Flow-control-induced vibrations for power generation using pulsed plasma actuators

Journal of Fluids and Structures 34 (2012) 170–189

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Flow-control-induced vibrations for power generation using pulsed plasma actuators David Greenblatt n, Alexander Treizer, Alexander Eidelman, Hanns Mueller-Vahl Technion—Israel Institute of Technology, Technion City, Haifa 32000, Israel

a r t i c l e in f o

abstract

Article history: Received 18 September 2011 Accepted 10 June 2012 Available online 27 July 2012

This paper describes flow-control-induced vibrations using pulsed dielectric barrier discharge plasma actuators, in which boundary layer separation on a structure is actively controlled to produce periodic loads that lead to its vibration. The concept is intended for energy generation and is demonstrated experimentally using a onedegree-of-freedom pivoted cylindrical body mounted vertically within a blow-down wind tunnel. Subcritical Reynolds numbers, less than 105, were considered where typical shedding frequencies were several times larger than the system natural frequency. Static deflection experiments were performed to determine the maximum imposed aerodynamic loads as a function of control parameters and these were complemented with flow-field measurements. Periodic loading of the cylinder was achieved by periodic modulation of the actuator. Large amplitude oscillations were observed when the modulation frequency was close to the system natural frequency. In contrast to natural vortex induced vibration, the large amplitude oscillations were achieved by alternating dynamic separation and attachment of the boundary layer. Estimation of the transient loads was performed using a system identification technique and the power generated by the system was estimated on the basis of a piecewise linear model. Peak estimated power coefficients were relatively small (0.042) but can be improved by increasing the lateral force coefficients and by proportionately increasing the system’s physical size. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Flow control Flow-induced vibrations Dielectric barrier discharge plasma actuators Unsteady separation control Energy generation Wind energy

1. Introduction Flow-induced vibration (FIV) is a topic of interest in many engineering disciplines. The phenomenon is alternatively referred to as vortex induced vibration (VIV), lock-on or synchronization. A common definition of lock-on or synchronization is when a body’s oscillation frequency (f) and vortex formation frequency (fv), are close to the natural frequency (fn) of the body within a regime of large-amplitude vibration (e.g. Williamson and Govardhan, 2004). VIV is generally a problem that results in fatigue and structural failure of heat exchanger tubes, ocean constructions, bridges, chimney stacks and vehicle components. Due to the important need to avoid the phenomenon, many fundamental studies have been carried out (see e.g. Blevins, 2006). Although avoidance (e.g. Wong and Kokkalis, 1982) or active control (e.g. Cheng et al., 2003) are common engineering or research objectives, other approaches aim to do the opposite. Instead of reducing, eliminating or avoiding VIV, the phenomenon is exploited to harvest energy as done, for example, by Bernitsas et al. (2008). Analytical studies show that for these applications, flow control can be used in a feedback loop to further

n

Corresponding author. Tel.: þ 972 4 829 3473; fax: þ 972 4 829 5711. E-mail address: [email protected] (D. Greenblatt).

0889-9746/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jfluidstructs.2012.06.004

D. Greenblatt et al. / Journal of Fluids and Structures 34 (2012) 170–189

Nomenclature c c0 C CD CL Cm d l DC f fex fion fn fp fv FB FD FL Fþ h

absolute velocity, (u2 þv2)1/2 natural (self) damping coefficient linear damping due to external load cylinder drag-force coefficient, F D =1=2rU 21 dh cylinder lateral-force coefficient, F L =1=2rU 21 dh momentum coeffcient, F B =1=2rU 21 dh cylinder diameter rigid connecting rod length duty cycle body’s oscillation frequency structural excitation frequency, 1/ Tex plasma ionization frequency pendulum natural frequency plasma pulsing frequency, 1/ Tp natural vortex shedding frequency plasma body force cylinder drag-force cylinder lateral-force dimensionless plasma pulsing frequency, fpd/UN cylinder height

P Pp qN Re St t Tatt Tsep UN Un V Vpp x y

a af y

t oz

171

gross power produced plasma input power free-stream dynamic pressure, 1=2rU 21 cylinder-based Reynolds number, UNd/n cylinder-based Strouhal number, fvd/UN time time-scale associated with forced flow attachment time-scale associated with forced flow separation free-stream velocity reduced velocity, UN/fnd voltage peak-to-peak voltage free-stream direction cross-stream direction cylinder angle from forward stagnation point actuator forcing angle from forward stagnation point system deflection angle dimensionless time, TUN/d non-dimensional spanwise vorticity, (@v/@x–@u/@y)d/UN

