1. Doug Breden
The University of Texas at Austin
Department of Aerospace Engineering and Engineering
Mechanics
Simulations of Atmospheric Pressure
Streamer Plasma Discharges
20 May 2013
1
Dissertation Defense:

2. Introduction
2

3. Introduction to Plasma Discharges
High Pressure (Atmospheric)
Constricted, thermal, highly transient
plasma (sparks)
science.howstuffworks.com
Low Pressure (mTorr – Torr)
Volumetric, non-thermal plasma in a
quasi-steady state (glow)
http://lrrpublic.cli.det.nsw.edu.au/lrrSecure/Sites/Web/physics_ex
plorer/physics/lo/cathode_08/cathode_08_01.htm
3
 Plasma is quasi neutral mixture of positive and negative charged particles
 Formed by applying electric field to gas in process called breakdown

4. Electron Avalanche
 Secondary processes provide
electron source (surface
emission and photoionization)
 Electron accelerated by
electric field
4
At low pressures/voltages plasma forms due to succession
of electron avalanches (glow discharge)
 Electron collide with
background particles
 Ionizes background particles
forming an avalanche (primary
process)

5. Electron Avalanche
Image from Raizer, Y., Gas Discharge Physics, 1987
Charge separation due
to slower moving ions
Avalanche produces
induced electric field
5
At high pressures/voltages plasma forms due to single
electron avalanche event
𝐄𝐢𝐧𝐝𝐮𝐜𝐞𝐝 = 𝐄 𝐚𝐩𝐩𝐥𝐢𝐞𝐝
“Enhanced”
High E-field
“Shielded”
Low E-field
Streamer Head
(~Debye length)
Avalanche transitions to thin filamentary plasma called a streamer

6.  plasma column and head with active zone
 produces multiple electron avalanches
 replace with single effective avalanche
Streamer Propagation Mechanism
 electrons from avalanche neutralize head
 avalanche becomes new streamer head
Propagation due to phenomena known as
Fast Ionization Wave
6

7. Advantages
• Preferentially heats electrons to high energies
• Prevents plasma from transitioning to spark
Nanosecond Pulsing
Technique to efficiently ionize atmospheric pressure air*
High voltages applied over very short (1-100 ns) duration
Pulse long enough to ionize plasma but shorter than
electron recombination time
7
* C Kruger, C Laux, D Packan, Pierrot, “Non-equilibrium discharges in air and nitrogen plasmas at atmospheric pressure”,
Pure and Applied Chemistry, Vol. 74, No. 3, pp 337-347, 2002

8. Numerical Models
8

9. Continuity
Plasma Governing Equations

kk
k
G
t
n



VnnDnun kkkkkkkk  

k
kk
r
nZ
e
0
2


Electron Energy
 S
t
ee



Electron
Joule Heating
Inelastic
collisions
Elastic
collisions
Drift-Diffusion (momentum)
eeeee Tkupe  )(
 
i
kege
k
e
ebi
e
ie b
b
vTT
m
m
nkrEeEeS ,
)(
2
2
3

coupled with Electrostatic Potential
9

10. 𝑆 𝑝ℎ 𝑟 = 𝑆 𝑝ℎ
1
+ 𝑆 𝑝ℎ
2
+ 𝑆 𝑝ℎ
3
𝑺 𝒑𝒉 𝒓 =
𝑰 𝒓′ 𝒈 𝑹
𝟒𝝅𝑹 𝟐 𝒅𝑽
𝜵 𝟐
𝑺 𝒑𝒉
𝒋
− 𝝀𝒋 𝑷 𝑶𝟐
𝟐
𝑺 𝒑𝒉
𝒋
= −𝑨𝒋 𝑷 𝑶𝟐
𝟐
𝑰 𝒓
Approximate the absorption function with several terms
j = 1,2,3
Integral Model :
𝐼 𝑟 =
𝑃𝑞
𝑃 + 𝑃𝑞
𝜉𝑆𝑖 𝑟
𝑔 𝑅
𝑃𝑂2
=
𝑒−𝜒 𝑚𝑖𝑛(𝑃 𝑂2 𝑅) − 𝑒−𝜒 𝑚𝑎𝑥(𝑃 𝑂2 𝑅)
(𝑃𝑂2 𝑅) 𝑙𝑛 𝜒 𝑚𝑎𝑥/𝜒 𝑚𝑖𝑛
+ Bourdon A, Pasko NP, Liu NY, Celestin S, Segue P and Maroude E 2007 Plasma Sources Sci. Technol. 16 656
* Luque A, Ebert U, Montijn C and Hundsdorfer W 2007 Appl. Phys. Lett. 90 081501
Emission Function Absorption Function f(PO2R)
Photoionization model
Plasma Governing Equations
10

