SCMHTCSchadModified

Class that computes the convective heat transfer coefficient using the Schad-Modified correlation. Only use for fuel-pins.

The HTC closure models inherit from: SCMHTCClosureBase.

Schad-Modified Correlation for Turbulent Nusselt Number

The Schad-Modified correlation Kazimi and Carelli (1976) is used for calculating the Nusselt number in triangular fuel-pin bundles, considering the geometry of the bundle.

For $var element = document.getElementById("moose-equation-98e1f2d9-4626-4220-ba13-1ed0bc7f994e");katex.render("(1.1 \\le P/D \\le 1.5)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-f42e05de-ffda-4010-9e97-4734e8bff0f8");katex.render("(150 \\le \\mathrm{Pe} \\le 1000)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , the Nusselt number is:

$var element = document.getElementById("moose-equation-d3dd3e8f-21d0-4ac1-aaad-767e396405b7");katex.render("Nu = \\left[ -16.15 + 24.96\\left(P/D\\right) - 8.55\\left(P/D\\right)^2 \\right] \\mathrm{Pe}^{0.3}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

For $var element = document.getElementById("moose-equation-e7accacd-e863-4138-ae03-ab568a29cc72");katex.render("(\\mathrm{Pe} \\le 150)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , the correlation becomes:

$var element = document.getElementById("moose-equation-74f435c0-bfb5-4159-b0df-97f8f44dbd8e");katex.render("Nu = 4.496\\left[ -16.15 + 24.96\\left(P/D\\right) - 8.55\\left(P/D\\right)^2 \\right]", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where:

$var element = document.getElementById("moose-equation-9a758512-068f-4d2c-95a6-245333887ecf");katex.render("Nu", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : Nusselt number
$var element = document.getElementById("moose-equation-d3714a53-2bc7-4f67-afc8-e638947097af");katex.render("P", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : Pitch, the center-to-center distance between neighboring fuel-pins
$var element = document.getElementById("moose-equation-2ff78ad3-f6b5-4831-b31c-e5a65538c2e9");katex.render("D", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : Diameter of the fuel-pin
$var element = document.getElementById("moose-equation-598281d1-d373-44ad-b30f-a986bd34319e");katex.render("\\frac{P}{D}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : Pitch-to-diameter ratio
$var element = document.getElementById("moose-equation-338442b2-2e95-4341-9f68-2926a6c858fd");katex.render("Pe", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : Peclet number ( $var element = document.getElementById("moose-equation-e17a3ee6-9ba0-4f87-b7f4-cdcbbcb89d13");katex.render("Pe = Re \\times Pr", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ )
$var element = document.getElementById("moose-equation-a18ce98b-2d66-4e6c-8f16-39ed826d5e31");katex.render("Re", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : Reynolds number
$var element = document.getElementById("moose-equation-245f54f5-709a-4441-8b9b-81d32d83a71b");katex.render("Pr", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : Prandtl number

note

The Schad-Modified correlation is not currently implemented for computing the duct surface temperature.

The Borishanskii and Schad-modified correlations yield the best agreement over the entire range of P/D values Todreas and Kazimi (2021).

Input 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.

Advanced Parameters

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
Unit:(no unit assumed)
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.
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.

Material Property Retrieval Parameters

Input Files

(modules/subchannel/test/tests/problems/heat_transfer_correlations/XX09_SCM_SS17.i)

References

MS Kazimi and MD Carelli. Clinch river breeder reactor plant. heat transfer correlation for analysis of crbrp assemblies. Technical Report, Westinghouse Electric Corp., Madison, PA (United States). Advanced Reactors Div., 1976.

@techreport{kazimi1976,
    author = "Kazimi, MS and Carelli, MD",
    title = "Clinch River breeder reactor plant. Heat transfer correlation for analysis of CRBRP assemblies",
    year = "1976",
    institution = "Westinghouse Electric Corp., Madison, PA (United States). Advanced Reactors Div."
}

Neil E Todreas and Mujid S Kazimi. Nuclear systems volume I: Thermal hydraulic fundamentals. CRC press, 2021.

@book{todreas2021nuclear1,
    author = "Todreas, Neil E and Kazimi, Mujid S",
    title = "Nuclear systems volume I: Thermal hydraulic fundamentals",
    year = "2021",
    publisher = "CRC press"
}

(modules/subchannel/test/tests/problems/heat_transfer_correlations/XX09_SCM_SS17.i)

# Following Benchmark Specifications and Data Requirements for EBR-II Shutdown Heat Removal Tests SHRT-17 and SHRT-45R
# Available at: https://publications.anl.gov/anlpubs/2012/06/73647.pdf
###################################################
# Steady state subchannel calcultion
# Thermal-hydraulics parameters
###################################################
T_in = 624.70556 #Kelvin
Total_Surface_Area = 0.000854322 #m2
Mass_In = 2.45 #kg/sec
mass_flux_in = '${fparse Mass_In / Total_Surface_Area}' #kg/m2
P_out = 2.0e5 #Pa
Power_initial = 486200 #W (Page 26,35 of ANL document)
###################################################
# Geometric parameters
###################################################
scale_factor = 0.01
fuel_pin_pitch = '${fparse 0.5664*scale_factor}'
fuel_pin_diameter = '${fparse 0.4419*scale_factor}'
wire_z_spacing = '${fparse 15.24*scale_factor}'
wire_diameter = '${fparse 0.1244*scale_factor}'
inner_duct_in = '${fparse 4.64*scale_factor}'
n_rings = 5
heated_length = '${fparse 34.3*scale_factor}'
unheated_length_exit = '${fparse 26.9*scale_factor}'
###################################################

