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Spatially distributed control for optimal drag reduction of the flow past a circular cylinder

Published online by Cambridge University Press:  06 March 2008

PHILIPPE PONCET ,
ROLAND HILDEBRAND ,
GEORGES-HENRI COTTET  and
PETROS KOUMOUTSAKOS
PHILIPPE PONCET
Affiliation:
Université de Toulouse, INSA, GMM 135 avenue de Rangueil, F-31077 Toulouse, France CNRS, Institut de Mathématiques de Toulouse, Equipe MIP, F-31077 Toulouse, France
ROLAND HILDEBRAND
Affiliation:
Laboratoire Jean Kuntzmann, CNRS and Université de Grenoble, BP 53, F-38041 Grenoble, France
GEORGES-HENRI COTTET
Affiliation:
Laboratoire Jean Kuntzmann, CNRS and Université de Grenoble, BP 53, F-38041 Grenoble, France
PETROS KOUMOUTSAKOS
Affiliation:
Computational Science, ETH Zurich, CH-8092, Switzerland
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Abstract

We report high drag reduction in direct numerical simulations of controlled flows past circular cylinders at Reynolds numbers of 300 and 1000. The flow is controlled by the azimuthal component of the tangential velocity of the cylinder surface. Starting from a spanwise-uniform velocity profile that leads to high drag reduction, the optimization procedure identifies, for the same energy input, spanwise-varying velocity profiles that lead to higher drag reduction. The three-dimensional variations of the velocity field, corresponding to modes A and B of three-dimensional wake instabilities, are largely responsible for this drag reduction. The spanwise wall velocity variations introduce streamwise vortex braids in the wake that are responsible for reducing the drag induced by the primary spanwise vortices shed by the cylinder. The results demonstrate that extending two-dimensional controllers to three-dimensional flows is not optimal as three-dimensional control strategies can lead efficiently to higher drag reduction.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 599 , 25 March 2008 , pp. 111 - 120
Copyright
Copyright © Cambridge University Press 2008

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