Feedback control of slowly-varying transient growth by an array of plasma actuators

Abstract

Closed-loop feedback control of boundary layer streaks embedded in a laminar boundary layer and experiencing transient growth, which is inherent to bypass boundary layer transition, is experimentally investigated. Streaky disturbances are introduced by a spanwise array of cylindrical roughness elements, and a counter disturbance is provided by a spanwise array of plasma actuators, which are capable of generating spanwise-periodic counter rotating vortices in the boundary layer. Feedback is provided by a spanwise array of shear stress sensors. An input/output model of the system is obtained from measurements of the boundary layer response to steady forcing, and used to design and analyze a proportional-integral controller, which targets a specific spanwise wavenumber of the disturbance. Attention is directed towards a quasi-steady case in which the controller update is slower than the convective time scale. This choice enables addressing issues pertinent to sensing, actuation, and control strategy that are also relevant to the control of unsteady disturbances but without the full complexity of transient effects. The feedback controller and plasma actuators perform well, attenuating the streamwise streaks both in the vicinity of the sensors and farther downstream. The controller remains effective for a range of off-design flow conditions, such as when the free-stream velocity is varied.