On the Possibility of Cross-Flow Vortex Cancellation by Plasma Actuators

Abstract

Cancellation of the cross-flow vortices in a swept-wing boundary layer is attempted by plasma actuator array in numerical simulation. The response of the boundary layer to the stationary excitation by a single actuator section is measured experimentally and compared to the response obtained from the solution to the parabolized stability equations. A linear approach is shown to be held within the peak-to-peak magnitude of the stationary cross-flow vortices below 10% of the local potential flow velocity. Within the linear model, an optimal control strategy and a faster suboptimal one are developed to calculate voltage amplitude distribution across the electrodes, taking into account the forcing constraints. Simulation of the cancellation process is performed, showing up to a 20 dB reduction in the initial spanwise velocity modulation in the boundary layer. The minimal actuator resolution required for the successive implementation of the control is shown to be in the order of a quarter of the most amplified wavelength, or 3–4 displacement thickness of the boundary layer. Linear estimates predict up to a 150 mm (22% of flow acceleration region length) transition delay for an actuator momentum coefficient of 0.005%.

Keywords

• cross-flow instability
• laminar–turbulent transition
• plasma actuator
• dielectric barrier discharge
• control theory