Onset of Vortex Shedding in a Periodic Array of Circular Cylinders

[+] Author and Article Information
L. Zhang

Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, IL 61801

S. Balachandar

Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, IL 61801s-bala@uiuc.edu

J. Fluids Eng 128(5), 1101-1105 (Feb 15, 2006) (5 pages) doi:10.1115/1.2201630 History: Received November 09, 2004; Revised February 15, 2006

Hopf bifurcation of steady base flow and onset of vortex shedding over a transverse periodic array of circular cylinders is considered. The influence of transverse spacing on critical Reynolds number is investigated by systematically varying the gap between the cylinders from a small value to large separations. The critical Reynolds number behavior for the periodic array of circular cylinders is compared with the corresponding result for a periodic array of long rectangular cylinders considered in [Balanchandar, S., and Parker, S. J., 2002, “Onset of Vortex Shedding in an Inline and Staggered Array of Rectangular Cylinders  ,” Phys. Fluids, 14, pp. 3714–3732]. The differences between the two cases are interpreted in terms of differences between their wake profiles.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

(a) The geometric arrangement for uniform flow past a transverse array of cylinders of circular cross section and (b) streamlines of the steady symmetric base flow at Re=50 for Ly=4

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Figure 2

(a) Wake length and (b) minimum streamwise velocity along the wake centerline. Results are shown for both the circular cylinder investigated here and for the long rectangular cylinder considered by (6). For the circular cylinder results are presented for varying Ly at both Re=50 (results at other Re are qualitatively similar) and Re=Recr .

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Figure 3

Log-linear plot of ∥u′∥ versus time for Ly=1.5 and Re=38; the growth rate obtatined is 0.320

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Figure 4

Quadratic fit of growth rate versus Re for Ly=1.5 case. Recr is the critical Re at which the growth rate is zero. Extrapolation of the plot gives a Recr of 27.5. For Ly=1.5, Reynolds numbers greater than 27.5 will result in vortex shedding.

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Figure 5

Critical Reynolds number versus transverse separation for both the circular and the long rectangular cylinder geometries. The results for the long rectangular cylinder are from (6).

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Figure 6

The eigenvector of the unstable mode at Re=50 and Ly=2. Plotted are contours of (a) streamwise velocity, (b) transverse velocity, and (c) swirling strength (11).

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Figure 7

Streamwise velocity profiles at six different streamwise locations in the cylinder wake for Re=50 and Ly=4. The x locations are shown in Fig. 1.




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