Richard B. Miles and Mikhail N. Shneider

Princeton University, Princeton, New Jersey

Plasma Actuators for Turbomachinery Flow Control

Final Report 

NASA/CR—2012-217654

September 2012

Notice for Copyrighted Information 

This manuscript has been authored by employees of the Princeton University under Cooperative Agreement No. NNX07AC02A 

with the National Aeronautics and Space Administration and the Lockheed Martin Corporation. The United States Government 

has a nonexclusive, irrevocable, worldwide license to prepare derivative works, publish or reproduce this manuscript, and 

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Richard B. Miles and Mikhail N. Shneider

Princeton University, Princeton, New Jersey

Plasma Actuators for Turbomachinery Flow Control

Final Report 

NASA/CR—2012-217654

September 2012

Notice for Copyrighted Information 

This manuscript has been authored by employees of the Princeton University under Cooperative Agreement No. NNX07AC02A 

with the National Aeronautics and Space Administration and the Lockheed Martin Corporation. The United States Government 

has a nonexclusive, irrevocable, worldwide license to prepare derivative works, publish or reproduce this manuscript, and 

allow others to do so, for United States Government purposes. Any publisher accepting this manuscript for publication 

acknowledges that the United States Government retains such a license in any published form of this manuscript. All other 

rights are retained by the copyright owner. 

National Aeronautics and

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Prepared under Cooperative Agreement No. NNX07AC02A 
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Trade names and trademarks are used in this report for identifi cation 

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Acknowledgments

The authors express their appreciation to David E. Ashpis of the NASA Glenn Research Center for serving as the Grant 

Technical Monitor. His support and deep involvement in the project, useful discussions, input, and suggestions 

contributed greatly to the project.
Plasma Actuators for Turbomachinery Flow Control 

Final Report 

Richard B. Miles and Mikhail N. Shneider 

Princeton University 

Princeton, New Jersey 08544 

Summary 

Work completed under this NASA Grant and Cooperative Agreement was focused on of the 

operation of surface dielectric barrier discharge devices driven by high voltage, nanosecond scale pulses 

plus constant or time varying applied bias voltages. The main interest was in momentum production and 

the range of voltages applied eliminated significant heating effects. The approach was experimental 

measurements and was supplemented by computational modeling. All the experiments were conducted at 

Princeton University. NASA funding supported mainly the experimental work while the computational 

work was supported by other sources. Most of the computational work was conducted at Princeton 

University and was completed at the Pennsylvania State University. 

The project provided comprehensive understanding of the associated physical phenomena achieved 

by complementary measurements and modeling. Limitations on the performance of the devices for the 

generation of high velocity surface jets were established and various means for overcoming those 

limitations were proposed and tested. The major limitations included the maximum velocity limit of the 

jet due to electrical breakdown in air and across the dielectric, the occurrence of backward breakdown 

during the short pulse causing reverse thrust, the buildup of surface charge in the dielectric offsetting the 

forward driving potential of the bias voltage, and the interaction of the surface jet with the surface through 

viscous losses. It was also noted that the best performance occurred when the nanosecond pulse and the 

bias voltage were of opposite sign. Solutions include the development of partially conducting surface 

coatings to bleed off the surface charge, the development of a semiconductor diode inlaid surface material 

to suppress the backward breakdown. Extension to long discharge channels was studied and a new ozone 

imaging method developed for more quantitative determination of surface jet properties. 

Details of the work are given in publications and a Ph.D. thesis. A list is provided below. Reprints of 

archival journal articles are attached in the Appendix. The dissertation is provided as Part II of this final 

report and is published separately as NASA/CR—2012-217655. 

Research Personnel 

Personnel supported under this Grant and Cooperative Agreement include 

Graduate students: 

Dmitry F. Opaits, Ph.D. completed September, 2010 

Research Staff: 

Dr. Mikhail N. Shneider (partial support) 

Dr. Sohail Zaidi (partial support) 

Subcontract (to Lockheed Martin Corporation): 

Dr. Sergey Macheret (partial support) 

NASA/CR—2012-217654 1
Technical staff: 

Mr. Philip Howard (partial support) 

Faculty: 

Prof. Richard B. Miles (partial summer) 

The grant and cooperative agreement included a subcontract to Lockheed Martin Corporation for the 

partial support of Dr. Sergey Macheret who provided advice on the physics of the interaction of the 

dielectric barrier discharge with the surrounding air and on the modeling of those processes. He was 

initially at Princeton and a co-Principal Investigator on the proposal which was submitted in 2006, but left 

Princeton prior to the initiation of the award. He continued his participation through the subcontract. 

Another graduate student who worked on the project while at Princeton University was Dr. Alexandre 

Likhanskii. His financial support came from other sources, but was he advised and guided by Princeton 

University faculty and research staff that were partially supported by this NASA grant. His work was 

completed at The Pennsylvania State University. 

Publications 

The results have been reported in numerous peer reviewed and conference manuscript publications, 

and are contained in a doctoral dissertation. 

The archival journal papers are included in the Appendix of this report. 

The conference papers have not been included in this report since the material presented in those 

papers is incorporated into the peer reviewed publications and the dissertations of Dr. Opaits and 

Dr. Likhanskii. 

Doctoral Dissertations 

1. Dmitry Florievich Opaits “Dielectric Barrier Discharge Plasma Actuator for Flow Control,” Ph.D. 

Dissertation, Princeton University, September 2010. 

The Doctoral dissertation of Dr. Opaits is included as Part II of this report (published separately as 

NASA/CR—2012-217655). 

2. Alexandre Likhanskii “Study of Plasma Phenomena at High Electric Fields in Applications for Active 

Flow Control and Ultra-Short Pulse Laser Drilling,” Ph.D. Dissertation, The Pennsylvania State 

University, August 2009. 

The Doctoral dissertation of Dr. Likhanskii is available from The Pennsylvania State University. 

List of Peer-Reviewed Archival Journal Publications 

1. A. Likhanskii, M. Shneider, S. Macheret, R. Miles, Modeling of dielectric barrier discharge plasma 

actuators driven by repetitive nanosecond pulses, Physics of Plasmas, Vol. 14, 073501, 2007. 

2. D.F. Opaits, A.V. Likhanskii, G. Neretti, S. Zaidi, M.N. Shneider, R.B. Miles and S.O. Macheret, 

“Experimental Investigation of Dielectric Barrier Discharge Plasma Actuators Driven by Repetitive 

High-Voltage Nanosecond Pulses with DC or Low Frequency Sinusoidal Bias,” Journal of Applied 

Physics, Vol. 104, Issue 4, Article number 043304 (2008). 

NASA/CR—2012-217654 2
3. A. Likhanskii, M. Shneider, S. Macheret, R. Miles, “Modeling of dielectric barrier discharge plasma 

actuator in air,” Journal of Applied Physics, Vol. 103, 053305, 2008. 

4. D.F. Opaits, M.N. Shneider, R.B. Miles, “Surface Charge in Dielectric Barrier Discharge Plasma 

Actuators,” Physics of Plasmas, Volume 15, Issue 7, Article Number: 073505 (July 2008). 

5. D.F. Opaits, M.N. Shneider, R.B. Miles, “Electrodynamic effects in nanosecond-pulse sustained long 

dielectric-barrier-discharge plasma actuators,” Applied Physics Letters, Volume 94, Issue 6, Article 

Number: 061503 (Feb 9, 2009). 

6. R.B. Miles, D.F. Opaits, M.N. Shneider, S.H. Zaidi, and S.O. Macheret, Non-thermal atmospheric 

pressure plasmas for aeronautic applications, Eur. Phys. J. Appl. Phys. Vol. 47, 22802 (2009). 

List of Conference Manuscripts 

Conference manuscripts published under this Grant and Cooperative Agreement include 

1. D.F. Opaits, G. Neretti, A.V. Likhanskii, S. Zaidi, M.N. Shneider, R.B. Miles, and S.O. Macheret, 

“Experimental Investigation of DBD Plasma Actuators Driven by Repetitive High Voltage 

Nanosecond Pulses with DC or Low Frequency Sinusoidal Bias,” AIAA-2007-4532, 38th Plasma 

Dynamics and Lasers Conference, Miami, FL, 25-28 June 2007. 

2. A.V. Likhanskii, M.N. Shneider, D.F. Opaits, R.B. Miles, and S.O. Macheret, “Numerical Modeling 

of DBD Plasma Actuators and the Induced Air Flow,” AIAA-2007-4533, 38th Plasma Dynamics and 

Lasers Conference, Miami, FL, 25-28 June 2007. 

3. D. Opaits, G. Neretti, S. Zaidi M. Shneider, and R.B. Miles, Princeton University, Princeton, NJ; A. 

Likhanskii, Penn State University, University Park, PA and S. Macheret, Lockheed Martin, Palmdale, 

CA “DBD Plasma Actuators Driven by a Combination of Low Frequency Bias Voltage and 

Nanosecond Pulses,” AIAA-2008-1372, AIAA Aerospace Sciences Meeting, Reno, Nevada, Jan 7-

10, 2008. 

4. A. Likhanskii, V. Semak, M. Shneider, D. Opaits, R. Miles, S. Macheret, Parallel Code Development 

and Numerical Investigation of Surface Charge Build-Up in DBD Plasma Actuators, AIAA-2008-

1380, 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, Jan. 7-10, 2008. 

5. A. Likhanskii, V. Semak, M. Shneider, D. Opaits, R. Miles, S. Macheret, Multiprocessor Modeling of 

DBD Plasma Actuator, AIAA-2008-4284 38th Fluid Dynamics Conference and Exhibit, Seattle, 

Washington, June 23-26, 2008. 

6. R.B. Miles, D. Opaits, M.N. Shneider, S.H. Zaidi, “Non-Thermal Atmospheric Pressure Plasmas for 

Aeronautic Applications,” HAKONE XI Oleron Island, September 7-12, 2008. 

7. D. Opaits, M. Shneider, A. Likhanskii, S. Zaidi, Princeton University, Princeton, NJ; S. Macheret, 

and R. Miles, “Improving Thrust by Suppressing Charge Build- Up in Pulsed DBD Plasma 

Actuators,” AIAA-2009-487, 47th AIAA Aerospace Sciences Meeting, Orlando, FL, Jan 5-9, 2009. 

8. A. Likhanskii, V. Semak, D. Opaits, M. Shneider, R. Miles, S. Macheret, The role of the 

photoionization in the numerical modeling of the DBD plasma actuator, AIAA-2009-841, 47th AIAA 

Aerospace Sciences Meeting and Exhibit, Orlando, Florida, Jan. 5-8, 2009. 

NASA/CR—2012-217654 3
9. D. Opaits, A. Likhanskii, S. Zaidi, M. Shneider, S. Macheret, R. Miles, “Suppression of Dielectric 

Barrier Discharge Charge Build up Using a Partially Conducting Thin Film,” AIAA-2009-4189, 39th 

AIAA Fluid Dynamics Conference, San Antonio, Texas, June 22-25, 2009. 

10. A. Likhanskii, Tech-X, Boulder, CO; M. Shneider and D. Opaits, Princeton University, Princeton, 

NJ; S. Macheret, Lockheed Martin Corporation, Palmdale, CA; and R. Miles, Princeton University, 

Princeton, NJ, Limitations of the DBD effects on the external flow AIAA-2010-470, 48th AIAA 

Aerospace Sciences Meeting, Orlando, FL, Jan 4-7, 2010. 

11. D. Opaits, S. Zaidi, R. Miles, and M. Shneider, Princeton University, Princeton, NJ; A. Likhanskii, 

Tech-X Corporation, Boulder, CO; M. Edwards, Princeton university, Princeton, NJ; S. Macheret, 

Lockheed Martin Corporation, Palmdale, CA, Surface plasma induced wall jets, AIAA-2010-469, 

48th AIAA Aerospace Sciences Meeting, Orlando, FL, Jan 4-7, 2010. 

12. R.B. Miles, “Limitations and Potential of flow Control with Dielectric Barrier Discharges” Lecture 

Series Notes for Von Karman Institute Lectures Flow Control Meeting, February 21-24, 2011. 

Other Conference Proceedings 

1. D. Opaits, S. Zaidi, M. Shneider, R. Miles, A. Likhanskii, S. Macheret, Parametric studies on thrust 

produced by pulsed DBD plasma actuators, American Physical Society, 61th Gaseous Electronics 

Conference, Dallas, TX, October 13-17, 2008, abstract BAPS.2008.GEC.GW1.4. 

2. A. Likhanskii, V. Semak, D. Opaits, M. Shneider, S. Macheret, Multiprocessor Modeling of 

Dielectric Barrier Discharge Plasma Actuator, American Physical Society, 61th Gaseous Electronics 

Conference, Dallas, TX, October 13-17, 2008, abstract BAPS.2008.GEC.MWP1.94D. 

3. D. Opaits, G. Neretti, S. Zaidi, M. Shneider, R. Miles, A. Likhanskii, S. Macheret, Schlieren 

observation of vortex flow structures in asymmetric dielectric barrier discharges, American Physical 

Society, 60th Gaseous Electronics Conference, Arlington, VA, October 2-5, 2007, abstract 

BAPS.2007.GEC.SRP1.40. 

4. A. Likhanskii, D. Opaits, M. Shneider, R. Miles, S. Macheret, Investigation of asymmetric dielectric 

barrier discharge plasma actuator, driven by repetitive nanosecond pulses, American Physical 

Society, 60th Gaseous Electronics Conference, Arlington, VA, October 2-5, 2007, abstract 

BAPS.2007.GEC.LW2.7 

Workshop Presentations 

1. Mikhail Shneider, “State-of-the-art high-fidelity DBD plasma simulations,” presentation at the 

AFOSR DBD Plasma Actuator Workshop, Gainesville, FL, 24-25, February 2010. 

2. Dmitry Opaits, “DBD Actuator Developments,” presentation at the AFOSR DBD Plasma Actuator 

Workshop, Gainesville, FL, 24-25 February 2010. 

Each of these manuscripts had associated with it a presentation given by the lead author. 

NASA/CR—2012-217654 4
Appendix 

Reprints of Publications 

The appendix contains the following reprints of peer reviewed journal publications supported in full 

or in part by NASA Glenn Research Center Cooperative Agreement NNX07AC02A. Copyrighted papers 

are reprinted with permission of the publisher. 

1. A. Likhanskii, M. Shneider, S. Macheret, R. Miles, “Modeling of dielectric barrier discharge 

plasma actuators driven by repetitive nanosecond pulses,” Physics of Plasmas, Vol. 14, 073501, 

2007. 

Copyright 2007, reprinted with permission from the American Institute of Physics, 

http://pop.aip.org 

2. D.F. Opaits, A.V. Likhanskii, G. Neretti, S. Zaidi, M.N. Shneider, R.B. Miles and S.O. Macheret, 

“Experimental Investigation of Dielectric Barrier Discharge Plasma Actuators Driven by 

Repetitive High-Voltage Nanosecond Pulses with DC or Low Frequency Sinusoidal Bias,” 

Journal of Applied Physics, Vol. 104, Issue 4, Article number 043304 (2008). 

Copyright 2008, reprinted with permission from the American Institute of Physics, 

http://pop.aip.org 

3. Likhanskii, M. Shneider, S. Macheret, R. Miles, “Modeling of dielectric barrier discharge plasma 

actuator in air,” Journal of Applied Physics, Vol. 103, 053305, 2008. 

Copyright 2008, reprinted with permission from the American Institute of Physics, 

http://pop.aip.org 

4. D.F. Opaits, M.N. Shneider, R.B. Miles, “Surface Charge in Dielectric Barrier Discharge Plasma 

Actuators,” Physics of Plasmas, Volume 15, Issue 7, Article Number: 073505 (July 2008). 

Copyright 2008, Reprinted with permission from the American Institute of Physics, 

http://pop.aip.org 

5. D.F. Opaits, M.N. Shneider, R.B. Miles, “Electrodynamic effects in nanosecond-pulse sustained 

long dielectric-barrier-discharge plasma actuators,” Applied Physics Letters, Volume 94, Issue 6, 

Article Number: 061503 (February 9, 2009). 

Copyright 2009, Reprinted with permission from the American Institute of Physics, 

http://pop.aip.org 

6. R.B. Miles, D.F. Opaits, M.N. Shneider, S.H. Zaidi, and S.O. Macheret, “Non-thermal 

atmospheric pressure plasmas for aeronautic applications,” Eur. Phys. J. Appl. Phys., Vol. 47, 

22802 (2009). 

Copyright 2009, Reprinted with permission from the European Physical Journal Applied Physics, 

http://ww.edpsciences.org 

 

NASA/CR—2012-217654 5
Modeling of dielectric barrier discharge plasma actuators driven

by repetitive nanosecond pulses

Alexandre V. Likhanskii and Mikhail N. Shneider

Department of Mechanical and Aerospace Engineering, Princeton University,

Princeton, New Jersey 08544, USA

Sergey O. Macheret

Lockheed Martin Skunk Works, 1011 Lockheed Way, Palmdale, California 93599, USA

Richard B. Miles

Department of Mechanical and Aerospace Engineering, Princeton University,

Princeton, New Jersey 08544, USA

Received 26 January 2007; accepted 3 May 2007; published online 9 July 2007

A detailed physical model for an asymmetric dielectric barrier discharge DBDin air driven by

repetitive nanosecond voltage pulses is developed. In particular, modeling of DBD with high voltage

repetitive negative and positive nanosecond pulses combined with positive dc bias is carried out.

Operation at high voltage is compared with operation at low voltage, highlighting the advantage of

high voltages, however the effect of backward-directed breakdown in the case of negative pulses

results in a decrease of the integral momentum transferred to the gas. The use of positive repetitive

pulses with dc bias is demonstrated to be promising for DBD performance improvement. The effects

of the voltage waveform not only on force magnitude, but also on the spatial profile of the force, are

shown. The crucial role of background photoionization in numerical modeling of ionization waves

streamersin DBD plasmas is demonstrated. © 2007 American Institute of Physics.

DOI: 10.1063/1.2744227

I. INTRODUCTION

Asymmetric dielectric barrier discharge DBDplasma

actuators are known to be effective in aerodynamic control

see Refs. 1–16. Experimental investigations showed the

dramatic effect of DBD on the gas flow, resulting in flow

separation control. Despite the plasma-induced flow complexity, there is an agreement that the major effect on the

flow is due to the downstream force on the gas. The currently

achieved performance of DBD plasma actuators is limited to

relatively low gas velocities of the order of 1 – 30 m/ s. The

prevention of flow separation at higher velocities needs

stronger DBD effects on the gas, and optimization is required. A number of groups have explored different applied

voltage shapes, such as sinusoidal or sawtooth voltage waveforms at frequencies 1 – 100 kHz and amplitudes 2 – 20 kV or

repetitive pulses with full width at half-maximum FWHM

from 4 to 400 ns at different repetition rates. The results

showed that all the waveforms can prevent separation, but

the strength of the DBD effect on the flow does depend on

the voltage waveform.

Explanation of the experimental results and further optimization of plasma actuators has to rely on a firm foundation

of modeling. Due to the vast difference of time scales that

characterize plasma phenomena ionization, recombination,

evolution of electric field, etc.and gas dynamics, the problem can be broken into hydrodynamic and plasma parts. The

plasma part describes the local influence of the DBD actuator

on the flow, and the hydrodynamic part uses the timedependent distributed body force and heating terms from the

plasma calculations to determine global flow field effects.

The first attempt of the numerical modeling of plasma kinetics was made by Roy in Ref. 9. Notable results in hydrodynamic modeling of DBD have been obtained by Gaitonde et

al. see Ref. 14, however the plasma models used in his

calculations were incomplete.

Our group has developed a comprehensive physically

based numerical model see Ref. 1, which includes relevant

plasma kinetic phenomena. The results have shown that at

low voltages 1.5– 2 kV, a sinusoidal signal is not particularly effective in gas pushing due to the positive ion attraction to the upper electrode in the cathode half-cycle. Based

on the analysis, a new voltage waveform, repetitive negative

nanosecond pulses plus positive bias, has been proposed. In

the present paper, we describe further development of the

consistent, comprehensive, and physically based model, and

computational exploration of DBD performance over a wide

range of voltage amplitudes and waveforms.

II. PHYSICAL MODEL

The modeled configuration of the DBD plasma actuator

is presented in Fig. 1. It consists of two electrodes separated

by the dielectric. The geometrical sizes of the electrodes and

the dielectric are different for different numerical experiments and vary from 1.5 mm to 1 cm for electrode lengths

and from 100 to 300 m for dielectric thickness. The relative dielectric permittivity is chosen to be equal to 5. The

electrodes are considered to be infinitely thin. This assumption is based on the experimental data, which did not show

the dependence on electrode thickness and is used for modeling simplification. The voltage of arbitrary profile is apPHYSICS OF PLASMAS 14, 073501 2007

1070-664X/2007/147/073501/8/$23.00 14, 073501-1 © 2007 American Institute of Physics

NASA/CR—2012-217654 6
plied to the upper electrode and the lower plate is considered

grounded.

The modeled gas was air at room temperature constant

densityconsisting of neutrals, electrons, positive, and negative ions. The air was considered as a mixture of oxygen and

nitrogen. Air chemistry was not considered in detail. The

voltage applied to the upper electrode resulted in weakly

ionized plasma formation near the edge of electrode, which

subsequently spread to above the dielectric. The formation of

negative ions was due to attachment of electrons to oxygen

see Ref. 17. The plasma kinetics and interactions with neutral gas were modeled in a drift-diffusion approximation see

Ref. 11.

We denote number densities of electrons, positive and

negative ions, and neutrals as ne, n+, n−, and n, and fluxes of

charged particles as e, +, and −. Rate coefficients of ionization, electron-ion recombination, ion-ion recombination,

electron detachment from negative ions, and electron attachment to the neutrals will be denoted as , , ii, kd, and a.

For simplicity, we assume that masses of both positive and

negative ions are equal to the mass of a neutral molecule,

and any of those greatly exceeds the electron mass m. De, Di

,

e, and i are correspondingly the electron and ion diffusion

coefficients and mobilities.

Equations of motion for a four-fluid mixture are then as

follows: Continuity equation for electrons,

ne

t

+ jej = e − nen+ + kdnn− − ane. 1

Continuity equation for positive ions,

n+

t

+ j+j = e − nen+ − iin+n−. 2

Continuity equation for negative ions,

n−

t

+ j−j = − iin+n− − kdnn− + ane. 3

Electron flux,

ej = − eEjne − Dejne − Dene

jTe

Te

. 4

Positive ion flux,

+j = i

Ejn+ − Dijn+. 5

Negative ion flux,

−j = − i

Ejn− − Dijn−. 6

The electric potential and electric field distribution are calculated using the Poisson equation,

  = ene + n− − n+, 7

Ej = − j, 8

where E is the electric field, e is the charge of the electron, 

is the dielectric permittivity, and  is the electric potential.

Ionization and recombination coefficients, as well as attachment, detachment rates, charged particles mobilities, and

electron temperature, are considered as functions E/n, where

E is local electric field. The numerical values for rate of

ionization, electron-ion recombination, ion-ion recombination, ion mobilities, attachment, and detachment rates are

standard and given in Ref. 17. Ion temperature is considered

to be equal to gas temperature. Electron drift velocities Vdr

and electron temperatures, as functions E/N, are given in

Ref. 18. The electron mobilities are calculated using the following relation:

e = Vdr

E . 9

The diffusion coefficients are calculated using the Einstein

relation,

Di = i

Ti, 10

where i denotes the species electrons, ions.

The boundary conditions at the electrode surface are

en = − m+n if En 	 0, 11

+n = 0 if En 
 0, 12

and the boundary conditions at the dielectric surface are

en = − d+n if En 	 0 13

and

+n = 0 if En 
 0. 14

Here, m and d are the effective secondary emission coefficients from metal and dielectric, with numerical values 0.1

and 0.01 used in computations correspondingly; index n denotes the normal component of electric field and fluxes.

III. NUMERICAL METHODS

In our previous work see Ref. 1, we used the secondorder accurate MacCormack scheme see Ref. 19to model

plasma kinetics. This model worked very well at low voltages and gave accurate results. Nevertheless, the transition to

higher voltages could not be achieved because of the numerical instabilities that arose at sharp time gradients of the electric field. In order to overcome this problem, the flux corrected transport FCTsee Ref. 20was added to the

MacCormack scheme. The results, obtained using the FCT

scheme, are smoother and more accurate. Figure 2 shows a

FIG. 1. Color onlineAsymmetric dielectric barrier discharge

configuration.