increase the harvested energy (e.g. Meliga et al., 2011). The concept appears suited to ocean and other flowing water resources where relatively large aspect ratio cylinders (h/db1) must be used to ensure lock-on. Extracting energy via oscillatory or reciprocating motion, as opposed to using conventional rotary turbines, has been attempted at least since the 1970s. Bade (1976) developed a wing with passive-pitch articulation that was mounted on the end of a pivoted boom and Jeffery (1977) developed a vertical swinging-wing that was pivoted and made to ‘‘flap’’ in the wind. McKinney and DeLaurier (1981) conducted an analytical and experimental investigation of a wing that oscillates in both angle-of-attack and vertical translation with prescribed phasing between the two motions. This so-called ‘‘wingmill’’ was capable of efficiencies comparable to rotary designs. In this paper, we describe a technique of forced flow induced vibration that is not related to the natural vortex formation and its associated frequency fv; neither is it based on passive or active airfoil pitching. Instead, the flow about the body is actively controlled, or forced, with a view to drive the body at, or near, resonance. The technique is explored here by actively controlling dynamic separation and attachment of the boundary layer over a small aspect ratio cylindrical bob (i.e. h/d ¼1.33 with two free ends) of a rigid-rod pendulum with one degree-of-freedom. When compared to nominally two-dimensional studies, investigations on cylinders with two free ends are extremely limited (e.g. Wieselsberger, 1922; Zdravkovich et al., 1989). The free ends produce a reduction in drag and quasi-periodic vortex shedding, similar to that on an infinite cylinder, is observed for 2 oh/d o8. A larger number of investigations have been conducted on wall-mounted cylinders with one free end. For example, Farivar (1981) observed lower shedding frequencies near the free end compared to those on the nominally two-dimensional part and Sakamoto and Arie (1983) observed that this shedding changes from the typical Karman-type to so-called arch-type. For low aspect ratios of 1.0 and 1.5, Baban and So (1991) observed that vortex shedding is partially destroyed by the flow separation over the free end and its resultant recirculating flow in the wake. In a recent investigation with h/d¼3, Iungo et al. (2012) did not detect a distinct shedding frequency over approximately half of the cylinder height relative to the free end. Consistent with these observations, the fluctuating lift decreases substantially and this provides an explanation of why Bernitsas et al. (2008) required relatively large aspect ratio cylinders to achieve lock-on. Another important observation was that the unsteady drag forces increased significantly, with the characteristic frequency larger than that associated with the lift fluctuations. It is interesting to note that the presence of a wall on either side of the cylinder (i.e. no free end) produces significant increases in lift oscillations and spanwise correlation of the shedding (Szepessy and Bearman, 1992). In the present investigation both ends were left free and no attempt was made to add ‘‘walls’’ or end-plates to the cylinder free ends. For the experiments reported here, surface-mounted dielectric barrier discharge (DBD) plasma actuators (see Corke et al., 2007) were used to control flow separation, under subcritical conditions, by exciting the separated shear layer on the cylinder wall. DBD actuators were selected due to their effectiveness in controlling flow separation and vortex shedding on two-dimensional cylinders at subcritical Reynolds numbers (see Asghar and Jumper, 2009; Jukes and Choi, 2009; Thomas et al., 2008). This is essentially a novel way of producing reciprocating motion and hence one objective of this paper is to

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study the phenomenon by measuring the applied loads, unsteady motions and flowfield. As in the studies cited above, a second objective is to assess the viability of such a system for wind-energy generation in the form of oscillatory or reciprocating motion. To this end, employing DBD plasma actuators at low duty cycles, and hence low power on the order of milliwatts, renders them ideally suited to the present applications (e.g. Greenblatt et al., 2008). In order to study the phenomenon and its applicability to energy-generation, the following procedure was followed: a small wind tunnel model was constructed and equipped with DBD plasma actuators (Section 2). A simple linear system model was developed and this was used to estimate the theoretical maximum system power and, together with experimental data, the natural system damping (Section 3). This was followed by a parametric study (Section 4), complimented with flow-field measurements (Section 5), aimed at identifying conditions under which the effectiveness of the actuators is maximized. With this as background, open-loop forcing of the system was studied in order to illustrate the basic nature of flow-control-induced vibrations (Section 6). Estimation of the transient loads was performed using a system identification technique (Section 7) and this was used to develop a model for the forcing function and estimate the power produced. The viability of the system for wind energy generation is considered in Section 8 and this is followed by the main conclusions and recommendations in Section 9. 2. Experimental set-up Experiments were performed in a low-speed blow-down wind tunnel with a 1  0.61 m2 test section area and a maximum wind speed of 55 m/s. The maximum turbulence level in the center of the tunnel was 0.3% of the free-stream velocity. The model consisted of a one-degree-of-freedom pendulum constructed from Plexiglas: namely a cylindrical bob (mass M ¼1.022 kg, diameter d ¼150 mm and height h¼204 mm) joined to a rigid connecting rod (mass m¼0.057 kg, length l ¼292 mm) that was pivot-mounted at the tunnel ceiling using a ball-bearing (see Fig. 1(a)). The dimensions of the bob resulted in an area blockage ratio of 5%. The angular position on the cylinder, measured from the stagnation line, was designated as a. For convenience, we designate the length from the pivot to the cylinder center of mass: L¼l þh/2. For the experiments performed here, no external load or external damping of any kind was attached to the cylinder. Wind tunnel speeds UN between 4 m/s and 10 m/s were considered, corresponding to the subcritical Reynolds number range 40 000– 100 000 based on the cylinder diameter. The cylinder was equipped with a surface-mounted DBD plasma actuator mounted at a fixed location that extended along its entire height h. The high voltage wires were taped to the connecting rod and connected to a high voltage AC source above the wind tunnel. The cylinder was equipped with a cover that could be located and bolted at 101 increments. In this way the angular location of the actuator relative to the oncoming stream, or stagnation point (af), could be varied (see schematic in Fig. 1(b)). The DBD actuator used was an asymmetric wall-mounted configuration as described by Corke et al. (2007). The upper (exposed) and lower (encapsulated) electrodes (both 70 mm thick) were separated by three layers of 50 mm thick Kaptons tape. The actuator was driven at fion ¼10 kHz and 20 kHz at 6 kVpp rVr10 kVpp, sufficiently high to cause the air

attached to wind tunnel ceiling

θ

connecting rod

y DBD plasma actuator

cylinder deflected due to flow control

l

αf

cylinder un-deflected

U∞

α

d x

h

d Fig. 1. (a) Cylinder and connecting rod configuration viewed from upstream with relevant dimensions and definitions and (b) underside view schematic of the cylinder showing the actuator location (actuator thickness exaggerated for clarity).

