A Parametric Investigation of Plasma Streamwise
Vortex Generator Performance
Michael Wicks, Flint O. Thomas, David Schatzman, Partick Bowles, and Thomas C. Corke
University of Notre Dame, Notre Dame, IN, 46556
Mehul Patel and Alan B. Cain
Innovative Technology Applications Company, LLC, Chesterfield, MO, 63017
In this paper a parametric investigation of arrays of plasma streamwise vortex
generators (PSVG) is presented. The arrays are flush mounted to a flat plate on
which a nominally zero pressure gradient turbulent boundary layer develops
upstream of the array. The investigation is focused on characterization of the
influence of freestream velocity, applied voltage, length of the covered electrode and
spanwise inter-electrode spacing on actuator performance. The metrics used to
assess performance are measured spanwise wall normal component mean velocity
gradient, ¶V / ¶z , and spanwise longitudinal mean velocity gradient, ¶U / ¶z ,
downstream of the array. The former quantity is related to direct streamwise
vorticity production and the latter is related to spanwise vorticity redistribution to
the streamwise component through the term w z ¶U / ¶z . In addition, a direct
comparison is made between the PSVG and passive vortex generators under
identical flow conditions. Results demonstrate the ability of the PSVG to harvest
energy from the external flow in a manner very similar to the passive VG. This
unique feature of PSVG may be exploited for flow control applications.
Nomenclature
Up
U¥
U
= plasma induced jet velocity
L
= covered electrode length
Epp
= spanwise inter-electrode spacing
= peak-to-peak excitation voltage

U
V
x, y, z
¶U / ¶z
¶V / ¶z
wx

d*
G ( x)
Re x
= freestream velocity
= Spanwise cycle-average mean velocity
= streamwise mean velocity component
= wall normal mean velocity component
= streamwise, wall-normal and spanwise spatial coordinates, respectively.
= spanwise spatial derivative of streamwise mean velocity
= spanwise spatial derivative of wall-normal mean velocity
= streamwise component mean vorticity
= 99% boundary layer thickness
= boundary layer displacement thickness
= circulation
= Reynolds number
1
I. Motivation and Objectives
P
P
ASSIVE vortex generators (VGs) are widely used for separation control on both commercial and
military aircraft. There are a wide variety of passive vane type surface-mounted vortex generators as
reviewed by Lin [1] and Bushnell [2]. These often have vane heights on the order of the local boundary
layer thickness  or smaller. Some designs create pairs of counter-rotating streamwise vortices while
others produce co-rotating vortices. Regardless of the details of their design, the production of near-wall
streamwise vortices that persist over a significant downstream distance function to promote cross-stream
mixing of momentum across the boundary layer. This serves to transport relatively high momentum fluid
from the outer region toward the wall and the boundary layer is therefore much better able to withstand an
imposed adverse pressure gradient without undergoing separation. Passive VGs have several advantages.
They are simple, robust, proven devices that are easily retrofitted to the airframe. However, their major
detractor is a significant drag penalty incurred in portions of the flight envelope where they are not needed.
It is desirable to have the ability to generate streamwise voriticity when boundary layer separation is a
possibility and have the VG effectively disappear when not needed. This is the basis of plasma streamwise
vortex generators (PSVG) which are the focus of this paper.
Psvgs are flush mounted devices designed to utilize the body force associated with dielectric barrier
discharge (DBD) plasma actuation to create streamwise vortices. Readers unfamiliar with application of
DBD plasma actuators for aerodynamic flow control are referred to the recent comprehensive reviews on
the subject by Corke et al. [3] and Moreau [4]. One of the first applications of PSVGs for aerodynamic
flow control was reported by Huang et al. [5] where plasma-induced streamwise vorticity was used for
aeroacoustic control of a low-speed cavity resonance. More recently, Schatzman and Thomas [6] utilized
PSVGs to eliminate separation of an adverse pressure gradient turbulent boundary developing on a convex
ramp. PSVGs were also found to be quite effective in eliminating unsteady vortex shedding from a circular
cylinder in cross flow at high subcritical Reynolds number by Kozlov and Thomas [7] and in a tandem
cylinder flow configuration Kozlov and Thomas [8]. Okita et al. [9] reported delayed separation on a
NACA 0024 airfoil due to the streamwise vortex produced by a single, yawed DBD actuator that
essentially functioned as a PSVG. A detailed parametric investigation into DBD vortex generators was
recently reported by Jukes and Choi [10]. The plasma vortex generator used in that study consisted of a
DBD plasma actuator placed at a yawed angle with respect to the oncoming flow. The plasma-induced
spanwise wall jet interacted with the primary boundary layer flow to produce a streamwise vortex whose
streamwise evolution was examined via particle image velocimetry in local cross-flow planes. DBD
actuators producing both co-rotating and counter rotating vortices were demonstrated. The effect of
plasma-induced velocity, freestream velocity, surface electrode yaw angle and length were systematically
investigated. The benefits of electode length and yaw angles orthogonal to the oncoming flow were
documented.
