47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition
5 - 8 January 2009, Orlando, Florida
AIAA 2009-1622
Plasma-induced force and self-induced drag in the dielectric
barrier discharge aerodynamic plasma actuator
C. L. Enloe,* M. G. McHarg,† G. I. Font‡
Department of Physics, United States Air Force Academy, CO 80840
and
T. E. McLaughlin§
Department of Aeronautics, United States Air Force Academy, CO 80840
Through high-time-resolution laser interferometry, we observe the motion of a test
article under the influence of a dielectric barrier discharge aerodynamic plasma actuator,
and from this motion we deduce the time history of the force produced by the actuator to a
resolution substantially smaller than the period of the actuator’s AC cycle. We find that the
negative- and positive-going half cycles of the plasma discharge produce a force on the
surrounding neutral air in the same direction, but that only the negative-going half cycle
produces a force sufficient to substantially overcome the drag induced by accelerating the
air in the immediate vicinity of the aerodynamic surface (within the boundary layer under
normal circumstances).
I. Introduction
The aerodynamic plasma actuator,1-9 an asymmetric, surface-discharge-mode dielectric barrier
discharge10-17 (DBD) operated at atmospheric pressure, is a promising application of plasma physics to aerodynamic
flow control18-26 due to its inherent high bandwidth and lack of moving parts. The physics of the device’s operation,
however, remain the subject of intense research (and in some cases, vigorous debate) within the community. 27-40 The
device operates by imparting momentum into the neutral air in which the discharge is embedded. The device is also
inherently an AC device, requiring several kilovolts of amplitude in an applied high-voltage waveform in order to
operate, and the discharge is known to progress in separate events during the positive- and negative-going half
cycles of the applied voltage waveform, with the plasma extinguished between these two discharge events (see
Fig. 1).2-9 The buildup of charge on the surface of the material that forms the dielectric barrier in the device makes
the device locally self-limiting and means that the overall envelope of the discharge spreads out over the dielectric
surface, allowing the device to interact with an extended volume of air.
Determining the time history of the momentum input to the neutral fluid (or equivalently, the body force)
by the DBD plasma actuator is key to understanding by mechanism by which it operates. In a previous paper, 6 we
were able to resolve the momentum coupling (force production) from the device into the neutral fluid in which it
operates down to the timescale of one-half cycle of its AC operation. In this work, we improve the time resolution of
these force measurements by approximately an order of magnitude to reveal a more detailed view of the actuator’s
behavior.
This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.
*
†
‡
Professor of Physics, HQ USAFA/DFP, USAF Academy, CO 80840, Senior Member, AIAA.
Director, Space Physics and Atmospheric Research Center, HQ USAFA/DFP, USAF Academy, CO 80840.
Professor of Physics, HQ USAFA/DFP, USAF Academy, CO 80840, Member, AIAA.
§
Director, Aeronautics Research Center, HQ USAFA/DFAN, USAF Academy, CO 80840, Associate Fellow,
AIAA.
This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.
Figure 1. The aerodynamic plasma actuator is a surface-discharge-mode dielectric barrier discharge with
asymmetrical electrodes, (from Enloe et. al.2).
II. Experimental Procedure
In our previous work,6 we drove the plasma actuator at a frequency equal to the natural frequency of the
structure that supported it, and by observing the resonant response of the system we were able to infer that it was the
negative-going half cycle that produced the largest net momentum input into the neutral air. This conclusion was
consistent with the results of others’ experiments that observed the motion of the surrounding air directly used
particle image velocimetery.41 In principle, we could have determined the temporal variation in the force produced
by the actuator from the motion of the structure by subtracting the restoring force due to the elasticity of the
structure, but in practice this turned out to be difficult, since we were subtracting numbers of approximately equal
magnitudes and looking for the answer in the remainder. In the most recent set of experiments described here, we
replaced the stiff mechanical structure with a much looser torsional pendulum, as shown in Fig. 2, so that the
restoring force is much less than the force produced by the actuator during the time we are observing the effect of
the actuator.
Figure 2. A torsional pendulum allows us to directly observe the effects of the force produced by the
aerodynamic plasma actuator with a laser interferometer.
