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
A parametric investigation into the performance 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 peak-to-peak voltage, length of the covered electrode and spanwise inter-electrode spacing, on actuator performance. The metrics used to assess performance are the spanwise wall normal component mean velocity gradient,
¶
V /
¶ z , and spanwise longitudinal mean velocity gradient,
¶
U /
¶ z , measured 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 vorticity-strain rate interaction term, w z
¶
U /
¶ z . 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 a passive VG. This unique feature of PSVG may be exploited for flow control applications.
1

V p
= plasma induced wall-normal velocity
U
¥
= freestream velocity
U = Spanwise cycle-average mean velocity
L

E pp
= covered electrode length
= spanwise inter-electrode spacing
= peak-to-peak excitation voltage
U = streamwise mean velocity component
V = wall normal mean velocity component x , y , z = streamwise, wall-normal and spanwise spatial coordinates, respectively.
¶
U /
¶ z = spanwise spatial derivative of streamwise mean velocity
¶
V /
¶ z = spanwise spatial derivative of wall-normal mean velocity w x
= streamwise component mean vorticity

= 99% boundary layer thickness
 *
G ( )
= boundary layer displacement thickness
= circulation
Re x
= Reynolds number
P
ASSIVE vortex generators (VGs) are widely used for separation control on both commercial and
P 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, 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 consequently the boundary layer is 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.
In many applications it is desirable 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 the plasma streamwise vortex generators (PSVG) which are the focus of this paper.
2

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] in which 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 as reported by Kozlov and Thomas [7] and in aeroacoustic control in a tandem cylinder flow configuration by 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 (PIV) 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. This allows much higher applied ac
3

voltages in the current investigation. Furthermore, the PSVG array geometric design utilized in this study is quite 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 laminar boundary layers with 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.
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 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 test section sidewall and the 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 rendered CAD model of the test fixture is shown in Fig.
1a. The PSVG test fixture consists of a flat Plexiglas boundary layer development plate of 1.2 m (48 in) length and 1 cm a)
3 thickness with a rounded leading-edge containing (1),
1
2 distributed sand grain roughness in order to promote rapid boundary layer transition. The last 0.2 m of the plate consists of
(2), a 2.2
o linear, symmetric taper down to a trailing-edge b) thickness of 1.6 mm. The plate is sidewall mounted and spans the wind tunnel test section. Endplates minimize the influence
Figure 1. a) Rendered CAD model of boundary layer development plate, and b) close-up of PSVG array.
of the tunnel sidewall boundary layers.
As shown in Figure 1a, a PSVG actuator test fixture is flush mounted into a cavity machined into the
4

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 boundary layer growth prior to application of PSVG flow control. The cavity provides ample room for accommodating both the required high-voltage leads and the dielectric material that forms the PSVG. Figure 1b shows a close up view 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 , which 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.
Figure 2. Schematic of the geometry of the PSVG array, front view (left) and orthographic view
(right).
Due to the use of a common covered electrode, plasma forms on both sides of each surface electrode. This gives rise to a series of opposing wall jets in the spanwise direction that collide, thereby generating pairs of counter-rotating vortices with size O (  /2) . These become the basis for enhanced cross-stream mixing of momentum within the boundary layer for separation control.
As noted earlier, the dielectric material used in this study was either Delrin or quartz of 3.2 mm thickness (1/8 in). In both cases, the dielectric material extended 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 was protected by a layer of 2 mil
Kapton tape and an outer layer of 2 mil Teflon tape. These additional layers of thin dielectric tape have
5

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. This controlled the length of the plasma forming region on each surface electrode. 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 extended 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 were connected to high voltage wires that led out of the test fixture and connected 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. This voltage range may be compared to the sinusoidal ac voltage of 7 to 12 kV peak-to-peak used in [10]. d.
Parameters and Actuator Performance Metrics
The experimental study involved varying the following parameters: actuator peak-to-peak voltage, E pp
, 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 and required construction of multiple PSVG arrays, it was desirable to define a performance metric that was both physically relevant and 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 180 o backscatter mode. The
Doppler bursts were measured using a BSA F60 Flow processor and BSA Flow Software Version 4.10.
One-micron diameter DEHS seed particles were injected upstream of the wind tunnel inlet by means of a
TSI atomizer. 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
6

pressure gradient turbulent boundary layer, is also the centroid of mean spanwise vorticity. 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 wall-normal location