In this paper a parametric investigation of the performance of PSVG arrays is presented. The PSVG
arrays are flush mounted to a flat plate on which a nominally zero pressure gradient turbulent boundary
layer develops. The understanding gleaned from this parametric investigation is considered prerequisite to
optimizing PSVG arrays for specific flow control applications. Unlike the study by Jukes and Choi [10],
which utilized a thin, 250 m mylar dielectric barrier, this study exploits the work of Thomas et al. [11]
which demonstrated order-of-magnitude increases in the plasma-induced body force produced by plasma
actuators with comparatively thick dielectric barriers. Consequently, the PSVGs used in this study utilize
both Delrin and quartz dielectrics of 3.18 mm (1/8 in) thickness. Furthermore the PSVG array design
utilized in this study is different than the yawed DBD actuators used in [10] as detailed in the following
section. The freestream flow velocity used in the present study extends in excess of 40 m/s whereas most of
the experiments results presented in [10] are for freestream velocities less than 2 m/s. Perhaps more
significantly, the ratio of plasma-induced jet velocity, U p , to freestream velocity, U¥ , was as high as 0.85
in [10]. In the current study the values are more than an order of magnitude smaller.
II. Experimental Apparatus and Procedures
a. Wind Tunnel Facility
The PSVG parametric investigation was performed in one of the low-turbulence, subsonic, in-draft
wind tunnels located at the Hessert Laboratory for Aerospace Research at the University of Notre Dame.
The wind tunnel has an inlet contraction ratio of 20:1. A series of 12 turbulence management screens at the
2
front of the inlet give rise to tunnel freestream turbulence levels less than 0.1% (0.06% for frequencies
above 10 Hz). The maximum tunnel speed is approximately U¥ = 40 m/s. Experiments are performed in a
test section of 0.610 m square cross-section and 1.82 m in length. One sidewall and the test section ceiling
have optical access for non-intrusive laser flow field diagnostics; in this case, particle image velocimetry
(PIV), and laser Doppler velocimetry (LDV).
b. PSVG Test Fixture
a)
A rendered CAD model of the plate is shown in Fig. 1a.
3
The PSVG test fixture consists of a flat Plexiglas boundary
layer development plate of 1.2 m (48 in) length and 1 cm
thickness with a rounded leading-edge containing (1),
distributed sand grain roughness in order to promote rapid
boundary layer transition. The last 0.2 m of the plate consists of
1
(2), a 2.2o linear, symmetric taper down to a trailing-edge
2
thickness of 1.6 mm. The plate is sidewall mounted and spans
the wind tunnel test section. Endplates minimize the influence
b)
of the tunnel sidewall boundary layers.
As shown in (3) of Fig. 1a, PSVG actuator test fixtures are
flush mounted into a cavity machined into the plate surface at a
location 0.79 m (31 in) downstream of the leading-edge. This
streamwise distance from the leading-edge allows for turbulent Figure 1. a) Rendered CAD model of
boundary layer growth prior to application of PSVG flow boundary layer development plate, and b)
control. The cavity provides ample room for accommodating
close-up of PSVG array.
both the required high-voltage leads and the dielectric material
that forms the PSVG. Figure 1b shows a close up of one of the PSVG arrays ready for installation into the
plate cavity. A description of the PSVG geometry and details regarding construction are presented in the
following section.
c. PSVG Array
The basic geometry of the PSVG arrays examined in this study is shown schematically in Figure 2. As
indicated in the figure, this configuration uses a common covered electrode with streamwise length, L, and
is separated from the exposed electrodes by a sheet of dielectric barrier material. The multiple exposed
electrodes with spanwise inter-electrode spacing are aligned parallel to the oncoming flow. Due to the use
of a common covered electrode, plasma forms on both sides of each surface electrode and this gives rise to
a series of opposing wall jets in the spanwise direction that collide, thereby generating pairs of counterrotating vortices with size O(/2). These become the basis for enhanced cross-stream mixing of momentum
within the boundary layer for separation control.
Figure 2. Schematic of the geometry of the PSVG array, front view (left) and orthographic view
As noted earlier, the dielectric material used (right).
