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

Authors: Chevalier, M.C., Hoepffner, J.P.J., Åkervik, E.Å., Henningson, D.S.H.
Document Type: Article
Pubstate: Submitted
Journal: J. Fluid Mech.
Volume: 588   163-187
Year: 2007


This paper presents the application of feedback control to spatially developing boundary layers. It is the natural follow-up of Högberg and Henningson (2001), where exact knowledge of the entire flow state was assumed for control. We apply recent developments stochastic models for the external sources of disturbances that allow the efficient use of several wall measurement 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 at the upstream region in the computational box and are propagating in the boundary layer. Measurement 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.