UnobstructedPlanarViewFactor

Description

UnobstructedPlanarViewFactor.md computes the view factors between n planar sides in radiative heat exchange. These sides need to be such that they do not obstruct each other. This is in particular true if the sides fully enclose a convex volume. This is the intended purpose of this UserObject.

View factors $var element = document.getElementById("moose-equation-fe2cf622-2c37-4e98-aec2-66c14ba1d628");katex.render("F_{i,j}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ from side $var element = document.getElementById("moose-equation-0c5f166c-6d34-45ab-866b-3116725e7e8f");katex.render("i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ to side $var element = document.getElementById("moose-equation-56f38128-df23-4b38-a4dd-07e112da3514");katex.render("j", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ are computed via a double loop over side elements and the quadrature points defined on them. View factors are computed by numerically evaluating:

$var element = document.getElementById("moose-equation-18bd85b1-85e6-490e-b7db-0467b750c477");katex.render(" F_{1,2} = \\frac{1}{A_1 \\pi} \\int_{A_1} \\int_{A_2} \\frac{\\cos \\beta_1 \\cos \\beta_2}{r^2} dA_1 dA_2,", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

where $var element = document.getElementById("moose-equation-dd40e7e2-fca0-4b6e-8630-c67efd3989bf");katex.render("r", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the distance between two points on the surfaces $var element = document.getElementById("moose-equation-7c9f1d98-725c-4f7d-9be8-07d94d3751a7");katex.render("A_1", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-5722d2ba-87e7-43ad-bdb1-b55f6b7428eb");katex.render("A_2", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-c09cea2d-0bf9-4b8e-818e-dad08428d80d");katex.render("\\beta_1", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-79e7a773-0302-46fb-a985-1fca6d42210d");katex.render("\\beta_2", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ are the angles that the line connecting these two points make with the normals at surface one and two, respectively.

In two-dimensional geometries, a different formula is evaluated. It is derived from the original formula by considering a geometry that is extruded from $var element = document.getElementById("moose-equation-7eb4a07f-1faa-410a-bd01-3c048bd18fb5");katex.render("-\\infinity", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ to $var element = document.getElementById("moose-equation-0cb14ef2-15a9-4186-a8ef-a434a7833983");katex.render("\\infinity", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ along the $var element = document.getElementById("moose-equation-bb7492fd-fbef-48a0-b705-7ca08e80781d");katex.render("z", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ -axis. We denote by $var element = document.getElementById("moose-equation-ed56309a-0d98-4b18-92c5-fd065406d881");katex.render("r_0", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ the distance between two points on surface one and two projected onto the plane orthogonal to the $var element = document.getElementById("moose-equation-bc0db175-1489-4485-85a1-9a82c9aef52f");katex.render("z", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ -axis. The line projected on this plane makes angles $var element = document.getElementById("moose-equation-b5f7415e-49e5-4e47-8014-7ff148fc1fce");katex.render("\\beta_{1,0}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-4dd59ee1-aecd-4c9f-8644-a8958107a19e");katex.render("\\beta_{2,0}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ with the normals at surfaces one and two, respectively. Note that the normals have no component into the $var element = document.getElementById("moose-equation-0a7cadf7-4e7e-480a-b8e4-01a23a23e912");katex.render("z", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ -direction. The following relationships hold:

$var element = document.getElementById("moose-equation-a7d2b8e6-68e6-43ef-a106-9dc6424dda94");katex.render(" \\begin{aligned} r^2 &= r_0^2 + (z_1 - z_2)^2 \\\\ \\cos \\beta_{1,0} &= \\cos \\beta_{1} \\frac{r_0}{\\sqrt{r_0^2 + (z_1 - z_2)^2}}\\\\ \\cos \\beta_{2,0} &= \\cos \\beta_{2} \\frac{r_0}{\\sqrt{r_0^2 + (z_1 - z_2)^2}}\\\\ A_1 &= \\Delta z L_1 \\\\ dA_1&= dz_1 dl_1 \\\\ dA_2&= dz_2 dl_2. \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

The view factor is then given by:

$var element = document.getElementById("moose-equation-14c905b9-1450-45b8-9375-49017dc4cd38");katex.render(" F_{1,2} = \\lim\\limits_{\\Delta z \\rightarrow \\infty} \\frac{1}{L_1 \\Delta z \\pi} \\int_{L1} dl_1 \\int_{L2} dl_2 \\frac{\\cos \\beta_{1,0} \\cos \\beta_{2,0} r_0^2}{\\pi} \\left [ \\int_{- \\Delta z / 2}^{\\Delta z / 2} dz_1 \\int_{- \\Delta z / 2}^{\\Delta z / 2} dz_2 \\frac{1}{\\left( r_0^2 + (z_1 - z_2)^2 \\right)^2} \\right]", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