D. Greenblatt et al. / Journal of Fluids and Structures 34 (2012) 170–189

173

surrounding the covered electrode to ionize. The ionized air, in the presence of the electric field, produced the body forces that were exploited here for controlling flow separation. Furthermore, the actuators were pulsed at frequencies (10 Hz rfp r250 Hz) selected to represent the F þ fpd/UN range between O(0.1) and O(5), known to be effective for separation control (see Greenblatt and Wygnanski, 2000; Greenblatt et al., 2008). In all cases fion bfp. The duty cycle, namely the percentage (or fraction) of time that the actuator is operational, was varied in the range 0.1%rDCr50%. A typical ionization frequency, a pulsed plasma frequency and a duty cycle are represented in Fig. 2(a). To determine the plasma body force FB as a function of the power supplied Pin, the actuator was calibrated independently using a lever and balance setup similar to that of Enloe et al. (2004). This facilitated estimation of the plasma body force coefficient, more commonly termed the momentum coefficient: Cm ¼

FB 1=2rU 21 dh

:

ð1Þ

The location of the cylinder at any instant, and hence the determination of the deflection angle y, was achieved using a standard optical technique as follows: the lower circular surface of the cylinder was painted matt-black and the wind tunnel walls were lined with a white paper background to improve the contrast. A transparent Plexiglass wind tunnel floor was installed to facilitate optical access. A Casio EX-F1 high-speed camera (6 Mega-pixel; 1200fps) was used to film the cylinder from below the wind tunnel. The individual images were cropped and converted to grayscale. A threshold algorithm was then applied, isolating the pendulum, and allowing the calculation of its centroid. Releasing the cylinder in still air and recording its motion in the above-mentioned manner indicated a natural virtually un-damped frequency of 0.790 Hz. This compared favorably with the theoretical value of: rffiffiffi 1 g fn ¼ ¼ 0:794 Hz, ð2Þ 2p L when considering the cylinder as a point mass. In order to excite the cylinder, the pulsed plasma actuator was further modulated at the excitation frequency fex. This was achieved by periodically initiating and terminating the actuators for particular pulsed frequencies F þ  fpd/UN.

15 1/fion 10 kV actuation

Tp=1/fp 5 0 -5 DC=Ton/Tp

-10

Ton

-15 0

0.005

0.01

0.015

time (s) 15 Tex=1/fex

kV actuation

10 5 0 -5 -10

1/fp

-15 0

0.25

0.5

0.75 time (s)

1

1.25

Fig. 2. (a) Illustration of the pulsed plasma actuation where the plasma actuator is driven at 10 kHz and pulsed at 100 Hz with DC¼ 10%. (b) Illustration of the pulsed plasma actuation of 100 Hz corresponding to (a), modulated the structure excitation frequency fex at a duty cycle of 30%.

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The excitation time-scales are illustrated in Fig. 2(b), where fex 5fp; for all modulation at fex the duty cycle was maintained at 30% as shown in Fig. 2(b). Two dimensional particle image velocimetry (PIV) was performed at the cylinder center-span in order to assess the flow state with and without actuation. For these measurements the cylinder pivot was locked, thereby preventing transverse motion of the cylinder. A 200 mJ double-pulsed Nd-YAG laser was used in conjunction with a 4 megapixel CCD camera mounted below the tunnel. A commercial seeding particle generator was employed to generate particles of diameter 1 mm (based on the manufacturer’s specifications) within the tunnel plenum. Measurements for the baseline and selected control cases were performed using 200 image pairs. Tests performed showed that this number of image pairs produced adequate convergence of the velocity field. The resolution of the PIV images was 0.18 mm/pixel. A decreasing size multipass approach was adopted, using 8  8 pixel interrogation windows with 0% overlap for the final results. Three types of PIV measurements were performed: random data acquired for baseline and control cases; phaseresolved measurements within the forcing cycle; and phase-resolved measurements within the attachment and separation transients. These data are presented in Section 5. 3. The system model Development of the linear system model was performed by writing the equation governing the pendulum motion: Iy€ ¼ SM O ,

ð3Þ

where I is the mass moment of inertia and SMO is the sum of the moments about the pivot point O. I is made up of the contribution from the cylinder ML2, the contribution about its own axis (Mh2/12) and the contribution from the rod (ml2/3). Assuming small angles y, and in addition that m5M and h2/(12L2)51 we can write the linear equation of motion: ML2 y€ þ ðc0 L2 þ CÞy_ þ MgLy ¼ F L ðtÞL,

ð4Þ

0

where c is the natural (self) damping coefficient of the system and C is an assumed linear damping due to an external load. Although the cylinder experiments were conducted without an external load, we introduce this damping here for the purpose of estimating the system power output. 3.1. Maximum theoretical power To estimate the maximum power generated, we assume zero natural damping (c0 ¼0) and that the pendulum is driven by a sinusoidal lateral forcing function: F L ðtÞ ¼ C L q1 S sinðotÞ,

ð5Þ U 21 ,

where qN is the dynamic pressure 1=2r CL is the lateral-force coefficient and S is the cylinder projected area d  h. Dividing by ML2, Eq. (4) can now be written in the form:

y€ þ2zl on y_ þ on 2 y ¼

C L q1 S sinðotÞ, ML

ð6Þ

where on ¼2pfn and the load damping ratio is zl ¼(C/L2)/(2Mon). This equation has the well-known solution:

y¼

ðC L q1 S=MLo2n Þsin½ot þ fðoÞ 2

2

½f1ðo=on Þ2 g þ f2zo=on g 1=2

,

ð7Þ

where fðoÞ ¼ tan1 ½2zo=on =½1ðo=on Þ2 . The power produced by the system can be calculated by integration over one cycle thus Z o 2p=o P¼ F L ðtÞLy_ ðtÞdt: ð8Þ 2p 0 By forcing at the natural frequency (o ¼ on), we can show that P¼

r 8

C L on DU 21 As ,

ð9Þ

where As is the area swept by the cylinder, namely As ¼ 2hLymax . Finally, we can write the power coefficient: CP 

P 1=2rU 31 As

¼

p CL 2 Un

,

ð10Þ

where the reduced velocity Un ¼UN/fnd. Providing that we do not violate the linear assumptions, the peak power coefficient is only limited by the lateral force coefficient and reduced velocity. Methods for exploiting these parameters are discussed in Section 8. This should be contrasted with the maximum power coefficient of 16/27 (Betz limit) attainable by an open wind turbine.