* was deemed the most appropriate wall-normal location to measure both
¶
V /
¶ z
and
¶
U /
¶ z . The former metric was chosen since w x
µ¶
V /
¶ z and is therefore related to the direct production of mean streamwise vorticity.
The latter metric is related to the redistribution of initially spanwise vorticity to the streamwise direction through the vorticty-strain rate interaction term w z
¶
U /
¶ z in the vorticity transport equation. Thus the quantity
¶
V /
¶ z 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 which takes initially spanwise mean vorticity and turns it into the streamwise direction.
Parameter E pp
Table 1. Parameter space for PSVG parametric study
(kV) U
∞
(m/s) L (in) λ (in) Dielectric
Range 15 – 50 5 – 40 1 – 6 0.5 – 1.5 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
Figure 3. PIV experimental setup in the cross-stream plane.
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 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
7

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 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.
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 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 25 o . The center-to-center spacing was  = 50.8 mm (2 in).
8

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 local boundary layer displacement thickness. 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
£
U
¥
£ to 20 m/s (corresponding to the Reynolds number range of 0.672 million
£
Re x
£
1.08 million). In order to account for the variation in external velocity between trials, 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. Due to the scaling demonstrated in Fig. 4, the ordinate may be denoted as F ( z ) , and it follows that
¶
U /
¶ z
=
U
¥ dF / dz . That is, the spanwise velocity gradient
¶
U /
¶ z
is directly proportional to U
¥
.
Figure 5 presents peak values of
¶
U /
¶ z measured at a fixed location downstream of the passive VGs as a function of freestream speed. The proportionality to U
¥
suggested by the scaling in Figure 4 is fully
Figure 4. Scaled spanwise cyclic variation of mean velocity downstream of the passive VGs. confirmed.
Figure 5. Maximum amplitude of
¶
U /
¶ z for passive VGs as a function of external velocity.
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 length of 2.54 cm (1 in). The spanwise inter-electrode electrode spacing was 2.54 cm (1in) for the array (the same
9

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
( )
and
( ) 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,

*. As a representative example of the results obtained, Fig. 6 presents the variation of scaled mean velocity
( )
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, U , is subtracted and the result is normalized by the external velocity, U
¥
. 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
( )
downstream of the
PSVG.
A comparison of Figures 4 and 6 reveals that the functional form of F(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 due to colliding spanwise plasma-induced wall jets. Positive excursions are centered over the surface electrodes and are associated with transport of comparatively high velocity fluid toward the surface electrodes by the plasma induced body force. However, the collapse shown in Figure 6 for the PSVG results indicates that
¶
U /
¶ z
is also proportional to the external flow speed, U
¥
, as was the case for the passive VGs.
10

Figure 6. Spanwise variation of scaled streamwise-component mean velocity downstream of the
PSVG array (40kV Case); surface electrodes centered at z
=
0,
±
25.4,
±
50.8
mm .
Figure 7 presents an example of measured
¶
U /
¶ z for the PSVG operated at E pp
= 40 kV and an external flow speed of 15 m/s corresponding to the Re x
= 810,000 case. A second-order accurate central difference approximation was used to calculate the spatial derivatives
¶
U /
¶ z and
¶
V /
¶ z downstream of the PSVG array. Figure 7 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 to the passive VG is quite remarkable, with the PSVG producing somewhat larger
Figure 7. Spanwise variation of the PSVG array ( U
¥
¶
U /
=
15 m / s , 40kV )
¶ z downstream of
11
Figure 8. Comparison of peak-to-peak
¶
U /
¶ z versus
U
¥ for the passive VG and PSVG.

