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Research Papers: Heat Transfer Enhancement

A Comparative Study of Performance of Low Reynolds Number Turbulence Models for Various Heat Transfer Enhancement Simulations

[+] Author and Article Information
Ankit Tiwari

Department of MNE,
Penn State,
59 Old Lyme Drive Apartment 1,
Buffalo, NY 14221
e-mail: ankittalks@gmail.com

Savas Yavuzkurt

Professor
Department of MNE,
Penn State,
327 Reber,
University Park, PA 16802
e-mail: sqy@psu.edu

1Corresponding author.

2Present address: Gentherm Inc., Buffalo, NY 14221.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 21, 2018; final manuscript received March 20, 2019; published online May 14, 2019. Assoc. Editor: Srinath V. Ekkad.

J. Heat Transfer 141(7), 071902 (May 14, 2019) (12 pages) Paper No: HT-18-1691; doi: 10.1115/1.4043305 History: Received October 21, 2018; Revised March 20, 2019

The goal of this study is to evaluate the computational fluid dynamic (CFD) predictions of friction factor and Nusselt number from six different low Reynolds number k–ε (LRKE) models namely Chang–Hsieh–Chen (CHC), Launder–Sharma (LS), Abid, Lam–Bremhorst (LB), Yang–Shih (YS), and Abe–Kondoh–Nagano (AKN) for various heat transfer enhancement applications. Standard and realizable k–ε (RKE) models with enhanced wall treatment (EWT) were also studied. CFD predictions of Nusselt number, Stanton number, and friction factor were compared with experimental data from literature. Various parameters such as effect of type of mesh element and grid resolution were also studied. It is recommended that a model, which predicts reasonably accurate values for both friction factor and Nusselt number, should be chosen over disparate models, which may predict either of these quantities more accurately. This is based on the performance evaluation criterion developed by Webb and Kim (2006, Principles of Enhanced Heat Transfer, 2nd ed., Taylor and Francis Group, pp. 1–72) for heat transfer enhancement. It was found that all LRKE models failed to predict friction factor and Nusselt number accurately (within 30%) for transverse rectangular ribs, whereas standard and RKE with EWT predicted friction factor and Nusselt number within 25%. Conversely, for transverse grooves, AKN, AKN/CHC, and LS (with modified constants) models accurately predicted (within 30%) both friction factor and Nusselt number for rectangular, circular, and trapezoidal grooves, respectively. In these cases, standard and RKE predictions were inaccurate and inconsistent. For longitudinal fins, Standard/RKE model, AKN, LS and Abid LRKE models gave the friction factor and Nusselt number predictions within 25%, with the AKN model being the most accurate.

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References

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Figures

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Fig. 1

Boundary conditions for (a) circular grooves, (b) rectangular grooves, (c) trapezoidal grooves from Bilen et al. [6] and (d) ribs from Han et al. [4]. (a′), (b′), (c′) and (d ′) are the sectional views of computational domain meshes for circular grooves, rectangular grooves, trapezoidal grooves, and rectangular ribs, respectively.

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Fig. 2

(a) Boundary conditions and (b) computational domain for longitudinal fins from Jensen and Vlakancic [2]

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Fig. 3

Friction factor versus Reynolds number plots for circular grooves for different LRKE models compared with the correlation data from Bilen et al. [6]

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Fig. 4

Nusselt number versus Reynolds number plots for circular grooves for different LRKE models compared with the correlation data from Bilen et al. [6]

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Fig. 5

Friction factor versus Reynolds number plots for Rectangular grooves for different LRKE models compared with the correlation data from Bilen et al. [6]

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Fig. 6

Nusselt number versus Reynolds number plots for Rectangular grooves for different LRKE models compared with the correlation data from Bilen et al. [6]

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Fig. 7

Friction factor versus Reynolds Number plots for Trapezoidal grooves for different LRKE models compared with the correlation data from Bilen et al. [6]

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Fig. 8

Nusselt number versus Reynolds Number plots for Trapezoidal grooves for different LRKE models compared with the correlation data from Bilen et al. [6]

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Fig. 9

Near-wall nondimensional velocity (u+) versus nondimensional wall distance (y+) plots for circular grooves ((a) and (d)), rectangular grooves ((b) and (e)), and trapezoidal grooves ((c) and (f)). Best LRKE represents AKN model for circular and rectangular grooves and LS model with RKE model constants for trapezoidal grooves.

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Fig. 10

Grid convergence study of friction factor versus cell count for circular, rectangular, and trapezoidal grooves. The continuous lines show the fixed values of friction factor computed from correlations of circular, rectangular, and trapezoidal grooves at the test Reynolds number.

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Fig. 11

Grid convergence study of Nusselt number versus cell count for circular, rectangular, and trapezoidal grooves. The continuous lines show the fixed values of Nusselt number computed from correlations of circular, rectangular, and trapezoidal grooves at the test Reynolds number.

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Fig. 12

Friction factor versus Reynolds number plots for transverse rectangular ribs for different LRKE models compared with the correlation data from Han et al. [4]

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Fig. 13

Stanton number versus Reynolds number plots for transverse rectangular ribs for different LRKE models compared with the correlation data from Han et al. [4]

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Fig. 14

Near-wall nondimensional velocity (u+) versus nondimensional wall distance (y+) plots for transverse rectangular ribs (a) and longitudinal fins (b). Best LRKE represents AKN model for longitudinal fins.

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Fig. 15

Friction factor versus Reynolds number plots for longitudinal rectangular fins for different LRKE models compared with the correlation data from Jensen and Vlakancic [2]

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Fig. 16

Nusselt versus Reynolds number plots for longitudinal rectangular fins for different LRKE models compared with the correlation data from Jensen and Vlakancic [2]

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Fig. 17

Examples illustrating effect of mesh refinement on near-wall velocity profiles for (a) rectangular grooves (Re ∼ 34,000) and (b) rectangular ribs (Re ∼ 28,000)

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