D. Greenblatt et al. / Journal of Fluids and Structures 34 (2012) 170–189

175

3.2. Natural system damping The natural system damping was determined by setting a particular flow velocity in the range 4 m/srUN r10 m/s and then releasing the cylinder from its maximum deflection angle (y0 E27.51). The recorded centroid locations were used to determine y(t). In order to estimate the natural system damping, Eq. (4) was used in the form:

y€ þ 2zon y_ þ on 2 y ¼ 0,

ð11Þ

with the natural damping ratio z ¼c0 /(2Mon). The damping coefficient and drag on the cylinder were estimated in the following manner. Based on the velocity vectors shown in Fig. 3, consider the velocity relative to the cylinder, namely V 2rel ¼ U 21 þðLy_ Þ2 ,

ð12Þ

and the relative drag coefficient, defined as C D,rel ¼

F D,rel 1=2rV 2rel dh

,

ð13Þ

where FD,rel is the drag force acting on the cylinder parallel to Vrel. Hence the force acting to damp the oscillations, i.e. opposing the motion of the cylinder is F nd ¼ 1=2rV 2rel dhC D,rel sine,

ð14Þ

where sine ¼ ðLy_ Þ=V rel . If we assume small angles e ðLy_ max 5 U 1 , see below for validation of this assumption), then UN EVrel, CD E CD,rel and hence the natural damping moment can be written as F nd L ¼ 1=2rU 1 dhC D L2 y_ :

ð15Þ

Consequently, the damping coefficient: c0 ¼ 1=2rC D dhU 1 ,

ð16Þ

and the damping ratio:

z¼

rC D dhU 1 : 4M on

ð17Þ

Note that under these assumptions, the damping ratio is a linear function of the free-stream velocity. Eq. (11) is simply an unforced single degree-of-freedom system. For cases where 0o z o1 Eq. (11) has the well-known solution:

yðtÞ ¼ ezon t ðA cosðod tÞ þB sinðod tÞÞ,

ð18Þ qffiffiffiffiffiffiffiffiffiffiffiffi 2 _ where od ¼ on 1z . By applying the initial conditions y ¼ y0 and y ¼ 0, we get that A ¼ y0 and B ¼ zony0/od. To find the remaining parameters, we write the equation for the angular peaks, namely

yðtÞ ¼ y0 ezon t ,

ð19Þ

take logarithms and perform linear least-squares curve fitting to obtain on, od and z. This procedure was followed for UN ¼4, 6, 8 and 10 m/s and the individual experiments, together with the theoretical curves are shown in Fig. 4. To obtain representative values, each experiment was performed 20 times and the data was averaged. Two sets of calculations were performed: one with all contributions to the moment of inertia I discussed in Section 3 (full geometry); and the other with I¼ML2 (simplified geometry). For all estimates, the full geometry was used resulting in fd ¼0.78170.006 Hz. Data for the damping ratio as a function of tunnel speed is shown in Fig. 5; error bars representing 95% confidence intervals were typically the same size as the symbols used in the figure. It is evident that our linearizing small angle assumption is valid as the damping ratio is clearly a linear function of the tunnel speed. As expected, using the simplified geometry has a small effect on the damping ratio with consistent differences in damping coefficient of less than 3%.

U∞ ε Vrel

Fig. 3. Velocity vectors showing the flow relative to the cylinder as a result of the one-dimensional periodic oscillations.

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D. Greenblatt et al. / Journal of Fluids and Structures 34 (2012) 170–189

θ (°)

U∞=10m/s experimental data U∞=8m/s

curve fit

50°

U∞=6m/s

U∞=4m/s

0

10

20 time (s)

30

40

Fig. 4. Experimental data showing cylinder damping at different wind tunnel speeds together with linear model predictions based on least squares curve fitting.

2.0%

1.5%

ζ 1.0% full geometry simplified geometry

0.5%

0.0% 0

2

4

6 U∞ (m/s)

8

10

12

Fig. 5. Natural damping coefficient as a function of wind tunnel speed based on the linear approximation assumed here.

With the damping ratio estimated as a function of the tunnel speed, the drag coefficient was estimated from Eq. (17) and the data are shown in Fig. 6 as a function of Re. For the full geometry, the CD varies between 0.67 and 0.85 with the general trend of increasing with Reynolds number. These values are less than those for an infinite cylinder at subcritical conditions where CD E1.2 (e.g. Schlichting, 1979) and consistent with those reported in the literature. For example, with two free ends the drag coefficient decreases to the range 0.65–0.85 as a result of ‘‘venting’’ of the near wake, thereby increasing the back pressure (e.g. Wieselsberger, 1922; Zdravkovich et al., 1989). Similar observations were made on cylinders with one free end, as shown in the summary table of Baban and So (1991) and in the recent investigation of Iungo et al. (2012). In the present investigation we anticipate that the error reduces with free-stream velocity for two reasons. Firstly, as UN increases from 4 m/s to 10 m/s, the assumed small angle e reduces from 141 to 61. Secondly, the decreasing ratio Ly_ max =U 1 increases the validity of the implicitly assumed quasi-steady assumption. 4. Parametric study of static loads The objective of this section was to determine the static lateral-force coefficients as a function of the plasma control parameters. As in the previous section, experiments were performed at wind tunnel speeds UN between 4 m/s and 10 m/s, corresponding to reduced velocities Un ¼UN/fnd of 33–84 respectively. The frequencies corresponding to the Strouhal

D. Greenblatt et al. / Journal of Fluids and Structures 34 (2012) 170–189

177

1 0.8

CD

0.6 0.4

full geometry simplified geometry

0.2 0 20000

40000

60000 Re

80000

100000

Fig. 6. Drag coefficient estimation based on the natural damping coefficient of the linearized model.