The direction of the force produced by the actuator is determined by the asymmetry of its electrode
geometry.2, 4-7 In our experimental apparatus, the exposed (Fig. 2(a)) and encapsulated (Fig. 2(b)) electrodes are
arranged on the epoxy/fiberglass substrate (Fig. 2(c)) in an arrangement that produces a net torque on the torsional
pendulum. Electrical connection to each of the electrodes (Fig. 2(d)) is provided by a hanging lightweight metal
chain (available at hardware stores and usually used for pull-chains on lighting fixtures) so that the electrical
connection introduces no torque into the system. An insulating center rod (Fig. 2(e)) ensures that there is no
electrical breakdown between the exposed electrodes and the steel wire that suspends the pendulum (Fig. 2(f)). A
probe laser beam (Fig. 2(g)) reflects off of a small mirror (Fig. 2(h)) attached to one side of the substrate, so that the
angular motion of the pendulum can be measured using a Michaelson laser interferometer. The total length of
actuator on the pendulum is l = 12.0 ± 0.2 cm, with the average radius of the actuator being r = 3.8 ± 0.1 cm.
The laser used in the interferometer (Spectra Physics model 106-1) has a wavelength of λ = 612 nm. In the
final (recombined) leg of the interferometer, a concave lens is included so that the interference pattern can be
projected onto a flat white screen where it is photographed with a high-speed digital camera (Vision Research model
Phantom 7) at 50,000 frames/second. This removes any ambiguity in the sign of the phase shift of the interference
fringes, since the sequence of frames can be examined and any reversals of the phase can be accounted for in the
subsequent analysis, and eliminates the possibility of contamination of a photodetector signal by electrical noise.
The images of the interference pattern are numerically apertured and the resulting intensity signal is analyzed
assuming a sine-squared variation of intensity with phase; with this technique displacements of the mirror can easily
be resolved to < λ/30.
The displacement of the mirror surface at the radius of the laser spot is determined from the interference
pattern directly. The velocity of the mirror surface is calculated by taking the time derivative of the displacement. In
order that high-frequency noise does not dominate the derivatives, the input in each case is low-pass filtered
numerically using a moving window. This reduces the effective time resolution of the measurements from that
which the raw sampling rate of the camera would imply. Nonetheless, the effective time resolution is sufficient to
resolve motion faster than the repetition period of the plasma discharge; with the frequency of the applied highvoltage waveform f0 = 200 Hz, the moving window is the equivalent of applying a “soft” (low-filter-order) low-pass
filter with a cutoff frequency fc > 2f0. The moment of inertia, I, of the torsional pendulum is calculated to be
I = (4.3 ± 0.3) × 10−5 kg m2. From this, the force produced by the actuator can be readily calculated.
Figure 3. The angular displacement of the test article increases monotonically consistent with a constant
average force, but temporal periodicity in the displacement is evident in the data.
III. Experimental Results
The angular displacement of the torsional pendulum as a function of time is shown in Fig. 3, along with the
high voltage waveform applied to the actuator. The angular displacement is monotonically increasing as the square
of the time, t, indicating that the pendulum is under the influence of a constant average torque (one of the
figures of merit for the actuator commonly quoted in the literature 1-3,5), but oscillations are evident in the position
versus time plot, indicating that there is a periodic variation in the force produced by the actuator. When one plots
the angular velocity versus time along with the applied voltage waveform, as shown in Fig. 4, that periodicity is
clearly evident. The pendulum accelerates and decelerates twice during each AC cycle of the actuator’s operation,
once during the negative-going half cycle of the discharge, and once during the positive-going half cycle. Consistent
with our previous work, we designate the negative-going half cycle the “forward stroke” of the discharge, and the
positive-going half cycle the “backward stroke.”2,3
Figure 4. The angular velocity of the test article as a function of time shows that both positive and negative
acceleration occurs twice during each AC cycle of the discharge.
After each forward stroke, we find that the test article has acquired a net increase in angular velocity, which
we designate Δωf. Similarly, after the backward stroke another net change in velocity Δωb is evident, but we also see
that Δωb << Δωf. Taking multiple data sets with identical high-voltage applied waveforms, we find that for this
configuration, Δωf = 5.0 ± 0.2 mrad/s, and Δωb = 0.3 ± 0.2 mrad/s. From the moment of inertia of the test article and
the period of the applied waveform, we can readily determine that this is the equivalent of a net 4.5 mN force
produced by the actuator during the forward stroke, compared to a 0.3 mN force produced during the backward
stroke. In relative terms, then, 94% of the velocity increase experienced by the test article is a result of the forward
(negative-going) half-cycle of the DBD discharge. This is in agreement with our previous results, 6 in which time
resolution was limited to one-half AC period. Significantly, though, is the behavior that the higher time resolution of
this experiment reveals. Both Δωf and Δωb are smaller by a considerable factor than the maximum increase in
angular velocity we observe during each half-cycle. The plasma discharge seems equally effective, at least to lowest
order, in imparting momentum to the test object during both the negative-going and positive-going half cycles, but
in each case the majority of that momentum is lost by the time the plasma quenches at the maxima of the applied
voltage waveform.2-8 The difference appears to be that less of the imparted momentum is lost after the conclusion of
the forward (negative-going) stroke than on the backward (positive-going) stroke; in the latter case almost all the
momentum imparted by the plasma discharge disappears after the plasma quenches.
