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Research Papers: Flows in Complex Systems

Numerical Simulation of Vortex-Induced Vibration of Two Rigidly Connected Cylinders in Side-by-Side and Tandem Arrangements Using RANS Model

[+] Author and Article Information
Ming Zhao

School of Computing, Engineering
and Mathematics;
Institute for Infrastructure Engineering,
University of Western Sydney,
Locked Bag 1797,
Penrith, New South Wales 2751, Australia
e-mail: m.zhao@uws.edu.au

Joshua M. Murphy

School of Computing, Engineering
and Mathematics,
University of Western Sydney,
Locked Bag 1797,
Penrith, New South Wales 2751, Australia

Kenny Kwok

Institute for Infrastructure Engineering,
University of Western Sydney,
Locked Bag 1797,
Penrith, New South Wales 2751, Australia

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received November 2, 2014; final manuscript received May 19, 2015; published online September 3, 2015. Assoc. Editor: Francine Battaglia.

J. Fluids Eng 138(2), 021102 (Sep 03, 2015) (13 pages) Paper No: FE-14-1631; doi: 10.1115/1.4031257 History: Received November 02, 2014; Revised May 19, 2015

Vortex-induced vibration (VIV) of two rigidly connected circular cylinders in side-by-side and tandem arrangements in the cross-flow direction was investigated using two-dimensional (2D) numerical simulations. The 2D Reynolds-Averaged Navier–Stokes (RANS) equations were solved for the flow, and the equation of the motion was solved for the response of the cylinders. Simulations were conducted for a constant mass ratio of 2.5, gap ratios G (ratio of the gap between the cylinders to the cylinder diameter) in the range of 0.5 to 3, and reduced velocities in the range of 1 to 30. The effects of the gap ratio on the response of the cylinders were analyzed extensively. The maximum response amplitude in the lock-in regime was found to occur at G = 0.5 in the side-by-side arrangement, which is about twice that of a single cylinder. In the side-by-side arrangement, the response regime of the cylinders for gap ratios of 1.5, 2, 2.5, and 3 is much narrower than that of a single cylinder, because the vortex shedding from the two cylinders is in an out-of-phase pattern at large reduced velocities. In the tandem arrangement, the maximum response amplitude of the cylinders is greater than that of a single cylinder for all the calculated gap ratios. For the gap ratio of 0.5 in the tandem arrangement, the vortex shedding frequency from the upstream cylinder was not observed in the vibration at large reduced velocities, and the response is galloping.

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Figures

Grahic Jump Location
Fig. 1

Sketch for VIV of two rigidly connected cylinders. (a) Side-by-side arrangement and (b) tandem arrangement.

Grahic Jump Location
Fig. 2

Computational meshes. (a) G = 1 in the side-by-side arrangement and (b) G = 3 in the tandem arrangement.

Grahic Jump Location
Fig. 3

The results of the mesh dependency study. (a) Time history of Y for the side-by-side arrangement at G = 1, Vr = 6; (b) time history of Y for the tandem arrangement at G = 3, Vr = 7; (c) effect of Δr on the results for Nc = 96 side-by-side, G = 1; and (d) effect of Nc on the results for Δr = 0.0005 side-by-side, G = 1.

Grahic Jump Location
Fig. 4

FFT spectra of the cross-flow displacement of two side-by-side cylinders. (The variation of vibration frequency with reduced velocity is plotted on the f–Vr plane.) (a) G = 0.5, (b) G = 1, (c) G = 1.5, and (d) G = 3.

Grahic Jump Location
Fig. 5

Variations of the response amplitude and frequency with the reduced velocity for two cylinders in the side-by-side arrangement. (a) Amplitude, G = 0.5, 1, and 1.5; (b) amplitude, G = 2, 2.5, and 3; (c) frequency, G = 0.5, 1, and 1.5; and (d) frequency, G = 2, 2.5, and 3.

Grahic Jump Location
Fig. 6

FFT spectra of the averaged lift coefficient of the two cylinders in the side-by-side arrangement. (The variation of the vibration frequency of the cylinders with the reduced velocity is plotted the f–Vr plane.) (a) G = 0.5, (b) G = 1, (c) G = 1.5, and (d) G = 3.

Grahic Jump Location
Fig. 7

Vorticity contours for two cylinders in the side-by-side arrangement at G = 0.5. (a) Vr = 4.5, (b) Vr = 8, and (c) Vr = 12.

Grahic Jump Location
Fig. 8

Vorticity contours for two cylinders in the side-by-side arrangement at G = 1. (a) Vr = 5.5 and (b) Vr = 12.

Grahic Jump Location
Fig. 9

Vorticity contours for two cylinders in the side-by-side arrangement at G = 1.5, 2, 2.5, and 3. (a) G = 1.5, Vr = 5; (b) G = 2, Vr = 5; (c) G = 2.5, Vr = 5; and (d) G = 3, Vr = 5.

Grahic Jump Location
Fig. 10

Variations of the response amplitude and frequency with the reduced velocity for two cylinders in the tandem arrangement. (a) Amplitude, G = 0.5, 1, and 1.5; (b) amplitude, G = 2, 2.5, and 3; (c) frequency, G = 0.5, 1, and 1.5; and (d) frequency, G = 2, 2.5, and 3.

Grahic Jump Location
Fig. 11

FFT spectra of the cross-flow displacement for two cylinders in a tandem arrangement. (The variation of vibration frequency with reduced velocity is plotted on the f–Vr plane.) (a) G = 0.5, (b) G = 1, (c) G = 1.5, (d) G = 2, (e) G = 2.5, and (f) G = 3.

Grahic Jump Location
Fig. 12

FFT spectra of the averaged lift coefficient for two cylinders in a tandem arrangement. (The variation of vibration frequency with reduced velocity is plotted on the f–Vr plane.) (a) G = 0.5, (b) G = 1, (c) G = 1.5, (d) G = 2, (e) G = 2.5, and (f) G = 3.

Grahic Jump Location
Fig. 13

Vorticity contours for two cylinders in the tandem arrangement. (a) G = 0.5, Vr = 5; (b) G = 0.5 Vr = 7; (c) G = 0.5 Vr = 9; (d) G = 0.5 Vr = 16; (e) G = 1 Vr = 6; (f) G = 1.5 Vr = 5; (g) G = 1.5 Vr = 9; and (h) G = 3 Vr = 9.

Grahic Jump Location
Fig. 14

Variations of the time averaged excitation lift coefficients of the two cylinders in tandem arrangement. (a) G = 0.5, (b) G = 1, (c) G = 1.5, (d) G = 2, (e) G = 2.5, and (f) G = 3.

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