073501-2 Likhanskii et al. Phys. Plasmas 14, 073501 2007

NASA/CR—2012-217654 7
comparison between time-averaged body forces on the neutral gas using these two methods after three pulses. The results obtained with and without FCT agree well: both produce similar downstream forces with only minor variations

in the local force fields. A successive over-relaxation method

was used to solve the Poisson equation see Ref. 19.

Figure 3 shows the voltage-current characteristics during

the breakdown for the two numerical schemes. After the

pulse, the current is very small. These characteristics obtained with and without the FCT also agree well. A grid

convergence study showed some dependence of the results

on the grid size, however the qualitative results remained the

same. Decreasing the mesh size results in plasma propagation somewhat farther downstream and thereby slightly increases the momentum transfer to the gas.

Using the second-order accurate MacCormack method,

the low voltage cases up to 2 kVhave been modeled see

Ref. 1. The results showed that at low voltages, the conventional sinusoidal voltage was not the optimal profile, and a

new voltage profile was proposed: repetitive negative nanosecond pulses and positive bias. The addition of FCT now

allows the calculation of DBD with applied low voltage repetitive positive nanosecond pulses with positive bias. Figure

4 shows the time-averaged force acting on the gas at positive

pulse with amplitude 1.65 kV and positive bias of 500 V. It

is worth mentioning that this is not the streamer case, because voltages are too low. It is a positive corona regime.

The question then arises as to whether the operation of

the DBD will improve at higher voltages. What will happen

if the amplitude of applied negative pulses increases? Or

what is the effect of streamers on the gas in the case of

high-voltage positive pulses? The second-order MacCormack scheme and FCT method could not give the answers to

these questions due to numerical instabilities, which appear

at high voltages. This difficulty has been overcome using the

Scharfetter-Gummel method see Refs. 21 and 22for flux

FIG. 2. Color onlineTime-averaged force on the neutral gas. The left plot corresponds to computations with the MacCormack method without FCT, and the

right one to the FCT method. Pulse voltage: 1.5 kV amplitude, 4 ns FWHM, 500 kHz repetition rate, and 500 V bias.

FIG. 3. Color onlineCurrent and voltage in a representative repetitive-pulse case in the quasi-steady-state regime. The red line shows the voltage, and the

dashed line shows the current. The left plot corresponds to the MacCormack method without FCT, and the right one to the FCT method. Pulse voltage:

−1.5 kV amplitude, 4 ns FWHM, 500 kHz repetition rate, and 500 V bias.

073501-3 Modeling of dielectric barrier discharge plasma... Phys. Plasmas 14, 073501 2007

NASA/CR—2012-217654 8
calculation and the Modified Euler method for solving continuity equations see Ref. 23.

IV. HIGH-VOLTAGE RESULTS

A. Repetitive negative nanosecond pulses

with positive dc bias

Based on the numerical calculations for low voltages, it

was proposed to use negative nanosecond pulses and positive

dc bias to increase the effect on gas pushing in the asymmetric DBD plasma actuator. The basic principle of this voltage

performance was the creation of an ionization wave during

the short pulse. When the pulse was applied, the electrons

were created near the edge of an electrode due to the high

electric field in this region, then they moved along the electric field lines, ionizing the gas, and finally they attached to

the dielectric surface, creating a virtual cathode. Since a

large number of electrons were attached to the dielectric surface and the pulse time was too short to make positive ions

move, a positive ion cloud was formed above the dielectric

surface. After the pulse, this positive cloud was pushed from

the electrode toward the dielectric surface by an applied

positive dc bias and by the attraction of the electrons on the

dielectric.

The logical step to improve the performance of DBD

plasma actuator with applied repetitive negative nanosecond

pulses is to increase the peak voltage of the pulses. This

voltage increase should lead to an increase of the positive ion

number density in the air after the pulse, and therefore an

increase in the force acting on the air in the downstream

direction. In order to investigate this phenomenon, a numerical experiment has been carried out. The following geometry

was chosen: lengths of upper and lower electrodes were 1.5

and 8 mms, the computational domain was 10.5 cm, and

the grid size was 2525 m. The dielectric thickness was

100 m and there were no gaps in the horizontal direction

between electrodes. When the pulse is applied to the upper

electrode, the breakdown occurs and the electrons move to

the dielectric, producing weakly ionized plasma and leaving

a positive ion cloud behind them. However, after the voltage

reaches its peak, a reverse breakdown occurs. This reverse

breakdown looks like a cathode-directed streamer Figs. 5

and 6and significantly decreases the performance of the

DBD plasma actuator. Figure 7 shows the average force on

the gas after the pulse. There is a component near the edge of

the electrode, directed upstream, however the integral over

the volume average force is still directed downstream and is

greater than in the case of low voltages. The quantitative

comparison of these results will be given later in the paper.

B. Repetitive positive nanosecond pulses

with positive dc bias

Another possible way of pushing gas in a DBD plasma

actuator is by applying high-voltage repetitive positive

pulses plus a positive dc bias. The physics of the downstream

force acting on the gas in this case is different from the case

with negative pulses.

When a positive nanosecond pulse is applied to the upper electrode, at some voltage the electric field near the edge

of the electrode will be sufficient for the initiation of

cathode-directed streamer propagation. During the pulse, the

streamer propagates along the dielectric until the electric

field at the leading edge headof the streamer is not sufficient to produce further ionization in front of it. At that point

the streamer stops. From the theory of streamers and from

the calculations, it is well known that the body of the

streamer is quasineutral, but the head of the streamer carries

a positive charge in order to displace the electric potential

and produce the ionization in front of it. Therefore, after the

pulse there will be positive ion cloud in the front part of the

decaying streamer. An applied dc bias after the pulse forces

this cloud to move downstream and push the gas. Despite the

body of the streamer being quasineutral plasma, its effect on

the formation of force on the gas is negligible in comparison

with the force from the positive ion cloud in front of the

streamer. The reason is that the force is proportional to the

difference between concentrations of positive and negative

charge carriers. After the discharge, the electrons in the

quasineutral streamer body are rapidly attached to the oxygen during the time scales of the order of 10 ns. Between the

pulses, the drift of negative ions to the upper electrode is

compensated by the drift of positive ions downstream.

C. The role of background electron density

In order to correctly model the streamer propagation,

one has to solve the problem of radiation transfer and calculate the number density of photoelectrons ahead the streamer

head. The number density of photoelectrons depends on the

streamer and gas parameters. However, the problem of radiation transfer is quite complicated and solving this problem is

time-consuming. The simplified model considers the background charge in the air as having been created in the photoprocesses see Ref. 24. There are two important parameters we deal with: initial and background charge number

FIG. 4. Color onlineAverage force acting on neutral gas during one cycle.

Pulse voltage: amplitude 1.65 kV, FWHM 4 ns, repetition rate 500 kHz,

and bias 500 V.

073501-4 Likhanskii et al. Phys. Plasmas 14, 073501 2007

NASA/CR—2012-217654 9
density. The initial charge number density is the positive ion

and electron number densities in the air at the beginning of

calculations. Since plasma formation is an exponential process, without initial charges plasma cannot form. However,

the initial number density has to be small to have no influence on plasma formation. This fact leads to the problem of

streamer formation if the voltage of the upper electrode is

positive. In this case, the electrons will be sucked to the

electrode during hundreds of picoseconds and there will be

no way for the streamer to propagate. In reality, photoelectrons, which are formed ahead of the streamer head, resolve

this problem. In our model, we substitute them with background charge. It is the minimum charge number density in

the computational domain. If charge number density is less

than background in any computational point at some point of

time, the charge number density becomes background. This

addition of charge has a negligible influence on the precision

of the model of plasma-gas interaction because the background charge number density is several orders of magnitude

less than the plasma number density. The background charge

number density should be chosen empirically to satisfy the

experimental data on the streamer propagation speed and the

propagation distance. The dependence of streamer propagation parameters on the background and the initial conditions

has been investigated. For this, a geometry that is the same

as for the negative pulses was chosen. Single positive Gaussian pulses with 4 ns FWHM and 3 kV amplitude have been

applied to the upper electrode. Two parameters were

changed—the initial charge density and the background

charge density. If the initial and background charge density is

of the order of 1 – 10 1/m3

, the plasma cannot even appear. If

the initial number density is very high of the order of

1016 1/m3

even without background charge, the plasma

forms and a streamer propagates. The background does not

play a role in this case, because the Debye length is less than

the computational domain and electrons will always be able

to come from the outside of the Debye sphere. When the

initial number density drops to 1011 1/m3

, it plays a critical

FIG. 5. Color onlineReverse breakdown. Applied voltage: negative pulses with positive bias. Peak voltage is −4.5 kV, the bias is 0.5 kV, and the pulse

FWHM is 4 ns. The figure shows the electron and positive ion number densities, electric potential, and the instantaneous force on the gas at the moment

corresponding to the peak voltage.

073501-5 Modeling of dielectric barrier discharge plasma... Phys. Plasmas 14, 073501 2007

NASA/CR—2012-217654 10
role in the streamer formation. Without it, all electrons will

rapidly move to the electrode and there will be no “photo”

electrons, and the streamer will not be able to propagate. The

background charge supplies the electrons for the streamer.

The streamer stops propagating when the electric field at its

head is not enough for propagation. A similar situation happens when the background number densities drop to

107 1/m3

. Figure 8 shows a comparison of different initial

and background charge number density. In our modeling, the

background plasma was taken to be 107 1/m3

, corresponding

to the values in the literature. Figure 9 shows the typical

simulated streamer and Fig. 10 shows the time-average force

on the gas distribution.

It is worth mentioning that the background charge is not

essential for negative pulse modeling. In this case, the electrons appear on the electrode or dielectric due to secondary

emission and then move along the electric field line, producing the plasma. The reverse breakdown is also easily resolved, despite its streamer-like appearance. After the electron avalanche, there is plasma with an ionization fraction

much greater than 1 due to photoionization.

V. COMPARISON OF HIGH- AND LOW-VOLTAGE

CALCULATIONS

As predicted before see Ref. 1, higher voltages increase the DBD plasma actuator performance. Figure 11

shows a comparison of ilow-voltage repetitive negative

nanosecond pulses with positive bias, iihigh-voltage negative pulses with positive dc bias, and iiirepetitive positive

nanosecond pulses with positive bias. The higher voltages

transfer three times more momentum to the gas in contrast to

the low ones. Note that positive pulses with amplitudes of

3 kV give the same effect as the negative pulses with amplitudes of 4.5 kV. Modeling high voltages also allows for the

prediction of different ways of plasma formation in DBD and

different momentum transfer. For example, at low voltages

the streamer does not propagate in the case of positive

pulses, but at high voltages it does. The obtained results also

give an important conclusion about the scaling predictions in

numerical modeling. DBD plasma actuators operate at different regimes not only at different voltage profiles, but at different voltage amplitudes. Further predictions of DBD performance at voltages of the order of 10– 20 kV require more

extensive computational capabilities and the application of

parallel computing methods.

FIG. 6. Color onlineReverse breakdown. Applied voltage is negative

pulse with positive bias. Peak voltage is −4.5 kV, the bias is 0.5 kV, and the

pulse FWHM is 4 ns. The figure shows the electron and positive ion number

densities, electric potential, and the instantaneous force on the gas after the

pulse.

FIG. 7. Color onlineAverage force acting on neutral

gas during one cycle. Pulse voltage: amplitude is

−4.5 kV, FWHM is 4 ns, repetition rate is 500 kHz,

and the bias is 0.5 kV.

FIG. 8. Color onlineStreamer propagation speed in three different cases.

The green line corresponds to the initial and background electron number

density of 107 1/m3

; the purple line, to 1011 1/m3; and the blue line, to the

initial electron number density of 1016 1/m3 and no background charge.

Applied voltage waveform: positive pulses with positive bias. Peak voltage

is 3 kV, the bias is 1 kV, and the pulse FWHM is 4 ns.

073501-6 Likhanskii et al. Phys. Plasmas 14, 073501 2007

NASA/CR—2012-217654 11
VI. CONCLUSIONS

The comprehensive physical and numerical model of

DBD plasma actuators in air developed in this work allowed

us to investigate the essential physics of DBD driven by

repetitive short pulses with and without dc bias and to reveal

the effects of varying the parameters of this type of voltage

waveform. Modeling of high-voltage negative nanosecond

pulses generally agrees with scaling predictions based on

low-voltage cases, but a new effect, the reverse breakdown,

takes place at the higher voltages. The physics of the reverse

breakdown and its negative role in the DBD performance,

consisting in upstream-directed force, has been shown. Nevertheless, at higher pulse voltages, stronger forces on the gas

are produced and more momentum is transferred than at

lower voltages.

A new voltage waveform—positive nanosecond pulses

with positive dc bias—has been modeled. The results demonstrate that this waveform is promising for improvement of

DBD plasma actuator performance. Although this voltage

waveform is not very effective at low voltages, it becomes

very effective at high voltages. With this waveform, a performance similar to that provided by the negative pulses with

positive dc bias could be achieved with much lower voltage

amplitudes.

Computations have demonstrated a crucial influence of

background and initial electron densities on the DBD modeling of streamers in the anode stage. Although that background charge density can be several orders of magnitude

FIG. 9. Color onlineStreamer-like ionization wave. Applied voltage

waveform: positive pulses with positive bias. Peak voltage is 3 kV, the bias

is 1 kV, and the pulse FWHM is 4 ns. The figure shows the electron and

positive ion number densities, electric potential, and the instantaneous force

on the gas.

FIG. 10. Color onlineAverage force acting on neutral gas during one cycle. Pulse voltage: amplitude is 3 kV, FWHM is 4 ns, the repetition rate is 500 kHz,

and the bias is 1 kV.

FIG. 11. Color onlineMomentum transferred to the gas. Blue and green

lines correspond to the negative pulses with amplitudes −4.5 and −1.5 kV

with positive bias of 0.5 kV, and the red line corresponds to the positive

pulses with 3 kV amplitude and positive bias of 1 kV. FWHM for all pulses

is 4 ns.

073501-7 Modeling of dielectric barrier discharge plasma... Phys. Plasmas 14, 073501 2007

NASA/CR—2012-217654 12
lower than that in the fully developed plasma, streamer

propagation characteristics are extremely sensitive to the

background electron density.

A comparison of the results for low- and high-voltage

amplitudes shows that, depending on the details of voltage

waveform and on the voltage amplitude, different DBD regimes with different physics of plasma-air interaction can be

realized. Therefore, one should be very cautious with scaling

predictions, and such predictions must be based on full

physical modeling and experiments.

ACKNOWLEDGMENTS

This work was supported in part by the Air Force Office

of Scientific Research Dr. John Schmisseurand in part by

Boeing, St. Louis. Fellowship support for one of the authors

A.V.L.was provided by the Princeton Program in Plasma

Science and Technology.

1

A. V. Likhanskii, M. N. Shneider, S. O. Macheret, and R. B. Miles, Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno,

NV, 2006 AIAA, Washington, D.C., 2006, Paper AIAA-2006–1204. 2

C. L. Enloe, T. E. McLaughlin, R. D. VanDyken, K. D. Kachner, E. J.

Jumper, and T. C. Corke, AIAA J. 42, 89 2004. 3

C. L. Enloe, T. E. McLaughlin, R. D. VanDyken, K. D. Kachner, E. J.

Jumper, T. C. Corke, M. Post, and O. Haddad, AIAA J. 42, 595 2004. 4

M. Post and T. C. Corke, Proceedings of the 35th AIAA Fluid Dynamics

Conference and Exhibit, Toronto, Ontario, 2005 AIAA, Washington,

D.C., 2005, Paper AIAA-2005–4630. 5

T. C. Corke, E. J. Jumper, M. L. Post, D. Orlov, and T. E. McLaughlin,

Proceedings of the 40th AIAA Aerospace Sciences Meeting & Exhibit,

Reno, NV, 2002 AIAA, Washington, D.C., 2005, Paper AIAA—2002–

350.

6

M. L. Post and T. C. Corke, AIAA J. 42, 2177 2004.

7

D. F. Opaits, D. V. Roupassov, S. M. Starikovskaia, A. Yu. Starikovskii, I.

N. Zavialov, and S. G. Saddoughi, Proceedings of the 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 2005 AIAA, Washington,

D.C., 2005, Paper AIAA-2005–1180. 8

S. Roy and D. V. Gaitonde, Proceedings of the 43rd AIAA Aerospace

Sciences Meeting and Exhibit, Reno, NV, 2005 AIAA, Washington, D.C.,

2005, Paper AIAA 2005–160. 9

S. Roy, Appl. Phys. Lett. 86, 101502 2005. 10K. P. Singh and S. Roy, J. Appl. Phys. 98, 083303 2005. 11J. P. Boeuf and L. C. Pitchford, J. Appl. Phys. 97, 103307 2005. 12D. M. Orlov and T. C. Corke, Proceedings of the 43rd AIAA Aerospace

Sciences Meeting and Exhibit, Reno, NV, 2005 AIAA, Washington, D.C.,

2005, Paper AIAA 2005–1083. 13J. R. Roth and X. Dai, Proceedings of the 44th AIAA Aerospace Sciences

Meeting and Exhibit, Reno, NV, 2006 AIAA, Washington, D.C., 2006,

Paper AIAA-2006–1203. 14D. V. Gaitonde, M. R. Visbal, and S. Roy, Proceedings of the 44th AIAA

Aerospace Sciences Meeting and Exhibit, Reno, NV, 2006 AIAA, Washington, D.C., 2006, Paper AIAA-2006–1205. 15T. C. Corke, B. Mertz, and M. P. Patel, Proceedings of the 44th AIAA

Aerospace Sciences Meeting and Exhibit, Reno, NV, 2006 AIAA, Washington, D.C., 2006, Paper AIAA-2006–1208. 16R. Anderson and S. Roy, Proceedings of the 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 2006 AIAA, Washington, D.C.,

2006, Paper AIAA-2006–0369. 17S. O. Macheret, M. N. Shneider, and R. B. Miles, IEEE Trans. Plasma Sci.

30, 1301 2002. 18I. S. Grigoriev and E. Z. Meilikhov, Handbook of Physical Quantities

CRC, Boca Raton, FL, 1997, Chap. 20. 19D. A. Anderson, J. C. Tannehill, and R. H. Pletcher, Computational Fluid

Mechanics and Heat Transfer Hemisphere, New York, 1984. 20S. T. Zalezak, J. Comput. Phys. 31, 335 1979. 21H. K. Gummel, IEEE Trans. Electron Devices 11, 455 1964. 22D. L. Scharfetter and H. K. Gummel, IEEE Trans. Electron Devices 16,

64 1969. 23J. C. Butcher, The Numerical Analysis of Ordinary Differential Equations:

Runge-Kutta and General Linear Methods Wiley, New York, 1987. 24L. B. Loeb, Science 148, 141 1965.

073501-8 Likhanskii et al. Phys. Plasmas 14, 073501 2007

NASA/CR—2012-217654 13
Experimental investigation of dielectric barrier discharge plasma actuators

driven by repetitive high-voltage nanosecond pulses with dc or low

frequency sinusoidal bias

Dmitry F. Opaits,1,a Alexandre V. Likhanskii,1 Gabriele Neretti,1 Sohail Zaidi,1

Mikhail N. Shneider,1 Richard B. Miles,1 and Sergey O. Macheret2

1

Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA

2

Lockheed Martin Aeronautics Company, Palmdale, California 93599, USA

Received 14 August 2007; accepted 26 June 2008; published online 27 August 2008

Experimental studies were conducted of a flow induced in an initially quiescent room air by a single

asymmetric dielectric barrier discharge driven by voltage waveforms consisting of repetitive

nanosecond high-voltage pulses superimposed on dc or alternating sinusoidal or square-wave bias

voltage. To characterize the pulses and to optimize their matching to the plasma, a numerical code

for short pulse calculations with an arbitrary impedance load was developed. A new approach for

nonintrusive diagnostics of plasma actuator induced flows in quiescent gas was proposed, consisting

of three elements coupled together: the schlieren technique, burst mode of plasma actuator

operation, and two-dimensional numerical fluid modeling. The force and heating rate calculated by

a plasma model was used as an input to two-dimensional viscous flow solver to predict the

time-dependent dielectric barrier discharge induced flow field. This approach allowed us to restore

the entire two-dimensional unsteady plasma induced flow pattern as well as characteristics of the

plasma induced force. Both the experiments and computations showed the same vortex flow

structures induced by the actuator. Parametric studies of the vortices at different bias voltages, pulse

polarities, peak pulse voltages, and pulse repetition rates were conducted experimentally. The

significance of charge buildup on the dielectric surface was demonstrated. The charge buildup

decreases the effective electric field in the plasma and reduces the plasma actuator performance. The

accumulated surface charge can be removed by switching the bias polarity, which leads to a newly

proposed voltage waveform consisting of high-voltage nanosecond repetitive pulses superimposed

on a high-voltage low frequency sinusoidal voltage. Advantages of the new voltage waveform were

demonstrated experimentally. © 2008 American Institute of Physics. DOI: 10.1063/1.2968251

I. INTRODUCTION

Electrohydrodynamic EHDand magnetohydrodynamic

phenomena are being widely studied for aerodynamic applications. The major effects of these phenomena are heating of

the gas, body force generation, and enthalpy addition or

extraction.1–35 In particular, asymmetric dielectric barrier discharge DBDplasma actuators are known to be effective

EHD device in aerodynamic control.30–35 A number of experiments have shown the potential of DBD for flow separation control at low-to-moderate flow velocities 1–100 m/s.

There is an agreement that the DBD actuators generate nearsurface synthetic jets. The induced near-surface flow velocities using sinusoidal or sawtooth voltage waveforms at frequencies of 1–100 kHz and amplitudes of 2–20 kV are of the

order of 1–5 m/s. However, optimized voltage waveforms36

allow the increase in the induced gas velocities in the vicinity of plasma-gas interaction region.

Recent numerical studies with a detailed model based on

full plasma kinetics coupled with the dynamics of the electric

field developed by Likhanskii et al.37–40 provided consistent

physical explanations for the observed phenomena and suggested ways for improvement of actuator performances. Specifically, it was shown that a voltage waveform consisting of

high repetition rate short nanosecondpulses has the potential to produce a stronger effect on the flow than a conventional sinusoidal voltage. Additionally, it was predicted that

adding a positive bias voltage to the pulses should increase

the velocity of wall jet generated by the plasma actuator.

This paper presents results of experiments with a DBD

asymmetric discharge driven by repetitive high-voltage

nanosecond pulses. The purpose of the experiments was to

provide a better understanding of the physical processes and

to validate the numerical model. The experiments showed, as

will be discussed below, that adding the bias voltage has a

strong effect only for the first several hundred pulses. Then

the surface charge builds up shielding the applied bias voltage and reducing performance. To remove the surface

charge, we explored changing the bias voltage polarity periodically. Experiments reported in this paper have demonstrated that the new voltage profile which consists of nanosecond pulses superimposed on a high-voltage low frequency

sinusoidal bias voltage does indeed lead to higher performance.

To conduct experiments with DBD actuators driven by

repetitive voltage pulses, one needs to characterize and optimize the coupling of the pulses with the plasma and to develop reliable nonintrusive flow diagnostics. To address the a

Electronic mail: dopaits@princeton.edu.

JOURNAL OF APPLIED PHYSICS 104, 043304 2008

0021-8979/2008/1044/043304/15/$23.00 104, 043304-1 © 2008 American Institute of Physics

NASA/CR—2012-217654 14
first problem, a numerical code for short pulse calculation

with an arbitrary impedance load was developed. The code is

based on Kirchhoff’s laws and allowed minimization of

pulse reflection from the actuator.

Regarding the second problem, flow diagnostics, difficulties of diagnostics of the actuator induced flow arise from

its small approximately centimeterscale, low speed

m/s, and closeness to the plasma and the dielectric surface. Most common techniques to diagnose the induced wall

jet include particle image velocimetry, smoke visualization,

Pitot probes, etc. Unfortunately, these methods are intrusive

and must be used with great care. For example, in particle

image velocimetry measurements the particles may get

charged in the plasma and may not only depict the flow

incorrectly but may also affect the plasma and the gas flow.