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 (Re x
= 1.34 X 10 6 ). This saturation effect is unique to the PSVG and will be described in detail in the following section.
Fig 9. Spanwise variation of scaled wall-normal component mean velocity downstream of the PSVG array (40kV Case); surface electrodes centered at z
=
0,
±
25.4,
±
50.8
mm .
Figure 9 presents corresponding LDV measurements of the wall-normal mean velocity
( )
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 figure also clearly shows that locations over the surface electrodes (e.g. z = -25.4 mm, 0,
+25.4 mm) are associated with negative V . This is indicative of the plasma induced body force drawing fluid toward the wall. In contrast, locations midway between surface electrodes are characterized by positive V peaks that arise from the local upwelling associated with the collision of opposing wall jets emanating from adjacent electrodes.
12

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
Figure 10. Peak-to-peak
¶
V /
¶ z versus U
¥ for the PSVG (40 kV case). flow speeds leading to 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
E pp
= 40 kV. The associated schematic shown in Figure 11b shows that the measured
¶
V /
¶ z pattern is fully consistent with the existence of pairs of counter-rotating streamwise vortices downstream of the
PSVG. The figure shows that regions of negative
¶
V /
¶ z correspond to clockwise streamwise vortices while regions of positive
¶
V /
¶ z correspond to counter clockwise vortices.
Consistent with Figure 11a, the locations of zero vorticity are centered over the electrodes, and midway between adjacent electrodes.
It is apparent from the results presented in this section that the PSVGs extract energy from the primary flow like the 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 at fixed applied voltage actually increases with external velocity, U
¥
. Figures 8 and 10 show that the PSVGs 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 the PSVG saturation may be driven to higher velocities and in the course of this investigation, details of the vortex formation process are provided.
13

a) b)
Figure 11. a) Spanwise variation in
¶
V /
¶ z for U
¥
= 20 m/s and E pp
= 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. b.
Effect of Applied Voltage, E pp
In order to examine the effect of peak-to-peak applied voltage, E pp
, 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
(1-inch). 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. All measurements were obtained at y =

*.
Results of the measurements 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. In particular, the range of external velocity for which
¶
V /
¶ z
µ
U
¥ increases with applied voltage, which has the effect of shifting the PSVG saturation to higher freestream speeds. It should be noted that for the 0.32 cm (0.125 in) thick Delrin dielectric material used for this experiment, E pp
= 45 kV represented an effective upper applied voltage limit.
14

Figure 12. Measured peak-to-peak
¶
V /
¶ z as a function of U
¥ for a range of applied voltages (L =

= 2.54 cm). c.
Effect of Surface Electrode Length
Figure 13 presents measured peak-to-peak ¶
U /
¶ z for four different PSVG arrays with covered surface electrode lengths of L = 2.54, 5.08, 10.16 and 15.24 cm (1, 2, 4 and 6 inches). The spanwise inter-electrode spacing was kept fixed at  = 1 inch (2.54 cm), and the applied voltage was fixed at E pp
= 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 a fixed applied voltage, the effect of electrode length is to drive the PSVG saturation to higher flow speeds, and to extend the range of external velocity for which
¶
U /
¶ z is proportional to U
¥
. This allows larger values of ¶
U /
¶ z to be reached.
Figure 14 presents measured peak-to-peak ¶
V /
¶ z for the same covered electrode lengths. The applied voltage is again fixed at 35 kV pp
. The effect of increased electrode length is to drive the PSVG saturation to higher freestream speeds and to thereby to increase the velocity range over which ¶
V /
¶ z
µ
U
¥
. Again the benefit of the covered electrode length on vorticity production is apparent. The solid curve is the result of a scaling analysis to be presented in Section IV which describes the flow physics of PSVG operation.
15

Figure 13. Peak-to-peak
¶
U /
¶ z for different covered electrode lengths, L; E pp
= 35 kV.
Figure14. Peak-to-peak
¶
V /
¶ z for different covered electrode lengths, L; E pp
= 35 kV.
Solid curve refers to scaling described in
Section IV. 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 was constructed for installation into the test plate in which in the inter-electrode spacing was set at values of

= 1.91, 2.54, 3.18, and 3.81 cm (0.75, 1.0, 1.25 and 1.5 inches, respectively). In each case, the covered electrode length was kept fixed at L = 5.08 cm ( 2 inches). 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 l
OPT
»
1.25 in. (3.2 cm). Note, however, that there is a rather abrupt 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

