Application of reduced-order controller to turbulent flows for drag reduction

A reduced-order linear feedback controller is designed and applied to turbu lent channel flow for drag reduction. From the linearized two-dimensional N avier-Stokes equations a distributed feedback controller, which produces bl owing/suction at the wall based on the measured turbulent streamwise wall-s hear stress, is derived using model reduction techniques and linearquadrati c-Gaussian/loop-transfer-recovery control synthesis. The quadratic cost cri terion used for synthesis is composed of the streamwise wall-shear stress, which includes the control effort of blowing/suction. This distributed two- dimensional controller developed from a linear system theory is shown to re duce the skin friction by 10% in direct numerical simulations of a low-Reyn olds number turbulent nonlinear channel flow. Spanwise shear-stress variati on, not captured by the distributed two-dimensional controller, is suppress ed by augmentation of a simple spanwise ad hoc control scheme. This augment ed three-dimensional controller, which requires only the turbulent streamwi se velocity gradient, results in a further reduction in the skin-friction d rag. It is shown that the input power requirement is significantly less tha n the power saved by reduced drag. Other turbulence characteristics affecte d by these controllers are also discussed. (C) 2001 American Institute of P hysics.