number associated with vortex shedding, namely St fvd/UN 0.2 on a two-dimensional cylinder of these dimensions, are approximately 5.3 Hz–13.3 Hz. This system was designed in such a way that vortex induced vibrations would not play a significant role because (a) the range of vortex two-dimensional shedding frequencies was at least 6 times higher than the system natural frequency (0.790 Hz) and (b) the aspect ratio of the cylinder (h/d¼1.33) was smaller than the minimum (h/d¼2) for which quasi-periodic vortex shedding was observed by Zdravkovich et al. (1989). Static load experiments were performed by initiating the plasma and then recording the deflection angle as a function of time. As expected, the unloaded system, subjected to a constant lateral-force approximating a ramp function, behaved qualitatively like an under-damped second-order linear system. Sufficient time was allowed until the oscillations had decayed to a negligible amplitude. Following this, a sufficiently long time average was performed to determine the mean deflection angle, formally: Z 1 T y ¼ lim yðtÞdt: ð20Þ T-1 T 0 For practical purposes the following two conditions were enforced: T b 1=f n and T b 1=f v , such that T was also typically between 30 s and 60 s. The angles were calculated with respect to the un-deflected zero-angle (y0  01; see Fig. 1(a)) with no control of the boundary layer, determined by taking a long time average with no actuation. With the mean deflection angle so determined, the lateral-force FL acting on the cylinder was calculated using a simple static moment balance, thus   F L ¼ g siny ml=2 þML =L: ð21Þ The lateral-force coefficient was calculated by conventional non-dimensionalization: CL ¼

FL 1=2 rU 21 dh

,

ð22Þ

as discussed in the previous section. Perturbations were introduced in 101 increments as described in Section 2 for the range 301r af r1201. The greatest effect was observed when the perturbations were introduced close to the separation angle (see below). An example of lateral-force coefficient data as a function of reduced frequency F þ is shown in Fig. 7 for af ¼601, 701 and 801 with a plasma ionization frequency fion ¼10 kHz and DC ¼10%. As a general rule, the introduction of perturbations in the vicinity of the separation line (af E 701) shows a marked effect on the lateral-forces. It has been shown previously that amplification of the perturbations is rooted in the Kelvin–Helmholtz instability mechanism associated with the separating shear layer (e.g. Greenblatt and Wygnanski, 2000). When perturbations are introduced slightly upstream of the separation point, namely af ¼601, the perturbation amplitude decays initially because there is no perturbation amplification mechanism. Although the perturbations decay somewhat, they still have a significant effect on the separating shear layer and hence the lateral-force. With the perturbations introduced just downstream of the separation point (af ¼801) the lateral-force is maximized for all reduced frequencies considered. In general, the optimum F þ is between 1 and 2 and at F þ 42 the effectiveness decreases; the rate at which effectiveness decreases depends upon the actuation location. When the perturbations were introduced at a relatively large angle downstream of separation, namely af ¼901, no significant lateral-force was recorded. Repeat experiments conducted at fion ¼20 kHz produced similar results to those shown in Fig. 7. These data are consistent with the observations of Thomas et al. (2008) who studied separation control on twodimensional subcritical cylinder flows using both pulsed and non-pulsed DBD actuation. They observed that simultaneous application of forcing on both sides of the cylinder eliminated vortex shedding and the wake turbulence levels decreased significantly. Furthermore, they determined that forcing at F þ ¼1 was most effective in achieving these objectives. In a similar study, Jukes and Choi (2009) recorded more than 70% reduction in lift fluctuations with a 32% drag reduction at F þ ¼2 and Cm ¼0.32%. They observed narrowing of the wake as the perturbations promoted rolling-up of the shear-layer at

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0.8

0.6 CL 0.4

αf = 60° αf = 70° αf = 80°

0.2

0 0.1

1 F+

10

Fig. 7. Example of lateral-force coefficient data as a function of reduced frequency for different DBD plasma forcing angles (Re ¼ 80 000; Cm ¼0.17%, and DC ¼ 10%).

0.8

0.6 CL

0.4

fion=10kHz fion=20kHz

0.2

0 0.0001

0.001

0.01 DC

0.1

1

Fig. 8. Example of lateral-force coefficient data as a function of duty cycle. af ¼ 701, F þ ¼1.0 and Re ¼ 80 000.

the forcing frequency, but with no effect on the opposite side of the wake. Considering the similar values of F þ for these investigations, as compared to the present one, it is reasonable to assume that similar mechanisms are present in this investigation. An investigation of separation control on airfoils showed that duty cycles between 1% and 50% had similar effect in the lift force coefficients (Greenblatt et al., 2008). With perturbations introduced close to the separation angle a similar result was observed here. Fig. 8 illustrates that there is very little difference in lateral-force coefficient for the range 0.1%–50%. In the context of energy generation this result is important because the measured power input was seen to be linearly dependent on duty cycle. Calibration of the actuator at DC ¼100% described in Section 2 showed that at 10 kHz, exciting the actuators at 8 kVpp consumed Pin ¼75 W/m. On the cylinder of height 150 mm, this reduced proportionately to 11.25 W. Exciting the actuator at DC ¼0.1% thus required only 11.25 mW. For energy generation, two actuators are used alternately (see Section 7) and therefore not pulsed continuously. Furthermore, each actuator is typically operated for a time period oTex/2 (see Fig. 2(b); also see Section 7 and Fig. 18 below). Hence the total actuator Pin can be reduced to approximately 5 mW for the present setup. This observation served as a major motivating factor for using plasma actuators in the present investigation as it was a negligible fraction of the power produced by the system. 5. Particle image velocimetry measurements Flowfield measurements were conducted using PIV, as described in Section 2, where the pivot was fixed to prevent transverse motion of the cylinder. The absolute velocity c ¼(u2 þv2)1/2 together with velocity vectors and the nondimensional vorticity oz are shown for the baseline case (Fig. 9(a) and (b)) and the F þ ¼2.1, DC ¼10% and Cm ¼ 0.17% case (Fig. 10(a) and (b)). Based on these data, the baseline separation point was estimated to be a E801, which is similar to that observed on a two-dimensional cylinder (Jukes and Choi, 2009). With control applied the separation location moves aft on

D. Greenblatt et al. / Journal of Fluids and Structures 34 (2012) 170–189

179

Fig. 9. PIV flowfield measurements at the cylinder center-span for the baseline case at Re ¼80 000: (a) absolute velocity c¼ (u2 þ v2)1/2 and (b) spanwise vorticity oz.

