SCMFrictionChenTodreas

Class that computes the axial friction factor using the Chen-Todreas correlations.

Overview

This class is used to model the axial friction factor for a subchannel assembly with wire-wrapped/bare fuel pins in a triangular lattice or bare fuel pins in a quadrilateral lattice.

For triangular lattices, two Chen-Todreas friction-factor parameterizations are available:

Upgraded, based on the upgraded Chen-Todreas correlation (UCTD) Todreas and Kazimi (2021), Chen et al. (2018);
Pacio, based on the Pacio-Chen-Todreas parameterization (PCTD) Pacio et al. (2022).

Equation and table numbers below refer to the UCTD and PCTD papers cited above.

The desired triangular-lattice parameterization is selected using the friction_model parameter. The default is Upgraded.

The two models use the same general form of the Cheng-Todreas detailed subchannel friction correlation but use different empirical coefficients for the flow-regime transition, wire-drag and wire-sweep terms, and intermittent-regime interpolation.

Triangular lattices

Upgraded Chen-Todreas parameterization

For friction_model = Upgraded, the laminar and turbulent transition Reynolds numbers are given by Eqs. (3) and (2) of UCTD,

var element = document.getElementById("moose-equation-1d66db1e-5a8e-47b4-a858-53fe0afa37f2");katex.render("Re_L = 320 \\times 10^{P/D - 1},", element, {displayMode:true,throwOnError:false});

and

var element = document.getElementById("moose-equation-a37c3c64-10c7-4f83-b743-c8755046f597");katex.render("Re_T = 10^4 \\times 10^{0.7(P/D - 1)} .", element, {displayMode:true,throwOnError:false});

The turbulent wire-drag coefficient is evaluated as in Eq. (14) of UCTD, with the sign of the linear term corrected in Chen et al. (2018),

var element = document.getElementById("moose-equation-9f6c1846-81ef-4057-b1d2-cb60ed666281");katex.render("W_{dT} = \\left[ 19.56 - 98.71\\left(\\frac{D_w}{D}\\right) + 303.47\\left(\\frac{D_w}{D}\\right)^2 \\right] \\left(\\frac{H}{D}\\right)^{-0.541},", element, {displayMode:true,throwOnError:false});

with the laminar coefficient from Eq. (19) of UCTD,

var element = document.getElementById("moose-equation-dd23a300-aaa3-4e06-90a2-1211d5b2ae9a");katex.render("W_{dL} = 1.4 W_{dT} .", element, {displayMode:true,throwOnError:false});

The turbulent wire-sweep coefficient is given by Eq. (21) of UCTD,

var element = document.getElementById("moose-equation-78af45db-5adc-4f8f-9e6c-8508cd41a783");katex.render("W_{sT} = -11 \\log_{10}\\left(\\frac{H}{D}\\right) + 19,", element, {displayMode:true,throwOnError:false});

with Eq. (20) of UCTD,

var element = document.getElementById("moose-equation-9398ccea-036d-4041-b890-ca055960f10b");katex.render("W_{sL} = W_{sT} .", element, {displayMode:true,throwOnError:false});

The intermittent-regime interpolation, Eq. (4) of UCTD, uses

var element = document.getElementById("moose-equation-31fb69e0-d205-4986-a3b2-8b3af28fdba8");katex.render("\\lambda = 7, \\qquad \\gamma = \\frac{1}{3} .", element, {displayMode:true,throwOnError:false});

Pacio-Chen-Todreas parameterization

For friction_model = Pacio, the transition Reynolds numbers are independent of $var element = document.getElementById("moose-equation-67c07357-fc81-4013-be01-ef1e707f6b70");katex.render("P/D", element, {displayMode:false,throwOnError:false});$ and are given by Eqs. (13) and (12) of PCTD with the coefficients of its Table 5,

var element = document.getElementById("moose-equation-7d32a87c-c31c-421f-9d5e-88d5165308d0");katex.render("Re_L = 700, \\qquad Re_T = 10^4 .", element, {displayMode:true,throwOnError:false});

The turbulent wire-drag coefficient is evaluated using Eq. (21) of PCTD as

var element = document.getElementById("moose-equation-26cfe268-fefb-4ee2-972a-43ad1c1f176d");katex.render("W_{dT} = \\left[ 15.2 - 48.0\\left(\\frac{D_w}{D}\\right) + 148.6\\left(\\frac{D_w}{D}\\right)^2 \\right] \\left(\\frac{H}{D}\\right)^{-0.547},", element, {displayMode:true,throwOnError:false});

with the laminar coefficient from Eq. (22) of PCTD,

var element = document.getElementById("moose-equation-8e382098-f320-4831-8a34-e1d8b420cca2");katex.render("W_{dL} = 0.8 W_{dT} .", element, {displayMode:true,throwOnError:false});

