GrayLambertNeumannBC

This BC imposes a heat flux density that is computed from the GrayLambertSurfaceRadiationBase userobject.

This boundary condition computes the heat flux density resulting from the radiative heat transfer between surfaces adjacent to this boundary. These surfaces must be diffuse, gray radiators (Lambert radiators). The heat flux is computed by the net radiation method described in Modest (2013). More information is available here.

There are two modes available for operating this boundary condition. The mode can be switched by the reconstruct_emission parameter. If set to false, the object queries the net radiation object (GrayLambertSurfaceRadiationBase or derived class) object for the net heat flux density on the surface. This heat flux density is applied as a constant for each participating sideset. If the sidesets are large and the flat heat flux densities on two adjacent sidesets sufficiently different, then the temperature will be non-smooth.

A smoother temperature distribution on the surface is usually obtained by noting that a large fraction of the spatial distribution of the heat flux stems from the temperature distribution and hence from the emission. The approximation made is that the emission is allowed to spatially vary, while the irradiation from other sidesets to the given sideset is assumed to be spatially flat. The heat flux at location on sideset is computed by:

where is the Stefan-Boltzmann constat, the emissivity of sideset , and the average irradiation into sideset .

[Problem]
  kernel_coverage_check = false
[]

[Mesh]
  type = MeshGeneratorMesh

  [./cartesian]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1 1'
    ix = '2 2 2'
    dy = '5'
    iy = '10'
    subdomain_id = '1 2 3'
  [../]

  [./break_sides]
    type = BreakBoundaryOnSubdomainGenerator
    boundaries = 'bottom top'
    input = cartesian
  [../]

  [./left_interior]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 1
    paired_block = 2
    new_boundary = left_interior
    input = break_sides
  [../]

  [./right_interior]
    type = SideSetsBetweenSubdomainsGenerator
    primary_block = 3
    paired_block = 2
    new_boundary = right_interior
    input = left_interior
  [../]
  [./rename]
    type = RenameBlockGenerator
    input = right_interior
    old_block = '1 2 3'
    new_block = '1 4 3'
  [../]
[]

[Variables]
  [./temperature]
    initial_condition = 300
    block = '1 3'
  [../]
[]

[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temperature
    diffusion_coefficient = 1
    block = '1 3'
  [../]
[]

[UserObjects]
  [./cavity_radiation]
    type = ConstantViewFactorSurfaceRadiation
    boundary = 'left_interior right_interior bottom_to_2 top_to_2'
    temperature = temperature
    emissivity = '0.8 0.8 0.8 0.8'
    adiabatic_boundary = 'bottom_to_2 top_to_2'
    # these view factors are made up to exactly balance energy
    # transfer through the cavity
    view_factors = '0    0.8 0.1 0.1;
                    0.8  0   0.1 0.1;
                    0.45 0.45  0 0.1;
                    0.45 0.45 0.1  0'
    execute_on = 'INITIAL LINEAR TIMESTEP_END'
  [../]
[]

[BCs]
  [./bottom_left]
    type = DirichletBC
    preset = false
    variable = temperature
    boundary = bottom_to_1
    value = 1500
  [../]

  [./top_right]
    type = DirichletBC
    preset = false
    variable = temperature
    boundary = top_to_3
    value = 300
  [../]

  [./radiation]
    type = GrayLambertNeumannBC
    variable = temperature
    reconstruct_emission = false
    surface_radiation_object_name = cavity_radiation
    boundary = 'left_interior right_interior'
  [../]
[]

[Postprocessors]
  [./qdot_left]
    type = GrayLambertSurfaceRadiationPP
    boundary = left_interior
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]

  [./qdot_right]
    type = GrayLambertSurfaceRadiationPP
    boundary = right_interior
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]

  [./qdot_top]
    type = GrayLambertSurfaceRadiationPP
    boundary = top_to_2
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]

  [./qdot_bottom]
    type = GrayLambertSurfaceRadiationPP
    boundary = bottom_to_2
    surface_radiation_object_name = cavity_radiation
    return_type = HEAT_FLUX_DENSITY
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]
(moose/modules/heat_conduction/test/tests/gray_lambert_radiator/coupled_heat_conduction.i)

Input Parameters

  • 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

  • surface_radiation_object_nameName of the GrayLambertSurfaceRadiationBase UO

    C++ Type:UserObjectName

    Controllable:No

    Description:Name of the GrayLambertSurfaceRadiationBase UO

  • variableThe name of the variable that this residual object operates on

    C++ Type:NonlinearVariableName

    Controllable:No

    Description:The name of the variable that this residual object operates on

Required Parameters

  • displacementsThe displacements

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

    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

    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.

  • reconstruct_emissionTrueFlag to apply constant heat flux on sideset or reconstruct emission by T^4 law.

    Default:True

    C++ Type:bool

    Controllable:No

    Description:Flag to apply constant heat flux on sideset or reconstruct emission by T^4 law.

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

Tagging 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 BC'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>

    Controllable:No

    Description:The name of auxiliary variables to save this BC'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 BC'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>

    Controllable:No

    Description:The name of auxiliary variables to save this BC'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

References

  1. M.F. Modest. Radiative Heat Transfer. Elsevier Science, 2013. ISBN 9780123869906. URL: https://books.google.com/books?id=J2KZq0e4lCIC.[BibTeX]