0.28 e^{-0.007 \\frac{Pr}{Pr_t}} \\right) \\,,", element, {displayMode:true,throwOnError:false});$

where:

$var element = document.getElementById("moose-equation-7d9e02d6-ed9c-4966-b970-8da4ca72e171");katex.render("Pr", element, {displayMode:false,throwOnError:false});$ is the Prandtl number

For the buffer layer, i.e., in $var element = document.getElementById("moose-equation-e7c3870f-9ee5-4662-8d52-b920bb9e691b");katex.render("y^+ \\in (5, 30)", element, {displayMode:false,throwOnError:false});$ , the thermal diffusivity is defined via a linear blending function as follows:

$var element = document.getElementById("moose-equation-5ae95d2a-de99-4d69-97dc-4e34d310413b");katex.render(" \\alpha_b = \\alpha_t \\frac{(y^+ - 5)}{25} + \\alpha_l \\left[ 1 - \\frac{(y^+ - 5)}{25} \\right]", element, {displayMode:true,throwOnError:false});$

Finally, using the thermal diffusivity, the heat flux at the wall is defined as follows:

$var element = document.getElementById("moose-equation-e869f841-33bb-4acb-a96b-ee98608acbee");katex.render(" q''_w = - \\rho c_p \\alpha \\frac{T_w - T_p}{y_p} \\,,", element, {displayMode:true,throwOnError:false});$

where:

$var element = document.getElementById("moose-equation-8eb6d962-31f0-48f4-bff6-1213f220808d");katex.render("T_p", element, {displayMode:false,throwOnError:false});$ is the temperature at the centroid of the near-wall cell
$var element = document.getElementById("moose-equation-2a99ecd5-57d2-41ee-bb4c-a745d31c9371");katex.render("y_p", element, {displayMode:false,throwOnError:false});$ is the distance from the wall to the centroid of the near-wall cell

note

The thermal wall functions are only valid for regions in which the equilibrium momentum wall functions are valid, i.e., no flow detachment, recirculation, etc. For resolving non-equilibrium phenomena, we recommend refining the mesh.

Input Parameters

T_wThe wall temperature. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The wall temperature. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
boundaryThe list of boundary IDs from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundary IDs from the mesh where this object applies
cpThe specific heat at constant pressure. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The specific heat at constant pressure. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
muDynamic viscosity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:Dynamic viscosity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
rhoDensity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:Density. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
uThe velocity in the x direction. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The velocity in the x direction. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
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

C_mu0.09Coupled turbulent kinetic energy closure.
Default:0.09
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Coupled turbulent kinetic energy closure.
Pr_t0.58The turbulent Prandtl number. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
Default:0.58
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The turbulent Prandtl number. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
kappaThe thermal conductivity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The thermal conductivity. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
tkeTurbulent kinetic energy functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:Turbulent kinetic energy functor. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
vThe velocity in the y direction. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The velocity in the y direction. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
wThe velocity in the z direction. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
C++ Type:MooseFunctorName
Unit:(no unit assumed)
Controllable:No
Description:The velocity in the z direction. A functor is any of the following: a variable, a functor material property, a function, a postprocessor or a number.
wall_treatmentneqThe method used for computing the wall functions
Default:neq
C++ Type:MooseEnum
Options:eq_newton, eq_incremental, eq_linearized, neq
Controllable:No
Description:The method used for computing the wall functions

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.
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
newton_solveFalseWhether a Newton nonlinear solve is being used
Default:False
C++ Type:bool
Controllable:No
Description:Whether a Newton nonlinear solve is being used
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 Parameters