The turbulent wire-sweep coefficient is given by Eq. (1) of PCTD,

var element = document.getElementById("moose-equation-af59b8eb-bf1a-43e0-a3ba-1e8a10bef06e");katex.render("W_{sT} = -6.9 \\log_{10}\\left(\\frac{H}{D}\\right) + 12,", element, {displayMode:true,throwOnError:false});

with Eq. (26) of PCTD,

var element = document.getElementById("moose-equation-ab80de0f-b3aa-46b1-b9ea-bb7e58048e99");katex.render("W_{sL} = 1.2 W_{sT} .", element, {displayMode:true,throwOnError:false});

The intermittent-regime interpolation, Eq. (35) of PCTD, uses

var element = document.getElementById("moose-equation-c07526c2-9b9e-4a83-877b-a2e39710a3b2");katex.render("\\lambda = 6.7, \\qquad \\gamma = 0.362 .", element, {displayMode:true,throwOnError:false});

Flow-regime interpolation

For both triangular-lattice parameterizations, the interpolation factor in the intermittent regime is evaluated using the bulk Reynolds number as in Eq. (5) of UCTD and Eq. (34) of PCTD,

var element = document.getElementById("moose-equation-1c7c878b-864a-452b-b4c0-ed7abd9146f0");katex.render("\\psi = \\frac{\\ln(Re_b/Re_L)} {\\ln(Re_T/Re_L)} .", element, {displayMode:true,throwOnError:false});

The laminar and turbulent subchannel friction factors, Eqs. (A1) and (A2) of UCTD and Eqs. (16) and (15) of PCTD, are

var element = document.getElementById("moose-equation-cbc087d0-0646-49a8-9a0e-6f6c938cc504");katex.render("f_L = C_{fL} Re^{-1},", element, {displayMode:true,throwOnError:false});

and

var element = document.getElementById("moose-equation-d0a60470-ba99-4e6e-ab16-ec29f3731887");katex.render("f_T = C_{fT} Re^{-0.18},", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-e3c7b028-5f26-4ce8-ad0e-ecef425a8125");katex.render("Re", element, {displayMode:false,throwOnError:false});$ is the local subchannel Reynolds number and $var element = document.getElementById("moose-equation-2f37d61e-fe87-40d7-b09e-9b1882270a4b");katex.render("C_{fL}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-f6c9c70b-7dd8-448d-b0f1-12a11b6633f7");katex.render("C_{fT}", element, {displayMode:false,throwOnError:false});$ include the appropriate bare-pin and, when present, wire-wrap contributions.

The intermittent friction factor is calculated as in Eq. (4) of UCTD and Eq. (35) of PCTD,

var element = document.getElementById("moose-equation-dd8b8613-794b-4cd6-bc3c-7b1d9d731027");katex.render("f = f_L (1-\\psi)^\\gamma \\left(1-\\psi^\\lambda\\right) + f_T \\psi^\\gamma .", element, {displayMode:true,throwOnError:false});

The values of $var element = document.getElementById("moose-equation-b5af0a72-8b16-4b6e-b9e0-0c8a065470a8");katex.render("Re_L", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-ca3cec68-be8d-4d85-b5a5-19451a299158");katex.render("Re_T", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-16b99687-2dc6-43cc-a0cf-5cc4acc7a504");katex.render("\\lambda", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-45ed8fa8-0ce7-478f-9ee8-8f3b3b4bda80");katex.render("\\gamma", element, {displayMode:false,throwOnError:false});$ are determined by the selected friction_model. Table 5 of PCTD compares all coefficients of both parameterizations.

Both $var element = document.getElementById("moose-equation-16cdebcd-585b-456a-9ba9-8cf99dc51f40");katex.render("f_L", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-43980787-35ca-4158-a154-c2acd1c050d1");katex.render("f_T", element, {displayMode:false,throwOnError:false});$ are evaluated at the local Reynolds number of the subchannel, from its current mass flux, as Eq. (35) of PCTD is written. The example calculation of PCTD, its Section 6.1.3, instead evaluates $var element = document.getElementById("moose-equation-2d2dde1b-a4ac-47dd-ab24-60a56abbc056");katex.render("f_L", element, {displayMode:false,throwOnError:false});$ with the laminar flow split and $var element = document.getElementById("moose-equation-b06c92a2-0bbe-4ba1-ab6e-8b263dd4cc12");katex.render("f_T", element, {displayMode:false,throwOnError:false});$ with the turbulent flow split of the subchannel type, computed before the transition regime. In the transition regime this gives a different flow split than the PCTD curves of the paper, up to about 0.14 in the corner subchannel of a 37-pin bundle; the laminar and turbulent regimes are not affected. Friction Factor Closures Verification compares the two.