11. Mobility, Diffusion and Thermal Conductivity
Transport Properties and Reaction Rates
Finite Rate Chemistry 𝐺 𝑘= 𝑖
𝐼 𝑟𝑥𝑛𝑠
𝑟𝑘,𝑖
𝑟𝑘,𝑖 = 𝑘𝑖 𝑛 𝑎
α
𝑛 𝑏
γ 𝑖 = (1,2, … . . 𝑛 𝑟𝑥𝑛𝑠)
α Xa + γXb → Products
Elementary Reaction i
ν 𝑒,𝑘𝑘 𝑏
= 𝑛 𝑏 𝑔σCollision Freq. :
μ 𝑘 =
𝑍 𝑘 𝑒
𝑚ν 𝑒,𝑘𝑘 𝑏
𝐷 𝑘 =
𝑘 𝑏 𝑇𝑘
𝑚ν 𝑒,𝑘𝑘 𝑏
Mobility : Diffusion : Thermal Conductivity :
𝐾𝑘 =
5
2
𝑘 𝑏 𝐷 𝑘
𝑛 𝑘
Reaction rate coefficients ki from experimental data or offline Boltzmann solver
11 𝑘𝑖 = 𝐴𝑇βexp
−ϵ
𝑘𝑇
𝑘𝑖 = 𝑓
𝐸
𝑁
𝑘𝑖 = 𝑓 𝑒𝑡

12. r
vY
vY
vPe
Pv
vu
v
x
uY
uY
uPe
uv
Pu
u
F
n
t
n
tinviscid ˆ
....
)(ˆ
....
)(
1
1
2
1
1
2


















































 











r
r
Y
D
r
Y
D
x
x
Y
D
x
Y
D
F
n
n
r
yy
yx
n
n
i
x
xy
xx
viscous ˆ
...
0
ˆ
...
0
1
1
1
1
1
1
1































































 









 





n
k i
k
kk
i
irxii
x
Y
Dh
x
T
kvu
1

V
x
x
x
x
ij
i
j
j
i
ij 













 
Inviscid Flux Viscous Flux
)( 22
2
1
)1( vue P
t  
i
x
x
T
kq i



Discretized with AUSM splitting Discretized with Hasselbacher
12




1
1
n
i
in YY 























1
1
...
n
t
Y
Y
e
v
u
U






Conserved Vars
dVSdVSdAnFdAnFU
t V
plasma
VA
viscous
A
inviscid
V
 


ˆˆ
Multi-Species Navier-Stokes Equations

13. Multi-Species Navier-Stokes Equations
b
b
g
kege
k
e
eB
i
i
g
i
Hk
kkT TT
m
m
nkrEeEfZeS ,)(
2
2
3






 
Ion Joule Heating Inelastic Elastic
Plasma Heating Source Term
EnZef
k
kkES 
Electrostatic Forcing Term























0
...
0
0
VfS
f
f
S EST
y
x
plasma g
Plasma affects gas via forcing and heating source terms
13

14. Overview of Numerical Solver
14
 Validation : 1 Torr, air chemistry
(Mahadevan S and Raja L L, “Simulations of direct-current air glow discharge at pressures 1 Torr: Discharge
model validation”, Journal of Applied Physics 107 2010)
 Decouple equations and solve separately
(separate time steps based on stability/accuracy criterion for each eqn)
 Large time scale disparity
Time : 10-13 – 10-12 seconds (dielectric relaxation)
Length : 10-6 – 10-5 meters (Debye length)
 Unstructured finite volume scheme

15. Plasma-Flow Coupling
Plasma Solver
(100- 1000 time steps)
Flow Solver
(1 large time step)
Background
Mass Fractions
Temperature
Velocity
Electrostatic Forcing
Gas Heating
Background
Mass Fractions
Plasma and Bulk Flow are weakly coupled
• Plasma/Navier-Stokes equations solved in segregated manner
• Coupled via source terms
• Limited by the electron time step
15

