Laminar Boundary-Layer Response to Step Input by an Array of Plasma Actuators

Abstract

A spanwise array of streamwise oriented plasma actuators are simulated in a laminar boundary layer to examine the flow response to a step change in the forcing. The spatial distribution and magnitude of the modeled body force applied in the simulation are calibrated to an experimental dataset for both steady and unsteady flows. When the actuator forcing undergoes a step change from off to on, it is found that the flow response downstream of the actuators is initially inverted in terms of the streamwise vorticity, disturbance velocity, and wall shear stress before approaching the steady-state behavior. This behavior to a step change in actuator forcing, known as a nonminimum phase response, is consistent with the experimental data. At planes downstream of the actuators, the peak streamwise vorticity propagates toward the wall after the actuators are activated, which is consistent with a tilted structure in the boundary layer. Between the locations where the vorticity enters the downstream plane and the wall, a region of secondary streamwise vorticity of the opposite sense is found. This secondary streamwise vorticity causes the inverted disturbance velocity and shear during the off-to-on portion of the cycle. In addition, a starting vortex, which is generated above the steady wall jets produced by the actuators, leads to a peak output in the intensity of the streamwise vortices generated when the actuators are activated.