SCMHTCBorishanskii

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

The HTC closure models inherit from: SCMHTCClosureBase.

Borishanskii Correlation for Turbulent Nusselt Number

The Borishanskii correlation Borishanskii et al. (1969) is used for calculating the Nusselt number in fuel-pin bundles, considering the geometry of the bundle.

For $var element = document.getElementById("moose-equation-b17ffb4e-1ad7-4f26-9a73-c31052fccbc0");katex.render("(1.1 \\le P/D \\le 1.5)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-70ac0db3-ee8c-447a-87c7-3a19106b6d2c");katex.render("(200 \\le \\mathrm{Pe} \\le 2200)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , the Nusselt number is:

$var element = document.getElementById("moose-equation-d2e23c7e-d3e3-460b-82a7-c169b17d3c87");katex.render("\\mathrm{Nu} = 24.15 \\log\\left[ -8.12 + 12.76\\left(\\frac{P}{D}\\right) - 3.65\\left(\\frac{P}{D}\\right)^2 \\right] + 0.0174 \\left[1 - \\exp\\left(6 - 6\\frac{P}{D}\\right) \\right] (\\mathrm{Pe} - 200)^{0.9}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

For $var element = document.getElementById("moose-equation-30f37a00-2def-4cc9-ae76-591fd625e79b");katex.render("(1.1 \\le P/D \\le 1.5)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-935e2f29-b840-4b85-a5a0-2605a0b012f5");katex.render("(\\mathrm{Pe} \\le 200)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , the correlation reduces to:

$var element = document.getElementById("moose-equation-b1762e7b-07e9-4614-92bc-6d49b94763ec");katex.render("\\mathrm{Nu} = 24.15 \\log\\left[-8.12 + 12.76\\left(\\frac{P}{D}\\right) - 3.65\\left(\\frac{P}{D}\\right)^2 \\right]", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where:

$var element = document.getElementById("moose-equation-67e08c35-20d4-4e41-b947-69ff36f2e85c");katex.render("Nu", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : Nusselt number
$var element = document.getElementById("moose-equation-6bebf2ca-b0c7-496d-bef2-b98dcad3b6c4");katex.render("P", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : Pitch, the center-to-center distance between neighboring fuel-pins
$var element = document.getElementById("moose-equation-0f898633-c1ca-4a37-b5dc-299c74d6decd");katex.render("D", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : Diameter of the fuel-pin
$var element = document.getElementById("moose-equation-71605a00-597f-4aac-9596-e3aa2f66cffa");katex.render("\\frac{P}{D}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : Pitch-to-diameter ratio
$var element = document.getElementById("moose-equation-7869bf51-b5e7-4c87-9282-a72bdfdd1743");katex.render("Pe", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : Peclet number ( $var element = document.getElementById("moose-equation-4a196c8e-3d38-4375-8fd6-96a6e5547b7d");katex.render("Pe = Re \\times Pr", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ )
$var element = document.getElementById("moose-equation-0098d11b-e708-4a10-9ff6-227441846087");katex.render("Re", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : Reynolds number
$var element = document.getElementById("moose-equation-300af21b-c36c-4ed9-b99a-bcea0727d13c");katex.render("Pr", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ : Prandtl number

note

The Borishanskii 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

VM Borishanskii, MA Gotovskii, and EV Firsova. Heat transfer to liquid metals in longitudinally wetted bundles of rods. Soviet Atomic Energy, 27(6):1347–1350, 1969.

@article{borishanskii1969heat,
    author = "Borishanskii, VM and Gotovskii, MA and Firsova, EV",
    title = "Heat transfer to liquid metals in longitudinally wetted bundles of rods",
    journal = "Soviet Atomic Energy",
    volume = "27",
    number = "6",
    pages = "1347--1350",
    year = "1969",
    publisher = "Springer"
}

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
[]

Borishanskii Correlation for Turbulent Nusselt Number
Input Parameters
Input Files
References