16. Spatial Flux Discretization (1st Order)
Plasma Numerical Method
All equations modeled as unsteady, convection, diffusion, source
𝛹t+1 = 𝛹t −
∆𝑡
∆𝑉 𝑓
𝐹𝑎𝑐𝑒𝑠
𝐶 𝑡 𝛹t+1
𝑓 − D𝛻𝛹t
𝑓 ∙ 𝐴 𝑓+ ∆𝑡 𝐺 𝑒𝑙𝑒𝑐
𝑡
+ ∆𝑡 𝐺 𝑒𝑙𝑒𝑐(𝛹) 𝑡+1
System of equations numerically stiff (electron-Φ coupling)
Can improve stiffness using a predictor step
𝐶𝑓 𝛹t+1
𝑓
− D 𝑓 𝛻𝛹t+1
𝑓 = 𝑛 ∙ 𝐶𝐿/𝑅
𝛹𝐿 − 𝛹 𝑅
𝑒 𝑃𝑒 − 1
𝐶𝑓 𝛹t+1
𝑓
− D 𝑓 𝛻𝛹t+1
𝑓 = 𝑛 ∙ 𝐶𝐿/𝑅 𝛹𝐿/𝑅
𝑃𝑒 =
|𝐶|Δ𝑥
𝐷
Scharfetter-Gummel:
(conv-diff soln)
Upwind:
16

17. Electron Predictor Step
Start with Poisson
−𝛻 ∙ εr 𝛻Φt+1
=
e
ε0
Znt
ion − nt+1
elec
nt+1
elec = nt
elec − ∆𝑡𝛻 ∙ − 𝜇 𝑒𝑙𝑒𝑐 𝑛 𝑒𝑙𝑒𝑐
𝑡
𝛻Φt+1
− 𝐷𝑒𝑙𝑒𝑐 𝛻𝑛 𝑒𝑙𝑒𝑐
𝑡
+ ∆𝑡 𝐺 𝑒𝑙𝑒𝑐
𝑡
Predict the electron density 𝐧𝐭+𝟏
𝐞𝐥𝐞𝐜 at the new time
−𝛻 ∙ 𝜀 𝑟 −
𝑒
𝜀0
𝜇 𝑒𝑙𝑒𝑐 𝑛 𝑒𝑙𝑒𝑐
𝑡
∆𝑡 𝛻Φt+1
=
e
ε0
Znt
ion − nt
elec -
𝑒
𝜀0
𝐷𝑒𝑙𝑒𝑐 𝛻𝑛 𝑒𝑙𝑒𝑐
𝑡
+ 𝐺 𝑒𝑙𝑒𝑐
𝑡
The mobility term is moved to LHS
𝑫 𝚽 = 𝛆 𝐫
𝑨𝒙 = 𝒃
𝑨𝒙 = 𝒃
𝑫 𝚽 = 𝜀 𝑟 −
𝑒
𝜀0
𝜇 𝑒𝑙𝑒𝑐 𝑛 𝑒𝑙𝑒𝑐
𝑡∆𝑡
Diffusion Coeff. Modified Diffusion Coeff.
Increase time step 1-2 orders of magnitude for some problems
17

18. Equations formulated as separate Ax=b linear systems
(A generally not symmetric)
Numerical Method
Linear system solved using GMRES w/ Block Jacobi
preconditioning from PETSc software library
18
|𝑎𝑖𝑖|
𝑖≠𝑗 |𝑎𝑖𝑗|
≈ 1
|𝑎𝑖𝑖|
𝑖≠𝑗 |𝑎𝑖𝑗|
≫ 1
Poisson A Mat
 Symmetric
 Weakly Diag. Dominant
Spec Den/Elec. Energy
 Not Symmetric
 Diag. Dominant