in this study was either Delrin or quartz of 3.2 mm
thickness (1/8 in). In both cases, the dielectric material extends 0.57 m (22.5 in) in the spanwise direction
and 20.3 cm (8 in) in the streamwise direction. The PSVG actuator arrays were constructed with
interchangeable Delrin or quartz plates. Each side of the Delrin plates is protected by a layer of 2 mil
3
Kapton tape and an outer layer of 2 mil Teflon tape. These additional layers of thin tape have proven to
extend the lifetime of the actuator, while preserving the advantage associated with use of the thick
dielectric. Each plasma actuator electrode consisted of copper foil tape of 0.05 mm thickness. The
streamwise length of the covered electrode was varied in this investigation. Streamwise lengths of 2.54 cm,
5.08 cm, 10.2 cm and 15.24 cm (1, 2, 4, and 6 in) were examined. In each case the span was fixed at 46.4
cm (18.25 in). The exposed electrodes extend from a common electrode over the dielectric above the
covered electrode. These straight exposed electrodes are 3.2 mm (1/8 in) in width and have a length of
15.24 cm (6 in). Both the covered electrode and exposed electrode are connected to high voltage wires that
lead out of the test fixture and connect to the transformers of the plasma generation circuit. The circuit used
to operate the PSVG array is identical to that presented in Figure 6 of Kozlov and Thomas [7]. Unless
otherwise noted, the actuators were operated with an ac carrier consisting of a positive sawtooth waveform
of 2 kHz frequency and a peak-to-peak voltage that was varied from 15 to 50 kV.
d. Parameters and Actuator Performance Metrics
The experimental study involved varying the following parameters: actuator peak-to-peak voltage, Epp,
freestream velocity, U¥ , covered electrode length, L, and spanwise inter-electrode spacing, while noting
the effect on actuator performance. The range of values tested for each parameter is listed in Table 1.
Since the parameter space was large, it was desirable to define a performance metric that was indicative of
the actuator performance but relatively rapid to measure. To characterize the array performance, LDV
measurements were made in a cross flow plane at a fixed location 76.2 mm (3 in) downstream of the PSVG
array. Two-component LDV measurements were conducted using a Dantec Dynamics Fiber Flow LDV
system with a Spectra Physics Stabilite 2017 Argon Ion Laser. The Fiber optic LDV system was operated
in 180o backscatter mode. The Doppler bursts were measured using a BSA F60 Flow processor and BSA
Flow Software Version 4.10. The LDV probe volume was traversed in the spanwise direction, z, and the x
(streamwise) U , and y (wall-normal) V , mean velocity components were measured. The wall-normal
location of the traverse was set to the local oncoming boundary layer displacement thickness, d * , which
for a zero pressure gradient turbulent boundary layer, is the centroid of mean spanwise vorticity. This was
deemed the most appropriate wall-normal location to measure both ¶V / ¶z and ¶U / ¶z . Spanwise
traverses were also performed at wall normal locations 2 d * and 0.5 d * and showed results consistent
with those obtained at d * and will not be presented here. The quantity ¶V / ¶z is one component of the
mean streamwise vorticity, w x , and represents a metric related to the efficacy of the PSVG to produce
w x . The second quantity ¶U / ¶z is an important component of a source term in the transport equation
for streamwise vorticity, w z ¶U / ¶z . This term serves to take initially spanwise mean vorticity and turn it
into the streamwise direction. In this manner both were deemed relevant quantities in characterizing the
PSVG array performance.
Table 1. Parameter space for PSVG parametric study
Parameter
Epp (kV)
U∞ (m/s)
L (in)
λ (in)
Dielectric
Range
20 – 50
5 – 40
1–6
0.5 – 1.25
Delrin/Quartz
e. PIV Data Acquisition
A LaVision time-resolved PIV system was also used to non-intrusively acquire two-component velocity
data in selected cross-stream planes. The system consisted of a Litron LDY300 series Nd:YLF pulse laser,
a Photron SA 1.1 high-speed camera, and dedicated computer running DaVis 8.0 vector processing
software. The laser light sheet was directed through the side window of the wind tunnel. Sheet optics
consisting of a combination of a spherical and a cylindrical lens were used to create a 1 mm thick light
4
sheet at the measurement plane. The
high speed camera, equipped with a
Nikon 105-mm lens and 2x teleconverter
operating at f/2.8, was positioned on top
of the test section, upstream of the
measurement
region,
angled
approximately 30° to the flow direction.
This angular distortion was corrected
with an appropriately aligned calibration
plate, and calibrations were performed at Figure 3. PIV experimental setup in the cross-stream plane.
each discrete streamwise position. At
each streamwise location 1200 image pairs were captured in double-frame mode at a sample rate of 1 kHz
with t = 200 s. The interrogation region was approximately 640 x 640 pixels before image correction
and varied from (601 to 649) x (685 to 788) pixels afterward, corresponding to physical domains of
approximately 48.10 to 56.97 mm x 59.01 to 64.97 mm (depending on the calibration used). A TSI
atomizer produced nominally one-micron diameter DEHS seed particles injected upstream of the wind
tunnel inlet via a mixing box allowing for uniform particle dispersion in the measurement plane. The data
were preprocessed by subtracting the sliding minimum over the first 200 image pairs, thereby removing a
majority of image background noise. The vector processing software was operated in multipass mode in
which two passes were made with 64 x 64 window size with 50% overlap, and three passes with 32 x 32
window size with 50% overlap resulting in a 76 to 81 x 86 to 96 vector map for the given interrogation
region. A Peak ratio of 1.2, universal outlier detection, and interpolation were used in post-processing to
remove spurious vectors.