[TriSubChannelMesh]
  [sub_channel]
    type = SCMTriSubChannelMeshGenerator
    nrings = ${n_rings}
    n_cells = 20
    flat_to_flat = ${inner_duct_in}
    unheated_length_exit = ${unheated_length_exit}
    heated_length = ${heated_length}
    pin_diameter = ${fuel_pin_diameter}
    pitch = ${fuel_pin_pitch}
    dwire = ${wire_diameter}
    hwire = ${wire_z_spacing}
  []

  [fuel_pins]
    type = SCMTriPinMeshGenerator
    input = sub_channel
    nrings = ${n_rings}
    n_cells = 20
    unheated_length_exit = ${unheated_length_exit}
    heated_length = ${heated_length}
    pitch = ${fuel_pin_pitch}
  []

  [duct]
    type = SCMTriDuctMeshGenerator
    input = fuel_pins
    nrings = ${n_rings}
    n_cells = 20
    flat_to_flat = ${inner_duct_in}
    unheated_length_exit = ${unheated_length_exit}
    heated_length = ${heated_length}
    pitch = ${fuel_pin_pitch}
  []
[]

[Functions]
  [axial_heat_rate]
    type = ParsedFunction
    expression = '(pi/2)*sin(pi*z/L)*exp(-alpha*z)/(1.0/alpha*(1.0 - exp(-alpha*L)))*L'
    symbol_names = 'L alpha'
    symbol_values = '${heated_length} 1.8012'
  []
[]

[FluidProperties]
  [sodium]
    type = PBSodiumFluidProperties
  []
[]

[SubChannel]
  type = TriSubChannel1PhaseProblem
  fp = sodium
  n_blocks = 1
  P_out = ${P_out}
  compute_density = true
  compute_viscosity = true
  compute_power = true
  P_tol = 1.0e-4
  T_tol = 1.0e-5
  implicit = true
  segregated = false
  interpolation_scheme = 'upwind'
  verbose_subchannel = true
  friction_closure = 'cheng'
  full_output = true
  mixing_closure = 'cheng_todreas'

[]

[SCMClosures]
  [cheng]
    type = SCMFrictionUpdatedChengTodreas
  []
  [dittus-boelter]
    type = SCMHTCDittusBoelter
  []
  [gnielinski]
    type = SCMHTCGnielinski
  []
  [kazimi-carelli]
    type = SCMHTCKazimiCarelli
  []
  [schad-modified]
    type = SCMHTCSchadModified
  []
  [graber-rieger]
    type = SCMHTCGraberRieger
  []
  [borishanskii]
    type = SCMHTCBorishanskii
  []
  [cheng_todreas]
    type = SCMMixingChengTodreas
    CT = 2.6
  []
[]

# Keep T manually declared and unrestricted so this legacy regression continues
# to compare against the pre-scoped AuxVariable golds. The automatic
# SubChannelAddVariablesAction path remains block-restricted for normal inputs.
[AuxVariables]
  [T]
  []
[]

[ICs]


  [q_prime_IC]
    type = SCMTriPowerIC
    variable = q_prime
    power = ${Power_initial}
    filename = "pin_power_profile61_uniform.txt"
    axial_heat_rate = axial_heat_rate
  []

  [T_ic]
    type = ConstantIC
    variable = T
    value = ${T_in}
  []


  [P_ic]
    type = ConstantIC
    variable = P
    value = 0.0
  []

  [DP_ic]
    type = ConstantIC
    variable = DP
    value = 0.0
  []

  [Viscosity_ic]
    type = ViscosityIC
    variable = mu
    p = ${P_out}
    T = T
    fp = sodium
  []

  [rho_ic]
    type = RhoFromPressureTemperatureIC
    variable = rho
    p = ${P_out}
    T = T
    fp = sodium
  []

  [h_ic]
    type = SpecificEnthalpyFromPressureTemperatureIC
    variable = h
    p = ${P_out}
    T = T
    fp = sodium
  []

  [mdot_ic]
    type = ConstantIC
    variable = mdot
    value = 0.0
  []
[]

[AuxKernels]
  [T_in_bc]
    type = ConstantAux
    variable = T
    boundary = inlet
    value = ${T_in}
    execute_on = 'timestep_begin'
    block = sub_channel
  []
  [mdot_in_bc]
    type = SCMMassFlowRateAux
    variable = mdot
    boundary = inlet
    area = S
    mass_flux = ${mass_flux_in}
    execute_on = 'timestep_begin'
  []
[]

[Outputs]
  csv = true
[]

[Postprocessors]
  ### Central pin inlet temperature
  [Pin_Temp_0_Inlet]
    type = SCMPinSurfaceTemperature
    index = 0
    height = ${fparse heated_length*0.01}
  []
  ### Central pin center temperature
  [Pin_Temp_1_Center]
    type = SCMPinSurfaceTemperature
    index = 0
    height = ${fparse heated_length*0.5}
  []
  ### Central pin outlet temperature
  [Pin_Temp_2_Outlet]
    type = SCMPinSurfaceTemperature
    index = 0
    height = ${fparse heated_length*0.99}
  []
[]

[Executioner]
  type = Steady
[]

Schad - Modified Correlation for Turbulent Nusselt Number
Input Parameters
Input Files
References