Alexandre Likhanskii

Tech-X Corporation, Boulder, Colorado

Simulation Tool for Dielectric Barrier

Discharge Plasma Actuators at Atmospheric

and Sub-Atmospheric Pressures

SBIR Phase I Final Report

NASA/CR—2012-217260

February 2012
NASA STI Program . . . in Profi le

Since its founding, NASA has been dedicated to the 

advancement of aeronautics and space science. The 

NASA Scientifi c and Technical Information (STI) 

program plays a key part in helping NASA maintain 

this important role.

The NASA STI Program operates under the auspices 

of the Agency Chief Information Offi cer. It collects, 

organizes, provides for archiving, and disseminates 

NASA’s STI. The NASA STI program provides access 

to the NASA Aeronautics and Space Database and 

its public interface, the NASA Technical Reports 

Server, thus providing one of the largest collections 

of aeronautical and space science STI in the world. 

Results are published in both non-NASA channels 

and by NASA in the NASA STI Report Series, which 

includes the following report types:

• TECHNICAL PUBLICATION. Reports of 

completed research or a major signifi cant phase 

of research that present the results of NASA 

programs and include extensive data or theoretical 

analysis. Includes compilations of signifi cant 

scientifi c and technical data and information 

deemed to be of continuing reference value. 

NASA counterpart of peer-reviewed formal 

professional papers but has less stringent 

limitations on manuscript length and extent of 

graphic presentations.

• TECHNICAL MEMORANDUM. Scientifi c 

and technical fi ndings that are preliminary or 

of specialized interest, e.g., quick release 

reports, working papers, and bibliographies that 

contain minimal annotation. Does not contain 

extensive analysis.

• CONTRACTOR REPORT. Scientifi c and 

technical fi ndings by NASA-sponsored 

contractors and grantees.

• CONFERENCE PUBLICATION. Collected 

papers from scientifi c and technical 

conferences, symposia, seminars, or other 

meetings sponsored or cosponsored by NASA.

• SPECIAL PUBLICATION. Scientifi c, 

technical, or historical information from 

NASA programs, projects, and missions, often 

concerned with subjects having substantial 

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientifi c and 

technical material pertinent to NASA’s mission.

Specialized services also include creating custom 

thesauri, building customized databases, organizing 

and publishing research results.

For more information about the NASA STI 

program, see the following:

• Access the NASA STI program home page at 

http://www.sti.nasa.gov

• E-mail your question via the Internet to help@

sti.nasa.gov

• Fax your question to the NASA STI Help Desk 

at 443–757–5803

• Telephone the NASA STI Help Desk at

 443–757–5802

• Write to:

 NASA Center for AeroSpace Information (CASI)

 7115 Standard Drive

 Hanover, MD 21076–1320
Alexandre Likhanskii

Tech-X Corporation, Boulder, Colorado

Simulation Tool for Dielectric Barrier

Discharge Plasma Actuators at Atmospheric

and Sub-Atmospheric Pressures

SBIR Phase I Final Report

NASA/CR—2012-217260

February 2012

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared under Contract NNX10CE78P
Acknowledgments

This research was made possible by a NASA Small Business Innovation Research (SBIR) Phase I Contract (No. NNX10CE78P) 

in support of the Subsonic Fixed Wing Project of the Fundamental Aeronautics Program. The period of performance for this 

research effort was January 29, 2010–July 29, 2010. Princeton University (Dr. Dmitry Opaits and Dr. Mikhail Shneider) was 

the subcontractor performing the experimental part. Dr. David E. Ashpis was the Technical Offi cer (COTR). The author thanks

Dr. David E. Ashpis from the Turbomachinery and Heat Transfer Branch at the NASA Glenn Research Center (GRC), for helpful 

comments and support for this work.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by NASA technical management.

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.
NASA/CR—2012-217260 iii

Project Summary 

SBIR Phase I 

Period of Performance January 29, 2010–July 29, 2010 

Firm: Tech-X Corporation

Contract Number: NNX10CE78P

Project Title: Simulation Tool for Dielectric Barrier Discharge Plasma Actuators at Atmospheric 

and Sub-Atmospheric Pressures

Identification and Significance of Innovation: 

Identification of Innovation: 

 Simulation tool for dielectric barrier discharge (DBD) plasma actuator 

 Analyzes and predicts DBD operation at wide range of ambient gas pressures 

Significance of Innovation: 

 Traditional DBD codes are limited to low-speed applications and have weak prediction 

capabilities 

 Proposed tool allows DBD analysis/prediction for subsonic/hypersonic applications 

Technical Objectives and Work Plan: 

Objectives: 

 Demonstrate VORPAL’s capability of modeling DBD plasma actuator at low pressures 

using kinetic plasma modeling approach; 

 Demonstrate VORPAL’s capability of modeling DBD plasma actuator at moderate to 

atmospheric pressures using hydrodynamic plasma modeling approach; 

 Validate developed DBD simulation tool by comparison between simulation results and 

experimental data. 

Technical Accomplishments: (Limit 200 words or 2,000 characters whichever is less) 

 Developed prototype DBD simulation tool using kinetic approach and demonstrated 

simulations of the DBD plasma actuator, driven by nanosecond pulses, at reduced and 

atmospheric pressures; 

 Developed prototype DBD simulation tool using fluid approach and demonstrated 

simulations of the DBD plasma actuator, driven by nanosecond pulses, at atmospheric 

pressures; 

 Demonstrated hybrid capabilities of the prototype DBD simulation tool; 

 Integrated state-of-the-art numerical concepts, such as variable time step, parallel 

computing and variable weight particles into DBD simulation tool for increasing 

computational speed; 

 Performed complex experimental study of the DBD, driven by nanosecond pulses; 

 Qualitatively validated numerical results against experimental data. 