III. Experimental Results
In this section, key results of the parametric investigation into the performance of several PSVG arrays
are presented. In the first portion a comparison is made between passive trapezoidal VGs and PSVG under
identical flow conditions. Consideration is also given to the appropriate scaling of ¶U / ¶z and
¶V / ¶z produced by both devices.
a. Comparison of Passive VGs and PSVGs: Scaling Issues
In order to provide a baseline data set for comparison, the test fixture containing the PSVG was
temporarily replaced with one containing a spanwise array of five passive trapezoidal vortex generators. A
series of experiments was performed to provide a comparison between ¶U / ¶z and ¶V / ¶z downstream
of both the passive VGs and the PSVG. The passive vortex generators were of trapezoidal shape and about
6.35 mm (0.25 in) in height; smaller than the nominal local turbulent boundary thickness of 2.54 cm (1 in).
Their width was 12.7 mm (0.5 in) at the front and 25.4 mm (1 in) at the back with a length of 25.4 mm (1
in). The VG angle was 25o. The center-to-center spacing was  = 50.8 mm (2 in).
In order to characterize ¶U / ¶z , the LDV probe volume was traversed in the spanwise z-direction at a
fixed distance of 76.2 mm (3 in) downstream of the VGs and with the wall normal height fixed at d * , the
boundary layer displacement thickness. For the nominally zero pressure gradient boundary layer d *
represents the wall-normal location of the centroid of mean spanwise vorticity. Figure 4 presents the
spanwise variation of mean velocity U(z) downstream of the passive vortex generator for external
velocities ranging from 12.5 m/s
million £ Re x
£ U¥ £ to 20 m/s (corresponding to the Reynolds number range of 0.672
£ to 1.08 million). In order to account for the varying external velocity, the measurements
are presented by subtracting the spanwise cycle average mean velocity, U , and normalizing by the
external velocity, U¥ . The location z = 0 is centered on a vortex generator. Figure 4 shows that this
normalization provides a reasonable collapse for all the cases.
5
Due to the scaling demonstrated in Fig. 4, the ordinate may be denoted as F(z), and it follows that
That is, the spanwise velocity gradient ¶U / ¶z is directly proportional to U¥ .
¶U / ¶z =U¥ dF / dz .
Figure 5 presents peak values of ¶U / ¶z measured downstream of the passive VGs as a function of
freestream speed. The proportionality to U¥ suggested by Figure 4 is fully confirmed.
Figure 5. Maximum amplitude of ¶U / ¶z for
passive VGs as a function of external velocity.
Figure 4. Scaled spanwise variation of mean
velocity downstream of the passive VGs.
The initial PSVG experiments were performed with an array that consisted of 17 surface electrodes,
each of which were 7 cm (2.75 in) in length and 3.2 mm (1/8 in) in width with a covered electrode of length
2.54 cm (1 in). The spanwise inter-electrode electrode spacing was 2.54 cm (1in) for the array (the same as
for the passive VG). For the PSVG experiment, the origin of the spanwise coordinate z = 0 was centered
on one of the surface electrodes. The PSVG array was operated in a quasi-steady manner with an ac
frequency of 2kHz. The peak-to-peak ac voltage amplitude was varied from 20 kV to 40 kV. Experiments
were performed for a similar external velocity range as for the passive VGs. The experiment was focused
on characterizing the spanwise variation in mean velocity U
( z) and V ( z) induced by the PSVG array. As
with the passive VG, the LDV probe volume was traversed in the spanwsie direction at a streamwise
location 76.2 mm (3 in) downstream of the PSVG array with the height of the probe volume above the wall
again fixed at the oncoming boundary layer displacement thickness, d * . As a representative example of
the results obtained, Fig. 6 presents the variation of scaled mean velocity U(z) downstream of the PSVG
operated at 40kV and for external velocities ranging from 10 m/s to 30 m/s (corresponding to the Reynolds
number range of 0.54 million to 1.61 million). The ordinate scaling is the same as that applied to the
passive VG data in Fig. 4; the spanwise cycle average mean velocity,
normalized by the external velocity,
U¥ .
U
, is subtracted and the result is
As was the case for the passive VGs, Figure 6 shows that this
scaling also does an excellent job of collapsing the spanwise variation of
U ( z ) downstream of the PSVG.
Comparison of Figures 4 and 6 reveals that the functional form of F(z) =
(U ( z) - U ) /U is different
¥
for the passive VGs and the PSVG. Unlike the passive VGs where positive and negative excursions from
the cycle mean are comparable, Fig. 6 shows larger negative deviations than positive for the PSVG. These
negative peaks are centered between the surface electrodes and are associated with local upwelling of low
velocity fluid from the near wall region associated with the colliding plasma induced spanwise
6
Figure 6. Spanwise variation of scaled streamwise component mean velocity downstream of the
PSVG array (40kV Case)
wall jets. Positive excursions are centered over the surface electrodes and are associated with transport of
comparatively high velocity fluid toward the electrodes by the plasma induced body force. However, the
collapse shown in Figure 6 for the PSVG results indicates that ¶U / ¶z is proportional to the external flow
speed, U ¥ , as was the case for the passive VGs.
