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Effect of compressibility on the global stability of axisymmetric wake flows

Published online by Cambridge University Press:  19 August 2010

P. MELIGA ,
D. SIPP  and
J.-M. CHOMAZ
P. MELIGA*
Affiliation:
ONERA/DAFE, 8 rue des Vertugadins, 92190 Meudon, France
D. SIPP
Affiliation:
ONERA/DAFE, 8 rue des Vertugadins, 92190 Meudon, France
J.-M. CHOMAZ
Affiliation:
LadHyX, CNRS-Ecole Polytechnique, 91128 Palaiseau, France
*
†Email address for correspondence: philippe.meliga@epfl.ch
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Abstract

We study the linear dynamics of global eigenmodes in compressible axisymmetric wake flows, up to the high subsonic regime. We consider both an afterbody flow at zero angle of attack and a sphere, and find that the sequence of bifurcations destabilizing the axisymmetric steady flow is independent of the Mach number and reminiscent of that documented in the incompressible wake past a sphere and a disk (Natarajan & Acrivos, J. Fluid Mech., vol. 254, 1993, p. 323), hence suggesting that the onset of unsteadiness in this class of flows results from a global instability. We determine the boundary separating the stable and unstable domains in the (M, Re) plane, and show that an increase in the Mach number yields a stabilization of the afterbody flow, but a destabilization of the sphere flow. These compressible effects are further investigated by means of adjoint-based sensitivity analyses relying on the computation of gradients or sensitivity functions. Using this theoretical formalism, we show that they do not act through specific compressibility effects at the disturbance level but mainly through implicit base flow modifications, an effect that had not been taken into consideration by previous studies based on prescribed parallel base flow profiles. We propose a physical interpretation for the observed compressible effects, based on the competition between advection and production of disturbances, and provide evidence linking the stabilizing/destabilizing effect observed when varying the Mach number to a strengthening/weakening of the disturbance advection mechanism. We show, in particular, that the destabilizing effect of compressibility observed in the case of the sphere results from a significant increase of the backflow velocity in the whole recirculating bubble, which opposes the downstream advection of disturbances.

JFM classification

Compressible Flows: Compressible Flows Instability: Instability Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 660 , 10 October 2010 , pp. 499 - 526
Copyright
Copyright © Cambridge University Press 2010

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References

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