NASA Application(s): The primary NASA applications of the proposed DBD simulation tool are 

active flow control concepts for both subsonic and hypersonic flights. Predictable active flow 

separation control, achieved using the proposed tool, will benefit many NASA Projects, such as 

Subsonic Fixed Wing Project, Subsonic Rotary Wing Project and Hypersonic Project. In addition 

to the flow separation application, DBD simulation tool can be used for a number of NASA 

problems, associated with gas discharges at different pressures. For example, DBD simulation 

tool can be used for the description plasma-assisted combustion for the reduction of carbon 

emissions. 

Non-NASA Commercial Application(s): Proposed tool will be beneficial for subsonic/hypersonic 

programs which involve active flow separation control. These programs include, but are not 

limited to, flow separation control at commercial airplanes during take-off or landing, increase in 

lift for tiltrotor aircrafts, improvement of engine performance, active flow control at hypersonic 

vehicles. Besides the primary application for a description of DBD operation, DBD simulation tool 

can be used for a wide range of plasma aerodynamics applications, such as plasma-assisted 

combustion, flow control using different types of discharges, reduction of carbon emission, 

optimization of air vehicle operation, MHD and EHD application. 
NASA/CR—2012-217260 iv

Table of Contents 

Project Summary ................................................................................................. iii 

Table of Contents ................................................................................................. iv 

1. Introduction ....................................................................................................... 1 

2. Technical Objectives ......................................................................................... 2 

3. Technical Activities ........................................................................................... 3 

4. Potential Applications ..................................................................................... 24 
NASA/CR—2012-217260 1

Simulation Tool for Dielectric Barrier Discharge Plasma 

Actuators at Atmospheric and Sub-Atmospheric 

Pressures 

SBIR Phase I Final Report 

Alexandre Likhanskii 

Tech-X Corporation 

Boulder, Colorado 80303 

1. Introduction

Traditional approaches for active flow separation control using dielectric barrier discharge (DBD) 

plasma actuators are limited to relatively low-speed flows and atmospheric conditions. However, 

NASA missions target a number of applications, such as active flow control at turbine blades, 

fixed wings, rotary wings and hypersonic vehicles, which require a satisfactory performance of the 

DBD plasma actuators at wide range of conditions, including rarified flows and combustion 

mixtures. 

A simulation tool that analyzes and predicts the DBD operation at particular conditions would 

benefit scientists involved in DBD research, allowing them optimizing DBD operation via 

simulations and reducing amount of work and cost of experimental equipment. 

We proposed to develop a DBD plasma actuator simulation tool for a wide range of ambient gas 

pressures. At the completion of the Phase II of this work, scientists and engineers will be able to 

analyze and predict DBD operation at different flight regimes – from subsonic to hypersonic. The 

proposed tool will be validated by comparison with the experimental and numerical data on the 

DBD investigations. 

In order to achieve maximum reliability and best performance, the proposed tool will utilize stateof-the-art numerical and theoretical approaches to the description of the DBD plasma actuator. 

The choice of these approaches will be dictated by the DBD projected applications. 

Subsonic applications, such as active flow separation control at turbine blades or at airplane 

wings during take-off or landing, will require a comprehensive model of the DBD plasma actuator 

at atmospheric conditions. For these kinds of applications, DBD simulation tool will treat plasma 

as a multi-component fluid, consisting of neutral molecules, electrons and different types of 

positive and negative ions. The motion of the charged particles will be defined by the distribution 
NASA/CR—2012-217260 2

of local electric field. The feasibility of this approach has been shown in numerous research 

efforts on discharge simulation at atmospheric conditions. 

Hypersonic applications, such as flow separation control at scramjet vehicles, will require the 

ability to describe DBD at substantially reduced pressures. For this purposes, we will use kinetic 

approach for the discharge treatment. By utilizing kinetic approach, we will be able to develop the 

unique simulation tool for the DBD operation at sub-atmospheric pressures. 

In order to achieve efficient performance of the proposed simulation tool at experimental scales, 

we will use modern numerical and theoretical concepts, including multiprocessor computing, nonuniform and adaptive meshes, and a concept of self-adjusting time step. Our previous experience 

with DBD modeling demonstrated up to two orders of magnitude increase in computational speed 

by using parallel simulations. Non-uniform and adaptive meshes will lead to another one/two 

orders of magnitude increase in computational speed, compared to traditionally-used uniform 

meshes. The concept of self-adjusting time step reduces the computational time between the 

breakdowns (most of the time) by three orders of magnitude. By utilizing these concepts, we 

anticipate high feasibility of the DBD simulation tool for a wide range of applications. 

As an output of the DBD simulation tool, scientists will get the temporal and spatial distributions of 

the force, acting on the ambient gas and of rate of thermal energy deposition. By using these 

output data as an input file for 2D and 3D Navier-Stokes solvers, such as NASA developed code 

WIND-US or commercial code FLUENT, scientists will be able to simulate the DBD operation for 

different applications. 

The validity of the proposed innovation will be confirmed by the comparing simulation results with 

available numerical and experimental data. 

2. Technical Objectives 

During Phase I project, we focused on the feasibility of the innovation. The objectives for the 

Phase I were: 

Objective 1: Demonstrate VORPAL’s capability of modeling DBD plasma actuator at low using 

kinetic plasma modeling approach. 

Objective 2: Demonstrate VORPAL’s capability of modeling DBD plasma actuator at moderate 

to atmospheric pressures using hydrodynamic plasma modeling approach. 