Fig. 10. PIV flowfield measurements at the cylinder center-span for the F þ ¼2.1, DC ¼ 10%, and Cm ¼ 0.17% case at Re ¼80 000: (a) absolute velocity c ¼(u2 þ v2)1/2 and (b) spanwise vorticity oz.

the cylinder to a E1201. Additional PIV data acquired at F þ ¼1 showed qualitatively similar results to those in Fig. 10 (not shown); this was anticipated due to the similarity in the lateral-force measurements shown in Fig. 7. The relative insensitivity of the wake on the opposite side of the cylinder reported by Jukes and Choi (2009) was also observed here at the cylinder center-span as seen when comparing Figs. 9(b) and 10(b). Phase-resolved data during the attachment transient at F þ ¼2.1 is shown in Fig. 11(a)–(h), where data were acquired corresponding to the leading-edge of each plasma-pulse and phase-averaged (see definitions in Fig. 2(a) and (b)). The figure shows absolute velocity and vorticity for the cycles 1, 2, 4 and 6 following initiation of the perturbations. After one cycle of the perturbation (Fig. 11(a) and (b)) the separated shear layer is severed and a distinct rolled-up vortex is clearly visible in the wake. Moreover, the upstream shear layer close to the cylinder is deflected towards the cylinder surface. Thus we can conclude that within one cycle, or one dimensionless time unit (1/F þ ), there is already a meaningful change to the load on the cylinder. After 2 perturbation cycles (Fig. 11(c) and (d)), the vortex generated after one cycle is shed into the wake and a new vortex generated by the second plasma pulse is visible close to the cylinder surface. The upstream shear layer is also deflected closer to the cylinder surface. After 4 and 6 cycles, respectively, the flowfield changes are small with the vortex generated during the previous cycle moving closer to the surface as does the upstream shear layer. Data acquired after 6 cycles showed relatively small variation in the flowfield. The main change was an elongation of the downstream vortex and its merging with the upstream shear layer (see Fig. 12(a) and (b) shown after 20 cycles). Hence, under these forcing conditions, it was concluded that the attachment process occurs over the dimensional time tatt  TattUN/D E7/F þ , namely tatt E3.3.

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Fig. 11. Phase-averaged transient flowfield measurements at the cylinder center-span following initiation of the perturbations: (a) and (b) at Tp; (c) and (d) at 2Tp; (e) and (f) at 4Tp; (g) and (h) at 6Tp. Control conditions as in Figs 10(a) and (b).

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181

Fig. 12. Phase-averaged transient flowfield measurements at the cylinder center-span at, and following, termination of the perturbations: (a) and (b) correspond to the final pulse; (c) and (d) at 6Tp; (e) and (f) at 12Tp; (g) and (h) at 18Tp. Control conditions as in Figs 10(a) and (b).

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The transient separation process (Fig. 12(a)–(h)) was studied by terminating the forcing but still acquiring data locked to the forcing cycle frequency as done above in Fig. 11. The first data set (Fig. 12(a) and (b)) corresponds to 22 forcing cycles after initiation of the perturbations; after the 22nd perturbation the forcing was terminated. It was observed that the separation process was much slower than the attachment process. For example, after the equivalent of six cycles subsequent to termination of the perturbations (Fig. 12(c) and (d)), the shear layer is observed to be only slightly deflected away from the cylinder as compared to that prior to termination in Fig. 12(a) and (b). After another 6 cycles, the shear layer continues its rather gradual transient deflection away from the surface. After another 6 cycles, the shear layer approximates that of the fully separated flow, is not fully separated as can be seen by comparing it to Fig. 9(a) and (b). Under these conditions, we can conclude that the separation process occurs over the dimensionless time tsep TsepUN/D 418/F þ , namely tsep 48.6. 6. Flow-control-induced vibrations To demonstrate the use of separation control to drive the system, the pulsed plasma actuator was modulated at the excitation frequency fex. This was achieved by periodically initiating and terminating the actuators for particular pulsed frequencies F þ  fpd/UN, where fex 5fp. All experiments were initiated with the cylinder in its baseline uncontrolled state with y ¼ 01. After initiation of the modulated forcing, sufficient time was allowed for the transient behavior to decay. Instantaneous deflection angle data y(t) for F þ ¼0.9 and DC¼1% at different excitation frequencies, non-dimensionalized by the system natural frequency, are shown in Fig. 13. The data show that the response resembles that of a lightly damped second-order system. Namely, when forcing at fex/fn o1 and fex/fn 41 the response amplitudes are relatively small. However, as fex-fn the amplitude increases significantly. For the most part, the oscillations are either stationary or nearlystationary. It should be noted, however, that the amplitudes are relatively large, namely ymax r271 and a description of the system on the basis of a linear approximation may be something of an oversimplification. A summary of the amplitudes expressed as the root-mean-square is shown in Fig. 14. Here data for Re ¼40 000 and 80 000 at F þ ¼0.9 and 5.0 and are presented on the same system of axes. The Re ¼40 000 data in the range 0.95ofex/fn o1.05 correspond to the instantaneous y(t) data shown in Fig. 13. At this Reynolds number the response of the system can be clearly discerned and large amplitudes are achieved over a rather narrow range of fex/fn. At the higher Reynolds number of 80 000, the range of large amplitude oscillations increased significantly. This result was not unexpected as the aerodynamic lateral-forces increase by a factor of 4 with a doubling of the tunnel speed. Hence high oscillation amplitudes can be achieved at frequencies considerably different from fn. However, at the higher Reynolds number, there is no clearly discernible peak due to data missing in the region of high amplitudes that extends between approximately 0.95 o fex/fn o1.1. The reason for this was that the cylinder was limited in its motion by the wind tunnel walls. Specifically, the cylinder struck the wind tunnel wall on its actuated side and this limited the peak amplitude that could be estimated. This region of expected high-amplitude oscillation is indicated on the figure. Apart from the limited test section size, there does not appear to be any other factor limiting the amplitude of the oscillations. It is expected that even when the amplitudes well exceed the limits of the linear approximation there is no inherent fluid-structure-related phenomenon that would limit the oscillation amplitudes. This, however, would result in significantly non-linear behavior, perhaps even causing the pendulum to rotate, and is outside of the scope of our present objectives. It is evident, therefore, that flow-control-induced oscillations are fundamentally different from well-known vortex-induced vibrations because here forcing decouples the fluid behavior from the cylinder dynamics. For VIV, where the flow-induced vibrations are coupled with that of a nominally two-dimensional cylinder, the system attains maximum

40°

baseline fex/fn=0.878 fex/fn=0.909

θ (°)

fex/fn=0.943 fex/fn=0.979 fex/fn=1.019 fex/fn=1.040 fex/fn=1.061 fex/fn=1.108 0

10

20

30

40

50

60

time (s) Fig. 13. Examples of cylinder oscillation amplitudes as a function of time for modulation at excitation frequency fex in the vicinity of the natural frequency fn (Re ¼40 000, F þ ¼ 0.9 and DC ¼1%).

