Numerical Modelling of Dielectric Barrier Discharge Plasma Actuators

Dielectric Barrier Discharge plasma actuators are one of the most promising techniques of active flow control. They act by ionizing the air around them and generating a body force on the fluid which can be used to manipulate the airflow. Due to their many advantages, most of all their capability of inducing a self-limiting discharge, DBDs have multiple applications in aerodynamics, from delaying flow separation to enhancing jet mixing. Despite the interest that these actuators have drawn in the last couple of decades, the phenomena that they generate are not fully understood. Because of this, many models have been developed to study their operation. These models can be either phenomenological if they focus on the effect that the actuator has on the airflow, or first-principles based if they focus on the processes of plasma creation and evolution. In this thesis, we present a physical and chemical model for DBDs, based on the coupling between a Boltzmann Equation for electron energy distribution and a system of continuity equations for charged particles in their Drift-Diffusion approximation. A Local Field Approximation is applied to simplify the computation of transport and chemical properties, while only the most relevant chemical processes have been considered. A numerical scheme to solve such model is then described, with reflections on temporal scales and explicit and implicit methods. Finally, a collection of significant results is presented for the classical DBD configuration, known as Single-Dielectric Barrier Discharge actuator. A number of interesting parameters are computed and discussed, such as charge density, electric potential, and the body force exerted on the external flow, in order to understand the operational process of DBDs and the influence that input parameters, such as voltage and the relative dielectric constant, have on these actuators.