Applicability

For triangular lattices, the closure flags a solution warning when $var element = document.getElementById("moose-equation-ec7f913d-c650-42b7-8ae8-37050ea34703");katex.render("P/D", element, {displayMode:false,throwOnError:false});$ , wire-wrap $var element = document.getElementById("moose-equation-fc07eca9-20cb-43a7-806c-0aae632ef4c1");katex.render("H/D", element, {displayMode:false,throwOnError:false});$ , number of pins, or the bulk Reynolds number $var element = document.getElementById("moose-equation-09efb89f-a2d0-4a06-8c84-8311465a5a57");katex.render("Re_b", element, {displayMode:false,throwOnError:false});$ is outside the data range associated with the selected friction correlation. Both sets of ranges are the reported ranges of validity in Table 1 of PCTD.

For the Upgraded parameterization, the implemented applicability ranges are

var element = document.getElementById("moose-equation-e868f3a6-437d-4edd-ba76-270a43f39fb5");katex.render("1.0 \\leq P/D \\leq 1.42,", element, {displayMode:true,throwOnError:false});

var element = document.getElementById("moose-equation-020b8f26-d02c-44ab-a9ce-081437f90ed6");katex.render("8.0 \\leq H/D \\leq 52.0,", element, {displayMode:true,throwOnError:false});

var element = document.getElementById("moose-equation-aee1ea14-02e9-41b9-87b4-bcdb3dfafc10");katex.render("7 \\leq N_{\\mathrm{pin}} \\leq 217,", element, {displayMode:true,throwOnError:false});

and

var element = document.getElementById("moose-equation-3f0d70be-a668-4324-a84f-11131accab1d");katex.render("50 \\leq Re_b \\leq 10^6 .", element, {displayMode:true,throwOnError:false});

For the Pacio parameterization, the implemented applicability ranges are

var element = document.getElementById("moose-equation-3da1d648-cfb5-41f0-a30c-92475d261fae");katex.render("1.02 \\leq P/D \\leq 1.42,", element, {displayMode:true,throwOnError:false});

var element = document.getElementById("moose-equation-4a576daa-bd01-4271-9323-7d4a7f479119");katex.render("7.5 \\leq H/D \\leq 54.0,", element, {displayMode:true,throwOnError:false});

var element = document.getElementById("moose-equation-c696c05a-f764-451f-af99-4554a75bdc51");katex.render("19 \\leq N_{\\mathrm{pin}} \\leq 217,", element, {displayMode:true,throwOnError:false});

and

var element = document.getElementById("moose-equation-00f90ead-4f9b-40c3-b30e-c4a32d80ec45");katex.render("10 \\leq Re_b \\leq 3\\times10^5 .", element, {displayMode:true,throwOnError:false});

Quadrilateral lattices

The friction_model selection applies only to triangular lattices.

For quadrilateral lattices, the existing Cheng-Todreas bare-pin friction-factor formulation is retained. The transition Reynolds numbers are given by Eqs. (3) and (2) of UCTD,

var element = document.getElementById("moose-equation-2a6e60c9-db42-40ab-85d3-5f66a1c7119b");katex.render("Re_L = 320 \\times 10^{P/D - 1}, \\qquad Re_T = 10^4 \\times 10^{0.7(P/D - 1)},", element, {displayMode:true,throwOnError:false});

and the intermittent-regime interpolation, Eq. (4) of UCTD, uses

var element = document.getElementById("moose-equation-db3b2afb-1e86-4878-888b-2c233d3ca0a8");katex.render("\\lambda = 7, \\qquad \\gamma = \\frac{1}{3} .", element, {displayMode:true,throwOnError:false});

note

Plots of the friction factor versus Reynolds number for all SCM friction closures are given in Friction Factor Closures Verification.

Input Parameters

friction_modelUpgradedFriction-factor parameterization for triangular wire-wrapped Chen-Todreas correlations.
Default:Upgraded
C++ Type:MooseEnum
Options:Upgraded, Pacio
Controllable:No
Description:Friction-factor parameterization for triangular wire-wrapped Chen-Todreas correlations.

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.