19. Supersonic Flow Ignition and
Actuation
19

20. Introduction
20
Lout etal, “Ignition of Premixed Hydrocarbon-Air Flows
by Repetitively Pulsed, Nanosecond Pulse Duration
Plasma”, Proceedings Combustion Institute 31, 2007, 3327-3334.
High Voltage Nanosecond Pulse Plasma applied to
supersonic fuel-air mixtures
Opaits etal, “Experimental Investigation of DBD Plasma Actuators
Driven by Repetitive High Voltage Nanosecond Pulses
with DC or Low-Frequency Sinusoidal Bias”, AIAA 2007-4532-152
SUPERSONIC COMBUSTION
FLOW ACTUATION
• High E/N efficiently ionizes and
dissociates gas
• Rapidly produces radicals which reduce
ignition delay
• Fast gas heating can actuate
the flow

21. Simulation Configuration
21
Gas Sub Domain Plasma Sub Domain
8000 cells
0.25 cm
Trapezoidal Pulse
• 10 ns pulse
• 2.5 ns rise/fall time

22. Steady State Flow (O2-H2)
22
Laminar Boundary layer with lower number density
Gas Sub Domain contains leading edge shock

23. H2-O2 Chemistry
23
16 Species
e, O+, O2
+, O4
+, O-, O2
- , H+,H2
+, O, H, OH, O2, H2, O(1D), O2(a1Δg), O2(b1Σg
+)
87 Reversible and Irreversible Reactions
Hagelaar, G. J. M. and Pitchford, L. C. 2005, Plasma Sources Sci. Technol. Vol. 14, pp. pp. 722-733.
Gudmundsson, J. T. 2004, J. Phys. D: Appl. Phys. 37, pp. 2073-2081.
Jeong, J. Y., et al., et al. 2000, J. Phys. Chem. A 104, pp. 8027-8032.
Starik, A. M. and Titova, N. S. 1, pp 28-39, s.l. : Kinetics and Catalysis, 2003, Kinetics and Catalysis Vol. 44, No. 1, Vol. 44, pp. pp. 28-39.
Gudmundsson, J. T. 2002, J. Phys. D: Appl. Phys. 35, pp. 328-341.
Smith, G. P., et al., et al. GRI 3.0 Mechanism. [Online] http://www.me.berkeley.edu/gri mech/.
Meeks, E., et al., et al. 1998, American Vacuum Society, pp. S0734-2101 01902-2J.
Kossyi, I. A., et al., et al. 1992, Plasma Sources Sci. Technol 1, pp. 207-220.
Deconinck, T. and Raja, L. L. 5, s.l. : Plasma Processes and Polymers, 2009, Vol. 6.

24. O2-H2 Anodic vs Cathodic (4 kv)
24
O2
+ ion density [# m-3]
O2
+ ion density [# m-3]
Plasma forms entirely within boundary layer
CATHODIC (-4000 V)
ANODIC (4000 V)

25. Species Concentrations
25
IONS
RADICALS
O2
+ and O2
- dominant positive and negative charge carriers
O dominant radical

26. Power Deposition
26
ANODIC (4000 V) CATHODIC (-4000 V)
More (conduction) power deposited into gas for cathodic pulse
Greater gas heating (ion Joule heating) for cathodic pulse

27. O2-H2 Gas Heating
27
temperature [K] temperature [K]
pressure [Pa] pressure [Pa]
27
ANODIC (4000 V) CATHODIC (-4000 V)

28. Effect of Flow Field on Plasma
28
Thermal boundary layer lowers gas density
Encourages breakdown of gas at lower applied voltage (E/N)
Flow carries radicals downstream
over micro/milli second timescales

29. High Pressure Lean Ignition
29

30. Introduction
30
Photo From : University of Southern California Pulsed Power Research Group
http://www.usc.edu/dept/ee/Gundersen/combustion.html
www.etatech.us/Technical-Papers/ECCOS-Advanced-
Ignition-System.ppt
Coaxial Geometry
(Small Inter-electrode Gap ~mm)
Corona Geometry
(Large Inter-electrode Gap ~cm)
Spark (thermal plasma) is traditional ignition system for IC engines
• Ignition kernel highly localized
• Ineffective at igniting lean fuel-air mixtures
Recent research has focused on utilizing non-equilibrium plasma

31. Methane – Air Chemistry
31 Species
E, O, N2, O2, H, N2
+, O2
+, N4
+, O4
+, O2+N2, O2
-, O-, O2(a1), O2(b1), O2*, N2(A), N2(B),
N2C, N2(a1), CH4, CH3, CH2, CH4
+, CH3
+, CH2
-, and H-
85 Reactions
31

