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Optimal growth, model reduction and control in a separated boundary-layer flow using global eigenmodes

Published online by Cambridge University Press:  02 May 2007

ESPEN ÅKERVIK ,
JÉRÔME HŒPFFNER ,
UWE EHRENSTEIN  and
DAN S. HENNINGSON
ESPEN ÅKERVIK
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
JÉRÔME HŒPFFNER
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
UWE EHRENSTEIN
Affiliation:
IRPHÉ, Université de Provence, F-13384 Marseille Cedex 13, France
DAN S. HENNINGSON
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
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Abstract

Two-dimensional global eigenmodes are used as a projection basis both for analysing the dynamics and building a reduced model for control in a prototype separated boundary-layer flow. In the present configuration, a high-aspect-ratio smooth cavity-like geometry confines the separation bubble. Optimal growth analysis using the reduced basis shows that the sum of the highly non-normal global eigenmodes is able to describe a localized disturbance. Subject to this worst-case initial condition, a large transient growth associated with the development of a wavepacket along the shear layer followed by a global cycle related to the two unstable global eigenmodes is found. The flow simulation procedure is coupled to a measurement feedback controller, which senses the wall shear stress at the downstream lip of the cavity and actuates at the upstream lip. A reduced model for the control optimization is obtained by a projection on the least stable global eigenmodes, and the resulting linear-quadratic-Gaussian controller is applied to the Navier–Stokes time integration. It is shown that the controller is able to damp out the global oscillations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 579 , 25 May 2007 , pp. 305 - 314
Copyright
Copyright © Cambridge University Press 2007

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