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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

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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.

Information

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

References

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