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Three-dimensional Floquet stability analysis of the wake in cylinder arrays

Published online by Cambridge University Press:  14 November 2007

N. K.-R. KEVLAHAN
N. K.-R. KEVLAHAN*
Affiliation:
Department of Mathematics & Statistics, McMaster University, Hamilton L8S 4K1, Canada
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Abstract

Three-dimensional stability of the periodic wake of tightly packed rotated and inline cylinder arrays is investigated for 60 ≤ Re ≤ 270. Results are compared with existing numerical and experimental studies for an isolated cylinder. Numerical Floquet analysis shows that the two-dimensional wakes of the rotated and inline arrays with spacing P/D = 1.5 become unstable at Rec = 64 ± 0.5 and Rec = 132 ± 1 respectively. Two-dimensional vortex shedding flow is unlikely in practice for such flows. The dominant spanwise wavelength is λ/D = 0.9 ± 0.1 for the rotated array at Re = 100 and λ/D = 3.0 ± 0.1 for the inline array at Re = 200. Three-dimensional simulations show excellent agreement with the Floquet analysis for the rotated case, and reasonable agreement for the inline case. The instability mechanism appears to be similar to Mode A for an isolated cylinder, although the structure of the three-dimensional vorticity is different due to the spatial periodicity of the flow. Unlike the isolated cylinder, both array flows are unstable as λ → ∞ (like a thin shear layer). This is the first investigation of three-dimensional wake instability in cylinder arrays, a problem of significant practical and theoretical interest.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 592 , 10 December 2007 , pp. 79 - 88
Copyright
Copyright © Cambridge University Press 2007

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References

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