Objective 3: Validate developed DBD simulation tool by comparison between simulation 

results and experimental data. 
NASA/CR—2012-217260 3

3. Technical Activities 

3.1 Task 1: Develop prototype DBD simulation tool for low pressures 

3.1.1 Incorporating dielectrics into VORPAL’s Poisson Solver. 

Before the start of the project, VORPAL’s Poisson Solver included Dirichlet (constant potential), 

Neumann (constant electric field) and periodic boundary conditions. Dirichlet boundary 

conditions are to be applied at both grounded and exposed electrode, and Neumann boundary 

conditions are to be applied on the outer boundaries of the computational domain. In the case of 

an array of DBDs, periodic boundary conditions can be applied on left and right sides of the 

conventional simulation domain for DBD plasma actuators. In this subtask we successfully 

implemented boundary conditions for dielectrics. Now, user can specify the relative dielectric 

permittivity in the entire simulation domain. This implementation is beneficial not only for 

conventional DBD configuration, but also for recently proposed multilayer structures. Once the 

dielectrics were incorporated into the VORPAL’s Poisson Solver, we were able to compute 

electric field distribution in the DBD configuration based on the geometry, applied voltages, 

dielectric permittivity and charged particle distribution. 

3.1.2 Setup VORPAL simulation with air-like mixture, consisting of 

molecular nitrogen and oxygen as a neutral background gas. 

3.1.2.1 Setup VORPAL simulation with nitrogen

The goal of this technical activity was to demonstrate the ability of PIC approach to resolve 

plasma phenomena observed in DBD simulations using fluid codes. It includes but not limited to 

sheath formation and streamer propagation. For the preliminary simulations, we limited the gas to 

nitrogen and included only inelastic collisions (ionization) in the model. The simulations started 

with seed background of positive ions and electrons. We have also included a constant rate of 

electron and ion production in the simulation domain in order to account for photoionization, 

which is not currently included into the model, but is crucial for resolving streamer formation. The 

solver for particle motion was coupled to the Poisson Solver. 

Benchmark Results 

In order to reproduce DBD physics and address the objectives of the project, we ran three 

different cases: 

 DBD driven by positive nanosecond pulses at atmospheric conditions in 2D 

 DBD driven by positive nanosecond pulses at reduced pressures (0.1 atm) in 2D 

 DBD driven by positive nanosecond pulses at atmospheric conditions in 3D 
NASA/CR—2012-217260 4

We applied 3 kV 4 ns positive pulses for atmospheric conditions and 0.7 kV 4 ns positive pulses 

for reduced pressures. 

Figure 1 shows the formation and propagation of the streamer above the dielectric surface at 

atmospheric pressure. In order to verify that the observed discharge is in streamer regime, we 

plotted electric potential distribution. The electric potential inside the streamer is the close to the 

one of the exposed electrode. This phenomenon is typical for streamer propagation and is also 

observed in fluid codes. 

Figure 1. Distribution of positive ions during the streamer discharge (left) and 

potential propagation during the streamer discharge (right). 

In the case of the reduced pressures, we observe much longer plasma formation (Figure 2) – cm 

scales compared to mm scales for atmospheric pressure. 

Figure 2. Distribution of positive ions during the breakdown at reduced pressure. 

We also performed first 3D simulations of the DBD discharge using PIC method (Figure 3). We 

observed streamer propagation both in terms of generation new particles and associated 

streamer phenomena, such as transfer of maximum electric field region to the tip of the streamer. 

One the open problem in DBD research is the description of an effect of 3D structures (filament 

formation) in the DBD operation. These structures were not resolved due to the absence of 3D 

DBD simulations. Figure 4 demonstrates the distinct structure in the z-direction (across the 

filaments) of the z-component of electric field. The ability to resolve 3D structures of the DBD will 

be beneficial to the community and will be able to provide insight on physics of the structures 

formation as well as quantify this structure. 

Y, mm 

X, mm

Y, m 

X, m

X, cm

Y, cm 

φ, V
NASA/CR—2012-217260 5

Figure 3. 3D distribution of the positive ions (left) and electric field (right) in the streamer 

discharge. Domain size is 1 mmX1 mmX0.5 mm. 

Figure 4. Distribution of z-component of electric field in the streamer discharge 

(top view on the DBD). 

Note that running these demonstration simulations for code testing is also relevant to Task 4, 

resolution of anode breakdown stage for DBD operation. 

3.1.2.2 Setup VORPAL simulation in air-like mixture

In this subtask we set up simulations in air-like mixture and demonstrated the applicability of 

variable weight particle concept for DBD simulations using PIC approach. 

Z, m

Y, m

Ez, V/m
NASA/CR—2012-217260 6

Air-like mixture. 

We considered air as a mixture of molecular nitrogen and oxygen. Three major types of collisions 

were incorporated in VORPAL – ionization, excitation and elastic collisions. In the event of 

ionization, electron collision with neutral background gas led to generation of electron-ion pair. In 

the event of excitation or elastic collision, electron lost a portion of its kinetic energy. 

Variable weight particles

First of all, let us briefly remind the physical concept behind PIC simulations. Ideal PIC simulation 

would consider the motion of each separate charged particle. This particle experiences collisions 

and gains energy in the electric field. If we consider sample plasma simulation, where the grid 

size is chosen in order to resolve typical plasma scales, we will observe, that each simulation cell 

contains lots of almost identical charged species. In order to reduce simulation time, the concept 

of macroparticles is introduced in PIC. The macroparticle is a collection of identical N charged 

particles, with the charge, equal to N times the charge of one particle and with the mass equal to 

N times the mass of one particle. With time evolution, one can observe the dynamics of 

macroparticles instead of observing dynamics of an ensemble of identical N particles. It leads to 

N-times increase in computational speed without loss of any physical phenomena. This concept 

works well for the quasi-steady state problems, when the “density” (number of real particles per 

macroparticle) of macroparticles can be chosen in advance. 

However, the above described approach fails for the unsteady gas discharge problem. Gas 

discharge starts with relatively small density of charged particles. During the avalanche ionization 

stage, the density of charged particles increases several orders of magnitude. So, on one hand, 

one should choose relatively low “density” of macroparticles for the initial stage of the discharge 

in order to get correct physical representation. On the other hand, one does not need those low 

“density” macroparticles when the plasma is generated, because it would lead to significant 

slowdown of the simulations. 

