Modelling of a nanosecond surface discharge actuator

Surface dielectric barrier discharges (SDBDs) can modify the boundary layer of a flow and are studied as a possible means to control the flow over an airfoil. In SDBDs driven by sinusoidal voltages in the 1-10 kHz range, momentum is transferred from ions to the neutral gas, as in a corona discharge (ion wind), and the resulting electrohydrodynamic force can generate a flow of several ms(-1) in the boundary layer along the surface. In this paper we are interested in a different regime of SDBDs where nanosecond voltage pulses are applied between the electrodes. Recent experiments by the group of Starikovskii have demonstrated that such discharges are able to modify a flow although no significant ion wind can be detected. A two-dimensional self-consistent numerical model of the discharge and gas dynamics in conditions similar to those of these experiments has been developed. The model couples fluid discharge equations with compressible Navier-Stokes equations including momentum and thermal transfer from the plasma to the neutral gas. This is a difficult multi-scale problem and special care has been taken to accurately solve the equations over a large simulation domain and at a relatively low computational cost. The results show that under the conditions of the simulated experiments, fast gas heating takes place in the boundary layer, leading to the generation of a 'micro' shock wave, in agreement with the experiments.