ADWallHTCGnielinskiAnnularMaterial

The material computes the convective heat transfer coefficient using the Gnielinski correlation for turbulent flow in annular ducts (Gnielinski, 2010).

The Nusselt number is calculated as follows:

var element = document.getElementById("moose-equation-a2de7116-a51d-4a76-99cc-b3d072f90d09");katex.render("\\text{Nu} = \\frac{(f_\\text{ann}/8) \\text{Re} \\text{Pr}}{k_1 + 12.7\\sqrt{f_\\text{ann}/8}(\\text{Pr}^{2/3} - 1)} \\left[1 + \\left(\\frac{D_h}{L}\\right)^{2/3}\\right] F_\\text{ann} K \\,,", element, {displayMode:true,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-b3e19821-df78-476a-a837-f366930d38cd");katex.render("k_1 = 1.07 + \\frac{900}{\\text{Re}} - \\frac{0.63}{1 + 10\\text{Pr}} \\,,", element, {displayMode:true,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-caaa1258-d208-4af5-aaa9-557ce62c2964");katex.render("f_\\text{ann} = (1.8 \\log_{10}\\text{Re}^* - 1.5)^{-2} \\,,", element, {displayMode:true,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-f0385836-9dad-4a2c-8daa-e458c5d67345");katex.render("\\text{Re}^* = \\text{Re} \\frac{(1 + a^2)\\ln a + (1 - a^2)}{(1 - a)^2 \\ln a} \\,,", element, {displayMode:true,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-38829199-1c47-4d20-b471-75106e681f7e");katex.render("K = \\left\\{\\begin{array}{l l} \\left(\\frac{T}{T_w}\\right)^n & \\text{Fluid is gas} \\\\ \\left(\\frac{\\text{Pr}}{\\text{Pr}_w}\\right)^{0.11} & \\text{Fluid is liquid} \\end{array}\\right. \\,,", element, {displayMode:true,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-b6246384-1a94-4b3b-ad1c-773c916564e0");katex.render("F_\\text{ann} = \\left\\{\\begin{array}{l l} 0.75 a^{-0.17} & \\text{Heat transfer at inner wall} \\\\ 0.9 - 0.15 a^{0.6} & \\text{Heat transfer at outer wall} \\end{array}\\right. \\,,", element, {displayMode:true,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-a977f525-cd37-4819-be91-7926779ac573");katex.render("D_h = D_o - D_i \\,,", element, {displayMode:true,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-9061c994-4d34-4b27-a3f2-92a573894fd5");katex.render("a = \\frac{D_i}{D_o} \\,,", 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:

$var element = document.getElementById("moose-equation-a124adaa-2313-4934-a50e-2a7b80cd3b01");katex.render("\\text{Re}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the Reynolds number,
$var element = document.getElementById("moose-equation-6004d129-ee9f-474b-b87f-b58254cd7b58");katex.render("\\text{Pr}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the Prandtl number,
$var element = document.getElementById("moose-equation-91843fde-eef8-4396-a187-17e3c9211c6a");katex.render("\\text{Pr}_w", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the Prandtl number obtained by evaluating properties at the wall temperature,
$var element = document.getElementById("moose-equation-db88ec57-57aa-4e6f-98bb-1d03761ed936");katex.render("L", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the channel length,
$var element = document.getElementById("moose-equation-b597534e-c5f5-4046-ade8-8c03133c9640");katex.render("T", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the fluid temperature,
$var element = document.getElementById("moose-equation-a1d70be8-5430-465d-9e27-410e5a2dbb09");katex.render("T_w", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the wall temperature, and
$var element = document.getElementById("moose-equation-21501e2d-621e-44ac-8ce0-82c17646778c");katex.render("n", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the gas exponent, which varies by gas and situation.

