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

Authors: Åkervik, E.Å., Hoepffner, J.P.J., Ehrenstein, U, Henningson, D.S.H.
Document Type: Article
Pubstate: Published
Journal: J. Fluid Mech.
Volume: 579   305-314
Year: 2007


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 are 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.