Journal of Fluid Mechanics

Papers

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

ESPEN ÅKERVIKa1, JÉRÔME HŒPFFNERa1, UWE EHRENSTEINa2 and DAN S. HENNINGSONa1

a1 Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden

a2 IRPHÉ, Université de Provence, F-13384 Marseille Cedex 13, France

Abstract

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.

(Received October 31 2006)

(Revised February 13 2007)

Metrics