Frequency-Dependent Capacitance-Based Plasma Model for Direct Simulation of Navier–Stokes Equation

Abstract

The effects of single dielectric barrier discharge plasma actuators on flow control are studied using a new frequency and pressure-dependent capacitance-based model by calculating the spatiotemporal distribution of surface charge density in the present work. The proposed model is an improvement over earlier similar efforts, but it retains the superior features of previous macroscopic models. It can be used to accurately compute the spatiotemporal distribution of body force due to plasma actuation without computing the complex electrodynamics equations for charge density on microscopic scales. It has been shown that the proposed model estimates the time-averaged total body force more accurately than similar models developed earlier, as compared to experimental results. The effects of plasma excitation frequency and the voltage waveform were considered. The proposed model has been incorporated into a Navier–Stokes equation solver in a time-accurate manner to study single dielectric barrier discharge plasma actuation in a quiescent flow environment. The onset of plasma actuation causes the creation of a complex transient vortical flowfield: one of its actions is to create a wall jet. Computed instantaneous velocity profiles at downstream locations show this wall jet, and they are compared with the experimental results. The computed results of the evolution of a starting vortex in a quiescent air induced by initiation of single dielectric barrier discharge plasma actuation display an excellent match with the experimental results of Whalley and Choi (“The Starting Vortex in Quiescent Air Induced by Dielectric-Barrier-Discharge Plasma,” Journal of Fluid Mechanics, Vol. 55, July 2012, pp. 192–203).