HSBoundaryRadiation

This component is a heat structure boundary that applies radiative heat transfer boundary conditions.

Usage

The parameter "hs" specifies the name of the heat structure component, and "boundary" is a list of boundary names on the heat structure where the boundary condition is to be applied.

The parameter "T_ambient" gives the ambient temperature $var element = document.getElementById("moose-equation-77c6f4c7-9da6-4bea-ae77-adb1e8b1d433");katex.render("T_\\infty", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , "emissivity" gives the surface emissivity $var element = document.getElementById("moose-equation-6e6b58b9-eca1-4be4-93df-2c19e976f4ec");katex.render("\\epsilon", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , and "view_factor" gives the view factor $var element = document.getElementById("moose-equation-2fe8cf7a-ad6f-46cf-8986-f900cd4d659a");katex.render("F", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

The parameter "scale_pp" specifies the name of a post-processor $var element = document.getElementById("moose-equation-39cfd52a-6a7c-430c-a513-b5d5b8241a21");katex.render("f", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ that can scale the boundary conditions.

Input Parameters

T_ambientTemperature of environment [K]
C++ Type:FunctionName
Controllable:No
Description:Temperature of environment [K]
boundaryList of boundary names for which this component applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:List of boundary names for which this component applies
emissivityEmissivity of flow channel [-]
C++ Type:double
Controllable:No
Description:Emissivity of flow channel [-]
hsHeat structure name
C++ Type:std::string
Controllable:No
Description:Heat structure name

Required Parameters

scale_ppPost-processor by which to scale boundary condition
C++ Type:PostprocessorName
Controllable:No
Description:Post-processor by which to scale boundary condition
view_factor1View factor function [-]
Default:1
C++ Type:FunctionName
Controllable:No
Description:View factor function [-]

Optional 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:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Formulation

The heat conduction equation is the following: $var element = document.getElementById("moose-equation-32ffe815-8f0d-4ff8-8385-6f63b775e580");katex.render(" \\rho c_p \\pd{T}{t} - \\nabla \\cdot (k \\nabla T) = q''' \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where

$var element = document.getElementById("moose-equation-16dd84c8-cba1-4230-9620-b64963b01986");katex.render("\\rho", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is density,
$var element = document.getElementById("moose-equation-3cdf69a6-da53-4e7d-9538-ec7daf73f04a");katex.render("c_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is specific heat capacity,
$var element = document.getElementById("moose-equation-34fb674a-b5d2-4420-b77f-1e0b2c3fbc24");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is thermal conductivity,
$var element = document.getElementById("moose-equation-5cef3986-a270-4946-8d00-0c3e08ea42c8");katex.render("T", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is temperature, and
$var element = document.getElementById("moose-equation-b40d5555-4197-47f0-869a-ba8906133524");katex.render("q'''", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a volumetric heat source.

Multiplying by a test function $var element = document.getElementById("moose-equation-b24c0dc1-17b4-4d1c-acda-789c65121d53");katex.render("\\phi_i", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and integrating by parts over the domain $var element = document.getElementById("moose-equation-049d99aa-c01e-4643-af88-074a356dba0a");katex.render("\\Omega", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ gives $var element = document.getElementById("moose-equation-64d0cffb-c432-4a44-9aca-2a1adb8a1f46");katex.render(" \\pr{\\rho c_p \\pd{T}{t}, \\phi_i}_\\Omega + \\pr{k \\nabla T, \\nabla\\phi_i}_\\Omega - \\left\\langle k \\nabla T, \\phi_i\\mathbf{n}\\right\\rangle_{\\partial\\Omega} = \\pr{q''', \\phi_i}_\\Omega \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where $var element = document.getElementById("moose-equation-cba88b75-9fa2-4a8b-87ed-a8e1a2d5fd1e");katex.render("\\partial\\Omega", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the boundary of the domain $var element = document.getElementById("moose-equation-20bc0a8b-bf15-43f1-bf67-6b6845c6f866");katex.render("\\Omega", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

For Neumann boundary conditions on the boundary $var element = document.getElementById("moose-equation-f06974ef-5189-49c8-8fe2-cdac59c4cc39");katex.render("\\Gamma", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , $var element = document.getElementById("moose-equation-90b1b8bc-5389-4dff-8270-e7c90993766d");katex.render("k \\nabla T \\cdot \\mathbf{n}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is replaced with a known incoming heat flux function $var element = document.getElementById("moose-equation-faa83bff-ccbb-460c-a4b9-7c1572c50b67");katex.render("q_b", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ :

var element = document.getElementById("moose-equation-237fb663-83aa-4035-a102-b602297ff0b1");katex.render("k \\nabla T \\cdot \\mathbf{n} = q_b \\qquad \\mathbf{x} \\in \\Gamma \\eqp", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

