Numerical Optimization of Boundary-Layer Control using Dielectric Barrier Discharge Plasma Actuators

Abstract

A numerical investigation of active wave cancellation, using a plasma actuator in both continuous and pulsed operation modes, was carried out for a flat-plate boundary layer with an adverse pressure gradient at low Reynolds number. Pulsing was achieved by rectangular and sinusoidal modulation of the high-frequency plasma excitation voltage. A closed-loop control was developed and implemented using Large-Eddy Simulations into a CFD code (FASTEST). With this feed-back control algorithm it was found that the control can be limited to two operating parameters in order to significantly reduce Tollmien-Schlichting waves (TS-waves). The feed-back control algorithm was validated using two existing optimization methods which were also implemented in the code. The first method finds a local minimum of a function with several variables using a pattern search technique that compares function values at the three vertices of a triangle. The second method, known as the trust-region method, is based on quadratic models for derivative-free minimization. It was found that the developed feed-back control works efficiently and can be used to determine the optimum operating parameters of the plasma actuator for cancellation of TS-waves. The amplitude reduction of TS-waves is of interest since it allows for a delay of laminar-to-turbulent transition in the boundary layer, resulting in significant drag reduction.