Friction drag reduction based on a proportional-derivative control scheme

Dielectric barrier discharge plasma actuators (DBD-PAs) are deployed experimentally for the first time in a feed-forward proportional-derivative (PD) control system, where the fluctuating wall-pressure Pw is demonstrated to be an effective feed-forward signal, to manipulate a turbulent boundary layer for drag reduction. A floating-element force balance with an area of 50 mm (streamwise length) × 200 mm (spanwise length) is deployed to capture the spatially averaged drag variation behind the DBD-PAs. The DBD-PAs generate streamwise vortices, whose occurrence synchronizes with the output signal of the controller with a predominant frequency of 40 Hz under the optimally tuned PD control. The control system proves to be effective, achieving a spatially averaged drag reduction by 16%, and efficient, cutting down its energy consumption by 30% at a negligibly small expense of drag reduction compared with the open-loop control. It has been found that the optimally tuned PD control aptly increases the voltage applied to the DBD-PAs upon detecting large Pw fluctuations or coherent structures, accounting for the savings in input power, Pinput. The experimental data have been carefully analyzed, which cast light upon the underlying physical mechanism behind the drag reduction. The reason behind the efficient control is also clearly elaborated.