In order to tackle this problem, we used the concept of variable-weight particles. In this concept, 

macroparticle has two parameters – “nominal density” and “weight”. The “nominal density” of 

macroparticle is defined the similar way the “density” was defined before, i.e. the minimum 

(initially chosen) number of real particles in macroparticle. The “weight” of macroparticle defines 

the actual number of real particles in macroparticle. For example, if the “nominal density” of 

macroparticle is equal to 10, and the weight of macroparticle is equal to 5, there will be 5*10=50 

real particles in macroparticle. 
NASA/CR—2012-217260 7

Now, let us consider the application of this concept to the DBD problem. Initially, when there is 

almost no plasma, we assign “nominal density” of macroparticles to be 105

 particles per meter for 

2D simulations. All initially generated macroparticles contain 105

 real charged particles (electrons 

or ions) per meter distance. Once a discharge development starts, we end up with regions with 

100-1000 macroparticles in one cell. These macroparticles behave similar way, but the solution of 

equation of motion for each macroparticle needs computational resources. So, we implemented 

the sorting algorithm in VORPAL to change the weight of the particles in order not to lose 

computational speed. If the number of particles in one cell exceeds predefined limit (10 in our 

case), we combine two macroparticles into one with the weight equal to the sum of the weights of 

initial two. In this case we don’t lose any particle properties, but significantly reduce the simulation 

time (need to solve equation of motion for one particle instead of two, and so on). 

Benchmark Results 

In order to test the above described concepts, we performed 2D PIC simulation of the DBD in airlike mixture at atmospheric pressure. 3 kV 4 ns Gaussian positive pulse was applied in order to 

initiate the discharge. Figures 5 show the distribution of positive molecular nitrogen and oxygen 

ions during the streamer propagation (3 ns after the start of the pulse). Figure 6 shows 

distribution of electric potential and x-component of electric field at the same moment of time. 

After the air-like mixture was added to VORPAL capabilities, the discharge characteristic 

(breakdown electric field, plasma number density) became much closer to one observed 

experimentally, compared to simulations in nitrogen with only ionization included. Figure 7 shows 

the evolution of macroparticle weight distribution. Initially, all macroparticles had weight equal to 1 

(which is the same to the case with constant weight macroparticles). Once the breakdown starts, 

and number of macroparticles in the cell exceeds the threshold limit (10 for this particular 

simulation), macroparticles start to combine, and their weight increases. 

Figure 5. Distribution of N2

+

 (red) and O2

+

 (green) ions during the streamer discharge in air. 

Positive 3 kV, 4 ns Gaussian pulse, 3 ns after the start of the pulse. 

Y, m 

X, m 
NASA/CR—2012-217260 8

 (a) (b) 

Figure 6. Distribution of electric potential (a) and x-component of electric field (b) during 

the streamer discharge in air. Positive 3 kV, 4 ns Gaussian pulse, 3 ns after the start of the 

pulse. 

 

(a) (b) (c) 

Figure 7. Concept of variable-weight particles during the gas discharge. Plots show the 

particles with corresponding weight and x-coordinate during the breakdown. (a) 

corresponds to 0.3 ns after the start of the pulse – breakdown has not started. (b) 

corresponds to 1.5 ns after the start of the pulse – initial stage of the breakdown, 

macroparticles start to combine near the edge of the exposed electrode. (c) – corresponds 

to 3 ns after the start of the breakdown – many macroparticles are combined to particles 

with “weights” from 2 to 200. 

3.2 Task 2: Develop prototype DBD simulation tool for moderate to 

atmospheric pressures 

3.2.1 Prototype rate equation model in VORPAL. 

The goal of this technical activity was to develop a fluid plasma model for DBD simulations based 

on the drift-diffusion approximation. We started the implementation with the choice of appropriate 

infrastructure based on the discussions with COTR for adding the hybrid capabilities of the DBD 

simulation tool (see discussion in Additional Activities section). The chosen infrastructure was 

Multifields concept in VORPAL. Its benefits are as follows. The Multifield infrastructure allows 

user defining the field of variables (such as number densities, plasma parameters, etc) and apply 

finite-difference schemes at each time step. This infrastructure also includes messaging between 

X, m 

X, m 

Y, m Y, m 

X, m 

X, m X, m 

Weight Weight Weight 

φ, V

Ex, V/m
NASA/CR—2012-217260 9

processors, making it easy to run parallel simulations without extra code development. Finally, 

this infrastructure has a communication with the PIC part of the VORPAL, making the 

development of hybrid model possible. The developed fluid code consists of 5 major blocks – 

Poisson Solver for electric potential distribution (same as for PIC simulations), definition of initial 

conditions, calculation of all plasma parameters based on local electric field, gas number density 

and temperature, block for boundary conditions and solver for continuity equations for all charged 

species. The model is developed both in 2D and 3D. 

Benchmark Results 

In order to verify the developed model, we ran simulations for DBD, driven by positive 

nanosecond pulses (3 kV and 4 ns). At the beginning of the pulse, since there is only background 

(very low density) electrons and ions present in the simulation domain, we observed standard 

potential distribution between two electrodes (Figure 8 (left)). After the plasma was generated 

(peak of the pulse), we observed the propagation of the electric potential above the dielectric 

(Figure 8 (right)). The potential in highly conductive streamer is the same to the potential of the 

exposed electrode. We observed the same phenomena in PIC simulation. Figure 9 shows the 

distribution of the positive ions in linear and decibel (20*log) scale. Figure 10 demonstrates the 

effect of transfer of maximum electric field region to the tip of the head of the streamer. 

Figure 8. Electric potential distribution at the beginning of the pulse (no plasma) 

and at the peak of the pulse (streamer is generated). 

Y, m Y, m

X, m X, m

φ, V φ, V
NASA/CR—2012-217260 10

Figure 9. Distribution of positive ions in linear scale (left) and decibel scale (right). 

Figure 10. Transfer of maximum electric field region to the tip of the streamer head 

during streamer propagation. 

