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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

REFERENCES

Abd-Rabbo, A. & Weaver, D. S. 1986 A flow visualization study of flow development in a staggered tube array. J. Sound Vibr. 106, 241–256.CrossRefGoogle Scholar
Barkley, D. & Henderson, R. D. 1996 Three-dimensional floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215–241.CrossRefGoogle Scholar
Brevdo, L. & Bridges, T. J. 1996 Absolute and convective instabilities of spatially periodic flows. Phi. Trans. R. Soc A 354, 1027–1064.Google Scholar
Drazin, P. G. 2002 Introduction to Hydrodynamic Stability, chap. 8. Cambridge University Press.CrossRefGoogle Scholar
Edwards, W.S., Tuckerman, L. S., Friesner, R. A. & Sorensen, D. C. 1994 Krylov methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 110, 82–102.CrossRefGoogle Scholar
Kevlahan, N. & Ghidaglia, J.-M. 2001 Computation of turbulent flow past an array of cylinders using a spectral method with brinkman penalization. Eur. J. Mech. B 20, 333–350.CrossRefGoogle Scholar
Kevlahan, N. K.-R. & Wadsley, J. 2005 Suppression of three-dimensional flow instabilities in tube bundles. J. Fluids Struc. 20, 611–620.CrossRefGoogle Scholar
Moulinec, C., Hunt, J. C. R. & Nieuwstadt, F. T. M. 2004 Disappearing wakes and dispersion in numerically simulated flows through tube bundles. Flow, Turbulence Combust.73, 95–116.CrossRefGoogle Scholar
Owen, P. R. 1965 Buffeting excitation of boiler tube vibration.J. Mech. Engng Sci. 7, 431–439.CrossRefGoogle Scholar
Weaver, D. S., Fitzpatrick, J. A. & Elkashlan, M. 1987 Strouhal numbers for heat-exchanger tube arrays in cross flow.J. Pressure Vessel Tech. 109, 219–223.CrossRefGoogle Scholar
Williamson, C. H. K. 1988 Defining a universal and continuous strouhal-Reynolds number relationship for the laminar vortex shedding of a circular cylinder. Phys. Fluids 31, 2742.CrossRefGoogle Scholar
Williamson, C. H. K. 1996 Three-dimensional wake transition. J. Fluid Mech. 328, 345–407.CrossRefGoogle Scholar