Figure 7 presents an example of measured ¶U / ¶z for the PSVG operated at 40 kV and an external
flow speed of 15 m/s corresponding to the Rex = 810,000 case. This figure shows the large spanwise
periodic mean velocity gradient set up by the PSVG due to the generation of spanwise counter-rotating
streamwise vortices.
Figure 8 compares peak values of ¶U / ¶z as a function of external velocity for the passive VGs and
the PSVG. The similarity is quite remarkable with the PSVG producing somewhat larger values over most
of the range of external velocities tested. Note, however, the reduction in peak ¶U / ¶z for the PSVG
measurement at U ¥ = 25 m/s (Rex = 1.34 X 106). This saturation effect is unique to the PSVG and will be
described in detail in the following section. It is conjectured that this reduction is associated with the
reduced residence time L/ U ¥ of the flow over the PSVG electrodes (where L denotes the electrode length)
at higher external velocities.
Figure 7. Spanwise variation of ¶U / ¶z downstream of
the PSVG array ( U¥ =15m / s , 40kV )
Figure 8. Comparison of peak-to-peak ¶U / ¶z versus
U¥ for the passive VG and PSVG.
7
z
Figure 9. Spanwise variation of scaled
wall-normal component mean velocity
(mm)
downstream of the PSVG array (40kV Case). Spanwise coordinate z in mm.
Figure 9 presents corresponding LDV measurements of the wall-normal mean velocity V (z) scaled in
the same manner as the streamwise component shown previously in Figure 6. These results are for a 2.54
cm (1 in) covered electrode, a 2.54 cm (1 in) inter-electrode spacing and an applied voltage of 40kV. With
the exception of peak positive V which shows some reduction at the higher freestream speeds, there is
again a reasonable collapse of the profiles suggesting that ¶V / ¶z is also proportional to external flow
speed, U¥ . This plot shows that locations over the surface electrodes (e.g. z = -25.4 mm, 0, +25.4 mm) are
V . This is associated with the plasma body force drawing fluid toward the wall.
In contrast, locations midway between adjacent electrodes are characterized by positive V peaks that arise
associated with negative
from the upwelling associated with colliding wall jets from adjacent electrodes.
Figure 10 presents the peak-to-peak value of
¶V / ¶z measured downstream of the PSVG as a
function of external velocity. As was suggested by
the scaling shown in Fig. 9, this figure shows that
¶V / ¶z is initially proportional to U¥ . A
saturation effect comes into play for the highest U¥
tested. This is to be expected from Fig. 9 where it
may be noted that the positive V peaks located
between the electrodes are reduced in amplitude at
the highest flow speeds giving a deviation from the
similarity scaling that occurs at the lower speeds.
Figure 11a presents an example of the spanwise
variation of ¶V / ¶z for the case of U¥ = 20 m/s
and Epp = 40 kV. The associated schematic shown
Figure 10. Peak-to-peak ¶V / ¶z versus U ¥ for
Figure 11b shows that the measured ¶V / ¶z
pattern is fully consistent with the existence of pairs the PSVG (40 kV case).
of counter-rotating streamwise vortices downstream
of the PSVG. In the figure negative ¶V / ¶z corresponds to clockwise streamwise vortices while positive
¶V / ¶z corresponds to counter clockwise vortices. Consistent with figure 11a the locations of zero
vorticity are centered over the electrodes and midway between adjacent electrodes.
8
a)
b)
Figure 11. a) Spanwise variation in ¶V / ¶z for U¥ = 20 m/s and Epp = 40 kV.
(Electrodes are located at z = -50.8 mm, -25.4 mm, 0, +25.4 mm, 50.8 mm) and b)
Schematic of the counter –rotating srtreamwise vortices produced by the PSVG array.
It is apparent from the results presented in this section that the PSVG’s extract energy from the
primary flow as is the case for passive vortex generators. In previously published applications of DBD
plasma actuators for separation control, authority at fixed applied voltage gradually degrades with
increased flow speed (i.e. Reynolds number). This is not the case for the PSVGs. The experiments have
shown that the magnitude of streamwise vorticty produced by a PSVG array actually increases with
external velocity, U¥ . Figures 8 and 10 show that the PSVG do, however, exhibit a saturation effect at
sufficiently high U¥ . This is obviously not the case for the passive VG. In the remaining section of this
paper a parametric study is presented in order to examine how to drive the PSVG saturation to higher
velocities and in the course of this investigation the details of the vortex formation process are also
examined.
b. Effect of Applied Voltage, Epp
In order to examine the effect of peak-to-peak applied voltage on PSVG performance an actuator array
was used in which both the covered electrode length and inter-electrode spacing was fixed at 2.54 cm (1inch). Delrin was used as the dielectric. The peak-to-peak voltage was varied from 20 to 45 kV and the
peak ¶V / ¶z was measured via LDV at a location 7.62 cm (3 inch) downstream of the array for
freestream velocities in the range 5 m/s £ U¥ £ 30 m/s. The measurements were obtained at y = *.
