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

Onset of global instability in the flow past a circular cylinder cascade
Onset of global instability in the flow past a circular cylinder cascade
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.
instability, separated flows, wakes/jets
0022-1120
304-334
Boppana, V.B.L.
817ed7fa-d262-451f-a442-ee8c9b8a2cb0
Gajjar, J.S.B
572ad621-15b9-499c-9a0d-f71b329a36a9
Boppana, V.B.L.
817ed7fa-d262-451f-a442-ee8c9b8a2cb0
Gajjar, J.S.B
572ad621-15b9-499c-9a0d-f71b329a36a9

Boppana, V.B.L. and Gajjar, J.S.B (2010) Onset of global instability in the flow past a circular cylinder cascade. Journal of Fluid Mechanics, 668, 304-334. (doi:10.1017/S0022112010004684).

Record type: Article

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.

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More information

Published date: 3 December 2010
Keywords: instability, separated flows, wakes/jets
Organisations: Aerodynamics & Flight Mechanics Group

Identifiers

Local EPrints ID: 195725
URI: https://eprints.soton.ac.uk/id/eprint/195725
ISSN: 0022-1120
PURE UUID: fffe08a5-8d30-4044-9b89-493668a59943

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Date deposited: 26 Aug 2011 08:04
Last modified: 18 Jul 2017 11:24

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