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183

motion limited by wall

20

Re=40,000, F+ = 0.9

16

Re=80,000, F+ = 0.9

θrms(°)

Re=40,000, F+ = 5.0 Re=80,000, F+ = 5.0

12 8 4 0 0.4

0.6

0.8

1 fex/fn

1.2

1.4

1.6

Fig. 14. Examples of system frequency response for selected modulation excitation frequencies fex/fn.

amplitude in the limit of zero system damping (Griffin, 1980; Klamo et al., 2005, Skop and Griffin, 1975). The ability to vary oscillation amplitudes by means of flow control, at frequencies totally unrelated to the vortex shedding frequency, opens new opportunities for fundamental studies and engineering applications. For example, the large amplitude oscillation, together with the external excitation of the system, may render this concept suitable for wind energy generation. 7. System performance estimates 7.1. Estimation of transient loads This section is concerned with modeling the transient variation of the lateral-force FL(t) during the process of attachment and separation. In Section 7.2, the transient attachment and separation processes are combined to produce a system forcing model. In particular, we are interested in measuring the time-scale associated with the attachment and separation processes. Once these transient processes are characterized the full forcing function can be modeled. Darabi and Wygnanski (2004a, 2004b) studied the attachment and separation processes of a fully turbulent boundary layer over a straight deflected flap of length Lf by initiating and terminating periodic sinusoidal perturbations. They determined that the minimum time-scales of the attachment and separation processes (Tatt and Tsep) were comparable with 15rTUN/ Lf r20. However, the time-scales were significantly affected by the input parameters, namely the reduced frequency and amplitude initiated to force attachment and terminated to force separation. In this investigation, the plasma actuation was initiated at t ¼0 and then the dynamic response of the system was measured. The system was modeled using an autoregressive model (see Ljung, 1987) that provides as output the damping coefficient and natural frequency ( z and on), but requires a model of the input function FL(t). The autoregressive model is one of a group of linear prediction formulas that attempt to predict an output of a system based on the input and previous outputs. The system is described at sample times kDT as a recursive difference equation, so that the output y(t ¼kDT) is computed as a linear combination of past outputs and past inputs:

yk ¼ a1 yk1 a2 yk2     ana ykna þ b0 F k þ b1 F k1 þ    þ bnb F knb :

ð23Þ

Here yk and Fk are the output and input respectively at t ¼kDT. The system identification problem consists of choosing the appropriate model structure (order of polynomials na, nb) and estimating the parameters (coefficients ai, bi) in (23). By defining s ¼ [a1,a2,...,ana,b0,b1,...,bnb]T we can rewrite (23) as the equation y ¼As, where y is a vector of present output measurements and A is a matrix of past output and input measurements. An initial estimation for s is achieved using least squares, then by performing an iterative technique (based on the truncated Taylor series) we get the optimal set of parameters s. Initial trials were performed using a ramp function described below: ( t F T att , 0 r t oT att : ð24Þ F L ðtÞ ¼ F, t ZT att The two parameters F and Tatt were varied systematically until the differences between the model and the data (rms error E) were minimized, namely " min½E ¼ min

# 9ymod,rms ydata,rms 9 : 9ydata,rms 9

ð25Þ

D. Greenblatt et al. / Journal of Fluids and Structures 34 (2012) 170–189

forcing amplitude F (N)

184

1.20

35

1.12

30 25

1.04

20

0.96

15

0.88 10

0.80 5

0.72 50

100

150 time (ms)

200

250

rms error (%)

Fig. 15. Error plot (E) for the arbitrary forcing amplitude F versus Tatt showing the results of the iterative process.

0.25

0.2

θ (rad)

0.15

data

data

model

model

error

error

0.1

0.05

0 0

0.5

1

1.5

2

0

0.5

time (s)

1

1.5

2

time (s)

0.25

0.2

θ (rad)

0.15

data

data

model

model

error

error

0.1

0.05

0 0

0.5

1 time (s)

1.5

2

0

0.5

1

1.5

2

time (s)

Fig. 16. Plots of the measured and modeled angular deflection following initiation of actuation. Modeled parameters: (a) F ¼ 0.8 N, Tatt ¼ 167 ms; (b) F ¼ 0.973 N, Tatt ¼ 167 ms; (c) F ¼ 0.8 N, Tatt ¼ 70 ms; (d) F ¼ 0.973 N, Tatt ¼ 70 ms.