IV. Interpretation
That the test article experiences a force when the plasma is ignited is the expected result, and it is
uncontroversial to assert that the positive momentum coupling when the plasma is ignited arises from electric field
interactions with the charged particles in the plasma and subsequent collisions with the neutrals air molecules. That
both the positive- and negative going half-cycles of the discharge produce a force in the same direction and
approximately the same magnitude is a result with which numerical simulations16-24 need to contend. The most
important new information in this work, however, is the degree to which momentum coupled into the neutral fluid is
lost once the plasma is quenched. That effect should not come as a surprise. It is well established that the plasma
actuator can induce flows of several meters per second in the neutral air (3-4 m/s is the most commonly observed
range1,2 ,4,7,8). It is also well known that this velocity is induced within a few millimeters of the surface−within the
boundary layer, under normal circumstances.4, 5, 8 The moving air has inertia and will continue moving close to the
surface, even when, as in the case of this experiment, the motion of the pendulum’s structure relative to the bulk of
the surrounding air is vanishingly small. The negative force experienced by the pendulum in between plasma
discharges is nothing more than the drag due to the relatively high-velocity flow very near the surface. That the ratio
of the positive to negative force is such that there is a net force predominately on the negative-going half cycle is
also an important result from these new measurements. (We note in passing that the velocity-versus-time profile is
in general agreement with the behavior that one can infer from measurements of the acoustic output of the
actuator,42 a feature of the device with which any actuator experimentalist is acquainted.)
There is evidence that the reason for the difference between the two discharge events is tied up in the
details of how each polarity of the discharge progresses. As these discharge processes are the subject of extensive
numerical and theoretical investigations,16-24 we are loathe to offer much in the way of the ad-hoc explanations, as
these would be mostly speculative, but we present here the results of a companion series of tests in which the
exposed electrode is modified by the substitution of a conducting wire on the downstream edge that considerably
Figure 5. Gross (effect of plasma alone) and net (effect of plasma plus drag) angular velocity changes per
discharge half-cycle for two different exposed electrode configurations.
modifies the radius of curvature of this edge and therefore modifies the local electric field there. (All other
parameters of the system remain unchanged.) These results are summarized and compared with the results from the
nominal configuration in Fig. 5. In this figure, the “gross” angular velocity changes refer to the maximum change
observed after the plasma quenches during a given half-cycle, while the “net” angular velocity change includes the
effects of drag as shown in Fig. 4. We see that the actuator with the wire exposed electrode is at least as effective as
the conventional actuator in imparting momentum to the fluid (and hence to the substrate), but that the net
effectiveness of the new configuration is considerably less, to the point where the “backward stroke” is a net
negative momentum input into the system.
To investigate whether the wire is less effective simply because it presents more area exposed above the
aerodynamic surface, we affixed a non-conducting (nylon) line of the same diameter to the edge of the exposed,
conventional electrode, and we did not observe any variation in the device’s behavior. From this, we conclude that
the change in behavior is tied to the structure of the plasma. We note the evidence our previous electrical and optical
measurements provide showing that the positive- and negative-going discharges are structurally very different and
occupy different volumes above the dielectric surface. 9 It stands to reason that the nearer the surface the air is set to
motion by the plasma, the greater the drag that will be induced when the plasma extinguishes, since the shear stress
(surface drag) is proportional to du/dy, where u is the fluid velocity and y is the distance of a given location above
the aerodynamic surface.
At the very least, the results presented here indicate that a complete description of the aerodynamic plasma
actuator must include analysis not only of the plasma discharge and its interaction with the neutral fluid, but also of
the neutral fluid’s interaction with the actuator structure when the plasma has (temporarily) quenched, as the
magnitude of both interactions are of the same magnitude.
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