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

References

SK Chen, YM Chen, and NE Todreas. Corrigendum to “the upgraded cheng and todreas correlation for pressure drop in hexagonal wire-wrapped rod bundles” [nucl. eng. des. 335 (2018) 356–373]. Nuclear Engineering and Design, 340:414, 2018.

BibTeX

@article{chen2018corrigendum,
    author = "Chen, SK and Chen, YM and Todreas, NE",
    title = "Corrigendum to ``The upgraded Cheng and Todreas correlation for pressure drop in hexagonal wire-wrapped rod bundles'' [Nucl. Eng. Des. 335 (2018) 356--373]",
    journal = "Nuclear Engineering and Design",
    volume = "340",
    pages = "414",
    year = "2018",
    publisher = "Elsevier"
}

RIS

TY  - JOUR
AU  - Chen, SK
AU  - Chen, YM
AU  - Todreas, NE
TI  - Corrigendum to “The upgraded Cheng and Todreas correlation for pressure drop in hexagonal wire-wrapped rod bundles” [Nucl. Eng. Des. 335 (2018) 356–373]
JO  - Nuclear Engineering and Design
PY  - 2018
VL  - 340
PB  - Elsevier
SP  - 414
ER  -

Plain Text

SK Chen, YM Chen, and NE Todreas. Corrigendum to “the upgraded cheng and todreas correlation for pressure drop in hexagonal wire-wrapped rod bundles” [nucl. eng. des. 335 (2018) 356–373]. Nuclear Engineering and Design, 340:414, 2018.

SK Chen, YM Chen, and NE Todreas. The upgraded cheng and todreas correlation for pressure drop in hexagonal wire-wrapped rod bundles. Nuclear Engineering and Design, 335:356–373, 2018.

BibTeX

@article{chen2018upgraded,
    author = "Chen, SK and Chen, YM and Todreas, NE",
    title = "The upgraded Cheng and Todreas correlation for pressure drop in hexagonal wire-wrapped rod bundles",
    journal = "Nuclear Engineering and Design",
    volume = "335",
    pages = "356--373",
    year = "2018",
    publisher = "Elsevier"
}

RIS

TY  - JOUR
AU  - Chen, SK
AU  - Chen, YM
AU  - Todreas, NE
TI  - The upgraded Cheng and Todreas correlation for pressure drop in hexagonal wire-wrapped rod bundles
JO  - Nuclear Engineering and Design
PY  - 2018
VL  - 335
PB  - Elsevier
SP  - 356
EP  - 373
ER  -

Plain Text

SK Chen, YM Chen, and NE Todreas. The upgraded cheng and todreas correlation for pressure drop in hexagonal wire-wrapped rod bundles. Nuclear Engineering and Design, 335:356–373, 2018.

J Pacio, SK Chen, YM Chen, and NE Todreas. Analysis of pressure losses and flow distribution in wire-wrapped hexagonal rod bundles for licensing. part i: the pacio-chen-todreas detailed model (pctd). Nuclear Engineering and Design, 388:111607, 2022.

BibTeX

@article{pacio2022analysis,
    author = "Pacio, J and Chen, SK and Chen, YM and Todreas, NE",
    title = "Analysis of pressure losses and flow distribution in wire-wrapped hexagonal rod bundles for licensing. Part I: The Pacio-Chen-Todreas Detailed model (PCTD)",
    journal = "Nuclear Engineering and Design",
    volume = "388",
    pages = "111607",
    year = "2022",
    publisher = "Elsevier"
}

RIS

TY  - JOUR
AU  - Pacio, J
AU  - Chen, SK
AU  - Chen, YM
AU  - Todreas, NE
TI  - Analysis of pressure losses and flow distribution in wire-wrapped hexagonal rod bundles for licensing. Part I: The Pacio-Chen-Todreas Detailed model (PCTD)
JO  - Nuclear Engineering and Design
PY  - 2022
VL  - 388
PB  - Elsevier
SP  - 111607
ER  -

Plain Text

J Pacio, SK Chen, YM Chen, and NE Todreas. Analysis of pressure losses and flow distribution in wire-wrapped hexagonal rod bundles for licensing. part i: the pacio-chen-todreas detailed model (pctd). Nuclear Engineering and Design, 388:111607, 2022.

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

BibTeX

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

RIS

TY  - BOOK
AU  - Todreas, Neil E
AU  - Kazimi, Mujid S
TI  - Nuclear systems volume I: Thermal hydraulic fundamentals
PY  - 2021
PB  - CRC press
ER  -

Plain Text

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

Overview
Triangular lattices
Quadrilateral lattices
Input Parameters
References