For radiation boundary conditions, the incoming boundary heat flux $var element = document.getElementById("moose-equation-c9e1e1f9-8c1c-450d-8308-8f66d19645fc");katex.render("q_b", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is computed as

$var element = document.getElementById("moose-equation-e7a38a9f-3a9a-4126-9c76-6831473c6015");katex.render(" q_b = f \\sigma \\epsilon F (T^4_\\infty - T^4) \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where

$var element = document.getElementById("moose-equation-cd9155e8-a04f-4b74-b7a8-2f2f3219d1a2");katex.render("\\sigma", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the Stefan-Boltzmann constant,
$var element = document.getElementById("moose-equation-35aa43b5-c6f4-4fe7-94fb-0b7a6bf16969");katex.render("\\epsilon", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the emissivity of the surface,
$var element = document.getElementById("moose-equation-bf6a54ab-525b-4a29-8757-92422c2d5027");katex.render("F", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the view factor function,
$var element = document.getElementById("moose-equation-efb143ed-5169-48df-a742-800f69d2c763");katex.render("T", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the temperature of the surface,
$var element = document.getElementById("moose-equation-f79c394d-d574-42ce-991f-97343410b916");katex.render("T_\\infty", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the ambient temperature, and
$var element = document.getElementById("moose-equation-794b2d14-2917-4ffc-abcd-b11efaaabd83");katex.render("f", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is an optional scaling factor.

Input Files

(modules/thermal_hydraulics/test/tests/components/hs_boundary_radiation/from_file_3d.i)
(modules/thermal_hydraulics/test/tests/components/hs_boundary_radiation/cylindrical.i)
(modules/thermal_hydraulics/test/tests/components/hs_boundary_radiation/plate.i)

(modules/thermal_hydraulics/test/tests/components/hs_boundary_radiation/from_file_3d.i)

T_hs = 1200
T_ambient = 1500
emissivity = 0.3
view_factor = 0.6
t = 5.0

# dimensions of the side 'left'
height = 5
depth = 2

# SS 316
density = 8.0272e3
specific_heat_capacity = 502.1
conductivity = 16.26

stefan_boltzmann = 5.670367e-8
A = ${fparse height * depth}
heat_flux = ${fparse stefan_boltzmann * emissivity * view_factor * (T_ambient^4 - T_hs^4)}
scale = 0.8
E_change = ${fparse scale * heat_flux * A * t}

[Materials]
  [mat]
    type = ADGenericConstantMaterial
    block = 'hs:brick'
    prop_names = 'density specific_heat thermal_conductivity'
    prop_values = '${density} ${specific_heat_capacity} ${conductivity}'
  []
[]

[Components]
  [hs]
    type = HeatStructureFromFile3D
    file = box.e
    position = '0 0 0'
    initial_T = ${T_hs}
  []

  [hs_boundary]
    type = HSBoundaryRadiation
    boundary = 'hs:left'
    hs = hs
    T_ambient = ${T_ambient}
    emissivity = ${emissivity}
    view_factor = ${view_factor}
    scale_pp = bc_scale_pp
  []
[]

[Postprocessors]
  [bc_scale_pp]
    type = FunctionValuePostprocessor
    function = ${scale}
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [E_hs]
    type = ADHeatStructureEnergy3D
    block = 'hs:brick'
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [E_hs_change]
    type = ChangeOverTimePostprocessor
    postprocessor = E_hs
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [E_change_relerr]
    type = RelativeDifferencePostprocessor
    value1 = E_hs_change
    value2 = ${E_change}
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Executioner]
  type = Transient

  [TimeIntegrator]
    type = ActuallyExplicitEuler
  []
  dt = ${t}
  num_steps = 1
  abort_on_solve_fail = true
[]

[Outputs]
  [out]
    type = CSV
    show = 'E_change_relerr'
    execute_on = 'FINAL'
  []
[]

(modules/thermal_hydraulics/test/tests/components/hs_boundary_radiation/cylindrical.i)

