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Onset of global instability in the flow past a circular cylinder cascade

Published online by Cambridge University Press:  03 December 2010

V. B. L. BOPPANA  and
J. S. B. GAJJAR
V. B. L. BOPPANA
Affiliation:
School of Engineering Sciences, University of Southampton, Highfield, Southampton, SO17 1BJ, UK
J. S. B. GAJJAR*
Affiliation:
School of Mathematics, The University of Manchester, Alan Turing Building, Manchester, M13 9PL, UK
*
†Email address for correspondence: [email protected]
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Abstract

The effect of blockage on the onset of instability in the two-dimensional uniform flow past a cascade of cylinders is investigated. The same techniques as those described in Gajjar & Azzam (J. Fluid Mech., vol. 520, 2004, p. 51) are used to tackle the generalized eigenvalue problem arising from a global stability analysis of the linearized disturbance equations. Results have been obtained for the various mode classes, and our results show that for the odd–even modes, which correspond to anti-phase oscillatory motion about the midplane between the cylinders and are the modes most extensively studied in the literature, the effect of blockage has a marginal influence on the critical Reynolds numbers for instability. This is in sharp contrast to results cited in many studies with a fully developed inlet flow past a cylinder placed between confining walls. We are also able to find other unstable modes and in particular for low blockage ratios, the odd–odd modes which correspond to the in-phase oscillatory motion about the midplane between the cylinders are the first to become unstable as compared with the odd–even modes, and with much lower frequencies.

JFM classification

Instability: Instability Wakes/Jets: Separated flows Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 668 , 10 February 2011 , pp. 304 - 334
Copyright
Copyright © Cambridge University Press 2010

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