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Optimal control of a separated boundary-layer flow over a bump

Published online by Cambridge University Press:  12 February 2018

Pierre-Yves Passaggia Open the ORCID record for Pierre-Yves Passaggia [Opens in a new window]  and
Uwe Ehrenstein
Pierre-Yves Passaggia*
Affiliation:
Department of Marine Sciences, University of North Carolina, Chapel Hill, NC 27599, USA
Uwe Ehrenstein
Affiliation:
Aix-Marseille Univ, CNRS, Centrale Marseille, M2P2, Marseille, France
*
†Email address for correspondence: [email protected]
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Abstract

The optimal control of a globally unstable two-dimensional separated boundary layer over a bump is considered using augmented Lagrangian optimization procedures. The present strategy allows for controlling of the flow from a fully developed nonlinear state back to the steady state using a single actuator. The method makes use of a decomposition between the slow dynamics associated with the base flow modification and the fast dynamics, known as flapping, characterized by a large scale oscillation of the recirculation region. Starting from a steady state forced by a suction actuator located near the separation point, the base flow modification is shown to be controlled by a vanishing suction strategy. For weakly unstable flow regimes, this control law can be further optimized by means of direct–adjoint iterations of the nonlinear Navier–Stokes equations. In the absence of external noise, this novel approach proves to be capable of controlling the transient dynamics and the base flow modification simultaneously.

JFM classification

Boundary Layers: Boundary layer separation Flow Control: Flow Control Flow Control: Instability control
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 840 , 10 April 2018 , pp. 238 - 265
Copyright
© 2018 Cambridge University Press 

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