> 1.5 inches (3.8 cm).
16

Figure 15. Variation of inter-electrode spacing,

. dU / dz
)
MAX with spanwise Figure 16. Variation of
¶
V /
¶ z
)
MAX with spanwise inter-electrode spacing,

.
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
as a function of l
/ d
. Peak values of
( ¶
U /
¶ z
)
MAX occur near λ /
δ = 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 upstream of the PSVG array was thickened by attaching a semicircular bump (15.9 mm in diameter) near
Figure 17. Peak
¶
U /
¶ z
)
MAX l
/ d as a function of l
/ d
;
( U
¥
=20 m/s).
17

the plate leading edge and followed by a downstream section of distributed 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-
Figure 18. Boundary layer development plate with leading edge semi-circular bump followed by distributed sand grain roughness. electrode spacing values

= 0.75, 1.0, 1.25 and
1.5 inches (1.905, 2.54, 3.18, and 3.81 cm, respectively) were again examined by LDV surveys to see if

OPT
scaled with the new boundary layer thickness,

. Sample results are shown in Figure 19, which presents normalized values of
( ¶
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 l
/ d
Figure 19. Comparison of normalized
¶
U /
¶ z for baseline and tripped case. 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
. In fact, the new peak value near l
/ d
= 0.6 is consistent with no change in

OPT
. Although not shown here, similar results were found to hold for
( ¶
V /
¶ z
)
MAX
. This suggests that the optimum value for spanwise inter-electrode spacing does not scale with the approach boundary layer thickness (at least for the quite limited range of
 examined here). However, the zero pressure gradient boundary layer is somewhat of a special case and this result should probably not be generalized. For instance, one can envision a variety of flows in which the spanwise inter-electrode spacing would couple to a spanwise wavenumber dependence of an underlying instability mechanism.
18

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 E pp
= 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. This comparatively low velocity was selected in order to maximize the particle residence time in the laser light sheet (stereo PIV was not utilized).
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 left-most image was 5.08 cm (2 in) upstream of the trailing edge of the actuator and the right-most image was at the actuator trailing edge. The formation of pairs of organized counter-rotating streamwise vortices within the boundary layer is apparent. The bottom two images show the evolution of the streamwise vortices downstream of the PSVG array. The left-most image was obtained 5.08 cm (2 in) downstream of the PSVG and the right-most image 10.16 cm (4 in) downstream of the PSVG. The counterrotating pairs of vortices remain well defined 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.
From the 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.
19

VG
w x
Figure 21 presents typical results for the streamwise variation of
G ( )
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, E pp
= 40 kV with U
¥
=
15 m / s . The symmetric development of
G ( )
exhibited by the CW and CCW vortices is apparent. Figure 21 also shows that the circulation increases approximately linearly 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 ( )
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 three-dimensional vorticity redistribution within the turbulent boundary layer.
20

Figure 21. Streamwise evolution of
G x
( ) for adjacent CW and CCW vortices. PSVG actuator location is denoted by shaded region on the abscissa.
Some key results of the parametric investigation into PSVG performance are qualitatively summarized in Figure 22. The response of the PSVG in terms of mean streamwise vorticity production, w x
, falls into two regimes. In regime 1 the response is directly proportional to external flow speed and there appears to be no explicit dependence on the covered electrode length, L , (other than an increase with L in the range of external velocity over which the linear behavior holds). In contrast, in regime 2 the response at fixed L is proportional to 1 / U
¥
, and is proportional to the covered electrode length L at fixed U
¥
. Taken in combination, this shows that in regime 2 the actuator response is directly proportional to the fluid residence time over the actuator, T
RES
» (
/ U
¥
)
. In this section, the mechanisms underlying streamwise vorticity production in these two regimes is examined using dimensional arguments.
21

