Modelling of a nanosecond surface discharge actuator

Abstract

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 m s−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.