

Article
Optimal growth, model reduction and control in a separated
boundarylayer 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
305314 
Year: 
2007 
AbstractTwodimensional global eigenmodes are used as a projection basis both for analysing the dynamics and building a reduced model for control in a prototype separated boundarylayer flow. In the present configuration, a high aspect ratio smooth cavitylike geometry confines the separation bubble. Optimal growth analysis using the reduced basis shows that the sum of the highly nonnormal global eigenmodes are able to describe a localized disturbance. Subject to this worstcase 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 linearquadraticgaussian controller is applied to the NavierStokes time integration. It is shown that the controller is able to damp out the global oscillations.