Figure 22. Schematic of general aspects of PSVG behavior observed in the parametric experiments. a. Regime 1
Consideration is first given to regime 1. This is the regime in which the PSVG exhibits energy harvesting from the mean flow. In this regime, the experiments are consistent with the notion that the production of streamwise vorticity occurs by vorticity redistribution mechanisms. Ignoring viscous diffusion (which operate on a much slower time scale than vorticity-strain rate interactions) the vorticity transport equation for the streamwise component mean vorticity w x is given by,
D w x
Dt
= w x
¶
U
¶ x
+ w y
¶
U
¶ y
+ w z
¶
U
¶ z
. (1)
For the flat plate used in the experiment reported here, the streamwise dilatation is negligible (i.e.
¶
U /
¶ x
»
0 ) and so the dominant vorticity transport terms on the right hand side of equation (1) are, w y
¶
U /
¶ y and w z
¶
U /
¶ z which serve to take initially wall-normal- and spanwise-component vorticity, respectively, and turn it into the streamwise direction. The wall-normal component of vorticity is w y
(
U /
¶ z
-¶
W /
¶ x
) » ¶
U /
¶ z
»
O
( D u / l )
, where
D u is a characteristic change in streamwisecomponent velocity occurring over the spanwise inter-electrode spacing,

. The mean strain rate is given
22

by
¶
U /
¶ y
» ( t
/ d
*
)
where u t
is the boundary layer friction velocity, and

* is the displacement thickness just upstream of the actuator. In this manner, the vorticity transport term may be written as, w y
¶
U
¶ y
»
O
æ u t d
*
D u l
æ
æ
. (2)
The spanwise vorticity is given by, w z
(
V /
¶ z
-¶
U /
¶ y
) » ¶
U /
¶ y , and the vorticity redistribution term may be approximated by w z
¶
U /
¶ z
(
U /
¶ y
) ¶
U /
¶ z . By scaling arguments similar to those presented above it is apparent that, w z
¶
U
¶ z
»
O
æ u t d
*
D u l
æ
æ
, (3) and both vorticity redistribution terms are of the same order-of-magnitude so that both will simultaneously serve to comparably increment the streamwise-component vorticity.
The streamwise velocity increment,
D u , occurs due to wall-normal fluid motions created by the PSVG actuator. In particular, these motions involve the transfer of relatively high-speed fluid down toward the wall at spanwise locations centered over the surface electrodes and the upwelling of low speed fluid in the inter-electrode gaps as clearly shown in the LDA measurements presented previously in Figures 6 and 9. In analogy with the mixing length concept, we can gauge the magnitude of the associated velocity increment
D u as, where
D u
»
O
( y
¶
U /
¶ y
)
»
O
( y u t
/ d
*
)
, (4) y
is a characteristic length scale for wall-normal plasma-induced motion set-up by the PSVG actuator. The rate of redistribution of wall-normal vorticity is then given by, w y
¶
U
¶ y
»
O
æ
ç
è y u t
/ d d
* / u t
* l ö
ø
÷
. (5)
Since both vorticity redistribution mechanisms operate in parallel, the steamwise vorticity increment,
D w x
, occurring over the characteristic redistribution time-scale, d
* / u t
,will be
D
The wall-normal length scale w x
»
O
æ
2 y u t d
* l
æ
æ
. (6) y
clearly cannot exceed the boundary layer thickness

