

Article
Linear and nonlinear optimal control in spatial boundary layer
Authors: 
Chevalier, M.C., Högberg, M., Berggren, M, Henningson, D.S.H. 
Document Type: 
Conference 
Pubstate: 
Accepted 
Journal: 
AIAA 20022755 
Volume: 

Year: 
2002 
AbstractInstabilities in a spatiallydeveloping threedimensional boundary layers are controlled through blowing and suction at the wall. The performance of the control is tested in direct numerical simulations (DNS) of the incompressible NavierStokes equations for TollmienSchlichting (TS) waves, optimal transiently growing streaks in a Blasius boundary layer, and cross flow vortices in a FalknerSkanCooke (FSC) flow. Two control strategies are compared. First, a quasiNewton optimization algorithm is applied to solve an offline optimal control problem. A solver for the adjoint equations has been implemented in the spectral DNS code used. This method adapts naturally, without modification, to nonlinearities such as a strongly varying mean flow. However, it is computationally expensive and storage demanding, needing numerous solves of the NavierStokes and associated adjoint equations. Second, feedback optimal control is applied, using a strategy designed to operate locally on a spatiallydeveloping flow. The feedback operator is constructed from the OrrSommerfeldSquire equations. Assuming the flow to be locally parallel makes it feasible to solve the associated Riccati equations for each wave number pair in the stream and spanwise directions. The feedback is applied to a DNS of the flows mentioned above. This method is much less computationally costly than the first nonlinear method. The method performs surprisingly well, in spite of the limitations with respect to being able to account for strong nonlinear effects. It is demonstrated that TS waves are stabilized and that transient growth is considerably lowered by the controller. Moreover, the controller successfully inhibits growth of steady cross flow vortices in the FSC flow.

