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Linear feedback control and estimation applied to instabilities in spatially developing boundary layers

Published online by Cambridge University Press:  24 September 2007

MATTIAS CHEVALIER ,
JÉRÔME HŒPFFNER ,
ESPEN ÅKERVIK  and
DAN S. HENNINGSON
MATTIAS CHEVALIER
Affiliation:
The Swedish Defence Research Agency (FOI), SE-164 90, Stockholm, Sweden Linné Flow Centre, KTH Mechanics, SE-100 44, Stockholm, Sweden
JÉRÔME HŒPFFNER
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44, Stockholm, Sweden
ESPEN ÅKERVIK
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44, Stockholm, Sweden
DAN S. HENNINGSON
Affiliation:
The Swedish Defence Research Agency (FOI), SE-164 90, Stockholm, Sweden Linné Flow Centre, KTH Mechanics, SE-100 44, Stockholm, Sweden
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Abstract

This paper presents the application of feedback control to spatially developing boundary layers. It is the natural follow-up of Högberg & Henningson (J. Fluid Mech. vol. 470, 2002, p. 151), where exact knowledge of the entire flow state was assumed for the control. We apply recent developments in stochastic models for the external sources of disturbances that allow the efficient use of several wall measurements for estimation of the flow evolution: the two components of the skin friction and the pressure fluctuation at the wall. Perturbations to base flow profiles of the family of Falkner–Skan–Cooke boundary layers are estimated by use of wall measurements. The estimated state is in turn fed back for control in order to reduce the kinetic energy of the perturbations. The control actuation is achieved by means of unsteady blowing and suction at the wall. Flow perturbations are generated in the upstream region in the computational box and propagate in the boundary layer. Measurements are extracted downstream over a thin strip, followed by a second thin strip where the actuation is performed. It is shown that flow disturbances can be efficiently estimated and controlled in spatially evolving boundary layers for a wide range of base flows and disturbances.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 588 , 10 October 2007 , pp. 163 - 187
Copyright
Copyright © Cambridge University Press 2007

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