Feedback control of wall turbulence with wall deformation

Abstract

Abstract Direct numerical simulation of turbulent channel flow was made in order to evaluate feedback control with deformable walls. When the local wall velocity is determined by an active cancellation control scheme similar to that of Choi et al. (Choi, H., Moin, P., Kim, J., 1994. J. Fluid Mech. 262, 75–110), the drag is decreased by about 12% with the wall deformation of the magnitude on the order of one viscous length. On the basis of the typical dimensions of the wall deformation thus obtained, a novel array of deformable actuators elongated in the streamwise direction is proposed. A new realizable control scheme by using wall information is developed based on physical arguments of the near-wall coherent structures. The location of quasi-streamwise vortices accompanied with streak meandering is successfully detected about 50 viscous lengths downstream from the sensing location, at which the spanwise gradients of wall shear stresses are measured. The wall velocity of each actuator is determined to counteract the wall-normal velocity induced by the streamwise vortices. By the present control scheme with the arrayed sensors and actuators, 10% drag reduction is achieved through selective manipulation of the streamwise vortices and streak meandering. It is also found that the energy input of the present control is one order of magnitude smaller than the pumping power saved.