New Frequency Dependent Capacitance Based SDBD Plasma Model for Direct Simulation of 2D Navier-Stokes Equation

Abstract

The effects of single dielectric barrier discharge (SDBD) plasma actuators on flow control are studied using a new frequency and pressure dependent capacitance based model by calculating the spatio-temporal distribution of surface charge density in the present work. The proposed model is an improvement over earlier similar efforts, while retaining the superior features of previous macroscopic models. It can be used to accurately compute the spatio-temporal 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. We have also considered the effects of plasma excitation frequency and the voltage wave-form. The proposed model has been incorporated into a Navier-Stokes equation (NSE) solver in time-accurate manner to study SDBD plasma actuation in a quiescent flow environment. The onset of plasma actuation causes creation of a complex transient vortical flow field, one of its actions is to create a wall-jet. Computed instantaneous velocity profiles at downstream locations show this wall-jet and are compared with the experimental results. Computed results of the evolution of a starting vortex in a quiescent air induced by initiation of SDBD plasma actuation, displays an excellent match with experimental results of Whalley and Choi (J. Fluid Mech., 703, 192-203, 2012).