Results are presented in Figure 12. This figure shows that the effectiveness of the PSVG in terms of
streamwise vorticity production increases with both applied voltage and external velocity. The range of
external velocity for which ¶V / ¶z µU¥ increases with applied voltage which, has the effect of shifting
the PSVG saturation to higher freestream speeds. It should be noted that for the Delrin dielectric material
used for this experiment, Epp = 45 kV represented an effective upper applied voltage limit.
9
Figure 12. Measured peak-to-peak
¶V / ¶z
as a function of
 = 2.54 cm).
U¥ for a range of applied voltages
(L =
c. Effect of Surface Electrode Length
Figure 13 presents measured peak-to-peak ¶U / ¶z for different PSVG arrays with covered surface
electrode lengths of 1, 2, 4 and 6 inches (2.54, 5.08, 10.16 and 15.24 cm). The spanwise inter-electrode
spacing was fixed at 1 inch (2.54 cm) and the applied voltage was fixed at 35 kV. The dielectric material
was Delrin. This figure clearly shows the benefit of increased actuator covered electrode length on PSVG
performance. In particular, at fixed applied voltage, the effect of electrode length is to drive the PSVG
saturation to higher flow speeds and extend the range of velocity for which ¶U / ¶z is proportional to U¥ .
This allows larger values of
¶U / ¶z to be reached.
Figure 13. Peak-to-peak ¶U / ¶z for different
electrode lengths, L ; Epp = 35 kV.
Figure 14. Peak-to-peak ¶V / ¶z for different
electrode lengths, L ; Epp = 35 kV.
Figure 14 presents measured peak-to-peak ¶V / ¶z for different streamwise electrode lengths. The
applied voltage is fixed at 35 kVpp. The effect of increased electrode length is to drive the PSVG saturation
to higher freestream speeds and to thereby increase the velocity range over which ¶V / ¶z µU¥ . Again
the benefit of covered electrode length is apparent.
10
d. Effect of Spanwise Inter-electrode Spacing
A series of experiments were performed in order to assess the effect of spanwise inter-electrode spacing
on PSVG performance. For these experiments a series of four PSVG arrays were constructed for
installation on the test plate in which in the inter-electrode spacing was set at values  = 0.75, 1.0, 1.25 and
1.5 inches (1.91, 2.54, 3.18, and 3.81 cm, respectively). In each case, the covered electrode length was kept
fixed at L = 2 inches (5.08 cm). Spanwise LDV traverses were performed at a wall normal location equal
to the local displacement thickness, *, corresponding to the centroid of boundary layer mean vorticity.
Figure 15 presents measured values of
¶U / ¶z ) max as a function of PSVG inter-electrode spacing, .
Results for three applied voltages are shown. In each case, there is clearly an optimum spacing of
approximately lOPT » 1.25 in. (3.2 cm). Note that there is a rather sudden reduction in PSVG
performance for > OPT.
Figure 16 presents measured values of
¶V / ¶z) max as a function of PSVG inter-electrode spacing, .
These data were acquired simultaneously with those presented in Figure 15. Figure 16 clearly suggests that
optimum performance of the PSVG in terms of mean streamwise vorticity production occurs for values
of between 1 and 1.25 inches (2.54 and 3.2 cm). Again there is a very rapid drop off in performance for l
> 1.5 inches (3.8 cm).
Figure 15.
Variation of
dU / dz) MAX with
Figure 16. Variation of
spanwise
inter-electrode spacing, .
inter-electrode spacing, .
11
¶V / ¶z) MAX with
spanwise
The optimum value of spanwise inter-electrode spacing for both
¶U / ¶z ) MAX and ¶V / ¶z) MAX is
approximately equal to the local 99% boundary layer thickness on the plate upstream of the PSVG array.
This is clearly shown in Figure 17, which presents
¶U / ¶z ) MAX occur near l / d
¶U / ¶z ) MAX as a function of l / d .
Peak values of
= 1.