The main disadvantage of Pitot-probe measurements is low

sensitivity. The measurements have to be taken at some distance downstream from the actuator in order not to perturb

the plasma. Pitot measurements are also local, and to obtain

the entire flow pattern, a scan through the entire flow region

should be performed. The task becomes much more complicated with nonstationary flows. Attempts to use nonintrusive

optical methods were made in a number of works. A laser

deflection technique was used to measure density by probing

index of refraction gradients in the air.41 Being nonintrusive,

this approach, however, gives only local measurements and,

like the Pitot-probe one, is hard to apply to nonstationary

flows.

The use of the schlieren technique for DBD induced

flow measurements was reported.42,43 In the first paper42 the

authors used conventional schlieren technique for flow visualization. The technique is based on following thermal disturbances in the jet and extracting the flow speed from that.

However, the authors42 found this insufficient for quantitative speed measurements and used schlieren streak video instead. Another, similar, application of the schlieren technique

to DBD plasma actuator was demonstrated in Ref. 43. Turbulent eddies were treated as tracers in the flow. A new,

helium based technique of schlieren image processing was

suggested to observe the flow field. In the region outside the

turbulent flow a helium jet was injected in order to produce

the necessary contrast. The helium jet, however, can disturb

the plasma and the flow field. All of the above techniques are

based on disturbances and/or turbulence in the induced flow.

As noted in Ref. 43 the technique is not applicable for laminar flows.

In this paper, we used a new approach for the induced

flow visualization and velocity measurements. Since the discharge slightly heats the air, it is possible to visualize the

induced wall jet. The principal feature of our schlieren technique, distinguishing it from other studies, is the modulation

of the voltage waveform applied to the discharge so that the

plasma actuator is operated in pulse-burst mode. In the burst

mode, separate pulse jets are created by each burst. The advantage of the proposed technique is the ability to visualize

two-dimensional 2D, laminar, low speed, small, nonstationary plasma induced jets. An advantage of studies with quiescent air is that it is possible to notice some features of the

induced flow which otherwise would be washed out by an

external flow. A numerical model based on 2D Navier–

Stokes equations predicts similar structures and allows us to

extrapolate the entire flow pattern by matching the schlieren

images of a single vortex. The numerical modeling also allows us to infer the magnitude of the body forces exerted by

the DBD actuator on the gas.

As will be discussed in the paper, the schlieren imaging

in the pulse-burst mode demonstrated that the DBD actuator

produces vortices. Note that similar structures were observed

in DBD experiments using smoke visualization44 and

schlieren technique,45 in DBD induced flow numerical

simulations,46,47 and also in plane wall jet experiments and

numerical simulations.48–50 However, in this work, we demonstrate that the strength of the vortices and frequency of

their generation can be controlled by the voltage waveform,

which has practical implications.

II. EXPERIMENTAL SETUP

The plasma actuator consisted of two electrodes placed

asymmetrically on either side of the dielectric, with one electrode encapsulated, and the other exposed to the atmospheric

air, as shown at Fig. 1.

51 The electrodes were made of copper

foil. The width of the electrodes was equal to 25 mm and

their spanwise dimension was 50 mm. A 100 m thick kapton tape was used as the dielectric. The discharge was ignited

by applying high voltage to one of the electrodes. The other

electrode was grounded. The actuator was placed inside a

sealed cylindrical aluminum chamber 45 cm high and 40 cm

in diameterto eliminate the interaction between the plasma

induced flow 1 m/sand air in the room and to enable

experiments at different pressures and with different gases.

For the plasma actuator induced flow visualization we

used a conventional schlieren system Fig. 2

52 which consisted of a mercury lamp, a 50 m pinhole, and two lenses

FIG. 1. Color onlineAsymmetric DBD plasma actuator.

FIG. 2. Color onlineSchlieren

system.

043304-2 Opaits et al. J. Appl. Phys. 104, 043304 2008

NASA/CR—2012-217654 15
FL= 25 cm, D= 6 cm. A vertical knife edge was put into

the focus of the second lens. The image was projected on a

ground glass screen and then captured by a Princeton Scientific Instruments 4-D charge coupled device camera. The

camera took 28 consecutive images with 1 ms exposure time

and no significant delay between the images.

In the experiments, we used a voltage waveform consisting of repetitive nanosecond pulses in burst mode superimposed on a bias voltage. Although during the experiments the

bias voltage waveform evolved from constant to sinusoidal,

the same electric circuit, shown in Fig. 3, was used. The

circuit is designed so as to superimpose short pulses on a low

frequency bias voltage without interference between the

pulser and the low frequency power supply. Adding a 470 pF

capacitor in series with the actuator shielded the pulser from

the bias voltage. Since the capacitance of the actuator was

only 4 pF, the main voltage drop occurred just at the plasma

actuator. The 220 kresistors did not let the pulse go to the

power supply. The charging time for the capacitor through

the corresponding resistors was =RC= 220 k470 pF

100 s, which corresponds to 10 kHz60 Hz. The

10 Mresistor was put in parallel with the actuator for

safety reasons. It discharged the high-voltage electrode after

experiments. Its high impedance did not influence the circuit

in any way. Also, a noninductive 250 resistor was added

in parallel with the actuator to minimize the pulse reflection.

The pulser used in the experiments was a FID Technology 4 ns full width at half maximum FWHMpulser capable of running with pulse repetition rate PRRof up to

100 KHz and triggered by a 10 V pulse from a Stanford

Box. The peak output voltage of the pulser was up to 10 kV

which was fed to three separate 3 m long 75 coaxial lines.

The three copropagating pulses were converted into a single

pulse by taking advantage of the short physical “length” of

the pulses less than 1 m. By connecting the center conductor of the first coaxial line to the outer conductor of the

second and the center conductor of the second to the outer

conductor of the third, an amplified pulse is produced between the center conductor of the third line and the outer

conductor of the first. This essentially is a transformer made

of sections of transmission lines, and it is well described in

the literature.53

A source of constant bias voltage used in the experiments was High Voltage DC Supply model 412 by John

Fluke MFG Co, Inc., capable of producing output voltages

up to 2 kV both polarities. Ozone generator transformer by

Plasma Technics, Inc., was used for producing sinusoidal

bias voltage.

The pulser was able to produce pulses of negative polarity only. The bias voltage could be of any polarity but could

be added to the pulsed electrode only due to the circuit properties. The terminology used in this paper came from the

numerical simulations, where the encapsulated electrode was

supposed grounded, and the voltage waveform was applied

to the exposed electrode. Following the same terminology,

we consider the encapsulated electrode to be at zero potential. That means that the term “positive” refers to a case

when the electric field is directed from the exposed electrode

to the encapsulated one, i.e., parallel to the induced jet, and

negative when in the opposite direction. Thus, applying

negative pulses to the lower encapsulatedelectrode will

henceforth be referred to as positive pulses. Further, applying

negative bias voltage to the top exposedelectrode will be

called a negative bias, whereas applying negative bias voltage to the lower encapsulatedelectrode will be referred to

as positive bias. See Fig. 4 for further examples.

III. NANOSECOND PULSE PROFILE

Special attention was paid to the electric pulse waveform. It was measured by a LeCroy high-voltage probe PPE6

kV 400 MHz bandwidth, 50 Minput resistance, 6 pF

input capacitanceconnected to a Tektronix digital oscilloscope TDS 380 400 MHz bandwidth. Since the pulses were

only several nanoseconds long, they were reflected back

from the plasma actuator and then reflected again by the

pulser toward the actuator. Therefore, each pulse actually

looked like a series of damped pulses. To reduce this ringing,

a computer code incorporating the actuator’s and the probe’s

capacitances was developed. The code calculated the reflection of a pulse from a RLC load. The code was based on

Kirchhoff’s laws written for an LRC load connected to a 3

75 = 225 cable. A schematic of the transformer made

of sections of transmission lines connected to a RLC load is

shown in Fig. 5a. In the figure, Z is the cable impedance, Z0

is defined by parasitic impedances and/or impedance of cable

connecting wires, C is the capacitance of the actuator and the

voltage probe, R is resistance of a noninductive matching

FIG. 3. Color onlineElectric circuit. The circuit is designed so as to

combine short pulses with a low frequency bias voltage without interference

between the pulser and the low frequency power supply. In experiments with

sinusoidal bias, the dc power supply was replaced by a high-voltage

transformer. FIG. 4. Color onlineTerminology used in the paper for the pulse and bias

voltage polarities. The encapsulated electrode is always considered to be at

zero potential. The sign of potential of the exposed electrode relative to the

encapsulated one determines the pulse and bias polarity.

043304-3 Opaits et al. J. Appl. Phys. 104, 043304 2008

NASA/CR—2012-217654 16
resistor, and LR and LC are inductances of the connecting

wires. Note that usually Z0nZ, where n is the number of

the cables. This simplifies the circuit to the one shown in Fig.

5b. Kirchhoff’s laws for this circuit can be written as

6E = 3Z0IRL + ILC+ IRLR + LR

dIRL

dt , 1

6E = 3Z0IRL + ILC+ V + LC

dILC

dt , 2

V = 1

C

o

t

ILCd. 3

From these, we get the following set of two integrodifferential equations for the currents:

dIRL

dt = 1LR

6E − 3Z0IRL + ILC− IRLR, 4

dILC

dt = 1LC

6E − 3Z0IRL + ILC− 1

C

o

t

ILCd	. 5

Solving the set of equations using first order explicit Euler’s

method, we obtain the dependence of the currents on time.

From that, the time-dependent voltage on the plasma actuator

and of the reflected pulse is calculated as

Vreflected = 3Z0IRL + ILC− 3E. 6

In the absence of a reactive load, this gives a well-known

result—the ringing can be eliminated by a matching load. In

our case, it was 225 . In the experiments, the connecting

wires had finite dimensions, i.e., inductances. To evaluate the

inductances, we used an approximate expression for circular

loop inductance,

Lcircle  R0
ln

8R

a 	 − 2, 7

where R is the radius of the loop, a is the radius of the wire,

and 0 is the permeability of free space. In the experiments,

the wires connecting the resistance formed a loop with

1 cm radius, while the wires connecting the actuator were

longer and the corresponding radius was 5 cm. This corresponds to inductances of LR= 0.038 H and LR

= 0.294 H. Substituting these numbers into the numerical

code, the pulse reflection can be calculated. Calculations

showed that at these values of inductances, there is almost no

difference if a 250 resistor is used as the matching impedance instead of the 225 one. Therefore, in the experiments, 250 resistor was used due to its availability in the

laboratory. Unfortunately, the reflection of the pulse from the

pulser back to the actuator could not be calculated because of

the complex structure of the pulser. Therefore, the numerical

results are for single reflection only, whereas the experimental ones show all the ringing which takes place between the

actuator and the pulser. Note that increasing the actuator’s

capacitance leads to a lower peak voltage and to increased

pulse duration. The voltage over the actuator and the reflected pulse is shown in Fig. 6. By choosing the right resistance, we were able to reduce the ratio of the reflected pulse

to the voltage over the actuator from 60% to 40%. The main

reason for the 40% reflection is the inductance of the connecting wires. The numerical model also predicted the pulse

duration increase from 4 to 5.5 ns. This result agrees well

FIG. 5. An equivalent scheme of the transformer made of sections of transmission lines connected to the RLC load. aFull circuit; breduced circuit.

FIG. 6. Color onlineNumerical calculation of the nanosecond pulses. The plots show profiles of the pulse originally generated by the pulser, the voltage

profile over the actuator, and the pulse reflected back into the cables. Left plot is for nonoptimized load. Right plot is for optimized load with 250 

noninductive resistor. Adding the resistor decreases the ratio of the reflected pulse to the voltage on the actuator from 60% to 40%. These 40% are due to

inductances of the connecting wires.

043304-4 Opaits et al. J. Appl. Phys. 104, 043304 2008

NASA/CR—2012-217654 17
with the experiment. The measured pulse profiles before and

after optimization are shown in Fig. 7.

Experiments showed that covering the exposed electrode

by a kapton tape, thus preventing the discharge ignition,

changed the amplitude of reflected pulse by only a few percent. Thus it was concluded that the plasma impedance plays

an insignificant role in the impedance matching problem.

IV. RESULTS

The schlieren technique provides the coupling between

the theoretical investigation of the plasma-gas interaction

and the experiment. The plasma model predicts the heating

rate and the force exerted on the gas. The output parameters

from the plasma calculations can be then used as an input for

the time-accurate numerical computational fluid dynamics

CFDmodel based on 2D Navier–Stokes equations. The

experiments showed that the DBD actuator run in pulse-burst

mode generates periodic wall jets which evolve into vortical

structures. The numerical model predicts similar vertical

structures and allows us to restore the entire flow pattern by

matching the schlieren images of a single vortex.

FIG. 8. Color onlineAir density and velocity distribution 14 ms after the

burst.

FIG. 9. Color onlineAn example of experimental leftand simulated

rightschlieren images of the DBD plasma jets. The images are 20

10 mm2 each and correspond to 7, 14, and 21 ms after the burst start.

FIG. 10. Color onlineVortex propagation velocity as a function of the

distance from DBD at different forces in the interaction region. The maximum velocities of the induced flow at the vicinity of interaction region are

designated as “max flow velocities.”

FIG. 11. Color onlineVarying the bias voltage in constant bias experiments. The pulse voltage is unchanged, thus change in bias voltage leads to

the same change in the peak voltage.

FIG. 7. Color onlineThe measured pulse profile before and after

optimization.

043304-5 Opaits et al. J. Appl. Phys. 104, 043304 2008

NASA/CR—2012-217654 18
FIG. 12. Color onlineThe induced flow speed vs distance at different constant bias voltages. The error bar is 0.04 m/s.

FIG. 13. Color onlineBias voltage switch experiments. The columns represent images taken 7, 14, and 21 ms after the burst started. Different rows

represent different bias profiles. The electrode arrangement is indicated. The

results are presented for 5 kV negative pulses, 50 kHz, 50% duty cycle. The

bias voltage was +/−2 kV. The view field is 2010 mm2

.

FIG. 14. Surface wipe experiments. The experiments were done for 0 kV

left columnand +2 kV right columnbias voltages with 5 kV, 50 kHz,

50% duty cycle positive pulses and time delays of 10, 20, and 60 s. Wiped

runs were done with 10 s time delay during which the charge was removed

from the surface by a grounded wet cloth. The last picture in the left column

shows the very first run of the day, when the surface was still charge-free.

The last picture in the right column shows a bias switch experiment in which

the bias voltage was changed from 0 to +2 kV. The images were taken 12

ms after the burst start. The field of view of each image is 2010 mm2

.

FIG. 15. Color onlineNanosecond

pulses combined with sinusoidal bias

voltage. 5 kV, 50 kHz positive left

columnand negative right column

pulses combined with 2.6 kV peak-topeak 60 Hz sinusoidal bias voltage.

The field of view of each image is

2010 mm2

.

043304-6 Opaits et al. J. Appl. Phys. 104, 043304 2008

NASA/CR—2012-217654 19
The 2D Navier–Stokes equations were solved using second order accurate MacCormack scheme.54 The computational domain was 52 cm2

. The time step was determined

by the Courant-Friedrichs-Lewy CFLcondition. The modeling has been performed for quiescent air at initial temperature of 300 K. The gas constants have been taken from Ref.

54. The dielectric surface temperature 1 mm downstream

from the exposed electrode was considered to be 350 K.

Several cases have been studied. We considered the plasma

region to be 100500 m. The force on the gas was considered to act only in horizontal direction downstream and to

be uniformly distributed in the interaction region. In the

simulations, the force magnitude and heating in the interaction region were varied.

In the experiment the pulser was run in burst mode at 50

kHz PRR and 50% duty cycle, giving 10 ms bursts with 500

pulses in each burst every 20 ms. The pulse voltage was 5

kV. In addition 2 kV bias voltage was applied to the electrodes.

Consider the flow induced by the DBD plasma actuator

in pulse-burst mode. When the DBD is on, the gas in the

interaction region is being heated and receives momentum in

the downstream direction from left to right. The motion of

the gas generates pressure gradient in the vicinity of interaction region. The gas is being sucked in that region from the

left and from above, creating an upstream vorticity. At the

same time another vortex is generated by the induced gas jet

Fig. 8. There are important differences between the two

vortices. One of them is the sign of vorticity. The vorticities

of upstream and downstream vortices are negative and positive, respectively. Another principal difference is the gas density in these vortices. The upstream vortex involves motion

of the quiescent air at room temperature, thus its temperature

is constant. In contrast, the downstream vortex is generated

due to the motion of heated gas jet. Thus, it is characterized

by well-defined temperature and density profiles. In the

schlieren experiments on DBD induced flow, only density

gradients can be visualized, i.e., the downstream vortex is

observed and the upstream one is not detected. These results

can be important in theoretical investigations of the flow

separation control using DBD: the gas flow will interact not

only with the observed downstream vortex but also with the

“hidden” upstream one. Representative examples of such

vortical structures, both experimental and reproduced in the

numerical modeling, are shown in Fig. 9. By comparing the

experimental and computational results, it was thus possible

to reconstruct the entire evolving flow pattern and to infer

both induced velocity field and the magnitude of plasma induced body force. For this example the motion of the vortex

was around 0.5 m/s 17 mm downstream and that was driven

by a surface jet with a velocity of 7 m/s in the plasma vicinity.

In our previous work37–40 we calculated the integral momentum transferred to the gas by means of positive and

negative nanosecond pulses with dc bias, as well as the heating rate in the interaction region. We have now extracted that

data and used it as an input to the Navier–Stokes solver. An

important assumption in the modeling was that there are no

saturation effects due to surface charging. The pulser was

considered to operate at 500 kHz repetition rate. The computed vortex propagation velocity as a function of distance

from the exposed electrode is shown in Fig. 10. Taking the

results for momentum transfer from Refs. 38 and 39 for positive 3 kV pulses 4 ns FWHMwith 1 kV dc bias and distributing it equally in the interaction region, we get the force

in that region, 1.4105 N/m3

. The numerical results for

this calculation are between the green roundand blue

squaredata points in Fig. 10. The other curves correspond

FIG. 16. Color onlineVortex speed vs distance for different PRRs with positive polarity of the pulses. The schlieren images were taken at the same moment

of time for 20, 50, and 100 kHz. A slow vortex is created by a jet from positive bias half-cycle, then from 5 – 7 mm it is accelerated by a jet from the

negative bias half-cycle burst. The field of view of each schlieren image is 2010 mm2

.

043304-7 Opaits et al. J. Appl. Phys. 104, 043304 2008

NASA/CR—2012-217654 20
to the different force magnitudes in the interaction region at

constant heating rate. It can be clearly seen that the translational vortex velocity significantly drops with the propagation along the surface. This fact is very important, since using the schlieren technique in the experiments we can extract

the density gradients at several temporal points and thus determine the vortex propagation speed. The developed model

thus allows inferring the induced flow velocity right at the

edge of the plasma and the force magnitude in the interaction

region by matching the experimental pictures with numerically obtained ones. The effect of heating was also investigated; however, the results showed that the vortex size has

almost no dependence on the heating in the interaction region. Only the temperature of the gas within the vortex varies. Note that the gas temperature cannot be measured by the

schlieren technique, and additional measurements with other

techniques should be used to provide an additional insight

into the plasma-flow interaction.

To examine experimentally how the actuator induced

flow speed depends on the constant bias voltage, we ran

experiments with fixed pulse voltage and different bias voltages, as shown in Fig. 11. The vortex translational speed

versus coordinate at different bias voltages is shown in Fig.

12 for both polarities of the pulses. The experiments showed

that in the case of negative pulses there is only a weak,

within the error bars, dependence of the induced flow velocity on the bias voltage. Bias voltage of either polarity increased the induced jet speed only slightly. For the positive

pulses, there was no clear dependence on the bias voltage.

These results did not agree with the expectations based on

FIG. 17. Color onlineVortex speed vs distance for different PRRs with negative polarity of the pulses. The schlieren images were taken at the same moment

of time for 30, 50, and 70 kHz. In the bottom images, a vortex from the negative bias half-cycle is shown. The vortex consists of two parts: head vortex and

tail vortex. In the top image, jet from positive bias half-cycle hitting the tail part of the negative vortex is shown. The speed of the positive vortex greatly

depends on the PRR, while the speed of the negative one does not. The field of view of each schlieren image is 2010 mm2

.

043304-8 Opaits et al. J. Appl. Phys. 104, 043304 2008

NASA/CR—2012-217654 21
the numerical plasma model that predicted significant increase in the induced flow velocity with the bias voltage.

However, during the experiment, an interesting phenomenon was noticed: a rapid switch of the bias polarity increased the jet velocity for the first several pulse bursts. To

observe the details of the first vortices after the bias switch,

the camera was triggered at the very beginning of every run

so that it captured the first bursts. The actuator was thus run

at some value of the bias voltage for 5 s, and then the pulses

were turned off. After 10 s off, the pulses were turned on

again, and the first burst of this second run was captured.

This second run was done at either the same or a different

value of the bias voltage compared to the first run. As in the

previous experiments, the pulser was run in burst mode at 50

kHz PRR and 50% duty cycle, giving 10 ms bursts with 500

pulses in each burst every 20 ms. The pulse voltage was 5

kV, and the bias voltage was changed from −2 to +2 kV.

The results are presented in Fig. 13. Columns represent images taken 7, 14, and 21 ms after the burst started. Different

rows represent different biases. The electrode arrangement is

indicated. The results show that switching the polarity of the

bias voltage has a dramatic effect on the DBD operation:

much faster jets and vortices are generated compared to the

constant bias cases. An interesting feature can also be seen

when switching from positive to negative bias. The induced

wall jet from the first burst makes what looks like a jump.

The jet created by the second burst, however, does not

“jump” anymore. The location of the jump is around the

region where the plasma ends. In the case of positive pulses,

a similar jump can be observed when switching from negaFIG. 18. Color onlineVortex speed vs distance for different pulse voltages with positive polarity of the pulses. The schlieren images were taken at the same

moment of time for 3.3, 5.0, and 7.4 kV. In the top images, slow jet from positive bias half-cycle is shown. In the bottom images, a vortex from the negative

bias half-cycle is shown. The speed of this vortex is high and depends strongly on the pulse voltage. In the pictures for 5.0 and 7.4 kV, this vortex is colliding

with the positive one. The field of view of each schlieren image is 2010 mm2

.

043304-9 Opaits et al. J. Appl. Phys. 104, 043304 2008

NASA/CR—2012-217654 22
tive to positive bias voltage. In addition, in that case the

second vortex also “jumps.” The same behavior was observed during switches from −2 to 0, 0 to −2, 0 to +2, and +2

to 0 kV for both polarities of the pulses. However, the jet

velocity increase and the jump were not as strong as in the

cases of switching between negative and positive polarities

of the bias voltage.

Likely explanation for the observed behavior is accumulation of surface charge on the dielectric. During the run, the

dielectric surface is charged, and shielding of the applied

bias electric field occurs, reducing the force on the gas and

the jet velocity. This explains why in the first series of experiments the effect was determined by the difference between the peak voltage and the bias voltage and not so much

by the peak voltage or the bias voltage separately. Switching

the polarity of the bias removes the surface charge and enhances the actuator performance for a short time, until the

surface charge builds up again. One reason for the jump

behavior could be an interaction of residual space charge

with the surface charge. More studies are needed to better

understand these phenomena.

To check if there really is a surface charge accumulated

on the dielectric, the next set of experiments was conducted.

The conditions were similar to the previous experiments.

First the actuator was run for 5 s. Then after some time being

off it was run again without switching the bias voltage. The

first burst of the second run was captured. The aim was to

see how the generated vortex depends on the time delay between the runs. The experiments were done for −2, 0, and

+2 kV bias voltages with 5 kV, 50 kHz, 50% duty cycle

positive pulses and time delays of 10, 20, and 60 s. Another

run was done with 10 s time delay during which the charge

FIG. 19. Color onlineVortex speed vs distance for different pulse voltages with negative polarity of the pulses. The schlieren images were taken at the same

moment of time for 3.3, 5.0, and 7.4 kV. In the top images, jet from positive bias half-cycle is shown. In the bottom images, a jet from the negative bias

half-cycle is shown, consisting of two parts: head vortex and tail vortex. There is no dependence of the speed of the vortices on the pulse voltage. The field

of view of each schlieren image is 2010 mm2

.

043304-10 Opaits et al. J. Appl. Phys. 104, 043304 2008

NASA/CR—2012-217654 23
was removed from the surface. The surface charge removal

was done with a wet grounded cloth. The water provided a

good contact with the entire surface, and after a wipe the

surface was slightly wet and quickly dried out by itself. The

whole procedure took less then 10 s at the end of which the

surface was dry and discharged. Wiping the surface with a

dry cloth to remove the water might lead to charging through

friction. The results are presented in Fig. 14. It is seen that

the vortex-generating performance persists for the times up

to 1 min. If the observed behavior was due to some heating

effects, there would not have been such a long hysteresis as

1 min. This provides evidence in favor of the surface charge.

