HSBoundaryAmbientConvection

This component is a heat structure boundary that applies convective 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 $var element = document.getElementById("moose-equation-85d4dca7-05f3-4cce-b4c1-db5cfb0b2964");katex.render("T_\\infty", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , and "htc_ambient" gives the heat transfer coefficient $var element = document.getElementById("moose-equation-cf94a936-706b-42fa-8581-255eeff053fb");katex.render("\\mathcal{H}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

The parameter "scale_pp" specifies the name of a post-processor $var element = document.getElementById("moose-equation-c4e95a1e-0d45-4cba-a948-8bfd3ce30b39");katex.render("f", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ that can scale the boundary conditions.

Input Parameters

T_ambientAmbient temperature function [K]
C++ Type:FunctionName
Controllable:No
Description:Ambient temperature function [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
hsHeat structure name
C++ Type:std::string
Controllable:No
Description:Heat structure name
htc_ambientAmbient Convective heat transfer coefficient function [W/(m^2-K)]
C++ Type:FunctionName
Controllable:No
Description:Ambient Convective heat transfer coefficient function [W/(m^2-K)]

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

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: $var element = document.getElementById("moose-equation-e05add79-4abc-4fd8-94cd-4d78044f60ba");katex.render(" \\rho c_p \\pd{T}{t} - \\nabla \\cdot (k \\nabla T) = q''' \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where

$var element = document.getElementById("moose-equation-69e1bc69-bf1b-48ec-afab-fc7dd3d85fb6");katex.render("\\rho", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is density,
$var element = document.getElementById("moose-equation-27a540f7-4314-4179-9fa6-2026201fe090");katex.render("c_p", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is specific heat capacity,
$var element = document.getElementById("moose-equation-5102c4ff-b539-4257-b20a-6dafbb925b93");katex.render("k", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is thermal conductivity,
$var element = document.getElementById("moose-equation-62e79808-44b7-4455-b1e3-0a075d15bb52");katex.render("T", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is temperature, and
$var element = document.getElementById("moose-equation-bf51708d-c01d-4485-a8b7-4b3bfcab2468");katex.render("q'''", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a volumetric heat source.

Multiplying by a test function $var element = document.getElementById("moose-equation-e3aa6b6b-2ab2-470b-9da5-c3cd066a71ae");katex.render("\\phi_i", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and integrating by parts over the domain $var element = document.getElementById("moose-equation-6259b32d-a837-4873-bc23-a8ad5d8fd654");katex.render("\\Omega", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ gives $var element = document.getElementById("moose-equation-0716373f-86e6-4593-b94a-846e7e0f6d0b");katex.render(" \\pr{\\rho c_p \\pd{T}{t}, \\phi_i}_\\Omega + \\pr{k \\nabla T, \\nabla\\phi_i}_\\Omega - \\left\\langle k \\nabla T, \\phi_i\\mathbf{n}\\right\\rangle_{\\partial\\Omega} = \\pr{q''', \\phi_i}_\\Omega \\eqc", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where $var element = document.getElementById("moose-equation-b9b54dbb-4e37-4500-9afe-656cf9c3fe0d");katex.render("\\partial\\Omega", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the boundary of the domain $var element = document.getElementById("moose-equation-fcfc40c5-b359-4975-aeca-3edaf7bd624f");katex.render("\\Omega", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ .

For Neumann boundary conditions on the boundary $var element = document.getElementById("moose-equation-4f255c82-a967-4d0a-a480-1dc64cd56d61");katex.render("\\Gamma", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , $var element = document.getElementById("moose-equation-e4bacfdc-eef8-423b-8817-aac502761830");katex.render("k \\nabla T \\cdot \\mathbf{n}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is replaced with a known incoming heat flux function $var element = document.getElementById("moose-equation-0ac65fc3-48b1-4b8f-b684-7e47bd48d1e0");katex.render("q_b", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ :

var element = document.getElementById("moose-equation-e9735357-bf40-45d0-b358-a19a44229110");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 convection boundary conditions, the incoming boundary heat flux $var element = document.getElementById("moose-equation-e6f14967-a333-4a27-aee6-7127e408cf19");katex.render("q_b", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is computed as

var element = document.getElementById("moose-equation-c2613565-2774-4aa2-aed1-74ef5de63c1d");katex.render("q_b = f \\mathcal{H} (T_\\infty - T) \\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

$var element = document.getElementById("moose-equation-1653fde6-006f-4e4f-a378-e968da853d8e");katex.render("\\mathcal{H}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the heat transfer coefficient,
$var element = document.getElementById("moose-equation-78c0b804-92f8-48c8-95a4-65d0afa52b91");katex.render("T", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the temperature of the surface,
$var element = document.getElementById("moose-equation-d2134e74-cecc-445a-91ad-f3667d7c6858");katex.render("T_\\infty", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the ambient temperature, and
$var element = document.getElementById("moose-equation-125d3080-53d5-4fad-9782-c1da445582b2");katex.render("f", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is an optional scaling factor.