3.2.2 Prototype a post processor for DBD relevant parameters.

Typical DBD relevant parameters are: spatial distribution of instant body force; spatial distribution 

of instant rate of thermal energy; spatial distribution of the momentum, transferred to the gas; 

spatial distribution of thermal energy, released to the gas; total gas momentum due induced by 

the DBD; total energy, released by DBD plasma. We computed these parameters according to 

the following expressions: 

Instant force distribution: e EnnneF  (  ) 

Rate of thermal energy release distribution: jEP

  , where j is the discharge current. 

Momentum distribution:  Momentum  dtF



Energy release distribution:  Energy  Pdt

Y, m 

Y, m Y, m

X, m X, m

X, m

Np, m-3 20*log(Np) 

E, V/m
NASA/CR—2012-217260 11

Total momentum:  TMomentum  ** dtdVF

Total Energy:  TEnergy  ** dtdVP 

Benchmark Results 

In order to demonstrate post-processing capabilities and experimental scale simulation 

capabilities for short times, we set up the following simulation. The simulation domain was 5x0.5 

milllimeters. The grid size was 1x1 microns. Dielectric thickness was 100 microns. Lengths of 

exposed and grounded electrodes were 200 microns and 4.6 millimeters. Applied voltage profile, 

which is typical for experimental DBD studies, is shown in Figure 11. The results of the simulation 

12 ns after the start of the pulse are presented in Figures 12-14. These results demonstrate 

developed post-processing capabilities of the DBD simulation tool. Figure 12 shows distribution of 

x-component of instant force, acting on the gas, during the streamer breakdown (a) and spatial 

distribution of the x-component of the momentum, transferred to the gas (b). Figure 13 shows 

distribution of instant rate of thermal energy release (a) and distribution of energy release (b). 

Figure 14 shows time evolution of average (within the domain) x-component of instant force, 

acting on the gas, and average (within the domain) x-component of the momentum, transferred to 

the gas. During last two months of the projects we implement the time evolution of spatially 

integrated instant force, acting on the gas, and spatially integrated momentum, transferred to the 

gas. The results on this development are presented in technical activities for Task 4. 

Figure 11. Positive pulse profile. 

0

1000

2000

3000

4000

5000

6000

0 3E‐09 6E‐09 9E‐09 1.2E‐08 1.5E‐08 1.8E‐08 2.1E‐08

Voltage,

V

Time, seconds
NASA/CR—2012-217260 12

Figure 12. Distribution of the instant force and time-integrated force, acting on the gas 

during the breakdown. 

Figure 13. Distribution of instant rate of thermal energy release (left, in dB scale) and 

distribution of thermal energy release (right, in dB scale). 

Figure 14. Time evolution of the averaged (over the domain) x-component of the instant 

force, acting on the gas (top), and averaged (over the domain) x-component of the 

momentum, transferred to the gas (bottom). 

Time, seconds 

Y, m

X, m X, m

Y, m Y, m

X, m

Y, m

Average 

 Force, 

N/m3

20*log(Energy Release) 

F, N/m3 

Momentum, N*s/m3 

X, m

20*log(Rate of Energy Release)

Time, seconds

Average 

Momentum, 

N*sec/m3
NASA/CR—2012-217260 13

3.2.3 Enabling variable time steps in VORPAL. 

An idea of using variable time step for reducing simulation time for the proposed tool comes from 

the fact, that most of the DBD operation time electron number density is much less than negative 

ion density. Electrons are important only during the breakdown stage of the DBD operation 

(several nanoseconds). After the breakdown, electrons are rapidly attached to the molecular 

oxygen, forming negative ions. If electrons are present in the system, they define time step in the 

simulations, since they are the fastest particles in the system. In order to take advantage of the 

fact that between the breakdowns plasma is ion-ion, we artificially attach all electrons after the 

breakdown to molecular oxygen. This process results in getting pure ion-ion plasma. After all 

electrons are attached, we compute only ion dynamics using the time step, defined by ion drift 

velocity. Figure 15 shows the evolution of positive ion number density for DBD, driven by a 

combination of positive nanosecond pulse and positive bias. After pulse ends, we artificially 

attach electron, and compute plasma dynamics based on ion time. Using this concept, we 

reduced simulation time between breakdowns by a factor of 20 and got stable correct results. 

Figure 15. Distribution of positive ions in decibel scale right after the breakdown and 

200 ns after the breakdown. Applied voltage is 3 kV 4 ns positive pulse and 1 kV dc bias. 

3.3 Task 3: Perform experimental study of the Pulses+Bias DBD 

configuration 

The experiments were conducted at Princeton University (D. Opaits and M. Shneider) via 

subcontract. 

 3.3.1 Power measurements in pulsed DBD’s 

Voltage and current profile measurements have been performed to quantify power consumption 

in DBD plasma actuators. The profiles were measured using LeCroy PPE20kV, 100 MHz high 

voltage probe and LeCroy CP031, 100MHz current probe connected to a LeCroy WavePro 

7300A, 3GHz, 20GS/s oscilloscope. The nanosecond pulses were produced by FID Technology 

FPG 25-200MC4 pulser. The schematic of the electric circuit is shown at Figure 16. The DBD 

plasma actuator was made of 100 micron thick kapton tape and copper tape electrodes. The 

X,m X,m

Y,m Y,m

20*log(Np) 20*log(Np)
NASA/CR—2012-217260 14

length of the actuator was 75 mm. The high voltage pulse was applied to the top electrode at 

frequency 10 Hz while the encapsulated one was grounded. To reduce the noise the scope was 

averaging over 10 profiles. The profiles were measured for both positive and negative polarities, 

the entire range of peak values allowed by the pulser and various length of the applied pulse 

voltage (5.5, 10, 17 ns FWHM). A typical voltage and current profiles are presented at Figure 17. 

Also, experiments were done with the top electrode encapsulated. Corona dope was used to 

cover the electrode and avoid the plasma formation. This approach allows estimation of plasma’s 

contribution to the power consumption and separate it from radiative and dielectric losses. 