Also the wiped-surface runs with bias look like a switch

from zero bias voltage. This shows that the effect does occur

due to the surface charge which depends on the bias voltage.

It can be seen that the vortex is very similar to the one from

the wiped-surface run, which means that both the wipe and

the run at 0 kV bias voltage discharge the surface. Again it

can be seen that the surface charge shields the applied bias

voltage. However, if the surface charge is removed, the

plasma feels the bias voltage, but only until new charge

builds up on the dielectric surface.

It was not possible to conduct similar experiments with

the negative pulses. As mentioned above, the bias voltage

was applied to the same electrode as the pulses, i.e., for the

negative pulses that would be the exposed electrode. Manually wiping the surface to remove the charge in the close

vicinity of the electrode at a few kilovolts potential would be

unsafe.

Since the jet-enhancement effect disappears as soon as

FIG. 20. Color onlineVortex speed vs distance for different peak-to-peak sinusoidal bias voltages with positive polarity of the pulses. The schlieren images

were taken at the same moment of time for 5, 10, and 13 kV. In the top images, a slow jet from positive bias half-cycle is shown; when a strong jet from the

negative half-cycle arrives, it pushes the positive jet forward, which explains the acceleration in 6–11 mm range. In the bottom images, a vortex from the

negative bias half-cycle is shown. Its speed is high and strongly depends on the pulse voltage. In the pictures for 5.0 kV, the collision is still in progress, which

explains the complex shape of the vortex. The field of view of each schlieren image is 2010 mm2

.

043304-11 Opaits et al. J. Appl. Phys. 104, 043304 2008

NASA/CR—2012-217654 24
the charge builds up on the dielectric and shields the bias

field, to let the effect go on continuously, one needs to keep

switching the bias. Thus, a new voltage waveform was used

in the subsequent experiments: high-voltage sinusoidal signal 2.6 kV peak to peak, 60 Hzplus nanosecond pulses 50

kHz, 5 kV, positive or negative. Three versions of the voltage waveform were examined: a100% duty cycle pulses

+ sinusoidal bias voltage, b50% duty cycle pulses, bursts

near the peak of the sinusoidal voltage+ sinusoidal bias voltage, and c50% duty cycle pulses, bursts at the slopes of the

sinusoidal voltage+ sinusoidal bias voltage, and were compared with the pulses without any bias voltage: d50% duty

cycle pulses with no bias.

Since this set of experiments involved 60 Hz sinusoidal

signal, a new modulation of the pulses had to be used. The

pulses were generated in bursts with 208 pulses per burst and

120 bursts per second. The results are presented in Fig. 15.

From the experimental results we can see that the sinusoidal bias significantly improves the actuator performance.

The jet speed increases from 30 cm/s near the discharge

in case dto 80 cm/s at 10 mm downstream in case a.

Thus, even a relatively low bias voltage 1.3 kV amplitude

comparing to 5 kV of the pulseshas a great effect on the

DBD actuator operation. Note that the bias voltage itself

could not ignite the plasma in the absence of the pulses.

Also, vortices are still observed in case adespite the fact

that the pulses are on all the time. This means that the inFIG. 21. Color onlineVortex speed vs distance for different peak-to-peak sinusoidal bias voltages with negative polarity of the pulses. The schlieren images

were taken at the same moment of time for 5, 10, and 13 kV. In the top images, jet from positive bias half-cycle is shown. The vortex speed strongly depends

on the negative pulse voltage. The field of view of each schlieren image is 2010 mm2

. The circle in the images is due to water condensation in the camera.

FIG. 22. Color onlineVoltage profiles with pulses near the bias voltage

peaks of one polarity only.

043304-12 Opaits et al. J. Appl. Phys. 104, 043304 2008

NASA/CR—2012-217654 25
duced wall jet speed strongly depends on instantaneous bias

voltage as well as on the surface charge on the dielectric. In

addition, vortices coming out of different bursts, i.e., of

bursts at different bias voltages, are different. The vortex

speed and size depend on whether it was generated during

positive/negative bias/slope of the bias voltage.

For further investigation we selected voltage waveform

with pulses near the peaks of the bias voltage, since this

waveform was more effective than the one with the pulse

bursts at the bias voltage slopes. Additionally, with this

waveform, it can be determined unambiguously which burst

the vortex came from, which makes the data easier for interpretation.

DBD actuator operation dependence on the new voltage

waveform parameters was investigated. As a baseline voltage

waveform, we chose 5 kV pulses at 50 kHz and 50% duty

cycle near the peaks of 10 kV peak-to-peak 60 Hz sinusoidal

bias voltage. Then varying one of the parameters at a time

the bias voltage, pulse voltage, and repetition ratewe observed the vortices for each polarity of the pulses. As mentioned above, the vortices coming out of different bias halfcycles differ in speed and size. Thus plots for both kinds of

vortices are presented in the figures when possible.

Consider first the actuator performance dependence on

PRR for positive pulses Fig. 16. The vortex coming out of

the positive bias half-cycle is slow. It does not move far

away from the plasma region by the time the next vortex

appears. The next vortex, which comes out of the negative

bias have-cycle, is very fast. It actually does not evolve into

a vortex immediately; it is still in its jet phase and thus is

hard to notice. Then, upon collision with the earlier generated slow vortex, it also becomes a vortex. Thus, actually

there is only one vortex in the schlieren image at a time. As

seen in Fig. 16, there is some weak dependence on the PRR.

The dependence of vortex parameters on PRR for negative pulses Fig. 17is different. The vortices created during

FIG. 23. Color onlineVortex speed vs distance for different voltage waveforms, see Fig. 20. The schlieren images were taken at the same moment of time

for pulses during negative half-cycle only, both half-cycles, and positive half-cycle only. The field of view of each schlieren image is 2010 mm2

.

043304-13 Opaits et al. J. Appl. Phys. 104, 043304 2008

NASA/CR—2012-217654 26
the negative bias half-cycles consist of two parts. The head

part is not observed for pulses repetition rate lower than 30

kHz. Its speed is relatively high and does not depend on the

PRR. The tail part is brighter and much slower. The vortex

created during positive bias half-cycle is faster. Its speed

strongly depends on the PRR, as seen in Fig. 17.

The next parameter varied in the experiments was the

pulse voltage. The results for the positive pulses are presented in Fig. 18. The speed of positive i.e., generated during the positive half-cycle of the bias voltagevortices

weakly depends on the pulse voltage. However, their brightness temperaturestrongly depends on the pulse voltage.

The pulse voltage has a dramatic effect on the speed of negative i.e., generated during the negative half-cycle of the bias

voltagevortices. For the negative polarity of the pulses, the

vortex speed is quite high, and the only effect of the higher

pulse voltage is stronger heating. The details are shown in

Fig. 19.

Among all the parameters, the sinusoidal bias voltage

has perhaps the strongest influence on the DBD plasma actuator operation. The results for the positive pulses are presented in Fig. 20. Again, positive vortices are rather slow,

and it is unclear if changing the bias voltage has any effect

on them because they propagate only several millimeters before the vortices from the negative bias half-cycles hit them

from behind. The speed of vortices from the negative halfcycles depends strongly on the bias voltage. For negative

pulses, the increase in bias voltage leads to a significant increase in effect in both half-cycles of the bias voltage. The

results are presented in Fig. 21.

Starting from 5 kV peak-to-peak bias voltage, selfsustained discharge was ignited in the absence of the highvoltage pulses. This discharge could remove the surface

charge by itself. Since positive pulses create a strong force

on the gas only during the negative bias half-cycle, it was

interesting to check if it is still important to have pulse bursts

during the positive half-cycle of the bias. Thus experiments

were run with the pulses during half-cycles of one polarity

only. The voltage waveforms are shown in Fig. 22. The results of the experiments are shown in Fig. 23. It can be seen

that in the absence of the pulse burst during the other halfcycle, the induced wall jet speed becomes two to three times

lower in all cases. This means that although some of the

pulse bursts do not create a strong wall jet, they still play an

important role in the DBD operation. Their task is to

discharge/recharge the dielectric surface and thus to increase

the efficiency of the other bursts. The experiments also

clearly show that the wall jets induced by negative pulses

evolve into two-vortex formations, whereas the ones from

the positive pulses do not. The mechanism of this behavior

should be investigated in future studies.

V. CONCLUSIONS

We have used a burst mode of plasma actuator operation

in conjunction with nonintrusive schlieren diagnostic of the

actuator induced flows in quiescent gas. With this technique,

the DBD actuator was observed to generate periodic pulsed

wall jets that evolve into vortices, and parametric studies of

the vortex speed and size versus parameters of the waveform

pulses in repetitive-burst mode plus dc or ac bias voltage

were performed. Matching 2D numerical fluid modeling to

the experimental results allowed us to infer the magnitude of

plasma-generated body force exerted on the gas. The knowledge of the body force magnitude can then be used to compute the entire flow field in both burst and continuous modes

of plasma actuator operation.

The experiments showed that although repetitive short

pulses do efficiently generate the plasma, a dc bias voltage

cannot push the gas efficiently because the charge buildup on

the dielectric surface shields the applied dc electric field.

To remove the surface charge, periodic switching of the

bias voltage polarity is required. Thus, we proposed a new

voltage waveform, consisting of high-voltage nanosecond repetitive pulses superimposed on a high-voltage low frequency sinusoidal or square-wave bias voltage.

The advantages of the new voltage waveform in significantly enhancing the wall jets and the vortices have been

demonstrated experimentally.

Note that in conventional DBD actuators driven by sinusoidal voltages, ionizing pulses streamer breakdownsalso

occur, but the magnitude and frequency of those ionizing

pulses depend entirely on the parameters of the sinusoidal

driving voltage. In contrast, we proposed and used what is

essentially non-self-sustained discharge: the plasma is generated by repetitive short pulses, and the pushing of the gas

occurs primarily due to the low frequency biasvoltage. The

advantage of this non-self-sustained discharge is that the parameters of ionizing pulses and the driving bias voltage can

be varied independently, which adds flexibility to control and

optimization of the actuator performance.

Future work should involve investigation of different dielectric surfaces due to the importance of surface charge

buildupand parametric studies of the induced flow velocity

versus frequency of the sinusoidal bias voltage. Nonsinusoidal bias voltage waveforms should also be investigated.

ACKNOWLEDGMENTS

This work was supported in part by NASA Glenn Research Center Dr. David Ashpis, in part by the Air Force

Office of Scientific Research Dr. John Schmisseur. Fellowship support for one of the authors A.V.L.was provided by

Princeton Program in Plasma Science and Technology.

1

S. O. Macheret, M. N. Shneider, and R. B. Miles, AIAA J. 42, 1378

2004. 2

S. O. Macheret, M. N. Shneider, R. B. Miles, and R. J. Lipinski, AIAA J.

39, 1127 2001. 3

S. O. Macheret, M. N. Shneider, and R. B. Miles, AIAA J. 40, 74 2002. 4

S. O. Macheret, M. N. Shneider, and R. B. Miles, J. Propul. Power 18, 424

2002. 5

M. N. Shneider, S. O. Macheret, and R. B. Miles, AIAA J. 42, 2303

2004. 6

S. O. Macheret, M. N. Shneider, and R. B. Miles, 34th AIAA Plasmadynamics and Lasers Conference, Orlando, FL, 23–26 June 2003, unpublished, Paper No. AIAA-2003-3763. 7

R. C. Murray, L. Vasilyak, M. R. Carraro, S. H. Zaidi, S. O. Macheret, M.

N. Shneider, and R. B. Miles, 42nd Aerospace Sciences Meeting and

Exhibit, Reno, NV, 5–8 January 2004 unpublished, Paper No. AIAA2004-1025.

8

S. O. Macheret, M. N. Shneider, and G. V. Candler, 42nd Aerospace

043304-14 Opaits et al. J. Appl. Phys. 104, 043304 2008

NASA/CR—2012-217654 27
Sciences Meeting and Exhibit, Reno, NV, 2004 unpublished, Paper No.

AIAA 2004-1024.

9

M. N. Shneider and S. O. Macheret, 35th AIAA Plasmadynamics and

Lasers Conference, Portland, OR, 2004 unpublished, Paper No. AIAA2004-2662.

10M. N. Shneider and S. O. Macheret, 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 10–13 January 2005 unpublished, Paper No.

AIAA-2005-0979.

11R. B. Miles, S. O. Macheret, M. N. Shneider, C. Steeves, R. C. Murray, T.

Smith, and S. H. Zaidi, 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 10–13 January 2005 unpublished, Paper No. AIAA2005-0561.

12A. L. Kuranov and E. G. Sheikin, 40th AIAA Aerospace Sciences Meeting

and Exhibit, Reno, NV, 14–17 January 2002 unpublished, Paper No.

AIAA-2002-0490.

13A. Vatazhin, V. Kopchenov, and O. Gouskov, Third AIAA Weakly Ionized

Gases Workshop, Norfolk, VA, 1–5 November 1999, Paper No. AIAA1999-4972.

14V. A. Bityurin, A. I. Klimov, S. B. Leonov, A. N. Bocharov, and J. T.

Lineberry, Third AIAA Weakly Ionized Gases Workshop, Norfolk, VA,

1–5 November 1999 unpublished, Paper No. AIAA-1999-4820. 15M. Nishihara, N. Jiang, J. W. Rich, W. R. Lempert, I. V. Adamovich, and

S. Gogineni, Phys. Fluids 17, 106102 2005. 16M. Nishihara, J. W. Rich, W. R. Lempert, I. V. Adamovich, and S. Gogineni, Phys. Fluids 18, 086101 2006. 17D. Gaitonde, 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno,

NV, 10–13 January 2005 unpublished, Paper No. AIAA-2005-560. 18S. T. Surzhikov and J. S. Shang, 43rd AIAA Aerospace Sciences Meeting

and Exhibit, Reno, NV, 10–13 January 2005 unpublished, Paper No.

AIAA-2005-0406.

19S. T. Surzhikov and J. S. Shang, J. Comput. Phys. 199, 437 2004. 20S. T. Surzhikov and J. S. Shang, 42nd Aerospace Sciences Meeting and

Exhibit, Reno, NV, 5–8 January 2004 unpublished, Paper No. AIAA2004-0508.

21S. T. Surzhikov and J. S. Shang, High Temp. 43, 19 2005. 22R. Kimmel, J. Hayes, J. Menart, and J. S. Shang, 42nd Aerospace Sciences

Meeting and Exhibit, Reno, NV, 5–8 January 2004 unpublished, Paper

No. AIAA-2004-0509.

23J. Poggie, 35th AIAA Plasmadynamics and Lasers Conference, Portland,

OR, 28 June–1 July 2004 unpublished, Paper No. AIAA-2004-2858. 24J. S. Shang, R. Kimmel, J. Hayes, C. Tyler, and J. Menart, J. Spacecr.

Rockets 42, 780 2005. 25J. S. Shang and S. T. Surzhikov, AIAA J. 43, 1633 2005. 26J. Menart, J. Shang, C. Atzbach, S. Magoteaux, M. Slagel, and B. Bilheimer, 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV,

10–13 January 2005 unpublished, Paper No. AIAA-2005-947. 27S. B. Leonov, D. A. Yarantsev, V. G. Gromov, and A. P. Kuriachy, 43rd

AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 10–13 January

2005 unpublished, Paper No. AIAA-2005-0780. 28S. O. Macheret, 44th AIAA Aerospace Sciences Meeting and Exhibit,

Reno, NV, 9–12 January 2006 unpublished, Paper No. AIAA-2006-1005. 29S. H. Zaidi, T. Smith, S. O. Macheret, and R. B. Miles, 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 9–12 January 2006 unpublished, Paper No. AIAA-2006-1006. 30C. L. Enloe, T. E. McLaughlin, R. D. VanDyken, K. D. Kachner, E. J.

Jumper, and T. C. Corke, AIAA J. 42, 589 2004. 31C. L. Enloe, T. E. McLaughlin, R. D. VanDyken, K. D. Kachner, E. J.

Jumper, T. C. Corke, M. Post, and O. Haddad, AIAA J. 42, 595 2004. 32M. Post and T. C. Corke, 35th AIAA Fluid Dynamics Conference and

Exhibit, Toronto, Ontario, 6–9 June 2005 unpublished, Paper No. AIAA2005-4630.

33T. C. Corke, E. J. Jumper, M. L. Post, D. Orlov, and T. E. McLaughlin,

40th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 14–17

January 2002 unpublished, Paper No. AIAA-2002-350. 34M. L. Post and T. C. Corke, AIAA J. 42, 2177 2004. 35D. F. Opaits, D. V. Roupassov, S. M. Starikovskaia, A. Yu. Starikovskii, I.

N. Zavialov, and S. G. Saddoughi, 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 10–13 January 2005 unpublished, Paper No.

AIAA-2005-1180.

36D. Opaits, A. Likhanskii, M. Shneider, G. Neretti, S. Zaidi, S. Macheret,

and R. Miles, 38th AIAA Plasmadynamics and Lasers Conference, Miami,

Florida, 25–28 June 2007 unpublished, Paper No. AIAA-2007-4532. 37A. Likhanskii, M. Shneider, S. Macheret, and R. Miles, 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 9–12 January 2006

unpublished, Paper No. AIAA-2006-1204. 38A. Likhanskii, M. Shneider, S. Macheret, and R. Miles, 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 10–13 January 2007 unpublished, Paper No. AIAA-2007-633. 39A. Likhanskii, M. Shneider, S. Macheret, and R. Miles, Phys. Plasmas 14,

073501 200740A. Likhanskii, M. Shneider, D. Opaits, S. Macheret, and R. Miles, 38th

AIAA Plasmadynamics and Lasers Conference, Miami, Florida, 2007 unpublished, Paper No. AIAA-2007-4533. 41C. Enloe, T. McLaughlin, G. Font, and J. Baughn, 44th AIAA Aerospace

Sciences Meeting and Exhibit, Reno, NV, 2006 unpublished, Paper No.

AIAA-2006-166.

42S. Leonov, D. Yarantsev, and A. Kuriachy, 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 2005 unpublished. 43R. Sosa, E. Arnaud, and G. Artana, International Simposium on Electrohydrodonamics ISEHD, Buenos Aires, Argentina, 2006 unpublished. 44T. Jukes, K. Choi, G. Johnson, and S. Scott, Third AIAA Flow Control

Conference, San Francisco, CA, 2006 unpublished, Paper No. AIAA2006-3693.

45A. M. Konchakov, V. M. Krivtsov, S. B. Leonov, V. R. Soloviev, and D.

A. Yarantsev, preprint of Institute of High Temperature RAS 2-491, 2006

unpublished. 46G. I. Font, S. Jung, C. L. Enloe, T. E. McLaughlin, W. L. Morgan, and J.

W. Baughn, 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno,

NV, 2006 unpublished, Paper No. AIAA-2006-167. 47M. R. Visbal and D. V. Gaitonde, 44th AIAA Aerospace Sciences Meeting

and Exhibit, Reno, NV, 2006 unpublished, Paper No. AIAA-2006-505. 48M. R. Visbal, D. V. Gaitonde, and S. P. Gogineni, 29th Fluid Dynamics

Conference, Albuquerque, NM, 1998 unpublished, Paper No. AIAA1998-2643.

49S. Gogineni, M. Visbal, and C. Shih, Exp. Fluids 27, 126 1999. 50S. Gogineni, M. Visbal, and C. Shih, 35th AIAA Aerospace Sciences

Meeting and Exhibit, Reno, NV, 1998 unpublished, Paper No. AIAA1997-0071.

51J. R. Roth, D. M. Sherman, and S. P. Wilkinson, 36th AIAA Aerospace

Sciences Meeting and Exhibit, Reno, NV, 1998 unpublished, Paper No.

AIAA-1998-0328.

52G. S. Settles, Schlieren and Shadowgraph Techniques Springer, NY,

2001. 53G. A. Mesiats, S. A. Nasibov, and V. V. Kremnev, Formirovanie Nanosecundnih Impulsov Visokogo Napriazhenia Energia, Moscow, 1970in

Russian. 54D. A. Anderson, J. C. Tannehill, and R. H. Pletcher, Computational Fluid

Mechanics and Heat Transfer Hemisphere, New York, 1984.

043304-15 Opaits et al. J. Appl. Phys. 104, 043304 2008

NASA/CR—2012-217654 28
Modeling of dielectric barrier discharge plasma actuator in air

Alexandre V. Likhanskii,1,a Mikhail N. Shneider,2 Sergey O. Macheret,3 and

Richard B. Miles2

1

Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park,

Pennsylvania 16802, USA

2

Department of Mechanical and Aerospace Engineering, Princeton University, Princeton,

New Jersey 08544, USA

3

Lockheed Martin Aeronautics Company, Palmdale, California 93599, USA

Received 24 January 2007; accepted 29 November 2007; published online 11 March 2008

A detailed physical model for asymmetric dielectric barrier discharge DBDin air at low voltages

1.5–2 kVis developed. Modeling of DBD with an applied sinusoidal voltage is carried out in two

dimensions. The leading role of charging the dielectric surface by electrons in the cathode phase is

shown to be critical, acting as a harpoon that pulls positive ions forward and accelerates the gas in

the anode phase. The positive ion motion back toward the exposed electrode is shown to be a major

source of inefficiency in the sinusoidal or near-sinusoidal voltage cases. Based on understanding of

the DBD physics, an optimal voltage waveform is proposed, consisting of high repetition rate, short

a few nanoseconds in duration, negative pulses combined with a positive dc bias applied to the

exposed electrode. © 2008 American Institute of Physics. DOI: 10.1063/1.2837890

I. INTRODUCTION

Plasma and magnetohydrodynamic MHDdevices can

potentially be used for internal and external flow control and

power extraction Refs. 1–37, and references therein. Body

forces can be exerted by electric and magnetic fields on

charged species electrons and ionsand coupled to the bulk

gas by collisions. These forces can then be used to extract

power or to control the flow. Plasma-induced gas heating can

also modify the flow Refs. 1–26, and references therein.

Both body forces and heating can be used as virtual shapes

for flow control in the absence of moving parts Refs. 1–27,

and references therein. There is also an increasing interest in

near-surface plasmas with and without magnetic field to control both laminar and turbulent boundary layers, shockboundary layer interactions, and particularly flow separation.

Air Force Research Laboratory researchers Kimmel, Shang

et al.studied dc surface plasmas in a Mach 5 tunnel.16–26

Leonov et al. at the Institute of High Temperatures Moscow,

Russiainvestigated flow control with high-current quasiequilibrium surface arcs.27 Adamovich et al. at the Ohio

State University has demonstrated MHD effects on the supersonic turbulent boundary layer15 and flow deceleration by

Lorentz force.16 Recently, the Princeton University group has

proposed and demonstrated cold nonequilibriumconstricted surface discharges “snowplow arcs”that are magnetically driven downstream or upstream at high velocity and

impart momentum to the boundary layer.11,28,29 All those

studies were devoted to high-speed, supersonic, or hypersonic flow control.

Significant and impressive experimental results have

been obtained by Corke and colleagues at Notre Dame University and the U.S. Air Force Academy,30–34 and by

Starikovskii et al.35 in Russia on the use of asymmetric dielectric barrier discharges DBDfor low-speed separation

control. Despite the successful demonstration of DBD

plasma actuators for flow control and the seeming simplicity

of DBD devices, the fundamental understanding of the underlying physics of their operation is still incomplete. It is

accepted that the experimentally observed near-surface gas

acceleration to several meters per second is due to the transfer of momentum from ions which are accelerated by the

electric field to the bulk gas molecules.

Challenges in modeling and understanding DBD plasma

actuators stem from the physics of the problem. Generation,

decay, drift, and diffusion of electrons and both positive and

negative ions must be correctly described by the model and

resolved by the numerical scheme. Since it is the electric

space charge that is responsible for the net force acting on

the gas, the Poisson equation for the electric potential must

be fully coupled with the other equations. The processes on

both dielectric and metallic surfaces, such as attachment of

electrons to the dielectric surface and the secondary electron

emission from both metallic and dielectric surfaces, must be

included. Additional complexity is due to the high gas density about 1 sea-level atmospheric densityat which DBD

actuators operate. This high density reduces both time and

length scales relevant to the problem. For example, avalanche ionization and sheath formation occur on a subnanosecond time scale, and sharp gradients of the electric field

and net charge density occur on a micron length scale. At the

same time, the model should also be able to compute the

plasma dynamics and kinetics on macroscopic time millisecondsand length millimeters or centimetersscales.