The integral in brackets evaluates to:

$var element = document.getElementById("moose-equation-aab09909-bcc1-46ba-879c-b6eafb9294cc");katex.render("\\int_{- \\Delta z / 2}^{\\Delta z / 2} dz_1 \\int_{- \\Delta z / 2}^{\\Delta z / 2} dz_2 \\frac{1}{\\left( r_0^2 + (z_1 - z_2)^2 \\right)^2} = \\frac{\\Delta z \\pi}{2 r_0^3}.", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

The view factors in two-dimensional geometry are consequently given by:

$var element = document.getElementById("moose-equation-9e6ee568-1280-4369-85b3-5a93b31ec690");katex.render(" F_{1,2} = \\frac{1}{2 L_1} \\int_{L1} \\int_{L2} \\frac{\\cos \\beta_{1,0} \\cos \\beta_{2,0}}{r_0} dl_1 dl_2", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

View factors should satisfy:

$var element = document.getElementById("moose-equation-662537de-5e0c-44f7-8520-bff7dd6fac00");katex.render(" \\sum\\limits_{j=1}^n F_{i,j} = 1,~i=1,..,n.", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ This can be checked by setting the parameter view_factor_tol and it can be enforced via normalization by setting the parameter normalize_view_factor.

It is stressed that this UserObject may give wrong results if obstruction is present

Example Input syntax

[Mesh]
  type = GeneratedMesh
  dim = 3
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  zmin = 0
  zmax = 1
  nx = 2
  ny = 2
  nz = 2
[]

[Problem]
  kernel_coverage_check = false
[]

[Variables]
  [./u]
  [../]
[]

[UserObjects]
  [./view_factor]
    type = UnobstructedPlanarViewFactor
    boundary = 'left right front back bottom top'
    execute_on = 'INITIAL'
  [../]
[]

[Postprocessors]
  [./left_right]
    type = ViewFactorPP
    from_boundary = left
    to_boundary = right
    view_factor_object_name = view_factor
  [../]

  [./left_top]
    type = ViewFactorPP
    from_boundary = left
    to_boundary = top
    view_factor_object_name = view_factor
  [../]

  [./left_back]
    type = ViewFactorPP
    from_boundary = left
    to_boundary = back
    view_factor_object_name = view_factor
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
[]

/opt/civet/build_0/moose/modules/heat_conduction/test/tests/view_factors/view_factor_cube.i

[Mesh]
  type = GeneratedMesh
  dim = 3
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  zmin = 0
  zmax = 1
  nx = 2
  ny = 2
  nz = 2
[]

[Problem]
  kernel_coverage_check = false
[]

[Variables]
  [./u]
  [../]
[]

[UserObjects]
  [./view_factor]
    type = UnobstructedPlanarViewFactor
    boundary = 'left right front back bottom top'
    execute_on = 'INITIAL'
  [../]
[]

[Postprocessors]
  [./left_right]
    type = ViewFactorPP
    from_boundary = left
    to_boundary = right
    view_factor_object_name = view_factor
  [../]

  [./left_top]
    type = ViewFactorPP
    from_boundary = left
    to_boundary = top
    view_factor_object_name = view_factor
  [../]

  [./left_back]
    type = ViewFactorPP
    from_boundary = left
    to_boundary = back
    view_factor_object_name = view_factor
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
[]

Input Parameters

boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies

Required Parameters

execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE INITIAL LINEAR NONLINEAR TIMESTEP_END TIMESTEP_BEGIN FINAL CUSTOM
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
normalize_view_factorTrueDetermines if view factors are normalized to sum to one (consistent with their definition).
Default:True
C++ Type:bool
Options:
Description:Determines if view factors are normalized to sum to one (consistent with their definition).
view_factor_tol1.79769e+308Tolerance for checking view factors. Default is to allow everything.
Default:1.79769e+308
C++ Type:double
Options:
Description:Tolerance for checking view factors. Default is to allow everything.