32. Coaxial Electrode Geometry
32
• 20 degree slice
• ~60,000 cells
• 27 deg tip
• 40 kV pulse

33. Plasma Formation
33
Primary streamer followed by secondary streamer

34. Coaxial Electrode Species Yields
34
4 mm
0.2 mm
Physical Domain Canonical Streamer Domain
Positive Ions Negative Ions Radicals
Lean Stoich Lean Stoich Lean Stoich

35. Coaxial Electrode O Radicals
35
4 mm
0.2 mm
Lean
Canonical Streamer Domain
Stoich
Radical Density Transients (LEAN)
9.7 ns
8.8 ns

36. Corona Geometry
36
ECCOS (Electrically Controlled Combustion Optimization System)
• 45 degree slice
• Inset plasma domain
• ~75,000 cells
• 115 kV pulse

37. Corona Geometry
37
1 ns 5 ns 10 ns 15 ns 20 ns 25 ns 30 ns

38. Corona Geometry Species Yields
38
4 mm
0.2 mm
Physical Domain Canonical Streamer Domain
Positive Ions Negative Ions Radicals
Lean Stoich Lean Stoich Lean Stoich

39. Corona Geometry O Radicals
39
4 mm
0.2 mm
Lean
Canonical Streamer Domain
Stoich
30 nanoseconds
Radical Density Transients (LEAN)

40. Atmospheric Pressure Plasma
Jets
40

41. Introduction
Shashurin et al, “Temporal behavior of cold atmospheric plasma jet”, APL 94, 2009
Cold plasma jets are an effective means of producing non-
equilibrium plasma
Typical Arrangement
• Thin dielectric tube with high voltage electrode
• Plasma discharge forms in jet plume
• Noble gas jet diffuses into air
41

42. Applications
Lu et al, “ A single electrode room-temperature plasma jet device
for biomedical applications” APL 92, 2008.
Atmospheric plasma jets have several useful properties
 Plasma is non-equilibrium (room temperature)
The greatest current application of interest is biomedicine42
D. Graves, J. Phys. D: Appl. Phys. 45 (2012)D L Bayliss, J L Walsh, G Shama, F Iza and M G Kong,
New. J. Phys. 11 (2009)
 Plasma formed outside the device (easy to apply to surfaces)
 Produces reactive products (O radicals, ozone, ions, etc.)

43. Experimental Observations
 Speed of discharge suggests photoionization
plays a prominent role
Laroussi and Akan, “Arc-free atmospheric pressure cold plasma jets: A Review”, Plasma Processes and
Polymers,2007, 4, 777-78843
 Consists of discreet packets of ionization
 Propagate at high velocities (100 s of km/s)

44. Experimental Observations (2)
 Imaging experiments indicate plasma “bullets” have a donut shape
N Mericam-Bourdet, M Laroussi , A Begum and E Karakas, “Experimental Investigations of Plasma Bullets”, J. Phys. D: Appl.
Phys. 42, 2009, 055207 (7pp)44
 Bullet travels along interface and penning ionization might play a role

45. Mesh Configuration
• 80,000 axisymmetric unstructured quad/tri cell mesh
• Parallel MPI (distributed memory) with 8-32 procs.
• Target modeled as thin (1mm) dielectric plate (εr = 6)
• Single 150 ns 10,000 kV pulse
45

46. Helium – Air Chemistry
31 Species
E O N NO NO2 N2 O2 O2(a1) O2(b1) O2(h) N2(A) N2(a’) N2(B) N2(C) O(1D) N2
+
O2
+ N4
+ O4
+ O2+N2 O2
- O- O3 O3
- NO+ O+ HE HE+ HE2
+ HEm HE2
m
135 Reactions
Ionin etal, Jo, 2007, Journal of Physics D: Applied Physics, pp. V. 40, R25-61.
Pitchford, Phelps. 1985, Phys. Rev. A. 31, p. 2932.
Lopez et. 2003, Int. Journal Mass Spec., pp. 25-37.
Kim and Desclaux. 012078, s.l. : Phys. rev. A., 2002, Phys. Rev. A 66, Vol. 66, p. 012078.
Yuan X. and Raja. L.L. 2003, IEEE Trans. Plasma Sci., p. 495.
Stafford, D. and Kushner, M., Journal of Applied Physics, 2004, Vol. 96.
Pancheshnyi S., Nudnova M. and Starikovskii A. 2005, Physical Review E. Vol. 71, p. 016407.
Aleksandrov, et al. Plasma Physics Reports, 2009, Vol. 25. pp 867-882.
Kossyi, I. A., et al., Plasma Sources Sco. Technol., 1992, Vol. 1. pp. 207-220.
Arakoni, Babaeva and Kushner. 2007, Journal Physics D: Appl. Phys. 40.
References
46

