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TECHNICAL PAPERS

The Asymmetry of the Large-Scale Structures in Turbulent Three-Dimensional Wall Jets Exiting Long Rectangular Channels

[+] Author and Article Information
J. W. Hall1

Department of Mechanical Engineering, McMaster University, Hamilton, Ontario, L8S 4L7, Canadajwhall@unb.ca

D. Ewing2

Department of Mechanical Engineering, McMaster University, Hamilton, Ontario, L8S 4L7, Canadaewingd@me.queensu.ca

1

Present address: Department of Mechanical Engineering, University of New Brunswick, 15 Dineen Drive, Fredericton, NB, E3B 5A3.

2

Present address: Department of Mechanical and Materials Engineering, Queens University, Kingston, ON, K7L 3N6 Canada.

J. Fluids Eng 129(7), 929-941 (Jan 15, 2007) (13 pages) doi:10.1115/1.2742721 History: Received November 16, 2005; Revised January 15, 2007

The development of the large-scale structures in three-dimensional wall jets formed using long rectangular channels with aspect ratios of 1 and 4 was investigated using measurements of the fluctuating wall pressure and point measurements of the turbulent velocity throughout the near and intermediate field. The instantaneous pressure fluctuations in both jets were laterally asymmetric causing the fluctuating wall pressure to be poorly correlated across the jet centerline. A frequency-dependent proper orthogonal decomposition (POD) of the fluctuating pressure measurements indicated that the first two mode shapes were opposite and each mode made similar contributions to the mean square fluctuations at all frequencies in order to capture the instantaneous asymmetry of the pressure field. The mode shapes in the intermediate field of both jets were strongly frequency dependent, and a subsequent wavelet analysis indicated that there are both large-scale horseshoe structures that span one-half of the jet and separate, smaller, near-wall structures located near the jet centerline. The initial development of the large-scale structures in the two jets differed, with the most energetic fluctuations being more antisymmetric in the square jet.

Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of a three-dimensional wall jet exiting a rectangular nozzle

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Figure 2

Proposed development of the vortex structure in a three-dimensional wall jet formed using a round nozzle (8)

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Figure 3

Schematic of: (a) The channel and flow conditioning for the variable aspect-ratio channel and (b) the wall-jet facility. All dimensions are in millimeters.

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Figure 4

Comparison of (∂W∕∂y)(h∕Umax) and prms at (a) and (b)x∕h=6, (c) and (d)x∕h=20, and (e) and (f)x∕h=40 for the wall jet formed using the Ar=4 channel

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Figure 5

Sequence of correlations of the fluctuating pressure at z∕z1∕2=−1 with the streamwise fluctuating velocity measured at x∕h=6

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Figure 6

Sequence of correlations of the fluctuating pressure at z∕z1∕2=−0.86 with the streamwise fluctuating velocity at x∕h=20

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Figure 7

Normalized two-point two-time correlation of the fluctuating wall pressure, ρpp(z∕z1∕2=zmax∕z1∕2,z′,τy1∕2∕Umax), at (a)x∕h=6, (b)x∕h=20, and (c)x∕h=40 in the jet exiting the Ar=4 channel. The contours of zero correlation are marked by the dashed lines.

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Figure 17

Transient pressure field normalized by the local dynamic head of the jet, 0.5ρoUmax2, reconstructed using the first three POD modes for frequencies 0<fUmax∕y1∕2≤0.5 at (a)x∕A=10, (b)x∕A=20 in jet formed using Ar=1 channel and for frequencies 0<fUmax∕y1∕2≤0.5 at (c)x∕A=10, and (d)x∕A=20 in jet formed using Ar=4 channel

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Figure 9

Comparison of (a) the eigenspectra and (b) the mode shapes of the first 3 POD modes at x∕h=20 in the jet formed using the Ar=4 channel: 엯n=1, ◻n=2, and ▵n=3

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Figure 8

Comparison of (a) the eigenspectra and (b) the mode shapes of the first 3 POD modes at x∕h=6 in the jet formed using the Ar=4 channel: 엯n=1, ◻n=2, and ▵n=3

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Figure 10

Comparison of (a) the eigenspectra and (b) the mode shapes of the first 3 POD modes at x∕h=40in the jet formed using the Ar=4 channel: 엯n=1, ◻n=2, and ▵n=3

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Figure 11

Transient fluctuating pressure field across the jet normalized by the local dynamic head of jet at x∕h=6: (a) original field, (b) reconstructed using only the first POD mode, (c) using only the second POD mode, (d) using only the third POD mode, (e) using the first and second POD modes, and (f) using the first three POD modes

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Figure 12

Transient fluctuating pressure field across the jet normalized by the local dynamic head of jet, 0.5ρoUmax2, reconstructed using the first three POD modes with frequencies 0<fUmax∕y1∕2≤0.4 at (a)x∕h=6, (b)x∕h=20, and (c)x∕h=40

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Figure 13

Comparison of (a) and (c) the modulus of the wavelet coefficients and (b) and (d) the real part of the wavelet coefficients for the contribution of the first three POD modes at (a) and (b)z∕z1∕2=−0.43, and (c) and (d)z∕z1∕2=−1.71

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Figure 14

Comparison of (∂W∕∂y)(h∕Umax), and prms at (a) and (b)x∕h=10 and (c) and (d)x∕h=20 for the jet formed using the Ar=1 channel

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Figure 15

Comparison of (a) the eigenspectra and (b) the mode shapes of the first three POD modes at x∕h=10 in the jet formed using the Ar=1, channel: 엯n=1, ◻n=2, and ▵n=3

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Figure 16

Comparison of (a) the eigenspectra and (b) the mode shapes of the first three POD modes at x∕h=20 in the jet formed using the Ar=1 channel: 엯n=1, ◻n=2, and ▵n=3

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