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Fundamental Issues and Canonical Flows

Wake Formation From a Pair of Circular Cylinders Traversing Between Small- and Large-Incidence Flow Regimes

[+] Author and Article Information
Mir M. A. Hayder

 Department of Engineering Technology Savannah State University 3219 College Street Savannah, GA 31404mir.hayder@mail.mcgill.ca

J. Fluids Eng 134(1), 011204 (Feb 24, 2012) (12 pages) doi:10.1115/1.4005726 History: Received June 27, 2010; Revised November 13, 2011; Published February 23, 2012; Online February 24, 2012

Cross flow past a pair of equal-diameter staggered circular cylinders, with either one of the pair subject to forced harmonic transverse oscillation, is investigated experimentally within Reynolds numbers Re = 525–750. The center-to-center pitch ratio and stagger angle of the cylinders at their mean position are 2.5° and 21°, respectively. Results with cylinder excitation frequencies in the range 0.07 ≤ fe D/U ≤ 1.18 (D = cylinder diameter, U = mean flow velocity) at a constant oscillation amplitude (peak-to-peak) of 0.44D are reported. Flow visualization of the wake formation region and hot-film measurements of the wake velocity are reported. Emphasis is placed on the mechanisms leading to vortex shedding. Results show that the wake undergoes considerable modification with the oscillation of either of the two cylinders; this modification depends strongly on the value of fe D/U. The flow patterns remain essentially the same as those of the corresponding static cases for fe D/U < 0.10. However, the flow at higher oscillation frequencies than that can no longer maintain those patterns. In particular, there are distinct regions of fundamental and superharmonic synchronizations between the dominant wake periodicities and the cylinder oscillation over the whole range of fe D/U. Moreover, the manner in which the wake responds to the cylinder oscillation depends strongly on whether it is the upstream or downstream cylinder which is being oscillated.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Locations of the hot-film probe. The dimensions P, L, T, D, and α represent the center-to center pitch, longitudinal pitch, transverse pitch, cylinder diameter, and stagger angle, respectively, for the nominal transverse position.

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Figure 2

Wake power-spectral plots when both cylinders are held stationary at: (a) T/D = 1.12 (Tmax ), position a; (b) T/D = 1.12 (Tmax ), position b; (c) T/D = 0.90 (Tnom ), position a; (d) T/D = 0.90 (Tnom ), position b; (e) T/D = 0.68 (Tmin ), position a; and (f) T/D = 0.68 (Tmin ), position b. f0 D/U indicates the dominant wake periodicity

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Figure 3

Sample flow visualization images for both cylinders held stationary at the (a) Tmax , (b) Tnom , and (c) Tmin positions

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Figure 4

Flow visualization images with both cylinders statically held at T/D = 1.12 (Tmax position), the time as a fraction of three periods, 3PSL of the flow periodicity assuming StSL ≈ 0.45 (PSL  = period of one shear layer shedding): (a) t/PSL  = 0.0; (b) t/PSL  = 0.67; (c) t/PSL  = 1.33; (d) t/PSL  = 2.0; (e) t/PSL  = 2.33; and (f) t/PSL  = 3.0

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Figure 5

Sample wake power-spectra measured at the Tnom position: (a) location a with Re = 13,139 and (b) location b with Re = 12,027

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Figure 6

Distinct peaks obtained from the wake spectra measured at positions a or b for upstream cylinder oscillation: • , dominant wake frequency; ○ , other distinct wake frequencies; —, lines showing integral relationships between wake and excitation frequency; ..., lines showing StSL  = 0.45 in (a) and StCW  = 0.15 in (b)

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Figure 7

Distinct peaks obtained from the wake spectra measured at positions c or d for downstream cylinder oscillation: • , dominant wake frequency; ○ , other distinct wake frequencies; —, lines showing integral relationships between wake and excitation frequency; ..., lines showing StSL  = 0.45 in (a) and StCW  = 0.15 in (b)

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Figure 8

Flow visualization images with the upstream cylinder oscillating at fe D/U ≈ 0.26. One complete cycle of oscillation is shown, time as a fraction of one period (P* ) of the oscillation.

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Figure 9

Flow visualization images with the downstream cylinder oscillating at fe D/U ≈ 0.18. One complete cycle of oscillation is shown, time as a fraction of one period (P* ) of the oscillation.

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Figure 10

Flow visualization images with the upstream cylinder oscillating at fe D/U ≈ 0.44. Three complete cycles of oscillation are shown, time as a fraction of one period (P* ) of the oscillation.

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Figure 11

Flow visualization images with the upstream cylinder oscillating at fe D/U ≈ 0.30. Two complete cycles of oscillation are shown, time as a fraction of one period (P* ) of the oscillation.

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Figure 12

Flow visualization images with the upstream cylinder oscillating at fe D/U ≈ 0.68. Two complete cycles of oscillation are shown, time as a fraction of one period (P* ) of the oscillation.

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Figure 13

Flow visualization images with the downstream cylinder oscillating at fe D/U ≈ 0.38. Two complete cycles of oscillation are shown, time as a fraction of one period (P* ) of the oscillation.

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Figure 14

Flow visualization images at the end of every third period with the downstream cylinder oscillating at fe D/U ≈ 0.51

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