T_hs = 1200
T_ambient = 1500
emissivity = 0.3
view_factor = 0.6
t = 5.0

L = 2
D_i = 0.2
thickness = 0.5

# SS 316
density = 8.0272e3
specific_heat_capacity = 502.1
conductivity = 16.26

stefan_boltzmann = 5.670367e-8
R_i = ${fparse 0.5 * D_i}
D_o = ${fparse D_i + 2 * thickness}
A = ${fparse pi * D_o * L}
heat_flux = ${fparse stefan_boltzmann * emissivity * view_factor * (T_ambient^4 - T_hs^4)}
scale = 0.8
E_change = ${fparse scale * heat_flux * A * t}

[HeatStructureMaterials]
  [hs_mat]
    type = SolidMaterialProperties
    rho = ${density}
    cp = ${specific_heat_capacity}
    k = ${conductivity}
  []
[]

[Components]
  [hs]
    type = HeatStructureCylindrical
    orientation = '0 0 1'
    position = '0 0 0'
    length = ${L}
    n_elems = 10

    inner_radius = ${R_i}
    widths = '${thickness}'
    n_part_elems = '10'
    materials = 'hs_mat'
    names = 'region'

    initial_T = ${T_hs}
  []

  [hs_boundary]
    type = HSBoundaryRadiation
    boundary = 'hs:outer'
    hs = hs
    T_ambient = ${T_ambient}
    emissivity = ${emissivity}
    view_factor = ${view_factor}
    scale_pp = bc_scale_pp
  []
[]

[Postprocessors]
  [bc_scale_pp]
    type = FunctionValuePostprocessor
    function = ${scale}
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [E_hs]
    type = ADHeatStructureEnergyRZ
    block = 'hs:region'
    axis_dir = '0 0 1'
    axis_point = '0 0 0'
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [E_hs_change]
    type = ChangeOverTimePostprocessor
    postprocessor = E_hs
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [E_change_relerr]
    type = RelativeDifferencePostprocessor
    value1 = E_hs_change
    value2 = ${E_change}
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Executioner]
  type = Transient

  [TimeIntegrator]
    type = ActuallyExplicitEuler
  []
  dt = ${t}
  num_steps = 1
  abort_on_solve_fail = true
[]

[Outputs]
  [out]
    type = CSV
    show = 'E_change_relerr'
    execute_on = 'FINAL'
  []
[]

(modules/thermal_hydraulics/test/tests/components/hs_boundary_radiation/plate.i)

T_hs = 1200
T_ambient = 1500
emissivity = 0.3
view_factor = 0.6
t = 5.0

L = 2
thickness = 0.5
depth = 0.6

# SS 316
density = 8.0272e3
specific_heat_capacity = 502.1
conductivity = 16.26

stefan_boltzmann = 5.670367e-8
A = ${fparse L * depth}
heat_flux = ${fparse stefan_boltzmann * emissivity * view_factor * (T_ambient^4 - T_hs^4)}
scale = 0.8
E_change = ${fparse scale * heat_flux * A * t}

[HeatStructureMaterials]
  [hs_mat]
    type = SolidMaterialProperties
    rho = ${density}
    cp = ${specific_heat_capacity}
    k = ${conductivity}
  []
[]

[Components]
  [hs]
    type = HeatStructurePlate
    orientation = '0 0 1'
    position = '0 0 0'
    length = ${L}
    n_elems = 10

    depth = ${depth}
    widths = '${thickness}'
    n_part_elems = '10'
    materials = 'hs_mat'
    names = 'region'

    initial_T = ${T_hs}
  []

  [hs_boundary]
    type = HSBoundaryRadiation
    boundary = 'hs:outer'
    hs = hs
    T_ambient = ${T_ambient}
    emissivity = ${emissivity}
    view_factor = ${view_factor}
    scale_pp = bc_scale_pp
  []
[]

[Postprocessors]
  [bc_scale_pp]
    type = FunctionValuePostprocessor
    function = ${scale}
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [E_hs]
    type = ADHeatStructureEnergy
    block = 'hs:region'
    plate_depth = ${depth}
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [E_hs_change]
    type = ChangeOverTimePostprocessor
    postprocessor = E_hs
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [E_change_relerr]
    type = RelativeDifferencePostprocessor
    value1 = E_hs_change
    value2 = ${E_change}
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Executioner]
  type = Transient

  [TimeIntegrator]
    type = ActuallyExplicitEuler
  []
  dt = ${t}
  num_steps = 1
  abort_on_solve_fail = true
[]

[Outputs]
  [out]
    type = CSV
    show = 'E_change_relerr'
    execute_on = 'FINAL'
  []
[]

Usage
Input Parameters
Formulation
Input Files

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