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TECHNICAL PAPERS: Forced Convection

Expansion Ratio Effects on Three-Dimensional Separated Flow and Heat Transfer Around Backward-Facing Steps

[+] Author and Article Information
Aya Kitoh

Department of Aerospace Engineering, Tohoku University, Sendai, Japan

Kazuaki Sugawara1

 Tohoku University, Sendai, Japan

Hiroyuki Yoshikawa

Department of Mechanical System Engineering, Kumamoto University, 2-39-1 Kurokami, Kumamoto 860-8555, Japanyoshi@kumamoto-u.ac.jp

Terukazu Ota

Department of Mechanical Systems and Design, Tohoku University, Sendai, Japan

1

Presently, Shin Nippon Air Technologies Co., Ltd., Tokyo, Japan.

J. Heat Transfer 129(9), 1141-1155 (Sep 28, 2006) (15 pages) doi:10.1115/1.2739619 History: Received March 20, 2006; Revised September 28, 2006

Direct numerical simulation methodology clarified the three-dimensional separated flow and heat transfer around three backward-facing steps in a rectangular channel, especially effects of channel expansion ratio ER upon them. ER treated in the present study was 1.5, 2.0, and 3.0 under a step aspect ratio of 36.0. The Reynolds number Re based on the mean velocity at inlet and the step height was varied from 300 to 1000. The present numerical results for ER=2.0 were found to be in very good agreement with the previous experimental and numerical ones in the present Reynolds number range for both the steady and unsteady flow states. The time averaged reattachment length on the center line increases with a decrease of ER. The flow became unsteady at RE=700, 600, and 500 for ER=1.5, 2.0, and 3.0, respectively, accompanying the remarkable increase of the three-dimensionality of the flow and temperature fields in spite of a very large step aspect ratio of 36.0. The Nusselt number increases in the reattachment flow region, in the neighborhood of the sidewalls, and also in the far downstream depending on both Re and ER.

Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Flow configuration and coordinates

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Figure 2

Grid dependency (Re=300, ER=2.0, AR=36.0, and z∕H=0)

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Figure 3

Comparison of streamwise velocity (z∕H=0)

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Figure 14

Nusselt number on lower wall (Re=300): (a) ER=1.5; (b) ER=2.0; (c) ER=3.0

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Figure 18

Time variation and power spectrum of ν′(Re=700): (a) ER=1.5; (b) ER=2.0; (c) ER=3.0

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Figure 15

Time averaged Nusselt number on lower wall (Re=700): (a) ER=1.5; (b) ER=2.0; (c) ER=3.0

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Figure 13

Time averaged limiting streamline on four walls (Re=700): (a) ER=1.5; (b) ER=2.0; (c) ER=3.0

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Figure 11

Time averaged streamline (Re=700): (a) ER=1.5; (b) ER=2.0; (c) ER=3.0

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Figure 10

Streamline (Re=300): (a) ER=1.5; (b) ER=2.0; (c) ER=3.0

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Figure 5

Effect of ER upon time averaged reattachment length (z∕H=0)

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Figure 4

Comparison of time averaged reattachment length (ER=2.0, and z∕H=0)

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Figure 17

Instantaneous Nusselt number on lower wall (Re=700, T=0): (a) ER=1.5; (b) ER=2.0; (c) ER=3.0

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Figure 16

Isosurface of instantaneous enstrophy (Re=700, Ω=2.0, and T=0): (a) ER=1.5; (b) ER=2.0; (c) ER=3.0

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Figure 12

Limiting streamline on four walls (Re=300): (a) ER=1.5; (b) ER=2.0; (c) ER=3.0

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Figure 9

Time averaged reattachment length and position of maximum Nusselt number (z∕H=0)

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Figure 8

Time averaged Nusselt number on lower wall: (a) Re=300; (b) Re=700

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Figure 7

Time averaged streamwise surface friction coefficient on upper wall: (a) Re=300; (b) Re=700

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Figure 6

Time averaged streamwise surface friction coefficient on lower wall: (a) Re=300; (b) Re=700

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