The question naturally arises whether
this is coincidental or whether the optimum
spanwise inter-electrode spacing actually
scales with the approach boundary layer
thickness. In order to investigate this, the
boundary layer thickness upstream of the
PSVG array was thickened by attaching a
semi-circular bump (15.9 mm in diameter)
near the plate leading edge followed by a
downstream section of surface roughness
extending 10.2 cm in the streamwise
direction. This is shown in the photograph in
Figure 18. This passive treatment gave rise to
a separation bubble followed by turbulent
reattachment, which increased the boundary
layer thickness just upstream of the PSVG
array by approximately 80%. The PSVG
arrays with inter-electrode spacing values  =
0.75, 1.0, 1.25 and 1.5 inches (1.905, 2.54, Figure 17. Peak
3.18, and 3.81 cm, respectively) were again
examined by LDV surveys to see if OPT ( U¥ =20 m/s).
scaled with the new boundary layer thickness,
. Sample results are shown in Figure 19,
which presents normalized values of
l /d
¶U / ¶z ) MAX as a function of l / d ;
¶U / ¶z ) MAX for both the original flat plate and
leading edge tripped cases as a function of
l / d . In both cases the external velocity was
fixed at U¥ = 20 m/s and the applied voltage
was 35 kV. Note that the thicker boundary layer
case peaks at a smaller value of l / d .
Although not shown here, similar results were
found to hold for
¶V / ¶z) MAX . This suggests
that the optimum value for spanwise interelectrode spacing does not scale with the Figure 18. Boundary layer development plate with
approach boundary layer thickness and is leading edge semi-circular bump followed by
instead determined by the governing equations distributed sand grain roughness.
for the electromagnetic field.
e. Streamwise Vortex Formation and Evolution
In order to clarify the mechanism of vortex formation by the PSVG array and its downstream evolution,
PIV measurements were made in the cross-flow plane at several representative streamwise locations both
over the PSVG actuator and at downstream locations. The quartz-based actuator was operated at Epp = 40
kV with L = 5.08 cm (4 in) and  = 2.54 cm (1 in). The freestream velocity was fixed at U¥ = 15 m/s.
12
Sample PIV results are presented in Figure 20,
which presents mean streamwise vorticty, w x , in
the cross-flow plane. The PIV image plane is
centered on the gap between two adjacent surface
electrodes, which are shown as black rectangles at
the bottom of each frame. As a reference, the local
boundary
layer
thickness
corresponds
to
approximately 25-30 on the ordinate scale. The top
two images are taken over the PSVG electrodes; the
leftmost image 5.08 cm (2 in) upstream of the
trailing edge of the actuator and the rightmost image
at the actuator trailing edge. The gradual formation
of pairs of organized counter-rotating streamwise
vortices within the boundary layer is apparent. The
l /d
bottom two images show the evolution of the Figure 19. Comparison of normalized ¶U / ¶z for
streamwise vortices downstream of the PSVG array. baseline and tripped case.
The leftmost image is obtained 5.08 cm (2 in)
downstream of the PSVG and the rightmost image 10.16 cm (4 in) downstream. The counter-rotating pairs
of vortices remain well defined well downstream of the PSVG actuator. The primary effect of streamwise
distance seems to be growth of the vortices and diffusion of the vortex core within the turbulent boundary
layer.
XVG"="4"in"(downstream"of"TE)"
x"="2"in"downstream"of"PSVG"
x"="4"in"downstream"of"PSVG"
Figure 20. PIV measurements of
w x in selected z-y cross-flow planes.
13
From PIV measurements of the cross-stream mean velocity components, the circulation
G º ò V ·d
was numerically evaluated over a fixed rectangular contour bounding a given
vortex at several streamwise locations. By Stoke’s theorem, this is equivalent to the mean
streamwise vorticity flux through the cross-stream area bounded by the integration contour. In
this manner, the streamwise development of w x over the PSVG actuator and its subsequent
evolution at locations downstream could be characterized. Figure 21 presents typical results for
the streamwise variation of G ( x ) for adjacent clockwise (CW) and counter-clockwise (CCW)
vortices. The streamwise coordinate x is centered at the downstream edge of the PSVG so
negative values indicate locations over the actuator and positive values are downstream locations.
The actuator operating conditions are identical to those corresponding to Fig. 20; L = 4 inch, Epp
= 40 kV with U¥ =15m / s . The symmetric development of G ( x ) exhibited by the CW and
CCW vortices is apparent. Figure 21 also shows that the circulation increases approximately
quadratically with x over the actuator and reaches a peak value at the trailing edge. Commencing
at the trailing edge of the actuator a plateau of peak circulation persists up to 2 inches
downstream (x = L/2) followed by a gradual reduction in G ( x ) farther downstream. It is
conjectured that this reduction in  is associated with both turbulent diffusion of the vortices (as
suggested by Figure 20) as well as vorticity redistribution within the turbulent boundary layer.
Figure 21. Streamwise evolution of G ( x ) for adjacent CW and CCW vortices. PSVG
actuator location is denoted by shaded region on the abscissa.
IV. Discussion
The experimental results presented in this paper have demonstrated that PSVGs harvest energy from the
external flow in a manner very similar to that exhibited by passive VGs. This increase in actuator
effectiveness with flow speed makes the PSVG unique among DBD plasma flow control devices. Unlike
14
passive VGs, there is a saturation in the effectiveness of the PSVG at sufficiently high freestream velocity.