Figure 16. Schematic of the electric circuit. 

Figure 17. Typical voltage (right) and current (left) profiles. 

By multiplying the voltage and current profile one will get instantaneous power consumption 

which can be integrated to find total energy dissipation. The difficulty is that due to very short 

periods of time involved the profiles should be synchronized with a high accuracy. Since the time 

which it takes for a signal to travel from the probes to the scope is unknown the difference can 

reach a few nanoseconds which will have a significant effect on the power calculations. The 
NASA/CR—2012-217260 15

calibration was done using a non-inductive resistor. Both voltage and current pulses measured at 

this load had the same shape and were shifted in time by 2.5 ns. This value of the time shift was 

used to adjust the experimental data. 

Figure 18 shows calculated energy dissipated in a single pulse in DBD. First of all, the results 

show that if the plasma is absent (the top electrode is covered with corona dope) power losses 

are still significant. It means that a big part of the energy consumed by DBD is lost due to 

dielectric and radiative losses. Second result is that the pulse duration has very little effect on the 

power consumption, at least in kapton made DBD’s. Third, negative pulses dissipate significantly 

higher energy than the positive ones. Overall the power consumption is low and equals to about 

10-20 mJ per meter per pulse. 

02468

0.0

0.5

1.0

1.5

2.0 Positive pulse:

 with discharge

 5ns

 10ns

 17ns

 without discharge

 5ns

 10ns

 17ns

Negative pulse:

 with discharge

 5ns

 10ns

 17ns

 without discharge

 5ns

 10ns

 17ns

Energy (mJ)

Peak voltage (kV)

Figure 18. Power consumption in pulsed DBD. 

Discharge dimensions 

Images of plasma were acquired to study dimensions of pulsed surface dielectric barrier 

discharge. The plasma actuator was made of two copper electrodes 100 micron thick and a 

kapton tape of the same thickness as the dielectric barrier. The actuator was pulsed by FID 
NASA/CR—2012-217260 16

Technology pulser FPG 25-200MC4 at frequency about 1 Hz. Pulses of both polarities and three 

different durations were applied to the top electrode, the lower one was grounded. Intensified 

CCD Princeton Instruments camera was used to capture images of the discharge. Exposure time 

was equal to 1 microsecond, field of 12 by 6 mm, resolution 512x256 pixels, i.e. 23 microns/pixel. 

The experiments were conducted in room air. 

Typical results of the discharge appearance (top view) along with the pulse voltage profile are 

shown in Figures 19 and 20. The top 1/3 part of the image is the top electrode; the lower 2/3 of 

the image is the dielectric and the bottom electrode under it. Note, the contrast and brightness of 

the images were changed for best appearance. It can be seen that positive discharge (especially 

at longer pulses) consists of uniformly distributed streamer, whereas the negative pulses produce 

more uniform glow. Still some irregular filamentation can be observed in negative polarity at 

higher peak voltages. 

Figure 19. Plasma appearance, top view, image size 12x6 mm. 

Voltage profile – 5.5 ns, 4 kV positive pulse, shown on the right.

Figure 20. Plasma appearance, top view, image size 12x6 mm. 

Voltage profile – 5.5 ns, 4 kV negative pulse, shown on the right.
NASA/CR—2012-217260 17

Profiles of the intensity distribution in DBD along the distance downstream is shown in Figure 21. 

Relative intensity in all plots is the same which makes possible comparison of the effect of the 

pulse polarity and duration on the intensity distribution. The intensity profiles demonstrate higher 

radiation close to the electrode edge. The intensity is higher for pulses of higher peak voltage and 

duration. Pulse polarity, although has some effect of the profile shape, does not make a big 

difference. 

Figure 22 shows the dependence of the discharge maximum intensity, total radiation (which was 

found by integration of the intensity over distance), and length as functions of the pulse voltage. 

The length of the discharge is defined as size of the region where the plasma radiation exceeds 

10% of its maximum value. Sometimes this definition of the discharge length may lead to 

confusion. For example, the size of the discharge created by 10 ns positive pulse increases with 

peak voltage as we can see from the intensity profiles. However the length measurements show 

that the discharge length suddenly decreases around 4 kV of the pulse voltage, see Figure 22. 

It can be seen from the plots that the maximum intensity, total emitted radiation, and the length of 

the discharge go up with the pulse voltage and duration. 

Thickness of the discharge 

Images of the discharge were acquired to measure its thickness. The actuator was 75 mm long 

and was made of 100 micron thick kapton tape and copper electrodes. The camera was placed 

downstream of the actuator as shown at Figure 23. The reason for that was to make sure that the 

entire discharge stays within the focal depth of the optical system (about 1 cm in this particular 

case). If the camera was taking side images of the discharge than the parts of the plasma which 

stick out of the focal plane of the optical system by more 5 mm would be out of focus and come 

out blurry. It can be misinterpreted as a thicker discharge. If the images are taken from the 

downstream this problem does not arise. 
NASA/CR—2012-217260 18

0246

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

 2.27 kV

 3.10 kV

 3.48 kV

 4.05 kV

 4.49 kV

 5.10 kV

Intensity, a.u.

Distance, mm

Positive pulses, 5ns

0246

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

 -1.79 kV

 -2.72 kV

 -3.48 kV

 -4.32 kV

 -5.24 kV

Intensity, a.u.

Distance, mm

Negative pulses, 5 ns

0246

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0 1.94 kV

 2.60 kV

 2.82 kV

 3.10 kV

 3.69 kV

 4.33 kV

 4.96 kV

 5.61 kV

Intensity, a.u.

Distance, mm

Positive pulses, 10ns

0246

-2

0

2

4

6

8

10

12

14

16

18

20 -2.34 kV

 -3.37 kV

 -4.47 kV

 -5.04 kV

 -5.76 kV

 -6.28 kV

 -6.60 kV

Intensity, a.u.

