Transcript Electric Circuit Model for Aerodynamic Plasma Actuator

Order of Magnitude Improvement of
SDBD Actuator Effect
T. Corke, F. Thomas, D. Orlov,
M. Iqbal, A. Kozlov,
H. Othman, D. Shatzman
Center for Flow Physics and Control
Aerospace and Mechanical Engineering
University of Notre Dame
Nov. 8, 2006
AF Academy Workshop
on Plasma Actuators
Questions:

How do we improve the performance of
SDBD plasma actuators?

What are the governing properties?

What is the ultimate performance limit?
Nov. 8, 2006
AF Academy Workshop
on Plasma Actuators
Approach:

Develop space-time model for ionization in
SDBD operation.
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
Include amplitude and frequency effects.
Not including maximum limits.
Compare to experiments.
Perform experiments that investigate
limiting conditions on SDBD design and
operation parameters.
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Nov. 8, 2006
Develop a theory to be included in space-time
model.
AF Academy Workshop
on Plasma Actuators
SDBD Actuators: What we know

Three time scales:

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Micro discharges (nsec)
a.c. period (.1ms)
Fluid response (10ms)
Ionization space-time dependent.
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Nov. 8, 2006
Static models give wrong results (e.g. fb~V2).
Temporal/space-uniform models give correct
V-dependence (fb~V7/2), need spatial weighting
Space-time models give correct V, frequency
and space dependence (Orlov, 2006).
AF Academy Workshop
on Plasma Actuators
Steps to model actuator in flow

Space-time electric potential, 

Space-time body force

Flow solver with body force added
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AF Academy Workshop
on Plasma Actuators
Space-time model
Physical space over the
encapsulated electrode is
divided into N parallel
networks.
Each parallel network
consists of air capacitor,
dielectric capacitor,
plasma resistive elements
and zenor diodes.
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AF Academy Workshop
on Plasma Actuators
Model circuit elements
air capacitor
dielectric capacitor
Voltage on the dielectric
surface in the n-th sub-circuit
Plasma current
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AF Academy Workshop
on Plasma Actuators
Model Time Series
Vn (t)
5
Vapp
n=1
n=2
n=3
n=4
n=5
2.0
5
4
n=1
n=2
n=3
n=4
n=5
3
Current, A
Voltage, kV
1.0
0.0
5
-1.0
Ipn (t)
-5
x 10
1
2
1
1
0
-2.0
0.0
Nov. 8, 2006
0.5
t / Ta.c.
t/T
a.c.
1.0
1.5
-1
0.0
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on Plasma Actuators
0.5
a.c.
t/Ta.c.
t/T
1.0
1.5
Model Space-time Characteristics
Experiment
Illumination
Model Ip(t)
(xp)max
dxp/dt
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AF Academy Workshop
on Plasma Actuators
Plasma Propagation Characteristics
Effect of Vapp
dxp/dt vs Vapp
Nov. 8, 2006
(xp)max vs Vapp
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on Plasma Actuators
Plasma Propagation Characteristics
Effect of fa.c.
dxp/dt vs fa.c.
Nov. 8, 2006
(xp)max vs fa.c.
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on Plasma Actuators
Numerical solution for (x,y,t)
Model provides time-dependent B.C. for
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on Plasma Actuators

y, mm
Y
Body Force, fb(x,t)
1.14
Normalized fb(x,t)
0.0
-5.08
0.0
x, mm
5.08
1.0
| fb |
0.5
0.0
y, mm
t/Ta.c.=0.2
-5.08
0.0
x, mm
5.08
-5.08
0.0
x, mm
5.08
1.14
0.0
1.0
| fb |
0.5
0.0
t/Ta.c.=0.7
-5.08
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AF Academy Workshop
on Plasma Actuators
0.0
x, mm
5.08
Frequency Dependence of fb & Wp
Impact: Optimum frequency for body force.
Depends on actuator capacitance.
Nov. 8, 2006
AF Academy Workshop
on Plasma Actuators
What limits maximum body force?

SDBD Plasma actuator is voltage driven,
fb~V7/2.

Not current driven like voice-coil type
actuators.

For fixed power (I·V), one needs to limit
current to maximize voltage.

What governs maximum achievable
voltage for fixed power?
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AF Academy Workshop
on Plasma Actuators
Maximum Voltage Optimization
Investigated different
parameters on thrust
produced by actuator
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AF Academy Workshop
on Plasma Actuators
Order of Magnitude Improvement
Imax
Material 
Quartz 3.8
Kapton 3.4
Teflon
2.0
Imax
Imax
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AF Academy Workshop
on Plasma Actuators
Imax
Premise

The maximum voltage at fixed power is
limited by local electric field exceeding
breakdown of air.
Thicker dielectrics and/or lower dielectric
constants reduce capacitance of actuator
and reduce concentration of electric field
lines.
 Other parameters?

Nov. 8, 2006
AF Academy Workshop
on Plasma Actuators
Effect of frequency on Vmax
1kHz
2kHz
0.25in. quartz glass
Vmax(f)
4kHz
8kHz
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on Plasma Actuators
Effect of dielectric thickness on
Vmax
quartz glass; 1,2,4,8kHz
fa.c. ~ (t/)d
Tmax ~ Vmax
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AF Academy Workshop
on Plasma Actuators
Tmax Efficiency
0.25in. quartz glass
Nov. 8, 2006
AF Academy Workshop
on Plasma Actuators
Answers to Questions:


To improve the performance of SDBD plasma actuators?

Maximize V for fixed power.

Minimize I by preventing formation of strong plasma filaments.
Governing properties?


Dielectric design (t & ) and a.c. frequency.
Ultimate performance limit?

Nov. 8, 2006
Maximum local E-field for air breakdown?
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Further Improvements: Additive Effect
Nov. 8, 2006
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on Plasma Actuators