Modeling and Simulation of Physical Processes in Aerodynamic Plasma Actuator Dielectric Barrier Discharges

This work on the physics and modeling of the dielectric barrier discharge aerodynamic plasma actuator is being supported by the U. S. Air Force through the U. S. Air Force Academy. The device, measurements, and modeling results are described in References [1] – [6]. This device, which is shown schematically in Figures 1 and 2 induces the flow of air over the surface when a high voltage is applied between the electrodes.

Figure 1

Figure 2

Figure 3 is a photograph of the discharge which shows the diffuse glow as well as the streamers that are characteristic of dielectric barrier discharges. The figures were taken from References 1-4.

Figure 3

The physical processes involved in inducing the flow of air along the discharge are simple: charged particles moving with electric field in the partially ionized gas collide with neutral atoms and molecules transferring momentum that causes convective motion o the gas. It can be described in one dimension by Euler’s equation of hydrodynamics

u(z)du(z)/dz = F(z)/M = (dp/dt)N_i/M

where u(z) is the flow velocity, F(z) is the force, M is the mass density, N_i is the ion density, and dp/dt is the momentum transfer rate per ion.

This is not a new phenomenon. The equivalent process in a corona discharge, which is known variously as the ion wind, or corona wind, or electric wind, has been known since 1709. Analyses of the phenomenon date from 1899. A similar process in electrolytic liquids is known as electro-osmosis.

The difficult aspect of the modeling problem is calculating the force term, F(Z) in the 1-D form of Euler’s equation shown above. As can be seen in Figure 3, the plasma is not homogeneous. The stochastic streamers, or plasma filaments, which have radii of a fraction of a millimeter and lifetimes of a few nanoseconds, are surrounded by a more uniform diffuse glow. The discharge is, in addition, dynamic. Over the course of a given AC half cycle the discharge expands over the surface of the lower dielectric, below which lies the second electrode. There are, of course, issues concerning sheaths and the charging and discharging of the dielectric.

The plasma chemistry of N₂ is not terribly complicated but becomes more so with the addition of O₂. Adding water vapor increases the complexity greatly. Although the details of plasma chemistry in applications such as plasma processing, which make use of the metastable atomic and molecular states and radicals produced in the plasma, are very important, such details are not so important here. Of greatest importance are spatial and temporal densities of the electrons, positive ions, and negative ions. These provide the momentum that is transferred to the gas molecules.

Momentum will be imparted to the neutral gas from electrons and ions in the streamers, the sheaths, and the diffuse plasma. What fraction of the total force on the gas comes from these various parts of the discharge is a critical question

The model that we have been working with is one of streamers as d-function sources of electrons and ions in time and space. These charged particles are then transported into the bulk plasma by diffusion and drift. The electrons and ions persist in the ambient electric field long enough to transfer observable momentum to the surrounding gas. For a parallel plate dielectric barrier discharge the charged particle source function would be of the form

N_j(r,z,t) = N_j(z)Delta(r-r_i)Delta(t-t_k)

In the present configuration this model would have to become more complex due to the dynamic behavior of the plasma over the dielectric surface.

It may not be feasible to model this problem using the codes that are usually used for modeling gas discharges.

Because this is essentially a surface discharge, it may be feasible to model it in 2-D rather than 3-D. The force F(x, y) could then be calculated and used in a fluid dynamics code to calculate the fluid flow properties.

References [4] – [6] describe the Particle-in-Cell (PIC) and Direct-Simulation-Monte-Carlo (DSMC) modeling of streamer development in the plasma actuator.

This is on-going research. This web page will be updated periodically to reflect new developments.

References

[1] C. L. Enloe, et al., “Mechanisms and responses of a single dielectric barrier plasma”, AIAA (2003).

[2] C. L. Enloe, et al., “Plasma structure in the aerodynamic plasma actuator”, AIAA (2004).

[3] C. L. Enloe, et al., “Parameterization of temporal structure in the single dielectric barrier aerodynamic plasma actuator”, AIAA (2005).

[4] G. I. Font, “Boundary layer control with atmospheric discharges”, AIAA (2004).

[5] G. I. Font and W. L. Morgan, “Plasma discharges in atmospheric pressure oxygen for boundary layer control”, AIAA (2005).

[6] G. I. Font and W. L. Morgan, AIAA (2005) Power Point presentation.