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Sensitivity analysis and passive control of cylinder flow

Published online by Cambridge University Press:  25 November 2008

OLIVIER MARQUET ,
DENIS SIPP  and
LAURENT JACQUIN
OLIVIER MARQUET
Affiliation:
ONERA/DAFE, 8 rue des Vertugadins, 92190 Meudon, France
DENIS SIPP
Affiliation:
ONERA/DAFE, 8 rue des Vertugadins, 92190 Meudon, France
LAURENT JACQUIN
Affiliation:
ONERA/DAFE, 8 rue des Vertugadins, 92190 Meudon, France
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Abstract

A general theoretical formalism is developed to assess how base-flow modifications may alter the stability properties of flows studied in a global approach of linear stability theory. It also comprises a systematic approach to the passive control of globally unstable flows by the use of small control devices. This formalism is based on a sensitivity analysis of any global eigenvalue to base-flow modifications. The base-flow modifications investigated are either arbitrary or specific ones induced by a steady force. This leads to a definition of the so-called sensitivity to base-flow modifications and sensitivity to a steady force. These sensitivity analyses are applied to the unstable global modes responsible for the onset of vortex shedding in the wake of a cylinder for Reynolds numbers in the range 47≤Re≤80. First, it is demonstrated how the sensitivity to arbitrary base-flow modifications may be used to identify regions and properties of the base flow that contribute to the onset of vortex shedding. Secondly, the sensitivity to a steady force determines the regions of the flow where a steady force acting on the base flow stabilizes the unstable global modes. Upon modelling the presence of a control device by a steady force acting on the base flow, these predictions are then extensively compared with the experimental results of Strykowski & Sreenivasan (J. Fluid Mech., vol. 218, 1990, p. 71). A physical interpretation of the suppression of vortex shedding by use of a control cylinder is proposed in the light of the sensitivity analysis.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 615 , 25 November 2008 , pp. 221 - 252
Copyright
Copyright © Cambridge University Press 2008

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References

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