47. Fast Ionization Wave
Confined Streamer propagates along diffusion layer
 Phase speed of ionization wave ~300 km/s
47
 Peak ionization along helium-air interface
 Ion and electron species mobilities are much slower (stationary)

48. Role of Helium-Air Jet/Diffusion Zone
Helium Ambient vs Air Ambient
Ambient air confines the streamer to the helium jet core
48 O2 and N2 harder to ionize than He

49. Role of Penning and (Air) Photoionization
Neither photo or Penning ionization necessary
No Photo
No Penning
No Photo
Penning
Photo
Penning
49

50. Role of Penning and (Air) Photoionization
Photoionization significantly impacts speed
Penning ionization results in small speed increase
50

51.  Slow convergence
Compressible Navier-Stokes equations stiff at low Mach #
Steady State Flow Field
2 cm gap 0.5 cm gap
 Solved to steady state using succession of meshes (coarse to fine)
 Laminar Helium Jet (Reynolds Number ~20)
51

52. Transition from guided streamer to surface driven discharge
Stages of Plasma Discharge
30 ns
50 ns
100 ns
Transition to constricted or guided streamer in gap
Plasma forms as surface discharge and streamer
Ceases to propagate when He:air ratio decreases (~0.67)52

53. Plume radicals (150 ns)
O (1022 m-3)
SDO (1021 m-3)
O3 (1020 m-3)
N (1020 m-3)
Most radicals produced in the helium plume “core” and in surface discharge
Short lived species (e.g. O, N) produced adjacent to surface
Long lived species (e.g. SDO, ozone) produced in jet and at surface
53
Lifetime
~1 hour

54. Surface Fluxes (100 ns)
Dominant positive charge is O4
+
(Peak wall impact energy ~1.3 eV)
Dominant radical is O (1022 m-3)
Dominant negative charge is e
(Peak wall impact energy ~0.4 eV)
Ions and radicals produced by surface discharge delivered to plate
54

55. Gas Heating Effect
Before Pulse – (0 ns)
steady state gas temperature ~ 299-300 K
After Pulse – (150 ns)
peak gas temperature increase ~10 K
temperature near plate ~302 K
1-2 degree temperature increase consistent with experiments55

56. Three Simulation Cases
1. Thin dielectric plate
2. Thick dielectric plate
3. Short gap
56

57. THIN PLATE
1 mm plate
2 cm gap
Electron (Plasma) Density
Thin Dielectric Plate (2 cm)
57

58. SHORT GAP
1 mm plate
0.5 cm gap
Electron (Plasma) Density
Gap Distance (0.5 cm)
58

59. THICK PLATE
1 cm plate
2 cm gap
Electron (Plasma) Density
Plate Thickness (1 cm)
59

60. Comparison of Simulations (log scale)
surface integrated ion flux surface integrated O radical flux
Long vs short gap
Discharge arrives at plate earlier, covers larger area
Thin vs thick plate
Discharge no longer propagates adjacent to plate
THIN PLATE
SHORT GAP
THICK PLATE
60

61. Grid Resolution
61

62. Grid Resolution : Streamers
25 k6250 100 k
62
 4 mm x 5 mm geometric domain
 1 atmosphere, 300 K air
 30 kV Voltage applied to pin (not shown)
40 micron cell length 20 micron cell length 10 micron cell length

63. Grid Resolution : Streamers
25 k
6250
100 k
1 ns 2 ns 3 ns 4 ns 5 ns
1 ns 2 ns 3 ns 4 ns
1 ns 2 ns 3 ns 3.5 ns
63

64. Grid Resolution : Plasma Jet
80k
25 ns
50 ns
75 ns
64
600k
10 microns~20-50 microns

65. Parallel Scaling
65

66. 80,000 APPJ mesh for 500 iterations on Lonestar
Strong Scaling
66

67. Potential Eqn
Electron
Density/Temperature Eqn
Gas Chemistry
Misc. Time
Numerical Solution Time
1 Processor 240 Processors
48 Processors 720 Processors
67