Input Files

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

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

T_hs = 300
T_ambient1 = 500
htc1 = 100
T_ambient2 = 400
htc2 = 300
t = 0.001

L = 2
D_i = 0.2
thickness = 0.5

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

R_i = ${fparse 0.5 * D_i}
D_o = ${fparse D_i + 2 * thickness}
A = ${fparse pi * D_o * L}
heat_flux_avg = ${fparse 0.5 * (htc1 * (T_ambient1 - T_hs) + htc2 * (T_ambient2 - T_hs))}
heat_flux_integral = ${fparse heat_flux_avg * A}
scale = 0.8
E_change = ${fparse scale * heat_flux_integral * t}

[Functions]
  [T_ambient_fn]
    type = PiecewiseConstant
    axis = z
    x = '0 1'
    y = '${T_ambient1} ${T_ambient2}'
  []
  [htc_ambient_fn]
    type = PiecewiseConstant
    axis = z
    x = '0 1'
    y = '${htc1} ${htc2}'
  []
[]

[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}
  []

  [ambient_convection]
    type = HSBoundaryAmbientConvection
    boundary = 'hs:outer'
    hs = hs
    T_ambient = T_ambient_fn
    htc_ambient = htc_ambient_fn
    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
    solve_type = lumped
  []
  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_ambient_convection/plate.i)

T_hs = 300
T_ambient1 = 500
htc1 = 100
T_ambient2 = 400
htc2 = 300
t = 0.001

L = 2
thickness = 0.5
depth = 0.6

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

A = ${fparse L * depth}
heat_flux_avg = ${fparse 0.5 * (htc1 * (T_ambient1 - T_hs) + htc2 * (T_ambient2 - T_hs))}
heat_flux_integral = ${fparse heat_flux_avg * A}
scale = 0.8
E_change = ${fparse scale * heat_flux_integral * t}

[Functions]
  [T_ambient_fn]
    type = PiecewiseConstant
    axis = z
    x = '0 1'
    y = '${T_ambient1} ${T_ambient2}'
  []
  [htc_ambient_fn]
    type = PiecewiseConstant
    axis = z
    x = '0 1'
    y = '${htc1} ${htc2}'
  []
[]

[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}
  []

  [ambient_convection]
    type = HSBoundaryAmbientConvection
    boundary = 'hs:outer'
    hs = hs
    T_ambient = T_ambient_fn
    htc_ambient = htc_ambient_fn
    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
    solve_type = lumped
  []
  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_ambient_convection/from_file_3d.i)

T_hs = 300
T_ambient1 = 500
htc1 = 100
T_ambient2 = 400
htc2 = 300
t = 0.001

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

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

A = ${fparse height * depth}
heat_flux_avg = ${fparse 0.5 * (htc1 * (T_ambient1 - T_hs) + htc2 * (T_ambient2 - T_hs))}
heat_flux_integral = ${fparse heat_flux_avg * A}
scale = 0.8
E_change = ${fparse scale * heat_flux_integral * t}

[Functions]
  [T_ambient_fn]
    type = PiecewiseConstant
    axis = z
    x = '-2.5 0'
    y = '${T_ambient1} ${T_ambient2}'
  []
  [htc_ambient_fn]
    type = PiecewiseConstant
    axis = z
    x = '-2.5 0'
    y = '${htc1} ${htc2}'
  []
[]

[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}
  []

  [ambient_convection]
    type = HSBoundaryAmbientConvection
    boundary = 'hs:left'
    hs = hs
    T_ambient = T_ambient_fn
    htc_ambient = htc_ambient_fn
    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
    solve_type = lumped
  []
  dt = ${t}
  num_steps = 1
  abort_on_solve_fail = true
[]

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

Usage
Input Parameters
Formulation
Input Files

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