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
Options:
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
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
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
Options:
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

Input Files

modules/heat_conduction/test/tests/radiation_transfer_action/radiative_transfer_no_action.i
modules/heat_conduction/test/tests/view_factors/view_factor_cube.i
modules/heat_conduction/test/tests/gray_lambert_radiator/gray_lambert_cavity_automatic_vf.i
modules/heat_conduction/test/tests/gray_lambert_radiator/gray_lambert_cavity_automatic_vf_3D.i

modules/heat_conduction/test/tests/radiation_transfer_action/radiative_transfer_no_action.i

[Problem]
  kernel_coverage_check = false
[]

[Mesh]
  type = MeshGeneratorMesh

  [./cmg]
    type = CartesianMeshGenerator
    dim = 2
    dx = '1 1.3 1.9'
    ix = '3 3 3'
    dy = '2 1.2 0.9'
    iy = '3 3 3'
    subdomain_id = '0 1 0
                    4 5 2
                    0 3 0'
  [../]

  [./inner_bottom]
    type = SideSetsBetweenSubdomainsGenerator
    input = cmg
    master_block = 1
    paired_block = 5
    new_boundary = 'inner_bottom'
  [../]

  [./inner_left]
    type = SideSetsBetweenSubdomainsGenerator
    input = inner_bottom
    master_block = 4
    paired_block = 5
    new_boundary = 'inner_left'
  [../]

  [./inner_right]
    type = SideSetsBetweenSubdomainsGenerator
    input = inner_left
    master_block = 2
    paired_block = 5
    new_boundary = 'inner_right'
  [../]

  [./inner_top]
    type = SideSetsBetweenSubdomainsGenerator
    input = inner_right
    master_block = 3
    paired_block = 5
    new_boundary = 'inner_top'
  [../]

  [./rename]
    type = RenameBlockGenerator
    old_block_id = '1 2 3 4'
    new_block_id = '0 0 0 0'
    input = inner_top
  [../]

  [./split_inner_bottom]
    type = PatchSidesetGenerator
    sideset = 4
    n_patches = 2
    partitioner = centroid
    centroid_partitioner_direction = x
    input = rename
  [../]

  [./split_inner_left]
    type = PatchSidesetGenerator
    sideset = 5
    n_patches = 2
    partitioner = centroid
    centroid_partitioner_direction = y
    input = split_inner_bottom
  [../]

  [./split_inner_right]
    type = PatchSidesetGenerator
    sideset = 6
    n_patches = 2
    partitioner = centroid
    centroid_partitioner_direction = y
    input = split_inner_left
  [../]

  [./split_inner_top]
    type = PatchSidesetGenerator
    sideset = 7
    n_patches = 3
    partitioner = centroid
    centroid_partitioner_direction = x
    input = split_inner_right
  [../]
[]

[Variables]
  [./temperature]
    block = 0
  [../]
[]

[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temperature
    block = 0
    diffusion_coefficient = 5
  [../]
[]

[UserObjects]
  [./gray_lambert]
    type = ViewFactorObjectSurfaceRadiation
    boundary = 'inner_bottom_0 inner_bottom_1
                inner_left_0 inner_left_1
                inner_right_0 inner_right_1
                inner_top_0 inner_top_1 inner_top_2'
    fixed_temperature_boundary = 'inner_bottom_0 inner_bottom_1'
    fixed_boundary_temperatures = '1200          1200'
    adiabatic_boundary = 'inner_top_0 inner_top_1 inner_top_2'
    emissivity = '0.9 0.9
                  0.8 0.8
                  0.4 0.4
                  1 1 1'
    temperature = temperature
    view_factor_object_name = view_factor
    execute_on = 'LINEAR TIMESTEP_END'
  [../]

  [./view_factor]
    type = UnobstructedPlanarViewFactor
    boundary = 'inner_bottom_0 inner_bottom_1
                inner_left_0 inner_left_1
                inner_right_0 inner_right_1
                inner_top_0 inner_top_1 inner_top_2'
    normalize_view_factor = true
    execute_on = 'INITIAL'
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 600
  [../]

  [./right]
    type = DirichletBC
    variable = temperature
    boundary = right
    value = 300
  [../]

  [./radiation]
    type = GrayLambertNeumannBC
    variable = temperature
    surface_radiation_object_name = gray_lambert
    boundary = 'inner_bottom_0 inner_bottom_1
                inner_left_0 inner_left_1
                inner_right_0 inner_right_1
                inner_top_0 inner_top_1 inner_top_2'
  [../]
[]

[Postprocessors]
  [./average_T_inner_right]
    type = SideAverageValue
    variable = temperature
    boundary = inner_right
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  exodus = true
[]

modules/heat_conduction/test/tests/view_factors/view_factor_cube.i

[Mesh]
  type = GeneratedMesh
  dim = 3
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  zmin = 0
  zmax = 1
  nx = 2
  ny = 2
  nz = 2
[]

[Problem]
  kernel_coverage_check = false
[]

[Variables]
  [./u]
  [../]
[]

[UserObjects]
  [./view_factor]
    type = UnobstructedPlanarViewFactor
    boundary = 'left right front back bottom top'
    execute_on = 'INITIAL'
  [../]
[]