Distance, mm

Negative pulses, 10ns

0246

-2

0

2

4

6

8

10

12

14

16 2.00

 2.54

 2.81

 3.10

 3.31

 3.80

 4.04

 4.50

 4.78

Intensity, a.u.

Distance, mm

Positive pulses, 17ns

0246

-1

0

1

2

3

4

5

6

7

8

9

10

11

12

Intensity, a.u.

Distance, mm

 -1.88 kV

 -2.33 kV

 -2.74 kV

 -3.08 kV

 -3.62 kV

 -4.04 kV

 -4.46 kV

Negative pulses, 17ns

Figure 21. Intensity distribution in DBD along the distance downstream. Relative intensity 

in all plots is the same. Electrodes edge located at 2 mm. 
NASA/CR—2012-217260 19

-6 -4 -2 0 2 4 6

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0 Positive pulse, 5 ns

 Negative pulse, 5 ns

 Positive pulse, 10 ns

 Negative pulse, 10 ns

 Positive pulse, 17 ns

 Negative pulse, 17 ns

Maximum intensity, a.u.

Pulse voltage, kV

-6 -4 -2 0 2 4 6

0

2

4

6

8

10 Positive pulse, 5 ns

 Negative pulse, 5 ns

 Positive pulse, 10 ns

 Negative pulse, 10 ns

 Positive pulse, 17 ns

 Negative pulse, 17 ns

Total radiation, a.u.

Pulse voltage, kV

-6 -4 -2 0 2 4 6

0

1

2

3

4

5

6

 Positive pulse, 5 ns

 Negative pulse, 5 ns

 Positive pulse, 10 ns

 Negative pulse, 10 ns

 Positive pulse, 17 ns

 Negative pulse, 17 ns

Length, mm

Pulse voltage, kV

Figure 22. The discharge maximum intensity, total radiation, and length measured at 10% 

of peak intensity versus pulse voltage. 
NASA/CR—2012-217260 20

Figure 23. Experimental layout. 

The image resolution was 512 by 512 pixel and the field of view was 40 by 40 mm. This 

corresponds to resolution 78 micron per pixel. Typical images for both polarities of the pulses are 

shown in Figure 24. It can be seen that the thickness of the discharge in the picture was only 2-3 

pixel what corresponds to about 150-200 microns. The thickness does not vary noticeably in the 

given range of pulse voltages (3-7 kV) and is similar for both polarities. A better optical system, 

namely a microscope, is required to perform exact plasma thickness measurements. 

Negative 

pulse 

40x10 mm 

Positive pulse 

40x10 mm 

Negative 

pulse 

40x2 mm 

Positive pulse 

40x2 mm 

Figure 24: Images of the discharge, front view, single pulse. 
NASA/CR—2012-217260 21

3.4 Task 4: Validate developed prototypes by comparing simulation and 

experimental results 

3.4.1 The anode breakdown stage of the DBD discharge. 

The goal of this technical activity was to demonstrate that developed prototype of DBD simulation 

tool can resolve all essential physical phenomena. We have accomplished this subtask during the 

testing of the developed prototype in Task 1 and 2 technical activities. We have studied DBD 

plasma actuator, driven by positive nanosecond pulses, and observed all phenomena, 

corresponding streamer propagation, such as transfer of region of maximum electric field to the 

tip of the streamer head, same potentials of the exposed electrode and streamer body, longer 

streamers at lower pressures. Besides it, we observed for the first time 3D structure in DBD 

discharge using 3D PIC simulations. These results are unique and show the high potential of the 

proposed DBD simulation tool for correct description of the DBD physical phenomena. 

3.4.2 Pulses+bias configuration

The goal of this technical activity was qualitative comparison between experimental and 

numerical results of the project and demonstration of potential of using DBD simulation tool for 

modeling experimental configurations. 

Qualitative comparison between experimental and numerical data

In order to demonstrate feasibility of the proposed DBD simulation tool, we performed qualitative 

comparison between the results of prototype model, developed during Phase I project and 

experimental results. Since detailed air-chemistry, photoionization and electric circuit models will 

be implemented during Phase II project, we anticipated getting only qualitative agreement. We 

have compared four plasma characteristics – plasma length, plasma thickness, general plasma 

appearance and power consumption. The comparison has been made for 3 kV 4 ns + 1 kV DC 

bias simulated positive pulses and 3 kV 5 ns experimental pulses. The numerical results on 

plasma length and plasma appearance for both PIC and fluid DBD simulations are taken from 

section 3.1.2 and 3.2.2 and experimental results are taken from section 3.3.1. As was mentioned 

in Task 3 Technical activities, we have also implemented a number of post-processing 

capabilities for DBD simulation tool in VORPAL. One of them is energy, deposited into plasma. 

Figure 25 shows the computed energy, deposited by nanosecond pulse, per DBD length. 
NASA/CR—2012-217260 22

Figure 25. Energy consumed by DBD as a function of DBD operational time. 

By comparing the results of simulations and experiments, we observe that qualitative plasma 

properties are similar and the results are in good agreement. Despite we observe the expected 

discrepancy in the quantitative comparison of the results, the values of the differences between 

numerical and simulations results are quite low. Once the detailed air chemistry, photoionization 

and electric circuit models are included into DBD simulation tool during Phase II project, we 

expect to get excellent quantitative agreement between the results. Table 1 summarizes the 

comparison between numerical and experimental results. 

DBD Property Experimental 

Results (3 kV, 5 ns) 

Numerical Results 

(3 kV, 4 ns) 

Qualitative 

Comparison 

Result 

Plasma length ~ 2 mm ~ 0.5 mm Good agreement 

Plasma thickness 

150-200 microns  100 microns for fluid 

approach 

 250 microns for 

kinetic approach 

Good agreement 

Consumed Energy per 

plasma volume 

~20 kJ/m3 ~18 kJ/m3 Excellent 

agreement 

Plasma appearance 

Starts from edge of 

exposed electrode 

and propagates along 

dielectric 

Starts from edge of 

exposed electrode 

and propagates 

along dielectric 

Excellent 

agreement 

Table 1. Results of comparison between DBD simulations and experiments. 