However, this study has also demonstrated that this saturation can be driven to higher freestream speeds by
increases in both actuator covered electrode length and applied voltage. For example, Figure 22 shows
measured ¶U / ¶z downstream of a PSVG array using quartz dielectric with 10.2 cm (4 inch) covered
electrodes operated at Epp = 50 kV. Note that the actuator saturation has been effectively eliminated over
the operating range of the wind tunnel.
Furthermore, comparison with the passive VG results presented previously in Figure 8 reveals that the
¶U / ¶z ) max produced by the PSVG exceeds that of the passive VG at corresponding flow speeds.
23 presents corresponding results for
Figure
¶V / ¶z) max for the same quartz PSVG actuator operated at Epp = 50
kV. Although actuator saturation is apparent, it has been pushed to the maximum wind tunnel speed. In
general, PSVG saturation for
¶V / ¶z) max occurs at a lower speed than for ¶U / ¶z ) max .
Figures 22 and 23 also revels that for any given flow speed peak-to-peak
propensity of PSVG to produce large values of
w z ¶U / ¶z ,
¶U / ¶z
>
¶V / ¶z .
In fact, this
¶U / ¶z ) max can also be exploited for flow control.
Figure 23. Peak-to-peak ¶V / ¶z for a PSVG
with quartz dielectric; Epp = 50 kV.
Figure 22. Peak-to-peak ¶U / ¶z for a PSVG
with quartz dielectric; Epp = 50 kV.
Large values of
¶U / ¶z
Comparison of
can be utilized to produce streamwise vorticity,
wx ,
through the term,
which serves to take initially spanwise oriented vorticity and turn it into the streamwise
direction. This is the basis of a “hybrid PSVG actuator” concept (HPSVG) in which spanwise vorticity is
artificially introduced just upstream of the PSVG array. This vorticity is subsequently turned into the
streamwise direction by the large PSVG-induced ¶U / ¶z . It is envisioned that the spanwise vorticity can
be introduced just upstream of the PSVG array by a spanwise oriented DBD plasma actuator using either
steady or unsteady streamwise blowing. However, for the initial proof-of-concept experiment reported here,
a very small scale mechanical ramp was used to create a separated shear layer very near the plate wall.
That is, instead of using a spanwise plasma actuator, additional w z was produced upstream of the PSVG
array by means of a ramp of height, h » d * , where d * is the local boundary layer displacement thickness,
as shown schematically in Figure 24. Figure 24 also serves to illustrate the concept of vortex turning that is
key in the hybrid PSVG (HPSVG) concept.
15
A proof-of-concept study was performed in order to investigate the ability of HPSVG to augment
streamwise vorticity. The LDV system was used to perform non-intrusive velocity measurements along the
spanwise z-axis. A second-order accurate central difference approximation was used to calculate the spatial
derivatives ¶U / ¶z and ¶V / ¶z downstream of the PSVG array. If the HPSVG works as shown
schematically in Fig. 24, then one expects significant increases in
changes in
¶V / ¶z
¶U / ¶z .
¶V / ¶z
and comparably modest
The maximum and spatially averaged peak-to-peak amplitudes of
¶U / ¶z and
are reported in Table 1. In both cases the covered electrode length, L = 5.08 cm (2 inch), the
spanwise inter-electrode spacing was l =
2.54 cm (1 inch) and Epp = 35 kV. As
expected, there seems to be relatively little
change in ¶U / ¶z between the two
configurations, with ~20 % increase on
average with a maximum increase of about
30 %. However, Table 1 shows a very
significant increase in the magnitude of
¶V / ¶z . Remarkably, there is a maximum
increase of about 80 % in peak-to-peak
amplitude of ¶V / ¶z ; that is, the HPSVG
configuration has greatly increased
actuator effectiveness in terms of direct
production of streamwise vorticity. It is
important to note that these results have
Figure 24. Schematic of HPSVG concept: a)
is
been obtained without any effort to
generated
by
the
ramp
element,
b)
is
turned
such
that
optimize this experimental configuration.
generated by PSVG is augmented, c) The resultant
As previously mentioned, the optimization
is increased.
of the HPSVG configuration may yield magnitude of
deeper insights into increasing actuator authority and should be subject of future study.
Table 1: Peak-to-Peak amplitude and increase of actuator metrics.
¶U / ¶z ) MAX (1/sec)
PSVG
HPSVG
Average Increase
Maximum Increase
1006.5
1241.3
23.3 %
29.4 %
16
¶V / ¶z) MAX (1/sec)
243.31
390.49
60.5 %
79.9 %
Acknowledgments
This work was supported by Innovative Technology Applications Company (ITAC), LLC under a Small Business
Innovation Research (SBIR) Phase II Contract No. N00014-11-C-0267 issued by the U.S. Department of the Navy.
The authors would like to thank Dr. Judah Milgram and Mr. John Kinzer of the Office of Naval Research (ONR) for
their support and encouragement during this effort. The authors would also like to acknowledge Mr. Eras Noel for
his important contributions to data acquisition.
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American Institute of Aeronautics and Astronautics