Lastly, the heat transfer coefficient is calculated as

var element = document.getElementById("moose-equation-75104dc1-96f1-439f-a87a-f16212be220e");katex.render("h = \\frac{\\text{Nu} k}{D_h} \\,.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

Input Parameters

D_innerInner diameter of the annulus [m]
C++ Type:double
Controllable:No
Description:Inner diameter of the annulus [m]
D_outerOuter diameter of the annulus [m]
C++ Type:double
Controllable:No
Description:Outer diameter of the annulus [m]
at_inner_wallFalseTrue if heat transfer is at inner wall
Default:False
C++ Type:bool
Controllable:No
Description:True if heat transfer is at inner wall
channel_lengthChannel length [m]
C++ Type:double
Controllable:No
Description:Channel length [m]
fluid_is_gasFalseTrue if the fluid is a gas
Default:False
C++ Type:bool
Controllable:No
Description:True if the fluid is a gas
fluid_propertiesFluid properties object
C++ Type:UserObjectName
Controllable:No
Description:Fluid properties object

Required Parameters

TTFluid temperature material property
Default:T
C++ Type:MaterialPropertyName
Controllable:No
Description:Fluid temperature material property
T_wallT_wallWall temperature material property
Default:T_wall
C++ Type:MaterialPropertyName
Controllable:No
Description:Wall temperature material property
blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
cpcpFluid isobaric specific heat capacity material property
Default:cp
C++ Type:MaterialPropertyName
Controllable:No
Description:Fluid isobaric specific heat capacity material property
declare_suffixAn optional suffix parameter that can be appended to any declared 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 declared properties. The suffix will be prepended with a '_' character.
gas_heating_correction_exponent0Exponent for the ratio of bulk fluid temperature to wall temperature for the Nusselt number correction factor when heating a gas
Default:0
C++ Type:double
Controllable:No
Description:Exponent for the ratio of bulk fluid temperature to wall temperature for the Nusselt number correction factor when heating a gas
htc_wallHwName to give the heat transfer coefficient material property
Default:Hw
C++ Type:MaterialPropertyName
Controllable:No
Description:Name to give the heat transfer coefficient material property
kkFluid thermal conductivity material property
Default:k
C++ Type:MaterialPropertyName
Controllable:No
Description:Fluid thermal conductivity material property
mumuFluid dynamic viscosity material property
Default:mu
C++ Type:MaterialPropertyName
Controllable:No
Description:Fluid dynamic viscosity material property
ppFluid pressure material property
Default:p
C++ Type:MaterialPropertyName
Controllable:No
Description:Fluid pressure material property
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.
rhorhoFluid density material property
Default:rho
C++ Type:MaterialPropertyName
Controllable:No
Description:Fluid density material property
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.
velvelFluid velocity material property
Default:vel
C++ Type:MaterialPropertyName
Controllable:No
Description:Fluid velocity material property

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: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
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

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

Input Files

(modules/thermal_hydraulics/test/tests/materials/ad_wall_htc_gnielinski_annular/ad_wall_htc_gnielinski_annular.i)

References

Volker Gnielinski. Heat transfer coefficients for turbulent flow in concentric annular ducts. Heat Transfer Engineering, pages 431–436, 2010. doi:10.1080/01457630802528661.

@article{gnielinski2010,
    author = "Gnielinski, Volker",
    title = "Heat Transfer Coefficients for Turbulent Flow in Concentric Annular Ducts",
    journal = "Heat Transfer Engineering",
    pages = "431--436",
    year = "2010",
    doi = "10.1080/01457630802528661"
}

(modules/thermal_hydraulics/test/tests/materials/ad_wall_htc_gnielinski_annular/ad_wall_htc_gnielinski_annular.i)

rho = 3.1176
vel = 100
k = 0.38220
mu = 4.8587e-05
cp = 5189.8
p = 100e3
T = 1073
T_wall = 1074
D_inner = 0.01
D_outer = 0.015
length = 0.5

[GlobalParams]
  execute_on = 'INITIAL'
[]

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 1
[]

[FluidProperties]
  [fp]
    type = IdealGasFluidProperties
  []
[]

[Materials]
  [props]
    type = ADGenericConstantMaterial
    prop_names = 'rho vel k mu cp p T T_wall'
    prop_values = '${rho} ${vel} ${k} ${mu} ${cp} ${p} ${T} ${T_wall}'
  []
  [test_material]
    type = ADWallHTCGnielinskiAnnularMaterial
    htc_wall = htc_wall
    D_inner = ${D_inner}
    D_outer = ${D_outer}
    channel_length = ${length}
    at_inner_wall = true
    fluid_is_gas = true
    gas_heating_correction_exponent = 0.15
    fluid_properties = fp
  []
[]

[Problem]
  solve = false
[]

[Executioner]
  type = Steady
[]

[Postprocessors]
  [htc_wall]
    type = ADElementAverageMaterialProperty
    mat_prop = htc_wall
  []
[]

[Outputs]
  csv = true
[]

Input Parameters
Input Files
References