3.5 Additional Technical Activities 

3.5.1 Demonstration of speedup for parallel simulations 

One of the key elements for the successful development of the commercial parallel simulation 

codes is the demonstration of the speedup with number of processors. Ee have performed such 

study for 1, 2, 4, 8, 16, 32 and 64 processors. We ran same sample simulation and measured the 

time, required for execution. Based on the measured time, we have computed the speedup, 

which is the ratio of simulation times for 1 processor and N processors. The results are presented 

in Figure 26. We observe very good scaling of the speedup with the number of processors. 

Time,seconds 

Energy, 

J/m 
NASA/CR—2012-217260 23

Figure 26. Speedup of parallel simulations. 

3.5.2 Demonstration of hybrid capabilities for DBD simulations for single 

processor 

Besides demonstration of PIC and fluid approaches for DBD plasma simulations, projected in 

Phase I proposal, we have also set up a simulation to show hybrid capabilities of the DBD 

simulation tool. For the demonstration purposes, we considered DBD in nitrogen with ionization 

collisions only. User was allowed to choose the time frames for PIC simulations and fluid 

simulations. In the following example, initial stage of the breakdown was computed using PIC 

approach. In order to proceed with fluid approach, the DBD simulation tool converted data on 

particle distribution to the distributions of number densities. This concept was successfully 

implemented for the single processor in VORPAL. Figure 27 shows the conversion of the nitrogen 

ion distribution in PIC approach (a) to the number density of nitrogen ions (b). The same applies 

to the electrons. Once the number densities are converted, simulations can continue using fluid 

approach. 

(a) (b) 

Figure 27. 2D distribution of positive ions at the beginning of streamer formation, obtained 

using PIC code (a). 2D distribution of positive ion number density at the beginning of 

streamer formation, converted into fluid code (b). 

 

1

4

16

64

1 4 16 64

SpeedUp

Number of Processors

Np,1/m3

Y,m Y,m

X,m X,m
NASA/CR—2012-217260 24

4. Potential Applications

4.1 Potential NASA applications 

The primary NASA applications of the proposed DBD simulation tool are active flow control 

concepts for both subsonic and hypersonic flights. Predictable active flow separation control, 

achieved using the proposed tool, will benefit many NASA Projects, such as Subsonic Fixed Wing 

Project, Subsonic Rotary Wing Project and Hypersonic Project. In addition to the flow separation 

application, DBD simulation tool can be used for a number of NASA problems, associated with 

gas discharges at different pressures. For example, DBD simulation tool can be used for the 

description plasma-assisted combustion for the reduction of carbon emissions. 

4.2 Potential non-NASA applications 

Active flow control using DBD plasma actuators is of interest to a number of government 

agencies, private industry and universities. Proposed tool will be beneficial for 

subsonic/hypersonic programs which involve active flow separation control. These programs 

include, but are not limited to, flow separation control at commercial airplanes during take-off or 

landing, increase in lift for tiltrotor aircrafts, improvement of engine performance, active flow 

control at hypersonic vehicles. Besides the primary application for a description of DBD operation, 

DBD simulation tool can be used for a wide range of plasma aerodynamics applications, such as 

plasma-assisted combustion, flow control using different types of discharges, reduction of carbon 

emission, optimization of air vehicle operation, MHD and EHD application. 
REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188 

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the 

data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this 

burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB 

control number. 

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 

1. REPORT DATE (DD-MM-YYYY)

01-02-2012 

2. REPORT TYPE

Final Contractor Report 

3. DATES COVERED (From - To)

January 29, 2010-July 29, 2010 

4. TITLE AND SUBTITLE

Simulation Tool for Dielectric Barrier Discharge Plasma Actuators at Atmospheric and SubAtmospheric Pressures 

SBIR Phase I Final Report

5a. CONTRACT NUMBER

NNX10CE78P 

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Likhanskii, Alexandre 

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 561581.02.08.03.21.13.02 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

Tech-X Corporation 

5621 Arapahoe Avenue, Suite A 

Boulder, Colorado 80303 

8. PERFORMING ORGANIZATION

 REPORT NUMBER

E-18015 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

10. SPONSORING/MONITOR'S

 ACRONYM(S)

NASA 

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/CR-2012-217260 

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Category: 02, 05, 07, 13, and 75 

Available electronically at http://www.sti.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

Technical Officer (COTR): David E. Ashpis, NASA Glenn Research Center 

14. ABSTRACT

This report is the final report of a SBIR Phase I project. It is identical to the final report submitted, after some proprietary information of 

administrative nature has been removed. The development of a numerical simulation tool for dielectric barrier discharge (DBD) plasma 

actuator is reported. The objectives of the project were to analyze and predict DBD operation at wide range of ambient gas pressures. It 

overcomes the limitations of traditional DBD codes which are limited to low-speed applications and have weak prediction capabilities. The 

software tool allows DBD actuator analysis and prediction for subsonic to hypersonic flow regime. The simulation tool is based on the 

VORPAL code developed by Tech-X Corporation. VORPAL’s capability of modeling DBD plasma actuator at low pressures (0.1 to 10 

torr) using kinetic plasma modeling approach, and at moderate to atmospheric pressures (1 to 10 atm) using hydrodynamic plasma modeling 

approach, were demonstrated. In addition, results of experiments with pulsed+bias DBD configuration that were performed for validation 

purposes are reported. 

15. SUBJECT TERMS

Jet engines; Aeropropulsion; Turbomachinery; Plasma; Dielectric barrier discharge; Flow control 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU 

18. NUMBER

 OF 

 PAGES

32 

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email:help@sti.nasa.gov) 

a. REPORT

U 

b. ABSTRACT

U 

c. THIS 

PAGE

U 

19b. TELEPHONE NUMBER (include area code)

443-757-5802 

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18