[Postprocessors]
  [./left_right]
    type = ViewFactorPP
    from_boundary = left
    to_boundary = right
    view_factor_object_name = view_factor
  [../]

  [./left_top]
    type = ViewFactorPP
    from_boundary = left
    to_boundary = top
    view_factor_object_name = view_factor
  [../]

  [./left_back]
    type = ViewFactorPP
    from_boundary = left
    to_boundary = back
    view_factor_object_name = view_factor
  [../]
[]

[Executioner]
  type = Steady
[]

[Outputs]
  csv = true
[]

modules/heat_conduction/test/tests/gray_lambert_radiator/gray_lambert_cavity_automatic_vf.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 2
  nx = 20
  ny = 20
[]

[Problem]
  kernel_coverage_check = false
[]

[Variables]
  [./temperature]
    initial_condition = 300
  [../]
[]

[UserObjects]
  [./gray_lambert]
    type = ViewFactorObjectSurfaceRadiation
    boundary = 'bottom top left right'
    fixed_temperature_boundary = 'bottom top'
    fixed_boundary_temperatures = '550 300'
    adiabatic_boundary = 'right left'
    emissivity = '1 0.75 0.75 0.75'
    temperature = temperature
    view_factor_object_name = view_factor
  [../]

  [./view_factor]
    type = UnobstructedPlanarViewFactor
    boundary = 'left right bottom top'
    normalize_view_factor = true
    execute_on = 'INITIAL'
  [../]
[]

[Postprocessors]
  [./heat_flux_density_bottom]
    type = GrayLambertSurfaceRadiationPP
    surface_radiation_object_name = gray_lambert
    return_type = HEAT_FLUX_DENSITY
    boundary = bottom
  [../]

  [./temperature_left]
    type = GrayLambertSurfaceRadiationPP
    surface_radiation_object_name = gray_lambert
    return_type = TEMPERATURE
    boundary = left
  [../]

  [./temperature_right]
    type = GrayLambertSurfaceRadiationPP
    surface_radiation_object_name = gray_lambert
    return_type = TEMPERATURE
    boundary = right
  [../]

  [./brightness_top]
    type = GrayLambertSurfaceRadiationPP
    surface_radiation_object_name = gray_lambert
    return_type = RADIOSITY
    boundary = top
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1
[]

[Outputs]
  csv = true
[]

modules/heat_conduction/test/tests/gray_lambert_radiator/gray_lambert_cavity_automatic_vf_3D.i

[Mesh]
  type = GeneratedMesh
  dim = 3
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 2
  zmin = 0
  zmax = 3
  nx = 4
  ny = 4
  nz = 4
[]

[Problem]
  kernel_coverage_check = false
[]

[Variables]
  [./temperature]
    initial_condition = 300
  [../]
[]

[UserObjects]
  [./gray_lambert]
    type = ViewFactorObjectSurfaceRadiation
    boundary = 'bottom top left right front back'
    fixed_temperature_boundary = 'bottom top'
    fixed_boundary_temperatures = '550 300'
    adiabatic_boundary = 'right left front back'
    emissivity = '1 0.75 0.75 0.75 0.75 0.75'
    temperature = temperature
    view_factor_object_name = view_factor
  [../]

  [./view_factor]
    type = UnobstructedPlanarViewFactor
    boundary = 'bottom top left right front back'
    normalize_view_factor = true
    execute_on = 'INITIAL'
  [../]
[]

[Postprocessors]
  [./heat_flux_density_bottom]
    type = GrayLambertSurfaceRadiationPP
    surface_radiation_object_name = gray_lambert
    return_type = HEAT_FLUX_DENSITY
    boundary = bottom
  [../]

  [./temperature_left]
    type = GrayLambertSurfaceRadiationPP
    surface_radiation_object_name = gray_lambert
    return_type = TEMPERATURE
    boundary = left
  [../]

  [./temperature_right]
    type = GrayLambertSurfaceRadiationPP
    surface_radiation_object_name = gray_lambert
    return_type = TEMPERATURE
    boundary = right
  [../]

  [./brightness_top]
    type = GrayLambertSurfaceRadiationPP
    surface_radiation_object_name = gray_lambert
    return_type = RADIOSITY
    boundary = top
  [../]

  [./brightness_front]
    type = GrayLambertSurfaceRadiationPP
    surface_radiation_object_name = gray_lambert
    return_type = RADIOSITY
    boundary = front
  [../]

  [./brightness_back]
    type = GrayLambertSurfaceRadiationPP
    surface_radiation_object_name = gray_lambert
    return_type = RADIOSITY
    boundary = back
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1
[]

[Outputs]
  csv = true
[]

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Example Input syntax
Input Parameters
Input Files

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