If one makes the reasonable assumption that y
»
O
( )
then we have,
23

D w x
»
O
æ
2 d u t d
* l
æ
æ
. (7)
Using appropriate measured values from the experiment, this grouping is plotted as the solid curve in
Figure 14. Given that this is only an order-of-magnitude analysis, the excellent agreement with experiment is possibly fortuitous, but it clearly serves to show that the response of the PSVG associated with vorticity redistribution mechanisms is directly proportional to external flow speed U
¥
and independent of covered electrode length L as observed in the experiments.
As indicated in (5), the vorticity redistribution takes place on a time-scale T
VR
»
O
( d
* / u t
)
. In order to allow sufficient time for vorticity redistribution mechanisms to work, it should be that T
VR
£
T res
. This requires, d
L
*
For the experiments reported in this paper, 0.125
£ u t
. (8)
U
¥
£ d
* / L
£
0.021 for covered electrodes lengths of 1 inch
£
L
£
6 inch, respectively. This may be compared to u t
/ U
¥
»
0.042 for the experiments. Strictly speaking then, only experiments with covered electrode lengths L
>
3 inches satisfy constraint (8). This likely explains the deviation from linear behavior at comparatively low speeds shown in Figures 13 and 14 for covered electrode lengths of L = 1 and 2 inches. b. Regime 2
Regime 2 involves the direct production of streamwise vorticity by the PSVG actuator. This will depend on the characteristic time required for streamwise vortex formation, T
F
»
O
( d
* / V
P
)
where V
P is the characteristic velocity of the plasma-induced wall-normal flow that leads to vortex formation. For the experiments reported in this paper, this time scale is on the of order of 1 ms. Comparing this to the timescale for vorticity redistribution T
VR
one finds that 0.2
<
T
F
/ T
VR
<
0.5
so that one expects direct production of steamwise vorticity to dominate for the lowest residence times over the actuator (i.e. small L and large
U
¥
). For direct production of vorticity, d w x
/ dt
»
O
æ
ç
è
4 V
P
/ d
* / V l
P
ö
ø
÷ »
O
ç
æ
è
4 V
P
2 d
* l
The increment in streamwise vorticity occurring over the time interval
ö
ø
÷
. (9)
T
RES
» (
L / U
¥
)
is just,
24

D
Consequently, at a fixed external speed,
D w x w x
»
O
æ
4 V
P
2 d
* l
æ
æ
æ
æ
L
U
æ
æ
æ
. (10)
µ
L , and at a fixed L ,
D w x
µ
1/ U
æ
, consistent with the results of the experiments.
Large values of
¶
U /
¶ z can be utilized to produce streamwise vorticity, w x
, through the vorticty-strain rate interaction term, w z
¶
U /
¶ z , 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 PSVGinduced
¶
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 instead to
Figure 23. Schematic of HPSVG concept: a) generated by the ramp element, b) w z
is w z
is turned such that w x
generated by the PSVG is augmented, c) The resultant magnitude of w z
is increased. create a separated shear layer very near the plate wall. That is, instead of using a spanwise plasma actuator, additional w z
was introduced 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 23. Figure 23 also serves to illustrate the concept of vortex turning that is key in the hybrid HPSVG concept.
A proof-of-concept study was performed in order to investigate the ability of an HPSVG to augment streamwise vorticity. The LDV system was used to perform non-intrusive velocity measurements along the spanwise z -axis. If the HPSVG concept works as shown schematically in Fig. 23, then one expects
25

Table 1: Peak-to-Peak amplitude and increase of actuator metrics.
¶
U /
¶ z
)
MAX
(1/sec) ¶
V /
¶ z
)
MAX
(1/sec)
PSVG
HPSVG
Average Increase
Maximum Increase
1006.5
1241.3
23.3 %
29.4 %
243.31
390.49
60.5 %
79.9 % significant increases in
¶
V /
¶ z and comparably modest changes in
¶
U /
¶ z . The maximum and spanwise spatially averaged peak-to-peak amplitudes of
¶
U /
¶ z and
¶
V /
¶ z 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 E pp
= 35 kV. As expected, there seems to be comparatively 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 production of streamwise vorticity. It is important to note that these results have been obtained without any effort to optimize this experimental configuration.
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 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 24 shows measured
¶
U /
¶ z downstream of a PSVG array using quartz dielectric with 10.2 cm (4 inch) covered electrodes operated at E pp
= 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.
26

Figure 24. Peak-to-peak
¶
U /
¶ z for a PSVG with quartz dielectric; E pp
= 50 kV.
Figure 25. Peak-to-peak
¶
V /
¶ z for a PSVG with quartz dielectric; E pp
= 50 kV.
Corresponding results for
( ¶
V /
¶ z
)
MAX for the same quartz PSVG actuator operated at E pp
= 50 kV is presented in Figure 25. 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
.
Comparison of Figures 24 and 25 also reveals that for any given flow speed, peak-to-peak
¶
U /
¶ z is greater than peak-to-peak
¶
V /
¶ z . In fact, this propensity of the PSVG actuator to produce large values of
( ¶
U /
¶ z
)
MAX can be exploited for flow control as described in the previous section regarding the hybrid
PSVG actuator.
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 the data acquisition.
27

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29
American Institute of Aeronautics and Astronautics