Because of this complexity, several recent modeling

efforts38–42 did not capture some essential features of kinetics

and dynamics of asymmetric DBD plasmas. The first attempts at DBD modeling were performed in Refs. 38–42.

However, the modeled regimes did not explain the observed

experimental results. Reference 41 shows the relevant

plasma kinetics and discharge development, but lacks the a

Electronic mail: alikhans@princeton.edu.

JOURNAL OF APPLIED PHYSICS 103, 053305 2008

0021-8979/2008/1035/053305/13/$23.00 103, 053305-1 © 2008 American Institute of Physics

NASA/CR—2012-217654 29
modeling of voltages used in DBD operation. The empirical

results, based on the DBD experiments, are shown in Ref.

42. But, this model has not resolved the processes in plasma.

All previous plasma modeling has been done in inert gases,

which did not allow an explanation of the features of DBD

operation, experimentally observed in air. For example, the

fact of DBD operation in “push-push” mode in a negative

half-cycle for sinusoidal voltages can be explained only by

the presence of negative ions, which are not present in inert

gases plasmas.

Therefore, it is necessary to develop a consistent, comprehensive, and physically based model that would qualitatively and quantitatively explain the operation of dielectric

barrier plasma actuators. This paper describes the successful

development of such a model. The ultimate goal of the

model development is to find a way of improving the DBD

actuator performance.

II. THE MODEL

The asymmetric DBD plasma actuator30–34 consists of

two electrodes separated by a dielectric layer Fig. 1. The

lower electrode is covered by the dielectric and is grounded,

and the voltage is applied to the upper exposedelectrode.

The electrodes are shifted with respect to each other thus,

the term “asymmetric”. Near the right edge of the upper

electrode the plasma is created, and according to the experimental data30–34 the gas is pushed from left to right.

The modeling was performed for air. The weakly ionized

air plasma was modeled as a four-fluid mixture: neutral molecules, electrons, and positive and negative ions. Note that

the presence of negative ions in air unlike the models for

inert gases or pure nitrogenis quite important for understanding of DBD physics, as will be shown later in this paper. The motion of the charged particles was considered in

the drift-diffusion approximation. We denote the number

densities of electrons, positive and negative ions, and neutrals as ne ,n+ ,n−, and n fluxes as e ,+ ,−. The rate of

ionization is , rates of electron-ion and ion-ion recombination are  and ii, the rate of electron detachment from negative ions is kd, the rate of electron attachment to the neutrals

is va, electron and ion diffusion coefficients and mobilities

are De, Di and e, i

, correspondingly; the thermodiffusion

relation is kt

.

The continuity equations for electrons, positive and

negative ions are then

ne

t

+ jej = e − nen+ + kdnn− − ane, 1

n+

t

+ j+j = e − nen+ − iin+n−, 2

n−

t

+ j−j = − iin+n− − kdnn− + ane, 3

where

ej = − eEjne − Dejne − kt

Dene

jTe

Te

, 4

+j = i

Ejn+ − Dijn+, 5

−j = − i

Ejn− − Dijn−. 6

Since the gas velocity is low in comparison with the drift

velocities of charged particles, for plasma behavior calculations the gas was considered stationary. Ionization and recombination coefficients, as well as attachment, detachment

rates, charged particles mobilities, and electron temperature

are considered as functions E/n, where E is the local electric

field .The numerical values for the rate of ionization,

electron-ion recombination, ion-ion recombination, ion mobilities, attachment and detachment rates are standard and

given in Refs. 43–45. The ion temperature is considered to

be equal to the gas temperature. Electron drift velocities Vdr

and electron temperatures, as functions E/N, are given in

Ref. 46. The electron mobilities are calculated using the following relation:

e = Vdr

E . 7

The diffusion coefficients are calculated using the Einstein

relation,

Di = i

Ti, 8

where i denotes the species electrons, ions.

The boundary conditions at the electrode surface are, for

the cathode,

en = − m+n, 9

and, at the anode,

+n = 0. 10

And, the boundary conditions at the dielectric surface are

en = − d+n, if En  0, 11

and

+n = 0, if En  0. 12

Here, m and d are the effective secondary emission coefficients from metal and dielectric.

The electric field and potential are related to the density

of charged species according to the Poisson equation,

FIG. 1. Color onlineAsymmetric dielectric barrier discharge

configuration.

053305-2 Likhanskii et al. J. Appl. Phys. 103, 053305 2008

NASA/CR—2012-217654 30
	  
= ene + n− − n+, 13

Ej = − j
. 14

The volumetric force on neutral gas can be generally expressed the following way:41

F = en+ − n− − neE + mee

dne

dt − m++

dn+

dt

+ m−−

dn−

dt E − nekTe + n+kT+ + n−kT−. 15

For the simulations, the following geometry was chosen. The

problem is considered two-dimensional, corresponding to the

plane of Fig. 1. The electrodes are considered infinitely thin.

This is justified, since a number of experiments performed

with both slightly protruding and buried electrodes showed

no considerable difference in DBD actuator

performance.30–34 The sizes of the electrode was from 0.1 to

1.5 mm, depending on the plasma length at different voltage

profiles. The cell size for the rectangular grid was chosen

according to the characteristic plasma and voltage scales and

geometrical sizes. Since the maximum charge density in the

DBD plasma was found to be on the order of 1021

−1022 m−3, and the applied voltage is on the order of kilovolts, the voltage drop on the order of several volts much

less than the applied voltagecorresponds to the cell size on

the order of 1–10 microns. It also explains the computational

difficulties of DBD numerical simulation in large scales.

Note that the maximum cell size should be the same even as

the size of DBD plasma is increased, in order to resolve the

relevant plasma dynamics, and increasing the geometrical

size would increase the number of computational points.

Two different numerical schemes were used in DBD

plasma kinetics modeling. For low voltages, a second-order

explicit McCormack scheme47 was able to resolve all physical processes. Using this scheme the low-voltage sinusoidal

case and low-voltage repetitive negative nanosecond pulses

were calculated. Some “wrinkles” on the presented figures

are due to dispersion of this numerical scheme. However, for

higher voltages this scheme could not resolve some plasma

phenomena, such as streamer propagation and back breakdown, due to the scheme dispersion. The

Scharfetter-Gummel48,49 method resolved these problems

and the high-voltage case was modeled using this scheme.

The successive over-relaxation method47 was used to

solve the Poisson equation. One of the difficulties in kinetic

simulations is the choice of time step. In the plasma modeling in this work, two parameters determine it. First, the time

step should allow the resolution of plasma formation and

sheath dynamics time which is of the order of nanoseconds,

and second, the time step should satisfy the CFL CourantFriedrichs-Lewycondition. The combination of these two

requirements leads to the time step of the order of picoseconds. In the modeling, the time step was recalculated on each

step according to the CFL condition and was from 1 to 10

picoseconds.

The complexity of the stated problem, such as resolution

of micron geometrical scales, picosecond time scale for the

nonlinear problem with particle generation, and the necessity

to compute the micro- to milliseconds time intervals and the

geometrical scales of the order of millimeters, sets some

limitations on the model for single-processor calculations.

First of all the model is two-dimensional. This fact does not

allow resolution of the 3D filament structures, experimentally observed in DBD investigations. However, due to overlapping of the streamers, the plasma becomes of diffusion

form, making the 2D assumption work quite well. Another

issue is that the 2D modeling qualitatively explains many

DBD features, but it would be better to compare the 2D

calculations with 3D ones, done on a multiprocessor cluster,

in order to verify the code. The second limitation is the geometrical and the time domain of the problem. Usually in the

modeling the size of the domain was 1 by 1 mm and the

computational time was several microseconds. The payoff

for increasing either the geometrical or time domain to experimental sizes was the decrease in the remaining domain.

Another issue is the range of applied voltages. The higher the

voltages applied, the smaller the grid should be. The decrease of the grid size twice leads to the 8-times increase of

the computational times. The model allowed calculations for

the peak voltages up to 3–4 kV. The above listed issues can

be possibly resolved using parallel computations, on which

our group is currently working.

III. LOW-VOLTAGE SINUSOIDAL SIGNAL

In a number of experiments,27,30–34 the sinusoidal shape

of the applied voltage on the exposed electrode was used as

a baseline. In order to understand the physics of DBD plasmas and the nature of the force exerted on the gas in those

experiments, a series of computations with small-scale geometry several hundred microns, see Sec. IIand high ac

frequency 1000 kHzwas performed. The small scales allow DBD simulations to be performed in a reasonable time

while showing the essential physics. However, it is very important to compare the results with those obtained with larger

plasma sizes in order to understand the scaling issues.

Figure 2 shows the applied voltage and calculated total

and displacement currents in a representative case with small

plasma size and sinusoidal voltage. During the negative halfFIG. 2. Color onlineApplied voltage and calculated current for 1.5 kV,

1000 kHz sinusoidal voltage. Red line shows the voltage shape, dashed blue

line the calculated total current, and dotted line the displacement current.

053305-3 Likhanskii et al. J. Appl. Phys. 103, 053305 2008

NASA/CR—2012-217654 31
cycle, the difference between the total and displacement currents is due to the breakdown. In the positive half-cycle the

difference can be explained by the motion of both negative

ions and the secondary electrons emitted from the dielectric

surfaceto the exposed anode.

Consider separately two half-cycles of sinusoidalvoltage DBD operation.

A. Negative half-cycle

During the first half of the negative half-cycle the exposed electrode is negative, its potential is decreasing, and

the covered electrode is grounded, the breakdown starts

when the instantaneous voltage reaches its critical value. If

the amplitude of the applied voltage is not very high, the

plasma development starts near the voltage peak, as shown

in Figs. 3aand 3b. Electrons are generated at the cathode

surface due to the secondary emission, and avalanche ionization then occurs in the strong electric field. Being light and

fast, electrons separate from positive ions and attach to the

dielectric surface, leaving behind a cloud of positive ions.

Some electrons, i.e., those at the front and upper edges of the

plasma, attach to oxygen and form negative ions Fig. 3b.

The plasma thus propagates along the surface and negatively

charges the surface during the propagation Fig. 4. The

propagation stops and the current is cut off when the negative potential on the dielectric surface becomes sufficiently

high, so that the difference in potential of the exposed electrode and the dielectric falls below the critical breakdown

value.

Increasing the applied voltage amplitude increases the

duration of this active phase, and also allows the plasma to

propagate farther along the surface. Under typical conditions,

the active avalanchephase duration is on the order of 100

ns for small-scale actuatorto about 1 microsecond for a

large-scale device, much shorter than the half-cycle of the

applied voltage. Therefore, during most of the negative halfperiod, no avalanche ionization occurs, and the plasma is

decaying. During this part of the cycle the negative ions push

the gas to the right downstream, while the cloud of positive

ions is attracted to the exposed electrode and pushes the gas

upstream and down, toward the surface Fig. 5.

Since the magnitude of the negative potential on the dielectric surface is always somewhat lower than the peak

negative potential on the exposed electrode-cathode, the

positive ion cloud always moves toward the cathode, creating the backward-directed force on the gas and reducing the

efficiency of generation of downstream-directed gas jet.

Moreover, in the computations for small-scale DBD actuator,

this backward motion of ions was found to be strong enough

to cause the overall negative backward-directedforce during the cathode half-period.

However, when the length scale of the plasma was increased the streamwise length of the electrode was increase

by a factor of 7, to several millimeters, the voltage amplitude increased to 3.5 kV, and the ac frequency decreased by

a factor of 10, then the reversal of the integrated force in the

cathode phase was reached. This is due to the fact that the

backward-directed force caused by the positive ions moving

to the cathode was found to vary only slightly with the scaling, while the downstream-directed force caused by the

negative ions increases with the increase in plasma size and

voltage amplitude. Consequently, the integrated force is now

directed downstream Fig. 6, as observed in the

experiments.26,29–33

Therefore, three factors are especially important in understanding why the force on the gas is directed downstream

even if the exposed electrode is at a negative potential: ithe

charging of dielectric surface by the attached electrons; ii

the formation of negative ions and their motion; and iiithe

relatively large scale of DBD actuators. It is also important

to note that the attraction of positive ions to the exposed

electrode in the cathode phase significantly reduces if not

reversesthe overall average force that pushes the gas. This

is a major source of inefficiency of plasma actuators.

FIG. 3. Color onlineNegative half-period: asine voltage waveform with

short active phase; billustration of processes during the active phase avalanche breakdown of the gas, charging of the dielectric surface, and propagation of the plasma; cillustration of processes during the decaying phase

positive space charge, ions drift toward the surface and away from the

exposed electrode, imparting momentum to the gas and recombining with

electrons deposited on the dielectric surface.

053305-4 Likhanskii et al. J. Appl. Phys. 103, 053305 2008

NASA/CR—2012-217654 32
B. Positive half-cycle

Two distinctly different regimes are possible in the positive half-cycle Fig. 7. If the applied voltage frequency is

low lower than about 2–3 kHz in millimeter or centimeterscale plasmas, then by the end of the negative half-period

almost all the electrons at the dielectric surface have been

destroyed in recombination with ions. Therefore, the plasma

around the positive exposed electrode can only exist as a

positive corona, as shown in Fig. 7b. Electrons generated in

the strong field when the electrode potential is near its peak

drift toward the exposed positive electrode anode, leaving

behind positive ions. The positive ions move in the opposite

direction, i.e., upwards away from the surfaceand along

the dielectric surface, imparting momentum to the gas. Thus,

the momentum imparted to the gas is in the same direction

away from the exposed electrodeas in the negative halfperiod. However, in this corona regime, the gas also can

receive some momentum directed from the surface.

Note that in this low-frequency corona regime the cloud

of positive ions near the tip of exposed electrode partially

FIG. 4. Color onlineaInstantaneous electron density distribution during the ionization avalanche sinusoidal voltage, amplitude 1.5 kV, frequency 1000

kHz. bInstantaneous positive ion density distribution during the ionization avalanche sinusoidal voltage, amplitude 1.5 kV, frequency 1000 kHz. c

Instantaneous negative ion density distribution during the ionization avalanche sinusoidal voltage, amplitude 1.5 kV, frequency 1000 kHz. dInstantaneous

electric potential distribution during the ionization avalanche sinusoidal voltage, amplitude 1.5 kV, frequency 1000 kHz. eInstantaneous force on neutral

gas during the ionization avalanche. The force always pushes the gas to the surface. The electrons push the gas downstream, and the positive ion cloud pushes

the gas upstream sinusoidal voltage, amplitude 1.5 kV, frequency 1000 kHz.

053305-5 Likhanskii et al. J. Appl. Phys. 103, 053305 2008

NASA/CR—2012-217654 33
shields the field and limits the current, stopping the avalanches. When the ions drift away, the shielding is removed,

and the breakdown can start again. This indicates the possibility of high-frequency oscillations superimposed on the

low-frequency discharge operation.

If the applied voltage frequency is high enough according to the calculations, at least 5–10 kHz, which agrees well

with experimental observationsso that the electrons attached to the dielectric surface are not significantly destroyed

FIG. 5. Color onlineaInstantaneous electron density distribution during the negative half-cycle after the ionization avalanche. The electrons are attached

to the dielectric surface sinusoidal voltage, amplitude 1.5 kV, frequency 1000 kHz. bInstantaneous positive ion density distribution during the negative

half-cycle after the ionization avalanche. The positive cloud is attracted to the cathode sinusoidal voltage, amplitude 1.5 kV, frequency 1000 kHz. c

Instantaneous negative ion density distribution during the negative half-cycle after the ionization avalanche. Negative ions drifts downstream sinusoidal

voltage, amplitude 1.5 kV, frequency 1000 kHz. dInstantaneous electric potential distribution during the negative half-cycle after the ionization avalanche

sinusoidal voltage, amplitude 1.5 kV, frequency 1000 kHz. eInstantaneous force on neutral gas during the negative half-cycle after the ionization

avalanche. Positive ion cloud is attracted to the exposed electrode and pushes gas upstream sinusoidal voltage, amplitude 1.5 kV, frequency 1000 kHz.

FIG. 6. Color onlineAverage force during the negative half-cycle for

sinusoidal applied voltage amplitude 3.5 kV, frequency 100 kHz.

053305-6 Likhanskii et al. J. Appl. Phys. 103, 053305 2008

NASA/CR—2012-217654 34
by the end of the negative half-period, then the electrons can

be pulled from the surface in the positive half-period by secondary emission impacts of high-energy ions and UV photons on the surface. These electrons can then generate avalanche ionization. The dielectric then plays the role of a

cathode in this half-period, as illustrated in Fig. 7c. The

motion of positive ions that imparts momentum to the gas is

toward the surface and along it Fig. 8. Note that in the

positive half-cycle, the negative ions move upstream, toward

the exposed electrode, and impart an upstream-directed momentum to the gas, thus reducing the overall downstreamdirected gas velocity.

C. Summary of the force exerted on the gas in

sinusoidal applied voltage cases

The average force acting on the gas for the small-scale

case is shown in Fig. 9. The first observation is that the gas

experiences a strong force normal to the surface and toward

it. This normal suction force, noted in Refs. 29–33, is due

primarily to the motion of positively charged ion cloud to the

exposed cathode in the negative half-cycle. In fact, this suction force turns out to be stronger than the average tangential

force. However, the same positive ion motion to the cathode

also creates a strong upstream-directed force. This upstream

force is even greater than the downstream-directed force created by the negative ions in the negative half-cycle, if the

device scale is small less than 1 mm. In a large-scale at

least several millimetersdevice, computations showed that

the negative ion generated downstream force becomes stronger than the upstream force due to positive ions, so that the

overall force is directed downstream even in the negative

half-cycle and the total force over the cycle is also in the

downstream direction see Fig. 6. However, the motion of

positive ions to the negatively biased exposed electrode remains a major source of inefficiency in generating tangential

velocity of the gas. Note also that negative ions play diametrically opposing roles in the negative and positive halfcycles. In the negative half-cycle, the negative ions are primarily responsible for the downstream force, while in the

positive half-cycle the negative ions move upstream and impede the downstream gas motion. The obtained results provide the first qualitative explanation of the DBD operation in

atmospheric air with applied sine voltage. The previous DBD

models38–42 had several weaknesses, which reflected the provided results. For example, all plasma modeling has been

done in inert gases. Thus, the formation of negative ions,

which explains the downstream-directed force in the cathode

cycle, was absent. Models38–40 used unreasonably large time

steps, which did not correctly resolve the ionization processes. Boeuf et al. developed a comprehensive model for

DBD simulations in nitrogen,41 but the real experimental

cases, such as applied sine voltage in air, were not considered.

Overall, despite the dominant downstream directionality

of the force, it is clear that a sinusoidal or near-sinusoidal

voltage signal is an inefficient way of generation of a

downstream-directed gas jet. In order to maximize the tangential force and the gas jet velocity, the inefficiencies discussed above should be eliminated or at least minimized.

IV. OPTIMAL WAVE FORM FOR LOW VOLTAGES:

REPETITIVE SHORT PULSES WITH DC BIAS

A. The physical principles

As shown in the discussion of the DBD actuator operation with a sine voltage signal, the gas is pushed downstream

due to the attraction of positive ions to the negatively

charged dielectric surface in the positive half-period and due

to negative ions in the negative half-period.

The charging of the dielectric plays the key role in understanding and optimizing the process. In the computed

DBD examples, this has been accomplished by the removal

of electrons from the plasma ionization wave onto the surface. However, in principle, other methods of charging the

dielectric surface can be used. A newly proposed principle

puts dielectric charging at the center.

Indeed, to push the gas along the surface in the direction

away from the exposed electrode, the motion of positive ions

should be predominantly in that direction. For that, the exFIG. 7. Color onlinePositive half-period: asine voltage waveform with

short active phase; billustration of “positive corona” regime at low frequency no charge on dielectric surface, electrons are drawn to the exposed

electrodes, ion clouds expand upward and away from the exposed electrode,

imparting momentum to the gas; cillustration of processes at high frequency negative charge remaining on dielectric surface from the negative

half-period, ions drift toward the surface and away from the exposed electrode, imparting momentum to the gas and recombining with electrons deposited on the dielectric surface.

053305-7 Likhanskii et al. J. Appl. Phys. 103, 053305 2008

NASA/CR—2012-217654 35
posed electrode should be positively biased. However, dc

current cannot just flow between neutral dielectric and the

positive exposed electrode. The dielectric itself is needed in

order to limit the current and thus to prevent transformation

of the plasma into hot, constricted, unstable arc. To make

the current flow possible in the regime when the exposed

electrode is positive, electrons should be deposited onto the

dielectric surface. That way, the electrons would be “lifted”

from the surface by recombination with ions that drift and

arrive at the surface and by secondary emission due to impact of energetic positive ions, and the operation would be

similar to the cathode in glow discharge.

FIG. 8. Color onlineaInstantaneous electron density distribution during the positive half-cycle sinusoidal voltage, amplitude 1.5 kV, frequency 1000

kHz. bInstantaneous positive ion density distribution during the positive half-cycle. The positive cloud pushes the gas downstream sinusoidal voltage,

amplitude 1.5 kV, frequency 1000 kHz. cInstantaneous negative ion density distribution during the positive half-cycle. The negative low density ion cloud

pushes the gas upstream sinusoidal voltage, amplitude 1.5 kV, frequency 1000 kHz. dInstantaneous electric potential distribution during the positive

half-cycle sinusoidal voltage, amplitude 1.5 kV, frequency 1000 kHz. eInstantaneous force on neutral gas during positive half-cycle. The unbalanced

positive ions drift from the anode to the dielectric surface sinusoidal voltage, amplitude 1.5 kV, frequency 1000 kHz.

053305-8 Likhanskii et al. J. Appl. Phys. 103, 053305 2008

NASA/CR—2012-217654 36
Since the actuator operation will entail the removal of

electrons from the surface, these surface-deposited electrons

should be periodically replenished.

The periodic replenishment of negative charge on the

dielectric should be done very rapidly to minimize the time

period of backward-directed positive ion motion. This can

indeed be accomplished by periodic application with repetition rate from tens to hundreds of kHzof very short 2–5

ns, strong, negative voltage pulses. In these short pulses, the

ionization avalanche developing from the exposed electrode

would quickly reach the dielectric surface and would deposit

electrons onto it, leaving behind the positive ions, so that the

main plasma actuator operation could resume.

B. Numerical results

The applied voltage and the corresponding calculated

current in the circuit in the representative repetitive-pulse

case is presented in Fig. 10. The breakdown occurs during

the pulse and the peak in the current curve corresponds to it.

In the representative case the following parameters were

chosen: the Gaussian pulse width was 4 ns, the pulse amplitude was −1.5 kV, the dc bias was 0.5 kV, and the repetition

rate was 500 kHz so that the interval between the pulses was

2 s. The small-scale geometry was the same as in the

sine-voltage cases. Figure 11 shows that after the pulse there

is a very high concentration of positive ions near the exposed

electrode. The electrons are attached to the dielectric surface,

creating an effective “cathode” which attracts the positive

cloud. Figures 11–13 show the evolution of the positive

cloud from the anode to the dielectric and the corresponding

instantaneous potential distributions. The cloud moves to the

right, neutralizing the surface charge and gradually dispersing. Figure 14 shows the average force acting on the gas

between two pulses. Comparison of Figs. 14 and 9 clearly

shows that the waveform with short repetitive pulses eliminates the upstream-directed force that was the principal inefficiency source in the sine-voltage cases.

A simple physical model can describe the pushing action

of plasma on the gas. Consider the gas in a region of length

L Fig. 15. A positive ion cloud with average ion number

density n+ and the width S is created near the exposed electrode.

The moving ion cloud acts as a porous piston: it moves

faster than the gas and accelerates the gas molecules that

experience collisions with ions. Since at thermal energies the

ion-molecule collision cross section is approximately in

1.510−14 cm2,

50 and the ion number density is typically

n+1011−1012 cm−3, the mean-free path of the molecule

with respect to collisions with ions is on the order of 1–10

m––much longer than the 0.3–3 mm width of the ion cloud.

Therefore, only a small fraction of molecules experiences

collisions with ions during the single sweep of the ion cloud,

which justifies the porous piston analogy.

