22P045-P
Numerical Simulation of Discharge Processes in DBD Plasma Actuator
DBD プラズマアクチュエータにおける電離過程の数値シミュレーション
Kazuya Sugimoto, Shoichi Ebato, and Naofumi Ohnishi
杉本和弥, 江波戸翔一, 大西直文
Department of Aerospace Engineering, Tohoku University
6-6-01 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, Japan東北大学大学院工学研究科航空宇宙工学専攻 〒 980-8579 仙台市青葉区荒巻字青葉 6-6-01
We have developed a numerical code based on PIC-MCC method to study flow generation mechanism in a dielectric barrier discharge (DBD) plasma actuator. Two-dimensional simulations of unsteady discharge processes were conducted with constant applied voltages. When a exposed electrodeis negatively biased against a buried electrode, charged particles are generated on the dielectric surface
because of electron avalanche, distort electric potential distribution, and spread as surrounding the exposed electrode. In the case of positively biasing, an ion cloud is generated on the exposed electrodeand spreads to a direction of the buried electrode followed by the plasma. The momentum coupling
between ions and neutrals primarily generates the force.
1. IntroductionRecently, applications of plasma flow have beenstudied for flow control and development of propulsion technique. A dielectric barrier discharge (DBD)
plasma actuator is one of the most popular applications and consists of two electrodes placed parallel toeach other [1–3]. One electrode is covered with a dielectric while the other is exposed to the flow. When asuﬃciently high voltage is applied between two electrodes, electrons are accelerated and aﬀect the surrounding electric field because of their charge. If theaccelerated electrons collide with suﬃcient energy,
activated neutrals can release new free electrons. The
newly created electrons are accelerated in the electric field and lead further ionization, so-called electron avalanche. A considerable number of ions are
created through the above process and also are accelerated.
The ions transfer their momenta to the neutrals
through elastic collisions, and the flow is induced.
However, some characteristics in the discharge processes have not been cleared completely yet. So, we
aim to find a dominant factor in the discharge processes in the DBD plasma actuator. In this paper, wehave numerically analyzed plasma formation process
and force generation mechanism.
2. Numerical Methods
In order to estimate a plasma flow in the DBD
plasma actuator, we should properly model the discharge processes with elastic and inelastic collisions.
Generally, the assumption of thermal equilibrium or
chemical equilibrium does not work out in the flow ofthe plasma actuator. Therefore, we employ ParticleIn-Cell (PIC) method to estimate the interaction between plasma and electric field, and simultaneously,
Monte Carlo Collision (MCC) method to estimate
the interaction between plasma and neutrals. In thePIC method, motions of charged particles which arelocated in each computational cell are solved withsome cell-assigned quantities representing electricfield. The governing equations are as follows:
dx
= qE,
dt
∇ · D = −ρ,D = εE,m(1)(2)(3)where m is the mass of particle, q is the particle
charge, and ρ is the charge density. In the present
paper, the electrostatic field is only considered, so wesolve Poisson equation for the electric potential. The
charge density is calculated with the particle positionand the particle charge. In the MCC method, many
sample particles are used, and the change of particle
velocity through collisions are estimated at each time
step in a stochastic manner.
3. Simulation Conditions and Results
We have performed particle dynamics in theDBD plasma actuator using the developed twodimensional code. The plasma actuator is modeled
in a rectangular domain. It consists of two electrodes separated by a dielectric. The exposed electrode is 0.5-mm thickness and 0.25-mm length, andthe buried electrode is 0.2-mm thickness and 1.25-4. Summary
We have modeled a DBD plasma actuator withsome representative reactions and developed a twodimensional numerical code to examine discharge
dynamics in it. Discharge processes were performed

y-position (mm)18×10 /m3

2.0

Exposed electrode

1.5

Buriedelectrode1.00-5

Dielectric
000.5

105

0.5-10
1.0

1.5

2.0

x-position (mm)Fig. 1 Net charge density at t =1.0 ns in the caseof negative voltage input.
183×10 /m

2.0

y-position (mm)mm length. 600×600 computational cells are used
for covering this domain. The buried electrode is set
to be ground, while on the exposed electrode, constant voltage is applied. Since the buried electrodeis covered with the dielectric, electrons are accumulated on it. The relative permittivity of the dielectric
layer is set as 2.7 of the value of Kapton. Secondary
electron emission coeﬃcient is set to be 0.3. The exposed electrode assumed as the complete absorption
boundary on which all electrons are absorbed, and allions become neutrals.
In order to study the discharge processes, we simulate direct current discharge in nitrogen gas using ourcode. When −3000 V is applied as a negative constant voltage input on the exposed electrode, a large
number of electrons are created and accumulated on
the dielectric. The electric potential is distorted dueto the high net charge density on the dielectric surface. The distorted potential generates high electric field intensity at the edge of the plasma. Electrons can be accelerated by the generated high electric field intensity. Since the electron avalanche iseasily caused in the region of the high electric field,
the plasma spreads as surrounding the exposed electrode (Fig. 1). Since it is one of the characteristics
of glow discharge, the discharge process in the caseof negative voltage is considered as glow-type discharge.
Next, on the exposed electrode, +3000 V is applied
as a positive constant voltage input. In this case, electrons are accelerated to the exposed electrode withleading the electron avalanche. On the exposed electrode, the electrons are absorbed, so the ion-rich region is generated on the surface of the exposed electrode. This ion-rich region is called as ion cloud anddistorts the electric potential. The region of high electric field intensity moves with the ion cloud toward
the right side of Fig. 2, and the plasma spreads byfollowing the ion cloud. Since it is one of the characteristics of streamer discharge, the discharge process in the case of positive voltage is considered asstreamer-type discharge.
The charged particles transfer their momenta to theneutrals via elastic collisions. In force generation
process, ion-neutral momentum coupling is dominantbecause of larger mass of the ion relative to the electron.

Exposed electrode

1.55Buried
electrode

1.0

1000.5-5

Dielectric
000.5

1.0

1.5

2.0-10x-position (mm)Fig. 2 Net charge density at t =1.0 ns in the caseof positive voltage input.

for the case of negative and positive voltages applied
to the exposed electrode. In the negative voltage case,though the region of high net charge density spreads
due to the electron avalanche, high electric field intensity in the vicinity of the exposed electrode ismaintained. On the other hand, in the positive voltage
case, after the ion cloud is generated in the vicinity ofthe exposed electrode, the region of high electric field
intensity moves with the ion cloud. The momentum
coupling between ions and neutrals primarily generates the force.
References[1] G. I. Font, “Boundary Layer Control with Atmospheric Plasma Discharge,” AIAA Paper
2004-3574, 2004.
[2] G. I. Font, “Plasma Discharge Characteristics and Experimentally Determined BoundaryConditions for a Plasma Actuator,” AIAA Paper
2007-188, 2007.
[3] T. C. Corke, “Numerical Simulation of Aerodynamic Plasma Actuator Eﬀects,” AIAA Paper
2005-1083, 2005.