68.  The potential equation is computationally most expensive
MPI communication time in predictor step
Linear solver (PETSc)
Optimization of Poisson Solve
GMRES (Iterative)
 Can takes hundreds of iterations to converge (slow)
 Pre-conditioner (e.g. Block Jacobi/ASM/etc), restart number, etc.
impact solution convergence rate
Sparse Direct Solvers (Mumps or SuperLU dist)
 Possibly more efficient than iterative solver (especially if
convergence rate is slow)
Electron Predictor Step
 Multiple communications required
68

69. Linear Solver Runtime
69
GMRES iteration count order of 500

70. Total Speedup Comparison
 Can gain about two orders magnitude speedup
 (~1 day on Lonestar for plasma jet simulation)70

71. Conclusions
Supersonic Ignition Enhancement
 Plasma produces O radicals that decrease ignition delay
 Significant gas heating possible
71
Internal Combustion Engine Ignition
 Short gap plasma primary + secondary streamer (most
radicals in secondary)
 Long gap plasma produces radicals uniformly
 Peak radical production occurs near prong tips
Atmospheric Pressure Plasma Jets
 Plasma forms as constricted streamer
 Primarily O radicals produced in gap and at surface

72. Future Work
Ignition Enhancement
 Investigate multiple pulses
 Improve chemistry mechanism (e.g. O4
+ dissociation)
 Track the entire ignition event
72
Atmospheric Pressure Plasma Jets
 Model complex surface chemistry interaction
 Include helium photoionization
Numerical
 Short Term
 Reduce simulation time (investigate GPU/MICs)
 Optimize or rewrite Poisson equation (current bottleneck)
 Long Term
 Adaptive mesh refinement

73. Publications
73

74. END OF PRESENTATION
74

75. 75
Voltage: Streamer Propagation
Higher voltages result
in stronger Electric
Field
Streamers propagate
further as voltage
increases

76. Voltage : Thermal Effects
76
Stronger Electric fields result in greater ion Joule heating

77. Introduction
Shashurin et al, “Temporal behavior of cold atmospheric plasma jet”, APL 94, 2009
Cold plasma jets are an effective means of producing non-
equilibrium plasma
Typical Arrangement
• Thin dielectric tube with high voltage electrode
• Plasma discharge forms in jet plume
• Noble gas jet diffuses into air
• Non-thermal (safe to touch)
77

78. Applications
Lu et al, “ A single electrode room-temperature plasma jet device
for biomedical applications” APL 92, 2008.
Atmospheric plasma jets have several useful properties
Plasma is non-equilibrium (room temperature)
Plasma formed outside the device (easy to apply to surfaces)
Produces reactive products (O radicals)
The greatest current application of interest is biomedicine78
D. Graves, J. Phys. D: Appl. Phys. 45 (2012)D L Bayliss, J L Walsh, G Shama, F Iza and M G Kong,
New. J. Phys. 11 (2009)

79. Streamer Ionization Rates (75 ns)
Electron impact ionization drives streamer propagation
Photoionization produced seed charge
79

80. Effect of Tube Radius
As Tube radius decreases …
- Streamer speeds increase
- Plasma densities increase80

81. Effect of Trace Air Impurities
Tube
N2 or O2 : Very Slight decrease in propagation speed
Air : significant increase in propagation speed
Ambient
Air, N2 or O2 : slight speed increase
Default
1 % O2
1% N2
1% N2 + O2
81

82. Diffusion Zone Width
Increasing width increases plasma volume and the structure is more diffuse
Increase in speed most likely due to decreasing radius of 99% He-Air zone
Diffusion zone width not crucial to plasma bullet propagation
82

83. Thin Dielectric Plate (2cm gap)
Propagates directly over target plate
83

84. Gap Distance (0.5 cm)
Propagates further along plate due to profile of helium jet84

85. Plate Thickness (1 cm)
Placing ground further back changes the potential profile
Discharge propagate along He-Air mixture layer instead of surface85