The force on a molecule inside the plasma column is

f = kinn+Mu+ − u, 16

where kin1.110−9 cm3 /s is the ion-molecule

momentum-transfer rate constant,51 M is the ion mass assumed equal to the molecule’s mass, u+ is the ion cloud

driftvelocity, and u is the gas velocity. Since the residence

time of a molecule inside the ion cloud is approximately t

S/u+ −u, the gas velocity increment in a single sweep of

the ion cloud is


V1 = kinn+S. 17

As the gas element in the boundary layer slowly moves

along the wall, it experiences many “hits” by the consecutive

rapidly moving ion clouds. The number of these hits is approximately equal to L/ ̃

u
t, where  ̃

u is the average gas

velocity, and 
t is the smaller of the interval between the

pulses and the time of ion drift over the distance L. Denoting

the initial gas velocity i.e., the velocity at the entrance to the

interaction regionas V0 and the final i.e., exitgas velocity

as V, we obtain

FIG. 9. Color onlineAverage force acting on neutral gas during the cycle

sinusoidal voltage, amplitude 1.5 kV, frequency 1000 kHz.

FIG. 10. Color onlineCurrent and voltage in a representative repetitivepulse case in quasi-steady-state regime. The solid line shows the voltage and

the dashed line shows the current. Pulse voltage: amplitude −1.5 kV,

FWHM is 4 ns, repetition rate is 500 kHz, and the bias is 500 V.

053305-9 Likhanskii et al. J. Appl. Phys. 103, 053305 2008

NASA/CR—2012-217654 37
V − V0 = L

1

2

V + V0
t


V1. 18

From Eqs. 17and 18, we obtain

V2 − V0

2 = 2Lkinn+S


t , 19

and assuming that initially the gas is at rest,

V = 	2Lkinn+S


t . 20

In the computed small-scale case with repetitive 500 kHz,

short 4 ns FWHM2 kV pulses and 500 V dc bias, the

approximate values of the parameters in Eq. 20are L

=0.3 mm, S=0.1 mm,
t=210−6 s, and n+ =5

1011 cm−3. Equation 20then gives the induced gas velocity of V=4 m/s. It is important to recognize that this

FIG. 11. Color onlineaElectron

density distribution at the peak pulse

voltage. The electron avalanche

charges the dielectric surface during

the pulse. Pulse voltage: amplitude

−1.5 kV, FWHM is 4 ns, repetition

rate is 500 kHz, and the bias is 500 V.

bPositive ion density distribution at

the peak pulse voltage. The positive

ion cloud is formed near the exposed

electrode during the pulse. Pulse voltage: amplitude −1.5 kV, FWHM is 4

ns, repetition rate is 500 kHz, and the

bias is 500 V.cInstantaneous force

on neutral gas at the peak pulse voltage. The gas is pushed by electrons

downstream and by ions upstream, but

during a very short time. Pulse voltage: amplitude −1.5 kV, FWHM is 4

ns, repetition rate is 500 kHz, and the

bias is 500 V.

FIG. 12. Color onlineaElectron

density distribution immediately after

the pulse. The electron avalanche has

charged the dielectric by the end of the

pulse. Pulse voltage: amplitude

−1.5 kV, FWHM is 4 ns, repetition

rate is 500 kHz, and the bias is 500 V.

bPositive ion density distribution

immediately after the pulse. Positive

ions start to move to the dielectric surface. Pulse voltage: amplitude

−1.5 kV, FWHM is 4 ns, repetition

rate is 500 kHz, and the bias is 500 V.

cInstantaneous force on neutral gas

immediately after the pulse. Positive

ions start to push the gas downstream.

Pulse voltage: amplitude −1.5 kV,

FWHM is 4 ns, repetition rate is 500

kHz, and the bias is 500 V.

053305-10 Likhanskii et al. J. Appl. Phys. 103, 053305 2008

NASA/CR—2012-217654 38
velocity is similar to that commonly observed in conventional asymmetric DBD actuators, but it is achieved with a

considerably lower voltage amplitude and an order of magnitude smaller plasma size compared with those in conventional DBD systems.30–34

V. DIFFERENT DBD REGIMES

As noted earlier in this paper, the voltage waveform consisting of repetitive short negative pulses and positive dc bias

makes the best use of the dielectric surface charging and

eliminates the inefficiencies present in sine-voltage cases.

Despite the clear physics in low-voltage cases, the scaling

predictions do not work for higher voltages, as the physics of

the discharge dramatically changes with scaling. In the case

of repetitive negative nanosecond pulses the proposed model

works for 1.5–2 kV applied voltages. However, if the voltage

is increased, the effects are unclear. On one hand, the positive ion cloud is increased, leading to a stronger pushing

force on the gas downstream52,53 But, on the other hand, the

back breakdown occurs, causing the backward-directed force

near the edge of the electrode. At high voltages another

mechanism of gas pushing can be produced: repetitive positive nanosecond pulses with positive bias.52,53 If the highvoltage positive pulses are applied to the exposed electrode,

one can get the streamerlike solution, Fig. 16. These cases

are discussed in detail in Refs. 52 and 53.

VI. CONCLUSIONS

A consistent, comprehensive, and physically based

model for an asymmetric dielectric barrier discharge plasma

FIG. 13. Color onlineaElectron

density distribution 0.5 s after the

pulse. The electrons are neutralized on

the surface by positive ions. Pulse

voltage: amplitude −1.5 kV, FWHM

is 4 ns, repetition rate is 500 kHz, and

the bias is 500 V.bPositive ion density distribution 0.5 s after the pulse.

The ions drift to the negatively

charged dielectric surface. Pulse voltage: amplitude −1.5 kV, FWHM is 4

ns, repetition rate is 500 kHz, and the

bias is 500 V.cInstantaneous force

on neutral gas 0.5 s after the pulse.

The force is due to positive ions drifting to the dielectric. Pulse voltage:

amplitude −1.5 kV, FWHM is 4 ns,

repetition rate is 500 kHz, and the bias

is 500 V.

FIG. 14. Color onlineAverage force acting on neutral gas during one

cycle. Pulse voltage: amplitude −1.5 kV, FWHM is 4 ns, repetition rate is

500 kHz, and the bias is 500 V.

FIG. 15. Color onlineSimplified physical model multiple sweeps by a

“porous piston”describing the momentum transfer to the neutral gas in

repetitive-pulse cases.

053305-11 Likhanskii et al. J. Appl. Phys. 103, 053305 2008

NASA/CR—2012-217654 39
actuator in air has been developed, and the modeling has

revealed the essential physics of DBD actuators. The charging of dielectric by electrons during the avalanche ionization

process lasts only a small fraction of the negative cathode

half-cycle, but plays a crucial role in DBD operation and gas

acceleration. The tangential force on the gas is directed

downstream in both cathode and anode half-cycles, and is

created by the downstream motion of the negative ions in the

cathode half-cycle and by the downstream motion of positive

ions in the anode half-cycle. The motion of positive ions

toward the exposed electrode in the cathode half-cycle was

found to not only create a strong suction effect, but to also

considerably decrease the integrated downstream-directed

tangential force, thus resulting in a major inefficiency of the

sine-voltage waveform. An additional inefficiency is due to

the negative ion motion upstream in the anode half-cycle.

The understanding of the detailed mechanism of DBD

actuator operation and the sources of inefficiency allowed us

to propose a voltage waveform making the maximum use of

dielectric charging and free from the above-mentioned inefficiencies. This optimal waveform consists of high repetition

rate, extremely short a few nanosecondspulses of negative

voltage in combination with a positive dc bias applied to the

exposed electrode. Computations and analytical estimates

showed that a repetitive-pulse waveform can induce gas velocities similar to those in conventional sine-voltage DBD

actuators at a considerably lower voltage and more than an

order of magnitude shorter streamwise plasma size.

ACKNOWLEDGMENTS

This work was supported by Boeing and by the USAFOSR Unsteady Aerodynamics and Hypersonics Program.

1

S. O. Macheret, M. N. Shneider, and R. B. Miles, AIAA J. 42, 1378

2004. 2

S. O. Macheret, M. N. Shneider, R. B. Miles, and R. J. Lipinski, AIAA J.

39, 1127 2001. 3

S. O. Macheret, M. N. Shneider, and R. B. Miles, AIAA J. 40, 74 2002. 4

S. O. Macheret, M. N. Shneider, and R. B. Miles, J. Propul. Power 18, 424

2002. 5

M. N. Shneider, S. O. Macheret, and R. B. Miles, AIAA J. 42, 2303

2004. 6

S. O. Macheret, M. N. Shneider, and R. B. Miles, “Optimum Performance

of Electron Beam Driven MHD Generators for Scramjet Inlet Control,”

Paper AIAA 2003–3763, in 34th AIAA Plasmadynamics and Lasers Conference, Orlando, FL, 23–26 June 2003.

7

R. C. Murray, L. Vasilyak, M. R. Carraro, S. H. Zaidi, S. O. Macheret, M.

N. Shneider, and R. B. Miles, “Observation of MHD Effects With Nonequilibrium Ionization in Cold Supersonic Air Flows,” Paper AIAA 2004–

1025, in 42nd Aerospace Sciences Meeting and Exhibit, Reno, NV, 5–8

January 2004.

8

S. O. Macheret, M. N. Shneider, and G. V. Candler, “Modeling of MHD

Power Generation On Board Reentry Vehicles,” Paper AIAA 2004–1024,

in 42nd Aerospace Sciences Meeting and Exhibit, Reno, NV, 5–8 January

2004.

9

M. N. Shneider and S. O. Macheret, “Modeling of Plasma Virtual Shape

Control of Ram/Scramjet Inlet and Isolator,” Paper AIAA 2004–2662, in

35th AIAA Plasmadynamics and Lasers Conference, Portland, OR, 28

June–1 July 2004.

10M. N. Shneider and S. O. Macheret, “Hypersonic Aerodynamic Control

and Thrust Vectoring by Nonequilibrium Cold-Air MHD Devices,” Paper

AIAA-2005–0979, in 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 10–13 January 2005.

11R. B. Miles, S. O. Macheret, M. N. Shneider, C. Steeves, R. C. Murray, T.

Smith, and S. H. Zaidi, “Plasma-Enhanced Hypersonic Performance Enabled by MHD Power Extraction,” Paper AIAA 2005–0561, in 43rd AIAA

Aerospace Sciences Meeting and Exhibit, Reno, NV, 10–13 January 2005.

12A. L. Kuranov and E. G. Sheikin, “MHD Control on Hypersonic Aircraft

under AJAX Concept: Possibilities of MHD Generator,” Paper AIAA

2002–0490, in 40th AIAA Aerospace Sciences Meeting and Exhibit, Reno,

NV, 14–17 January 2002.

13A. Vatazhin, V. Kopchenov, and O. Gouskov, “Some Estimations of Possibility to Use the MHD Control for Hypersonic Flow Deceleration,” PaFIG. 16. Color onlineStreamer

propagation in the case of repetitive

positive nanosecond pulse with bias.

Pictures shows the instant electron,

positive ion densities, electric potential distribution, and force on the gas

distribution right after the pulse.

Pulse voltage: amplitude 3 kV,

FWHM is 4 ns, repetition rate is 500

kHz, and the bias is 1000 V.

053305-12 Likhanskii et al. J. Appl. Phys. 103, 053305 2008

NASA/CR—2012-217654 40
per AIAA 1999–4972, in 3rd AIAA Weakly Ionized Gases Workshop,

Norfolk, VA, 1–5 November 1999.

14V. A. Bityurin, A. I. Klimov, S. B. Leonov, A. N. Bocharov, and J. T.

Lineberry, “Assessment of a Concept of Advanced Flow/Flight Control for

Hypersonic Flights in Atmosphere,” Paper AIAA 1999–4820, in 3rd AIAA

Weakly Ionized Gases Workshop, Norfolk, VA, 1–5 November 1999.

15M. Nishihara, N. Jiang, J. W. Rich, W. R. Lempert, I. V. Adamovich, and

S. Gogineni, Phys. Fluids 17, 106102 2005. 16M. Nishihara, J. W. Rich, W. R. Lempert, I. V. Adamovich, and S.

Gogineni, Phys. Fluids 18, 086101 2006. 17D. Gaitonde, “Simulations of Global and Local Flow Control with Magnetic Field,” Paper AIAA 2005–560, in 43rd AIAA Aerospace Sciences

Meeting and Exhibit, Reno, NV, 10–13 January 2005.

18S. T. Surzhikov and J. S. Shang, “Subsonic and Supersonic Flow Around

Wing with Localized Surface Gas Discharge,” Paper AIAA 2005–0406, in

43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 10–13

January 2005.

19S. T. Surzhikov and J. S. Shang, J. Comput. Phys. 199, 437 2004. 20S. T. Surzhikov and J. S. Shang, “Magneto-Fluid-Dynamic Interactions for

Hypersonic Flow Control,” Paper AIAA 2004–0508, in 42nd Aerospace

Sciences Meeting and Exhibit, Reno, NV, January 5–8, 2004.

21S. T. Surzhikov and J. S. Shang, High Temp. 43, 19 2005. 22R. Kimmel, J. Hayes, J. Menart, and J. S. Shang, “Effect of Surface

Plasma Discharge on Boundary Layer at Mach 5,” Paper AIAA 2004–

0509, in 42nd Aerospace Sciences Meeting and Exhibit, Reno, NV, 5–8

January 2004.

23J. Poggie, “Numerical Exploration of Flow Control with Glow Discharges,” Paper AIAA 2004–2858, in 35th AIAA Plasmadynamics and

Lasers Conference, Portland, OR, 28 1 June–1 July 2004.

24J. S. Shang, R. Kimmel, J. Hayes, C. Tyler, and J. Menart, J. Spacecr.

Rockets 42, 780 2005. 25J. S. Shang and S. T. Surzhikov, AIAA J. 43, 1633 2005. 26J. Menart, J. Shang, C. Atzbach, S. Magoteaux, M. Slagel, and B.

Bilheimer, “Total Drag and Lift Measurements in a Mach 5 Flow Affected

by a Plasma Discharge and a Magnetic Field,” Paper AIAA-2005–947, in

43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 10–13

January 2005.

27S. B. Leonov, D. A. Yarantsev, V. G. Gromov, and A. P. Kuriachy,

“Mechanisms of Flow Control by Near-Surface Electric Discharge Generation,” Paper AIAA 2005–0780, in 43rd AIAA Aerospace Sciences

Meeting and Exhibit, Reno, NV, 10–13 January 2005.

28S. O. Macheret, “Physics of Magnetically Accelerated Nonequilibrium

Surface Discharges in High-Speed Flow,” Paper AIAA 2006–1005, in

44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 9–12

January 2006.

29S. H. Zaidi, T. Smith, S. O. Macheret, and R. B. Miles, “Snowplow Surface Discharge in Magnetic Field for High Speed Boundary Layer Control,” Paper AIAA 2006–1006, in 44th AIAA Aerospace Sciences Meeting

and Exhibit, Reno, NV, 9–12 January 2006.

30C. L. Enloe, T. E. McLaughlin, R. D. VanDyken, K. D. Kachner, E. J.

Jumper, and T. C. Corke, AIAA J. 42, 589 2004. 31C. L. Enloe, T. E. McLaughlin, R. D. VanDyken, K. D. Kachner, E. J.

Jumper, T. C. Corke, M. Post, and O. Haddad, AIAA J. 42, 595 2004. 32M. Post and T. C. Corke, “Flow Control with Single Dielectric Barrier

Plasma Actuator,” Paper AIAA 2005–4630, in 35th AIAA Fluid Dynamics

Conference and Exhibit, Toronto, Ontario, 6–9 June 2005.

33T. C. Corke, E. J. Jumper, M. L. Post, D. Orlov, and T. E. McLaughlin,

“Application of Weakly-Ionized Plasmas as Wing Flow-Control Devices,”

Paper AIAA 2002–350, in 40th AIAA Aerospace Sciences Meeting and

Exhibit, Reno, NV, 14–17 January 2002.

34M. L. Post and T. C. Corke, AIAA J. 42, 2177 2004. 35D. F. Opaits, D. V. Roupassov, S. M. Starikovskaia, A. Yu. Starikovskii, I.

N. Zavialov, and S. G. Saddoughi, “Plasma Control of Boundary Layer

Using Low-Temperature Non-Equilibrium Plasma of Gas Discharge,” Paper AIAA 2005–1180, in 43rd AIAA Aerospace Sciences Meeting and

Exhibit, Reno, NV, 10–13 January 2005.

36F. Massines, A. Rabehi, F. Decomps, R. Ben Gadri, P. Ségur, and C.

Mayoux, J. Appl. Phys. 83, 2950 1998. 37J. R. Roth, D. M. Sherman, and S. P. Wilkinson, AIAA J. 38, 1173 2000. 38S. Roy and D. V. Gaitonde, “Modeling Surface Discharge Effects of Atmospheric RF on Gas Flow Control,” Paper AIAA 2005–160, 43rd AIAA

Aerospace Sciences Meeting and Exhibit, Reno, NV, 10–13 January 2005.

39S. Roy, Appl. Phys. Lett. 86, 101502 2005. 40K. P. Singh and S. Roy, J. Appl. Phys. 98, 083303 200541J. P. Boeuf and L. C. Pitchford, J. Appl. Phys. 97, 103307 2005. 42D. M. Orlov and T. C. Corke, “Numerical Simulation of Aerodynamic

Plasma Actuator Effects,” Paper AIAA 2005–1083, in 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 10–13 January 2005.

43S. O. Macheret, M. N. Shneider, and R. B. Miles, Phys. Plasmas 8, 1518

2001. 44S. O. Macheret, M. N. Shneider, and R. B. Miles, IEEE Trans. Plasma Sci.

30, 1301 2002. 45Yu. P. Raizer, Gas Discharge Physics Springer-Verlag, Berlin, 1997. 46I. S. Grigoriev and E. Z. Meilikhov, Handbook of Physical Quantities

CRC Press, Boca Raton, FL, 1997, Chap. 20. 47D. A. Anderson, J. C. Tannehill, and R. H. Pletcher, Computational Fluid

Mechanics and Heat Transfer Hemisphere, New York, 1984. 48H. K. Gummel, IEEE Trans. Electron Devices 11, 455 1964. 49Y. P. Raizer and M. N. Shneider, Sov. J. Plasma Phys. 14, 128 1988. 50M. N. Shneider, S. O. Macheret, and R. B. Miles, “Electric Charge

Build-Up in Hypersonic Wind Tunnels with Electron Beam Energy,” Paper AIAA-2003–4035, in 34th AIAA Plasmadynamics and Lasers Conference, Orlando, FL, 23–26 June 2003.

51D. L. Scharfetter and H. K.Gummel, IEEE Trans. Electron Devices 16, 64

1969. 52A. V. Likhanskii, M. N. Shneider, S. O. Macheret, and R. B. Miles, Paper

AIAA-2007–633, in 45th AIAA Aerospace Sciences Meeting and Exhibit,

Reno, NV, 2007.

53A. V. Likhanskii, M. N. Shneider, S. O. Macheret, and R. B. Miles, Phys.

Plasmas 14, 073501 2007.

053305-13 Likhanskii et al. J. Appl. Phys. 103, 053305 2008

NASA/CR—2012-217654 41
Surface charge in dielectric barrier discharge plasma actuators

D. F. Opaits,1,a M. N. Shneider,1 Richard B. Miles,1 A. V. Likhanskii,2 and S. O. Macheret3

1

Department of Mechanical and Aerospace Engineering, Princeton University, Princeton,

New Jersey 08544, USA

2

The Pennsylvania State University, University Park, Pennsylvania 16802, USA

3

Lockheed Martin Aeronautics Company, Palmdale, California 93599, USA

Received 10 April 2008; accepted 17 June 2008; published online 21 July 2008

Direct measurements of the dielectric surface potential and its dynamics in asymmetric dielectric

barrier discharge DBDplasma actuators show that the charge builds up at the dielectric surface

and extends far downstream of the plasma. The surface charge persists for a long time tens of

minutesafter the driving voltage has been turned off. For a sinusoidal voltage waveform, the

dielectric surface charges positively. With the voltage waveform consisting of nanosecond pulses

superimposed on a dc bias, the sign of the dielectric surface charge is the same as the sign polarity

of the bias voltage. The surface charging significantly affects DBD plasma actuator performance.

© 2008 American Institute of Physics. DOI: 10.1063/1.2955767

I. INTRODUCTION

Asymmetric dielectric barrier discharge DBDplasma

actuators have been reported in a number of works which

have addressed their potential use for aerodynamic

control.1–22,24–29 This application relies on a DBD-induced

wall jet with typical velocities of several meters per second.

It is understood that electric charge deposition on the dielectric surface limits the current and thus allows operation of

nonequilibrium discharges at atmospheric pressure. The important role of the surface charge and its finite relaxation

time the “memory voltage”in the discharge physics was

pointed out by Massines et al.30 and Gadri31 for the parallelplate DBD configuration, and by Roth et al.32 for One Atmosphere Uniform Glow Discharge Plasma OAUGDPTM.

Since the surface charge plays an important role in DBD

physics, it warrants a special study. In the work of Font

et al.,

21 the surface potential in a DBD driven by sinusoidal

voltage was measured using a V-dot probe technique, and the

voltage across the plasma was shown to be less than half of

that which is applied across the electrodes. Recently the

same group22 presented the time evolution and the spatial

extent of the surface potential. In this paper, we describe

electrostatic voltmeter measurements of surface charge in

DBD plasma actuators driven by various voltage profiles,

most notably by pulses plus dc bias but also by sinusoidal

voltages. The work reported here extends our previously reported work which also used the electrostatic probe.24 The

results for the sinusoidal profile recently reported by Enloe

et al.22 are consistent with the work reported here and with

our previous results. For sinusoidal voltages the two approaches are mutually complementary since Enloe et al.

measure the surface potential using a different method.

II. SURFACE POTENTIAL MEASUREMENTS

A. Experimental setup

For nonintrusive surface potential measurements we

used the Trek Model 247-3 Electrostatic Voltmeter with Trek

Model 6000B-13C Electrostatic Voltmeter Probe. It has high

resolution around 1 mm, fast response time less than 3 ms

for a 1 kV step, and an operating range from 0 to 3 kV dc

or peak ac.

The description of the asymmetric DBD plasma actuator

Fig. 1can be found in our earlier paper.24 The electrodes

were made of copper foil. The width of the electrodes was

equal to 25 mm and their spanwise dimension was 75 mm. A

100 micron thick kapton tape was used as the dielectric. The

discharge was ignited by applying high voltage to one of the

electrodes. The other electrode was grounded.

B. Sinusoidal voltage experiments

First, experiments were conducted for the 3 kHz 10 kV

peak-to-peak sinusoidal voltage profile. Since the sinusoidal

profile is widely used in DBD experiments,1–6,13–15,17–20 it is

interesting to compare its surface potential distribution with

the one obtained in pulsed DBD.16,24–29 The actuator was run

for 15 s and then the surface potential was measured. The

result is presented in Fig. 2, where the distance is measured

from the edge of the exposed electrode. The plasma extends

only a few millimeters downstream of the edge of the exposed electrode, whereas the dielectric charge extends centimeters away from it, far downstream of the plasma. The

maximum surface potential 1.5 kVis comparable to the

applied peak voltage 5 kV. This means that the electric

field of the surface charge can significantly distort the electric field produced by the voltage applied to the electrodes.

Also, even though the applied voltage is symmetrical sinusoidal with no bias voltagethe time-averaged surface charge

has a positive polarity. This is possibly due to the much

higher mobility of electrons compared to positive ions which a

Electronic mail: dopaits@princeton.edu.

PHYSICS OF PLASMAS 15, 073505 2008

1070-664X/2008/157/073505/5/$23.00 15, 073505-1 © 2008 American Institute of Physics

NASA/CR—2012-217654 42
leads to a much higher electron current into the exposed

electrode during the positive half-cycle of the sinusoidal

voltage compared to the positive ion current into the exposed

electrode during the negative half cycle. With this reasoning

one might conclude that there is a net negative current into

the exposed electrode and positive current flow from the

DBD to infinity. This picture is consistent with results from

other two experiments described in our earlier work.24 Similar behavior is observed in asymmetric rf discharges, where

there is a positive current flux to a virtual electrode at

infinity.23

The persistence of surface charge far downstream of the

plasma can be due either to surface mobility of the charges

or to deposition of the charges onto the surface from the gas

jet downstream of the plasma. Estimates show that while the

dielectric surface charge mobility is too low, the deposition

of ions from the DBD-generated tangential gas jet is likely to

persist downstream of the plasma. Indeed, in the DBD generated jet downstream of the visible plasma, plasma electrons, no longer regenerated by ionization, rapidly in tens of

nanosecondsrecombine with positive ions and attach to

oxygen molecules, which results in an ion-ion plasma jet

with an estimated ion-ion recombination time on the order of

several milliseconds. At a jet velocity of several m/s, this

translates into several centimeters of ion-ion plasma and thus

into several centimeters of dielectric surface charge.

