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Research Papers: Heat Exchangers

Determination of the Number of Tube Rows to Obtain Closure for Volume Averaging Theory Based Model of Fin-and-Tube Heat Exchangers

[+] Author and Article Information
Feng Zhou

School of Energy and Environment,  Southeast University, 2 Si Pai Lou, Nanjing 210096, China; Department of Mechanical and Aerospace Engineering, University of California, 48-121 Engineering IV, 420 Westwood Plaza, Los Angeles, CA 90095zhoufeng@ucla.edu

Nicholas E. Hansen, David J. Geb, Ivan Catton

Department of Mechanical and Aerospace Engineering,  University of California, 48–121 Engineering IV, 420 Westwood Plaza, Los Angeles, CA 90095hansenen@gmail.com

J. Heat Transfer 133(12), 121801 (Oct 06, 2011) (9 pages) doi:10.1115/1.4004478 History: Received January 03, 2011; Revised June 19, 2011; Accepted June 21, 2011; Published October 06, 2011; Online October 06, 2011

Modeling of fin-and-tube heat exchangers based on the volume averaging theory (VAT) requires proper closure of the VAT based governing equations. Closure can be obtained from reasonable lower scale solutions of a computational fluid dynamics (CFD) code, which means the tube row number chosen should be large enough, so that the closure can be evaluated for a representative elementary volume (REV) that is, not affected by the entrance or recirculation at the outlet of the fin gap. To determine the number of tube rows, three-dimensional numerical simulations for plate fin-and-tube heat exchangers were performed, with the Reynolds number varying from 500 to 6000 and the number of tube rows varying from 1 to 9. A clear perspective of the variations of both overall and local fiction factor and the Nusselt number as the tube row number increases are presented. These variation trends are explained from the view point of the field synergy principle (FSP). Our investigation shows that 4 + 1 + 1 tube rows is the minimum number to get reasonable lower scale solutions. A computational domain including 5 + 2 + 2 tube rows is recommended, so that the closure formulas for drag resistance coefficient and heat transfer coefficient could be evaluated for the sixth and seventh elementary volumes to close the VAT based model.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 7

Comparison between the variation trend of Nu and θm with Re

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Figure 8

Re  = 500, N = 3, (a) velocity, (b) temperature, and (c) intersection angle

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Figure 9

Re  = 3000, N = 3, (a) velocity, (b) temperature, and (c) intersection angle

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Figure 10

Re  = 6000, N = 3, (a) velocity, (b) temperature, and (c) intersection angle

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Figure 11

Effect of tube row number on the heat transfer and friction characteristics, according to Wang correlations [13]

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Figure 12

Variation of Nu and f with tube row number by CFD simulation

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Figure 1

A schematic diagram of a plain plate fin-and-tube heat exchanger

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Figure 2

Computational domain (It is not drawn to scale)

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Figure 3

Grid system for 2-row case

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Figure 4

Fluid flow and heat transfer over a backward step

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Figure 5

Comparison between the present CFD results and well-known correlations

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Figure 6

Variation curve of M/M0 with Re

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Figure 13

Variation of M and θm with tube row number N

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Figure 14

Re  = 3000, N = 6, (a) velocity, (b) temperature, and (c) intersection angle

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Figure 15

Re  = 3000, N = 9, (a) velocity, (b) temperature, and (c) intersection angle

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Figure 16

Variation of local values in the streamwise direction

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