C. Pulses plus dc bias experiments

In this set of experiments the voltage profile consisted of

3 kV 8-ns FWHMionization pulses superimposed on 2 kV

dc bias voltage. The pulse repetition rate was 10 kHz and the

plasma was run for 10 s. The results of surface potential

measurements are presented in Fig. 3. As in the case of a

sinusoidal voltage, the charge builds up far downstream the

plasma region. As can be seen from Fig. 3, the magnitude of

the surface potential is quite close to that of the bias voltage,

while the magnitude of the ionization pulse voltage has little

effect.

We next examined how quickly the surface charge builds

up. At a selected dc bias voltage, a predetermined number of

pulses were sent to the actuator, and then the surface potential was measured. A typical result is shown at Fig. 4. Even

though for a small number of pulses the accuracy of measurements is low, it can be seen that even a single pulse

creates a noticeable surface charge. As the number of pulses

increases, the surface charge builds up and moves farther

away from the plasma. After thousands of pulses, the surface

charge is close to its steady-state value. We have also found

that 2 kV bias voltage itself builds up some surface charge at

the dielectric. The charge is smaller then the one built by a

single pulse but is still significant. We have also found that

positive pulses added to positive bias are significantly more

efficient in depositing the charge on the surface than other

combinations of the pulse and bias polarities. This effect is

illustrated in Fig. 5.

The purpose of the next set of experiments was to study

the evolution of the surface charge with time after the discharge has been turned off. The results for positive polarity

of the bias voltage are presented in Fig. 6. In the case of

negative polarity the potential distribution looks very

similar.24As seen in Fig. 6, the charge persists for a very

long time. In 30 min it depletes by only 15%–20%. There is

uniformly slow charge depletion from the surface in the region of low gradients of the charge concentration and a relatively fast depletion close to the exposed electrode in the

region of high gradients. The fact that the depletion occurs at

the same rate for both positive and negative charge is consistent with the charged particles at the dielectric surface

being positive and negative ions from the gas rather than

electrons.

An experiment was conducted with a plasma actuator in

which a conventional Kapton tape was substituted by a lowstatic Kapton tape of the same thickness.24 The results show

that the depletion rate is faster for the low-static Kapton tape,

but the characteristic time is still of the order of tens of

minutes.

Note that Roth et al.32 also observed the slow depletion

of the residual surface charge on the dielectric after the driving voltage was turned off. The typical time periods were up

to 30 s, which is much shorter than the times we observed.

This difference may be associated with the difference in dielectric materials and configuration of the electrodes.

FIG. 2. Surface potential distribution. Applied voltage profile: Sinusoidal

3 kHz, 10 kV peak-to-peak. Electrodes edge at 0.

FIG. 1. Color onlineAsymmetric dielectric barrier discharge plasma

actuator.

073505-2 Opaits et al. Phys. Plasmas 15, 073505 2008

NASA/CR—2012-217654 43
III. CALCULATION OF THE SURFACE CHARGE

DENSITY

In order to interpret the experimental data and to infer

the surface charge density from the measured surface potential, we used a numerical model based on the twodimensional Poisson solver for the electric potential. We considered the DBD plasma actuator consisting of 2 electrodes

of length 2.5 cm, separated by the 100 micron Kapton tape,

i.e., the same configuration as in the experiments. The electrodes were assumed to be infinitely thin. The size of the

computational domain was 25 mm by 1 mm. The computational domain included the entire lower encapsulatedelectrode and 5 mm of the upper exposedelectrode. The reason

for neglecting the remaining part of the upper electrode is its

insignificant contribution to the electric potential on the surface. Since the electric potential distribution was measured

experimentally after the DBD was turned off, and the recombination time of the plasma is of the order of microseconds,

the gas above the dielectric was considered noncharged.

In the computations, the distribution of charge on the

dielectric surface that would match the experimentally measured profile was obtained. Thus, having the experimentally

measured potential, we reproduced the 2D electric potential

distribution and the surface charge for each temporal measurement as the charge decayed. Figure 7 shows the calculated 2D electric potential distribution for the case of 3 kV

negative pulses, 2 kV positive dc bias, right after the applied

voltage was turned off. Figure 8 shows the calculated surface

charge for the case of 3 kV negative pulses, 2 kV positive

bias. As seen in Fig. 8, the surface charge is mainly located

5 – 20 mm downstream of the exposed electrode. The peak

surface charge density corresponds to 1 ion per 5

5 nmRef. 2site, which is a coverage of a few percent.

IV. THREE-ELECTRODE CONFIGURATION

OF DBD PLASMA ACTUATORS

One of the results of our numerical simulations7,28 of

DBD actuators driven by repetitive nanosecond pulses superimposed on a dc bias was the prediction of a significant

effect of the dc bias voltage on the plasma produced tangential gas velocity and thrust. However, the experiments26 did

not show such an effect. The reason was found to be the

surface charge which builds up in tens or hundreds of pulses

and which shields the applied bias field. Indeed, the DBD

induced tangential flow velocity and thrust depend quite

strongly on the voltage amplitude.4–7,15,24–28 Thus, a reduction in the effective voltage on the plasma caused by the

surface charge results in a significant decrease in the actuator

performance. The numerical model7,27 could not include

large numbers of pulses and intervals between those due to

FIG. 3. Color onlineSurface potential distribution. Applied voltage profile: 2 kV dc bias, 3 kV pulses at 10 kHz PRR.

FIG. 4. Color onlineSurface potential for a fixed number of pulses. Applied voltage profile: Positive 2 kV dc bias, negative 3 kV pulses at 10 kHz

PRR.

FIG. 5. Color onlineSurface potential after five ionizing pulses for different pulses and bias polarities.

073505-3 Surface charge in dielectric barrier discharge plasma actuators Phys. Plasmas 15, 073505 2008

NASA/CR—2012-217654 44
numerical difficulties; the total number of pulses in the computations never exceeded 4–5. Since several pulses deposit

only little charge on the surface, the modeling did not capture the potential shielding and the performance decrease

that occur after hundreds and thousands of pulses.

As a solution to the surface charge build up problem, it

was proposed26 to switch the bias periodically. This improved the DBD actuator performance.26 However, in this

paper we found that the surface charge builds up far downstream from the plasma. It would therefore be desirable to

remove the surface charge as it builds up downstream of the

exposed electrode. We therefore proposed a modification to

the actuator configuration. In the new configuration, the dielectric covers only part of the lower electrode, leaving the

rest of the electrode exposed, as shown in Fig. 9. In such a

case the surface charge cannot build up far downstream and

the dc bias voltage is not shielded. Some preliminary results

of thrust measurements can be found in Ref. 24. The surface

potential profile for the configuration of Fig. 9 after 10 s of

running the plasma is shown in Fig. 10. A comparison of

Figs. 3 and 10 shows that the surface charge has indeed been

substantially reduced by exposing the electrode downstream

of the plasma. Although gas dynamic measurements are outside the scope of this paper, the surface charge reduction

accomplished by exposing the electrode downstream of the

plasma can be expected to result in enhanced induced gas

velocity and thrust.

Note that if a relatively thick dielectric layer is used,

then simply cutting the dielectric layer off over a part of the

lower electrode would produce a “step” which can be detrimental to aerodynamic drag. A simple modification of the

idea would then be to put a third electrode on the surface and

to electrically connect this electrode with the encapsulated

electrode, rather than cutting the dielectric off.

The three-electrode DBD configuration resembles that of

the sliding discharge.9–11 However, in sliding discharges the

plasma actually reaches both exposed electrodes. In contrast,

in the three-electrode DBD discharge proposed here, the

electrons would not reach the auxiliary electrode whose purpose is simply to reduce or eliminate the charge accumulation on the dielectric surface.

V. CONCLUSIONS

In this work, surface charge dynamics in DBD plasma

actuators were studied. Direct dielectric surface potential

measurements showed that the electric field of the surface

charge can dramatically distort the field produced by the

voltage applied to the electrodes and thus reduce the actuator

FIG. 6. Color onlineSurface potential vs time for positive surface charge.

Negative 3 kV pulses, positive 2 kV dc voltage.

FIG. 7. Color onlineCalculated 2D electric potential distribution based on

the experimental data for the electric potential on the dielectric surface right

after the voltage applied to DBD was turned off. Negative 3 kV pulses,

positive 2 kV dc voltage.

FIG. 8. Color onlineCalculated charge density on the dielectric surface at

different moments of time after the DBD was turned off. Negative 3 kV

pulses, positive 2 kV dc voltage.

FIG. 9. Color onlineModified DBD plasma actuator.

073505-4 Opaits et al. Phys. Plasmas 15, 073505 2008

NASA/CR—2012-217654 45
performance. For a sinusoidal voltage profile, significant

positive charge builds up at the dielectric surface in the region far downstream of the plasma. For the “pulses plus dc

bias” voltage waveform the dielectric surface potential depends primarily on the bias voltage. In particular, the sign of

the surface potential coincides with the bias polarity. The

surface charge builds up relatively quickly in a few pulses

and depletes slowly in tens of minutes. Based on the results

of the surface potential measurements, a three-electrode configuration of DBD plasma actuators was proposed.

ACKNOWLEDGMENTS

This work was supported in part by NASA Glenn Research Center Dr. David Ashpis, and in part by the Air

Force Office of Scientific Research Dr. John Schmisseur.

1

E. Moreau, J. Phys. D 40, 605 2007. 2

J. R. Roth, D. M. Sherman, and S. P. Wilkinson, Proceedings of the 46th

AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 1998 AIAA,

Washington, D.C., 1998, Paper No. AIAA-1998-328. 3

J. Pons, E. Moreau, and G. Touchard, J. Phys. D 38, 3635 2005. 4

D. Orlov, T. Corke, and M. Patel, Proceedings of the 46th AIAA Aerospace

Sciences Meeting and Exhibit, Reno, NV, 2006 AIAA, Washington, D.C.,

2006, Paper No. AIAA-2006-1206. 5

C. L. Enloe, T. E. McLaughlin, R. D. VanDyken, K. D. Kachner, E. J.

Jumper, and T. C. Corke, AIAA J. 42, 589 2004. 6

C. L. Enloe, T. E. McLaughlin, R. D. VanDyken, K. D. Kachner,

E. J. Jumper, T. C. Corke, M. Post, and O. Haddad, AIAA J. 42, 595

2004. 7

A. V. Likhanskii, M. N. Shneider, S. O. Macheret, and R. B. Miles, J.

Appl. Phys. 103, 053305 2008. 8

J. P. Boeuf and L. C. Pitchford, J. Appl. Phys. 97, 103307 2005. 9

C. Louste, G. Artana, E. Moreau, and G. Touchard, J. Electrost. 63, 615

2005.

10C. Louste, E. Moreau, and G. Touchard, Proceedings of the ESA-IAS-IEJ

Joint Symposium, Berkeley Laplacian Press, Morgan Hills, CA, 2006. 11B. Arad, Y. Gazit, and A. Ludmirsky, J. Phys. D 20, 360 1987. 12D. Orlov, G. Font, and D. Edelstein, Proceedings of the 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 2008 AIAA, Washington,

D.C., 2008, Paper No. AIAA-2008-1409. 13C. A. Borghi, A. Cristofolini, M. Carraro, and G. Neretti, Proceedings of

the 37th AIAA Plasma Dynamics and Lasers Conference, San Francisco,

CA, 2006 AIAA, Washington, D.C., 2006, Paper No. AIAA-2006-3380. 14Y. V. Shcherbakov, N. S. Isanov, N. D. Baryshev, V. S. Frolovskij, and V.

S. Syssoev, Proceedings of the 31st AIAA Plasma Dynamics and Lasers

Conference, Denver, CO, 2000 AIAA, Washington, D.C., 2000, Paper

No. AIAA-2000-2670. 15M. L. Post and T. C. Corke, Proceedings of the 43th AIAA Aerospace

Sciences Meeting and Exhibit, Reno, NV, 2005 AIAA, Washington, D.C.,

2005, Paper No. AIAA-2005-563. 16D. F. Opaits, D. V. Roupassov, A. Yu. Starikovskii, I. N. Zavialov, and S.

G. Saddoughi, Proceedings of the 43th AIAA Aerospace Sciences Meeting

and Exhibit, Reno, NV, 2005 AIAA, Washington, D.C., 2005, Paper No.

AIAA-2005-1180. 17L. S. Hultgren and D. E. Ashpis, Proceedings of the 41th AIAA Aerospace

Sciences Meeting and Exhibit, Reno, NV, 2003 AIAA, Washington, D.C.,

2003, Paper No. AIAA-2003-1025. 18J. R. Roth, Phys. Plasmas 10, 2117 2003. 19S. Grundmann and C. Tropea, Proceedings of the 46th AIAA Aerospace

Sciences Meeting and Exhibit, Reno, NV, 2008 AIAA, Washington, D.C.,

2008, Paper No. AIAA-2008-1369. 20A. Hoskinson and N. Hershkowitz, Proceedings of the 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 2008 AIAA, Washington,

D.C., 2008, Paper No. AIAA-2008-1370. 21G. I. Font, C. L. Enloe, T. E. McLaughlin, and D. Orlov, Proceedings of

the 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 2007

AIAA, Washington, D.C., 2007, Paper No. AIAA-2007-188. 22C. L. Enloe, T. E. McLaughlin, J. W. Gregory, R. A. Medina, and W. S.

Miller, Proceedings of the 46th AIAA Aerospace Sciences Meeting and

Exhibit, Reno, NV, 2008 AIAA, Washington, D.C., 2008, Paper No.

AIAA-2008-1103. 23Yu. P. Raizer, M. N. Shneider, and N. A. Yatsenko, Radio-Frequency

Capacitive Discharges CRC, Boca Raton, 2006. 24D. Opaits, A. Likhanskii, M. Shneider, G. Neretti, S. Zaidi, S. Macheret,

and R. Miles, Proceedings of the 46th AIAA Aerospace Sciences Meeting

and Exhibit, Reno, NV, 2008 AIAA, Washington, D.C., 2008, Paper No.

AIAA-2008-1372. 25A. Likhanskii, V. Semak, D. Opaits, M. Shneider, R. Miles, and S. Macheret, Proceedings of the 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 2008 AIAA, Washington, D.C., 2008, Paper No. AIAA2008-1380. 26D. Opaits, A. Likhanskii, M. Shneider, G. Neretti, S. Zaidi, S. Macheret,

and R. Miles, Proceedings of the 38th Plasma Dynamics and Lasers Conference, Miami, FL, 2007 AIAA, Washington, D.C., 2007, Paper No.

AIAA-2007-4532. 27A. Likhanskii, M. Shneider, D. Opaits, S. Macheret, and R. Miles, Proceedings of the 38th Plasma Dynamics and Lasers Conference, Miami,

FL, 2007 AIAA, Washington, D.C., 2007, Paper No. AIAA-2007-4533. 28A. Likhanskii, M. Shneider, S. Macheret, and R. Miles, Proceedings of the

44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 2006

AIAA, Washington, D.C., 2006, Paper No. AIAA-2006-1204. 29A. Likhanskii, M. Shneider, S. Macheret, and R. Miles, Proceedings of the

45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 2007

AIAA, Washington, D.C., 2007, Paper No. AIAA-2007-633. 30F. Massines, R. B. Gadri, A. Rabehi, Ph. Decomps, P. Segur, and Ch.

Mayoux, J. Appl. Phys. 83, 2950 1998. 31R. Ben Gadri, IEEE Trans. Plasma Sci. 27, 36 1999. 32J. R. Roth, J. Rahel, X. Dai, and D. M. Sherman, J. Phys. D 38, 555

2005.

FIG. 10. Color onlineSurface potential distribution at modified DBD

plasma actuator. Applied voltage profile: 2 kV dc bias, 3 kV pulses at

10 kHz PRR.

073505-5 Surface charge in dielectric barrier discharge plasma actuators Phys. Plasmas 15, 073505 2008

NASA/CR—2012-217654 46
Electrodynamic effects in nanosecond-pulse-sustained long

dielectric-barrier-discharge plasma actuators

D. F. Opaits,a M. N. Shneider, and R. B. Miles

Applied Physics Group, Mechanical and Aerospace Engineering, Princeton University,

Princeton, New Jersey 08540, USA

Received 17 November 2008; accepted 19 January 2009; published online 10 February 2009

Both numerical and experimental studies of the voltage distribution in a pulsed long dielectric

barrier discharge plasma actuator have been performed. The results demonstrate the importance of

electrodynamic effects in actuators for which the length is comparable with the length of the

propagating pulses. These effects lead to a nonuniform voltage distribution along the electrodes,

voltage doubling at the end of the actuator, nonoptimized power coupling to the actuator, and

ringing. In addition to the direct voltage measurements, images of the discharge were taken which

revealed its nonuniform structure. © 2009 American Institute of Physics.

DOI: 10.1063/1.3081027

The most promising prospective application of the asymmetric dielectric barrier discharge DBDplasma actuator is

flow control over an airfoil.1–6 Recently, a number of both

numerical7 and experimental8–10 works have demonstrated

the effectiveness of nanosecond, high voltage pulse sustained

DBDs in achieving improved performance for the generation

of surface flow for control authority. While these pulse sustained devices have worked well for laboratory size models

tens of centimeters in spanwise directionimportant issues

arise when it comes to scaling the pulse sustained actuator to

the practical airfoil sizes several meters spanwise.

If the actuator is extended across a wing its size may

become comparable with physical length of the high voltage

pulse or to the wavelength of the applied rf voltage if the

actuator discharge is sustained by a rf generator. In such case

the electrodes cannot be considered equipotential anymore

and the wave nature of the electromagnetic signal propagating along the long line the actuatormust be taken into

account. This effect can lead to variations in the voltage

along the actuator, voltage doubling at the end, nonoptimized

power coupling into the actuator, and ringing due to mismatched impedance of the cable and the actuator. The nonuniform voltage distribution across electrodes was observed

for the first time in rf driven CO2 lasers of slab geometry by

Lapucci et al.11 Theory of the phenomenon was later developed by Raizer and Shneider.12 Later a similar problem was

studied for large-area rf plasma chemical reactors by Lieberman et al.13

The plasma actuator used for this study was 2.4 m long

and was connected to the pulse generator at one end, as

shown in Fig. 1. The electrodes were made of copper foil.

The width and thickness of the electrodes were 25 mm and

100 m, respectively, which resulted in resistance R= 1.34

10−2  m−1. A 100 m thick kapton tape was used as

the dielectric. The actuator’s capacitance was measured

experimentally using a Fluke 189 multimeter and found to

be C= 127 pF m−1. Its inductance was found to be L

= 0.178 H m−1 by measuring the pulse propagation speed

v= 2.1108 m s−1 in the actuator and using the expression

v= 1/LC. The impedance of the actuator can be found from

the expression Zactuator=L/C= 37 . The voltage was

monitored with PP005A 500 MHz LeCroy voltage probe

connected to WavePro 7300A 3GHz LeCroy oscilloscope.

The experiments were conducted for low and high voltage pulses. The low voltage pulses were used to measure the

pulse propagation speed in the absence of the plasma, which

may introduce significant dissipation. A Stanford Research

Systems pulse generator was used as a source and the pulses

were applied to one end of the actuator through a 50 

cable. High voltage pulses of negative polarity were used to

ignite the plasma and observe the visible appearance of the

discharge. These pulses were generated by FPG 25–200MC4

pulser by FID Technology. The pulse profiles are shown in

Fig. 2.

The signal propagation in a long line is described by

telegraph equations

C

u

t

+ Gu +

i

x = 0, 1

L

i

t

+ Ri +

u

x = 0, 2

where u and i are voltage and current; L, C, G, and R are the

impedance parameters specified per unit length—inductance,

capacitance, leakage conductance, and resistance correspondingly. The values of the impedance parameters were

taken from the experiment and are specified above. The leakage conductance was considered to be negligibly low.

A numerical code has been developed to solve the set of

telegraph Eqs. 1and 2 using a second order Lax–

Wendroff method coupled with Flux Corrected Transport

a

Electronic mail: dopaits@princeton.edu.

FIG. 1. Color onlineDBD plasma actuator aand schematic representation of its elementary components b.

APPLIED PHYSICS LETTERS 94, 061503 2009

0003-6951/2009/946/061503/3/$25.00 94, 061503-1 © 2009 American Institute of Physics

NASA/CR—2012-217654 47
technique.14–16 Proper boundary conditions for forward and

reversed waves, see for instance,17 were imposed at the

cable/actuator connection point as well as at the end of actuator open circuit. The code allows simulation of the actuator with an arbitrary active noninductive resistoror reactive inductor, capacitorload at the end.

Results of both numerical simulation and experimental

measurements of the low voltage nanosecond pulse in the

long plasma actuator are presented in Fig. 3. The diagrams

show the time evolution of the voltage distribution along the

actuator. Negative values of the distance correspond to the

voltage in the connecting cable. The finite capacitance

11 pFof the voltage probe caused the small amount of

pulse broadening seen in the comparison of the modeled

voltage leftwith the measured voltage right.

Several phenomena characteristics of long lines can be

recognized in these diagrams. First of all, the voltage distribution is not uniform along the electrodes. Second, the pulse

doubles at the end of the actuator which we expect to happen

with a high impedance load. This leads to nonuniform discharge parameters along the actuator.

Also the impedance matching of the connecting cable

and the DBD actuator is important. The mismatch leads to

poor power coupling from the cable to the actuator as can be

seen from the modeling. In this particular case the impedances have values which are close Zcable= 50  and

Zactuator= 37 so the effect is not particularly strong, but it

is still observable. Similarly, a part of the pulse reflects on its

way back to the cable which creates a ringing effect, which

can be seen most clearly in the model results. By choosing

the proper dimensions and dielectric constant, the actuator

could be designed in a way to match the cable impedance. It

means that pulse would be transferred from the cable to the

actuator and back without any distortion and losses, so there

would not be any ringing effect or poor power coupling. The

finite conductivity of the electrodes did not play a significant

role in the pulse propagation.

Experiments with the high voltage nanosecond pulses

were conducted in order to observe the plasma nonuniformity visually. The pictures of the discharge at different pulse

voltages are shown in Fig. 4. The top left picture, Fig. 4a,

corresponds to the pulse voltage slightly below the breakdown value. The discharge ignites only at the far end where

the pulse voltage doubles. In the second picture, Fig. 4b,

the pulse voltage is higher than the breakdown value and the

discharge ignites along the whole length of the actuator. The

image in Fig. 4c, which is the top view of Fig. 4a, shows

the nonuniformity of the discharge, which becomes brighter

and wider toward the end of the actuator. Gaps in the discharge are due to local variations in the electrode edges.

Experiments on the nonuniformity of the pulse voltage

distribution in a long DBD plasma actuator have been conducted. Images of the discharge appearance have been taken

and direct voltage distribution measurements have been

made. The images demonstrate the discharge nonuniformity.

Numerical modeling of short pulse propagation in long lines

has also been performed and agreement between the experimental and the simulated voltage distribution was obtained.

The results show the importance of the wave nature of pulse

propagation. This results in a nonuniform potential distribution along the electrodes, a doubling of the pulse voltage, at

the end of the actuator, nonoptimized power coupling, ringing effects, etc.

This work was supported in part by a grant from the Air

Force Office of Scientific Research Dr. John Schmisseur,

Program Managerand in part by NASA Glenn Research

Center Dr. David Ashpis, Program Manager.

1

E. Moreau, J. Phys. D 40, 605 2007. 2

C. L. Enloe, T. E. McLaughlin, R. D. VanDyken, K. D. Kachner, E. J.

Jumper, and T. C. Corke, AIAA J. 42, 589 2004. 3

C. L. Enloe, T. E. McLaughlin, R. D. VanDyken, K. D. Kachner, E. J.

Jumper, T. C. Corke, M. Post, and O. Haddad, AIAA J. 42, 595 2004. 4

J. R. Roth, J. Rahel, X. Dai, and D. M. Sherman, J. Phys. D 38, 555

2005. 5

B. Jayaraman, Y.-C. Cho, and W. Shyy, Proceedings of the 38th

AIAA Plasmadynamics and Lasers Conference, Miami, Florida, 2007

unpublished. 6

M. A. Huerta and L. D. Ludeking, Proceedings of the 38th AIAA Plasmadynamics and Lasers Conference, Seattle, Washington, 2008

unpublished. 7

A. V. Likhanskii, M. N. Shneider, S. O. Macheret, and R. B. Miles, J.

Appl. Phys. 103, 053305 2008. 8

D. F. Opaits, A. V. Likhanskii, G. Neretti, S. Zaidi, M. N. Shneider, R. B.

FIG. 2. Low aand high bvoltage pulse profiles.

FIG. 3. Pulse propagation along the actuator. Numerical a, experimental

b.

FIG. 4. Color onlineImages of DBD at different voltages. alow voltage,

bhigh voltage, clow voltage seen from above.

061503-2 Opaits, Shneider, and Miles Appl. Phys. Lett. 94, 061503 2009

NASA/CR—2012-217654 48
Miles, and S. O. Macheret, J. Appl. Phys. 104, 043304 2008. 9

D. F. Opaits, D. V. Roupassov, A. Yu. Starikovskii, I. N. Zavialov, and S.

G. Saddoughi, Proceedings of the 43th AIAA Aerospace Sciences Meeting

and Exhibit, Reno, Nevada, 2005 unpublished. 10D. V. Roupassov, I. N. Zavyalov, and A. Yu. Starikovskii, Proceedings of

the 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada,

2006 unpublished. 11A. Lapucci, F. Rossetti, M. Giofini, and G. Orlando, IEEE J. Quantum

Electron. 31, 1537 1995. 12Y. P. Raizer and M. N. Shneider, IEEE Trans. Plasma Sci. 26, 1017

1998. 13M. A. Lieberman, J. P. Booth, P. Chabert, J. M. Rax, and M. M. Turner,

Plasma Sources Sci. Technol. 11, 283 2002. 14P. D. Lax and B. Wendroff, Commun. Pure Appl. Math. 13, 217 1960. 15E. S. Oran and J. P. Boris, Numerical Simulation of Reactive Flow Cambridge University Press, Cambridge, England, 2000. 16Y. N. Dnestrovskii and D. P. Kostomarov, Numerical Simulation of Plasmas Springer, Berlin, 1985. 17P. N. Herbert, Introductory Electromagnetics Wiley, New York, 1991.

061503-3 Opaits, Shneider, and Miles Appl. Phys. Lett. 94, 061503 2009

NASA/CR—2012-217654 49
Eur. Phys. J. Appl. Phys. 47, 22802 (2009)

DOI: 10.1051/epjap/2009081

Regular Article

THE EUROPEAN

PHYSICAL JOURNAL

APPLIED PHYSICS

Non-thermal atmospheric pressure plasmas for aeronautic

applications

R.B. Miles1,a, D.F. Opaits1, M.N. Shneider1, S.H. Zaidi1, and S.O. Macheret2

1 Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA 2 Lockheed Martin Aeronautics Company, Palmdale, CA 93599, USA

Received: 27 November 2008 / Accepted: 12 February 2009

Published online: 14 May 2009 – c EDP Sciences

Abstract. Dielectric barrier surface discharges (DBD) have the potential to act as flush mounted flow

control devices for separation control and other aeronautic applications. A pulse-sustained plasma with

the ions driven by a DC bias voltage is proposed for optimum performance. While characterizing these

devices, it was found that their performance is severely limited by surface charge build-up. That charge

builds up rapidly and remains for as long as hours. Work in this paper shows that the surface charge can be

mitigated by using a reversing DC bias potential or by using a constant DC bias potential with a partially

covered electrode.

PACS. 52.40.Hf Plasma-material interactions; boundary layer effects – 47.85.L- Flow control – 52.80.-S

Electric discharges

1 Introduction

Many recent studies have demonstrated the utility of dielectric barrier discharge (DBD) plasma actuators with

offset electrodes (Fig. 1a) for aerodynamic control [1–5].

In particular, they have been shown to suppress boundary

layer separation in low-speed flow on airfoils, so there has

been great practical interest in developing this technology

further. Typically, these DBD discharges are driven by

high peak-to-peak sinusoidal voltages (tens of kilovolts),

and they produce surface jets that are in the direction

of the offset covered electrode, as shown by the arrow in

Figure 1a. Understanding the physics of the process is still

proceeding, with the current picture being that charge separation and attachment of electrons to the surface play a

critical role. Modeling in our laboratory captured that process [6], and, with that insight, we predicted that a voltage

waveform consisting of high-voltage nanosecond repetitive

pulses superimposed on a DC bias voltage would produce

significantly enhanced wall jet velocities compared with

those generated with the conventional sinusoidal voltage.

In this case, the plasma is generated and the charge separation formed by the repetitive short ionization pulses,

and the momentum transfer to the neutral gas occurs due

to the ions that are driven by the charge separation enhanced by the DC bias voltage. The advantage of this nonself-sustained discharge is that the parameters of ionizing

pulses and the driving bias voltage can be varied indepena e-mail: miles@Princeton.EDU

dently, which adds efficiency and flexibility to control and

optimization of the actuator performance. The nanosecond pulses accelerate electrons to high velocity between

collisions, so the ionization process is more efficient, and

the timing and repetition rate of the pulses can be optimized to minimize power and maximize thrust. The DC

bias avoids the intermittent generation of thrust characteristic of AC driven systems, and thus can have a 100%

duty cycle.

However, laboratory measurements with this pulse

plus DC waveform did not yield the increased performance predicted. Upon closer inspection we observed that

the jet velocity was high for a few pulses when the DC

was turned on, but slowed significantly thereafter [7].

From this observation we determined that surface charge,

which built up over a number of pulses, was limiting

the performance [8,9]. This charge opposes the applied

DC potential. This build-up process is not captured in

the model because subnanosecond time steps are necessary, and the long build-up time exceeds the few microsecond single CPU computational limit. Further experiments [8–10] have shown that the same surface charge

builds up in the conventional sinusoidal-driven DBD configuration, so it is important to develop approaches that

will minimize its effect.

We have taken two approaches to overcome this charge

build up. Both still rely on the high voltage nanosecond

pulses to form the discharge. The first approach applies an

alternating bias, which sweeps the charge off the dielectric,

Article published by EDP Sciences

NASA/CR—2012-217654 50
The European Physical Journal Applied Physics

Fig. 1. (Color online) Dielectric barrier discharge configurations. (left) The standard configuration with an exposed upper

electrode and a lower electrode, offset from the upper and covered with a think dielectric material. (right) The new configuration designed to suppress charge build up. Here the lower

electrode is uncovered downstream to allow charge that builds

up on the dielectric to bleed-off.

and the second approach is a change in the electrode geometry, with the buried electrode uncovered a few millimeters downstream (Fig. 1b). Both of these have shown

some success in alleviating the problem [8,9].

2 Measurement of surface charge

The series of experiments we undertook to quantify the

charge build-up used a non-contacting Trek Model 247-3

Electrostatic Voltmeter with Trek Model 6000B-13C Electrostatic Voltmeter Probe [8,9]. This probe has high resolution, fast response time (less then 3 ms for a 1 kV step),

and an operating range from 0 to +/− 3 kV DC or peak

AC. The spatial resolution of the probe is around 1 mm.

Initial experiments were conducted for 3 kHz 10 kV peakto-peak sinusoidal voltage profile. Since the sinusoidal profile is widely used in DBD experiments, the initial experiments were conducted with a sinusoidal voltage driven

discharge (no pulses). The actuator was run for 15 s and

then the surface potential was measured. The result is presented in Figure 2. As can be seen in the figure, there is a

significant charge build-up on the dielectric in the region

far downstream of the plasma. The plasma extends only

a few millimeters downstream of the edge of the exposed

electrode whereas the dielectric charges up to centimeters

away from it. The maximum surface potential (1.5 kV)

is comparable with the applied peak voltage (5 kV). This

means that the electric field of the surface charge can dramatically distort the electric field produced by the voltage

applied to the electrodes. Also, even though the applied

voltage is symmetrical (sinusoidal with no bias voltage)

the surface charge has a positive polarity.

We then conducted experiments with the pulsesustained plasma using a DC bias. This was the configuration our modeling suggested would produce the highest

thrust. Four kilovolt (4 kV) nanosecond pulses were applied at a rate of 10 kHz along with a DC bias of + or

−2 kV. The plasma was run for 15 s. Results of surface

potential measurements are presented in Figure 3. As in

the case of a sinusoidal voltage, the charge builds up far

downstream the plasma region, and the magnitude of the

surface potential is primarily determined by the bias volt0 5 10 15 20 25

0.0

0.5

1.0

1.5

Surface potential, kV

Distance, mm

Fig. 2. Surface potential distribution. Applied voltage profile

− sinusoidal 3 kHz, 10 kV peak-to-peak. Electrodes edge at 0.

age. The ionization pulse voltage has little effect on it. In

order to determine how quickly the surface charge builds

up at a selected DC bias voltage, a pre-determined number

of pulses were sent to the actuator and then the surface potential was measured. The results are shown in Figure 4.

Even though this was for a small number of pulses and

the accuracy of measurements is low, it can be seen that

a single pulse creates a noticeable surface charge. As the

number of pulses increases, the surface charge builds up

and moves farther away from the plasma. After it builds

up, the surface charge remains for a very long time. Measurements shown in Figure 5 indicate that in 30 min it depletes only by 15–20 per cent. Since the depletion occurs

at the same rate for both positive and negative charge,

we can assume that the charged particles at the dielectric

surface are positive and negative ions from the gas, not

electrons or holes.

In order to interpret the experimental data a numerical model, based on the described above Poisson solver,

was developed [11]. The DBD plasma actuator consisted

of 2 electrodes of length 2.5 cm, separated by the 100 micron Kapton tape. The electrodes were assumed to be infinitely thin. The computational model [11] was able to

provide the distribution of charge on the dielectric surface, as shown in Figure 6. It is important to note that

numerical results shown in Figure 6 correspond to potential distribution shown in Figure 5.

3 Periodically reversing bias for charge build

up suppression

Our first approach to the minimization of the surface

charge build-up has been to use a time-varying bias together with the high repetition rate pulses. We observed

that, as long as the bias reverses, the build-up is of the

22802-p2

NASA/CR—2012-217654 51
R.B. Miles et al.: Non-thermal atmospheric pressure plasmas for aeronautic applications

-5 0 5 10 15 20 25

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

 Positive bias

 Zero bias

 Negative bias

Surface potential, kV

Distance, mm

Positive pulses

-5 0 5 10 15 20 25

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

 Positive bias

 Zero bias

 Negative bias

Surface potential, kV

Distance, mm

Negative pulses

Fig. 3. (Color online) Surface potential distribution. Applied voltage profile +/− 2 kV DC bias, 3 kV pulses at 10 kHz PRR.

-5 0 5 10 15 20 25

0.0

0.5

1.0

1.5

2.0

2.5

Surface potential, kV

Distance, mm

Number of pulses

 0

 1

 5

 10

 102

 103

 104

 105

Positive pulses

Positive bias

-5 0 5 10 15 20 25

0.0

-0.5

-1.0

-1.5

-2.0

-2.5

Surface potential, kV

Distance, mm

Number of pulses

 0

 1

 5

 10

 102

 103

 104

 105

Positive pulses

Negative bias

-5 0 5 10 15 20 25

0.0

0.5

1.0

1.5

2.0

2.5

Surface potential, kV

Distance, mm

Number of pulses

 0

 1

 5

 10

 102

 103

 104

 105

Negative pulses

Positive bias

-5 0 5 10 15 20 25

0.0

-0.5

-1.0

-1.5

-2.0

-2.5

Surface potential, kV

Distance, mm

Number of pulses

 0

 1

 5

 10

 102

 103

 104

 105

Negative pulses

Negative bias

Fig. 4. (Color online) Surface potential for a fixed number of pulses. Applied voltage profile +/− 2 kV DC bias, 3 kV pulses

at 10 kHz PRR.

Fig. 5. (Color online) Surface potential versus time for positive (left) and negative (right) surface charges.

22802-p3

NASA/CR—2012-217654 52
The European Physical Journal Applied Physics

Fig. 6. (Color online) Calculated charge density on the dielectric surface at different moments of time after the DBD was

turned off (negative 3 kV pulses, negative 2 kV DC voltage).

opposite sign, so the overall performance of the device

recovers each half cycle. Our experiments have used a

schlieren technique and a thrust stand to evaluate the

plasma actuator performance. The schlieren approach is

totally non-intrusive and permits studies of the induced

flow structure. The schlieren system illuminates the actuator from the side and images the induced surface jet. In

order to obtain good visibility, the nanosecond pulser is

run in a burst mode, synchronous with the time-varying

bias voltage. This produces sequential surface jets that

generate vortexes that propagate downstream. We have

also undertaken computational modeling of the effects of

these jets on the flow so that we can infer from the speed of

the vortex the original speed of the surface jet [11]. These

schlieren measurements allow us to determine the deleterious effects of long-time charge build-up on the surface

and permit us to explore different pulse sequences, different bias waveforms and polarizations, and different geometries. Figure 7 shows a series of such measurements where

the images on the left correspond to the pulse timing relative to sinusoidal bias sequences shown on the right. The

sign of the applied pulses and the bias is defined as positive if the exposed top electrode is positive relative to the

encapsulated bottom electrode. The bottom two images

are for positive and negative nanosecond pulses without

bias.

The measurement of the velocity of the vortex as it

propagates downstream gives a relative measure of the

speed of the surface jet. Computations indicate that the

surface jet at the electrode is about ten times the speed of

the propagating vortex [12]. The vortex speed is measured

as a function of distance downstream from the edge of the

upper electrode, and variations in the voltage, waveform,

and pulse repetition rate show that the highest speed occurs with negative nanosecond pulses. In that case, the

most important parameter controlling the speed of the jet

is the bias voltage. In the experiments, the vortexes originating from the positive half cycle and the negative half

cycle are separately recorded. Figure 8a shows the variation of the jet speed as a function of bias voltage for a

Fig. 7. (Color online) Images of surface vortexes taken at the

same time relative to the sinusoidal wave form showing the

variation is vortex speed for different pulse and bias configurations. Each full cycle of the bias voltage generates two vortexes,

one during the positive half cycle and one during the negative

half cycle.

sinusoidal bias with negative pulses applied at the peak

of the positive half cycle, and Figure 8b shows the vortex

speed for negative pulses applied at the peak of the negative half cycle. Both must be running at the same time

to avoid significant charge build up, so these data were

taken in sequence. Note that the peak vortex speed occurs for negative pulses during the positive bias half cycle

and is around 3 m/s at 12 kV, corresponding to surface

jet speeds of around 30 m/s.

Experiments on induced thrust measurements were

conducted using a PL303 Mettler Toledo balance [8]. A

Faraday cage was constructed to shield the balance from

electronic noise. The actuator was mounted on a dielectric

post and was operated with thrust either up or down so

buoyancy effects were determined to be negligible. Parametric studies were made of the thrust and Figure 9 shows

some of the results of those studies, indicating that the

thrust increase is most dramatic with increasing bias voltage, as previously expected from Schlieren images. What

is most interesting is that the thrust measured is much

higher than achieved elsewhere at low bias voltages, as

shown by the orange and blue lines on the left of Figures 10a and 10b. The same thrust is measured for 20 kV

peak-to-peak bias as for 40 kV in the more conventional

configuration. Note that the high bias voltages require

much thicker dielectrics to avoid breakdown. These results indicate that the pulse plus bias approach has great

promise for improved performance of DBD control devices.

In our experiments the peak bias voltage was limited by

the isolation circuit elements between the bias and the

pulse forming electronics.

4 Partially covered electrode configuration

for charge bleed off

Our second approach to the solution of the surface charge

problem is a new electrode configuration that is intended

to take advantage of the fact that the surface charge builds

up far downstream from the plasma. In this new configuration, the dielectric covers only part of the lower electrode,

22802-p4

NASA/CR—2012-217654 53
R.B. Miles et al.: Non-thermal atmospheric pressure plasmas for aeronautic applications

Fig. 8. (Color online) Vortex speed as a function of distance downstream of the upper electrode edge for negative high voltage

pulses and sinusoidal bias voltages ranging from 5 to 12 kV. (right) Vortexes generated during the positive half cycle of the bias

and (left) vortex generated during the negative half cycle of the bias.

2.0 2.5 3.0 3.5

0

2

4

6

8

10

12

Thrust, mN/m

Pulse voltage, kV

0 10 20 30 40 50

0

2

4

6

8

10

12

14

16

Thrust, mN/m

PRR, kHz

0 2 4 6 8 10 12

0

2

4

6

8

10

12

14

16

18

Thrust, mN/m

Bias voltage, peak-to-peak, kV

1 10 100 0

2

4

6

8

10

12

Thrust, mN/m

Bias frequency, Hz

Fig. 9. Thrust dependence on applied voltage parameters. Negative pulses. Bias: square, 10 kV peak-to-peak, 100 Hz.

Pulses: 3 kV, 25 kHz.

leaving the rest of the electrode exposed, as shown in Figure 1b. This configuration allows a return to the more

effective repetitive nanosecond pulses plus DC bias concept. In such a case, the surface charge cannot build up

far downstream and the shielding of the DC bias voltage is reduced. Some preliminary results are shown in

green (far left curve) in Figures 10a and 10b. The induced

thrust is greater than the DBD plasma actuator driven by

repetitive pulses with an alternating sign 100 Hz square

wave low frequency bias. The thrust for this new electrode configuration scales linearly with the bias voltage

and nanosecond pulse repetition rate, at least in the low

voltage regime that we have so far been able to explore.

This actuator has a simpler bias voltage profile (DC but

not AC) and there is 100% duty cycle because the bias

voltage does not have to reverse.

5 Summary

Our work indicates that sustaining the plasma with repetitive high voltage nanosecond pulses and driving the ions

with a bias leads to significantly improved performance of

the flush mounted DBD surface control jet as compared

22802-p5

NASA/CR—2012-217654 54
The European Physical Journal Applied Physics

0 20 40 60 80

0

20

40

60

80

100

120

140 Sinusoidal voltage profile

 6 mil Kapton, 4.4 kHz

 4 mil Kapton, 5 kHz

 1/4" Quartz, 1 kHz

 1/4" Quartz, 2 kHz

 1/4" Quartz, 4 kHz

 1/4" Quartz, 8 kHz

 Glass plate, 5 kHz, Thickness unknown

Pulses plus bias voltage profile

 1/16" MACOR, 100 Hz square bias

50 kHz 4.5 kV negative pulses

 4 mil Kapton, 100 Hz square bias

50 kHz 3.0 kV negative pulses

 Modified DBD plasma actuator,

4 mil kapton, DC positive bias,

10 kHz 3 kV negative pulses

Thrust, mN/m

Voltage, peak-to-peak, kV

0 5 10 15 20 25 0

10

20

30

40

Thrust, mN/m

Voltage, peak-to-peak, kV

Fig. 10. (Color online) Thrust per unit length of the DBD electrode as a function of sinusoidal bias voltage for different

configurations at Princeton and in the literature. (Right) is a close up of the left side of (left). The three curves on the left are

with the Princeton pulse sustained plasma system operating at 50 kHz with a 100 Hz square wave bias a DC bias and the lower

electrode partially covered with 4 mil kapton (green – farthest to the left).

to the conventional configuration driven with a sinusoidal

high voltage. Ion charge build up on the dielectric surface

inhibits the performance both for the conventional DBD

configuration and for the pulse sustained concept. In order to suppress the charge build up, we show that either

a reversing bias or a new electrode configuration can be

used. The new electrode configuration exposes the lower

electrode downstream of the dielectric coating, and thus

provides a route for charge bleed off. Using this configuration, a DC bias can be applied leading to 100% duty cycle

and high performance at low bias voltage. Scaling suggests

that higher DC biases will lead to much improved performance compared to both the pulse sustained reversing

bias configuration and the conventional sinusoidal configuration.

This work was supported in part by NASA Glenn Research

Center (Dr. David Ashpis, contract Number NNX07AC02A),

in part by the Air Force Office of Scientific Research (Dr. John

Schmisseur).

References

1. J. Reece Roth, J. Phys. D: Appl. Phys. 40 (2007)

2. E. Moreau, J. Phys. D: Appl. Phys. 40, 605 (2007)

3. R. Van Dyken, T. McLaughlin, C. Enloe, 42nd AIAA

Aerospace Sciences Meeting and Exhibit, Reno, NV, 2004

(US Air Force Academy, Colorado Springs, CO AIAA2004-846)

4. T. Corke, 44th AIAA Aerospace Sciences Meeting and

Exhibit, Reno, NV, 2006 (University of Notre Dame, Notre

Dame, IN, AIAA-2006-1208)

5. T.C. Corke, E.J. Jumper, M.L. Post, D. Orlov, T.E.

Mclaughlin, 40th AIAA Aerospace Sciences Meeting &

Exhibit, Reno, NV, 2002

6. A.V. Likhanskii, M.N. Shneider, S.O. Macheret et al., J.

Appl. Phys. 103, 053305 (2008)

7. D.F. Opaits, G. Neretti, A.V. Likhanskii, S. Zaidi,

M.N. Shneider, R.B. Miles, S.O. Macheret, 38th Plasma

Dynamics and Lasers Conference, Miami, FL, 2007

(AIAA-2007-4532)

8. D. Opaits, G. Neretti, S. Zaidi M. Shneider, R.B. Miles,

A. Likhanskii, S. Macheret, 46th AIAA Aerospace Sciences

Meeting, Reno, NV, 2008 (AIAA-2008-1372)

9. D.F. Opaits, M.N. Shneider, R.B. Miles, A.V. Likhanskii,

S.O. Macheret, Phys. Plasmas 15, 073505 (2008),

doi:10.1063/1.2955767

10. C. Enloe, T. McLaughlin, J. Gregory, R. Medina, W.

Miller, 46th AIAA Aerospace Sciences Meeting and

Exhibit, Reno, NV, 2008 (AIAA-2008-1103)

11. A.V. Likhanskii, V.V. Semak, M.N. Shneider, D.F. Opaits,

R.B. Miles, S.O. Macheret, 46th AIAA Aerospace Sciences

Meeting, Reno, NV, 2008 (AIAA-2008-1380), p. 604

12. A. Likhanskii, D. Opaits, M. Shneider, S. Macheret, R.

Miles, 38th AIAA Plasmadynamics and Lasers Conference,

Miami, FL, 2007 (AIAA-2007-4533)

22802-p6

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4. TITLE AND SUBTITLE

Plasma Actuators for Turbomachinery Flow Control 

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13. SUPPLEMENTARY NOTES

Grant technical monitor, David E. Ashpis, Aeropropulsion Division, Glenn Research Center, organization code RTTO, ashpis@nasa.gov 

14. ABSTRACT

This report is Part I of the final report of NASA Cooperative Agreement contract no. NNX07AC02A. The period of performance was 

January 1, 2007 to December 31, 2010. This report includes the project summary, a list of publications and reprints of the publications that 

appeared in archival journals. Part II of the final report includes a Ph.D. dissertation and is published separately as NASA/CR-2012-

2172655. The research performed under this project was focused on the operation of surface dielectric barrier discharge (DBD) devices 

driven by high voltage, nanosecond scale pulses plus constant or time varying bias voltages. The main interest was in momentum production 

and the range of voltages applied eliminated significant heating effects. The approach was experimental supplemented by computational 

modeling. All the experiments were conducted at Princeton University. The project provided comprehensive understanding of the associated 

physical phenomena. Limitations on the performance of the devices for the generation of high velocity surface jets were established and 

various means for overcoming those limitations were proposed and tested. The major limitations included the maximum velocity limit of the 

jet due to electrical breakdown in air and across the dielectric, the occurrence of backward breakdown during the short pulse causing reverse 

thrust, the buildup of surface charge in the dielectric offsetting the forward driving potential of the bias voltage, and the interaction of the 

surface jet with the surface through viscous losses. It was also noted that the best performance occurred when the nanosecond pulse and the 

bias voltage were of opposite sign. Solutions include the development of partially conducting surface coatings, the development of a 

semiconductor diode inlaid surface material to suppress the backward breakdown. Extension to long discharge channels was studied and a 

new ozone imaging method developed for more quantitative determination of surface jet properties.

15. SUBJECT TERMS

Flow control; Tubomachinery; Low pressure turbine; Turbulence; Wall jet; Separation; Dielectric barrier discharge plasma; DBD; 

Electric field; Dielectric; Electrode; Glow discharge nanosecond pulsing 

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