The results of a typical iteration cycle are shown in Fig. 15 which illustrates that the combination of F ¼0.973 N and Tatt ¼70 ms produces the smallest error with E¼1.9%. The error plot can be best understood by considering the model results presented in Fig. 16(a)–(d), where a direct comparison of the model and the experimental data are shown for different combinations of parameters F and Tatt. As shown in Fig. 16(a) the combination of both the parameters F¼0.8 N

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185

and Tatt ¼167 ms produces relatively large errors caused by both parameters (E¼ 24%); in Fig. 16(b) the main contributor to the error is the attachment time Tatt ¼167 ms (E¼13%); in Fig. 16(c) the error is caused primarily by the amplitude F ¼0.8 N (E¼18%); while the minimum error is produced by the parameter combination shown in Fig. 16(d) (E¼1.9%). Attempts were made to further reduce the errors and hence the parameter estimates by modeling the F(t) with higher order polynomials. However, these attempts did not yield significantly different estimates of F and Tatt. The same procedure was performed multiple times for each case and for a variety of data sets, where reduced frequency and duty cycle were systematically varied. The identical algorithm was also applied to the separation process. Here the ramp function took the form: ( Fð1t=T sep Þ, 0 r t oT sep F L ðtÞ ¼ , ð26Þ 0, t Z T sep and the minimum error associated with F and Tsep was obtained in the identical manner to that described above (see Eq. (25)). A summary of the time-scales associated with attachment and separation are shown in dimensionless form, namely tatt TattUN/D and tsep TsepUN/D in Fig. 17. The statistical uncertainty based on averages of multiple experiments (95% confidence interval) is shown for all data points. For the range of parameters considered here, the attachment process is faster than the separation process where tatt o7 while tsep 48. These measurements are fully consistent with the PIV measurements presented above in Section 5, where it was observed that at F þ ¼2.1 and DC¼10%, tatt E3.8 and tsep 48.6. These results are also consistent with the observations of Darabi and Wygnanski (2004a, 2004b). 7.2. Piecewise continuous model With the attachment and separation time-scales determined, a simple piecewise forcing model was developed. This is shown by way of example for the excitation cycle Tex of the cylinder as shown in Fig. 18. Here it was assumed that the cylinder was equipped with two actuators. The forcing functions of actuators 1 and 2 are shown for positive and negative values respectively, corresponding to alternating sides of the cylinder. It is also assumed that actuation on one side of the cylinder does not affect that on the other side, which is a reasonable assumption based on the PIV data presented in Section 5. At t ¼0, actuator 1 is initiated for the duration 0 rt rT1, where T1 ZTatt,1, namely the time taken for the flow on the side of actuator 1 to attach. At t 4T1, actuation is terminated and the flow on the side of actuator 1 separates over the time-scale Tsep,1. At t¼ T1 þTsep,1, actuator 2 is initiated for the duration T2. As with the flow on the side of actuator 1, the time taken for the flow on the side of actuator 2 is Tatt,2. Then, with actuator 2 terminated at t ¼T1 þTsep,1 þT2, the flow on the side of actuator 2 separates over the time-scale Tsep,2 and the forcing cycle is repeated. The forcing function shown in Fig. 18 can be represented by the Fourier series: FðtÞ ¼

1 X

½An sinðn2pf ex tÞ þBn cosðn2pf ex tÞ:

ð27Þ

n¼1

Note that the function is not even and we must include the cosine terms. Evaluating the coefficients indicated that the amplitude of the fundamental forcing frequency was significantly larger than the harmonics. The largest harmonic was A3/A1 ¼0.1 with the remaining An and Bn significantly smaller. Given the relatively small harmonics and the simplification associated with the piecewise forcing function shown in Fig. 18, the assumption of sinusoidal forcing as discussed in Section 3 is justified. Furthermore, if we assume that the natural damping is small (z 5 1, as shown in Section 3.2) with the

14 12 10

DC=10%, attachment DC=30%, attachment DC=10%, separation DC=30%, separation

8 τ 6 4 2 0 0

1

2

3

4

5

F+ Fig. 17. Summary of tatt and tsep data as a function of F þ for two duty cycles.

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Normaized Forcing Function

Tex 1 0.5 0 Tatt,1 -0.5

Tsep,1

T1

-1

Tatt,2 0

0.25

0.5

Tsep,2

T2

0.75 time (s)

1

1.25

Fig. 18. Assumed piecewise forcing function where forcing corresponding to actuators 1 and 2 are represented are represented by positive and negative values respectively.

Table 1 Predicted power coefficient/absolute power (mW) as a function of maximum lateral force coefficient and wind speed for the present system. CL

0.6 0.7 0.8 0.9

Wind Speed UN(m/s) 4

6

8

10

0.028/83 0.033/97 0.037/110 0.042/124

0.019/186 0.022/217 0.025/248 0.028/279

0.014/331 0.016/386 0.019/441 0.021/496

0.011/517 0.013/603 0.015/689 0.017/776

system load zl b z, then we can use the analysis of Section 3 to estimate the power coefficients. Based on the system dimensions considered here, the power coefficients (see Eq. (10)) and power (in mW) for different wind speeds and lateralforce coefficients are shown in Table 1. The largest value, for UN ¼4 m/s and CL ¼0.9, namely 0.042, is an order of magnitude less than that of a typical wind turbine. Hence, at these small scales, the present concept does not appear to be viable as an alternative to conventional wind turbines. It should also be noted that, although the absolute power produced here is small, between 83 mW and 776 mW, it is still relatively large compared to the plasma input power possible of  5 mW (see Section 3). 8. Viability for wind energy generation This paper was aimed at demonstrating the concept of flow-control-induced vibrations for the purposes of wind energy generation. As noted in the previous section, however, the maximum power coefficients anticipated are one order of magnitude less than those of a modern wind turbine. Within the limitations of the linear model developed in Section 3, and the resulting expression for CP presented in Eq. (10), we consider here a number of different techniques that could conceivably be used to render the present concept viable for medium- to large-scale wind energy generation. In particular, there are three independent methods of increasing the power coefficient: by increasing the maximum lateral force coefficient, by increasing the system natural frequency and by increasing the cylinder diameter. Lateral forces could in principle be increased using a more effective form of boundary layer control as discussed below in Section 8.1. On the other hand, the natural frequency and cylinder diameter would involve changes to the system geometry and this is discussed in Section 8.2. 8.1. Methods of boundary layer control As mentioned above, lateral force coefficients on the cylinder can be increased using a more effective form of boundary layer control (BLC). Obviously, the gain in power must exceed the power used to drive the BLC system. The lowest power systems are typically boundary layer trips, flaps or spoilers, because these generally require power input only during deployment. For example, Naim et al. (2007) showed that a passive boundary layer trip could produce two-dimensional lift coefficient Cl variations of 0.81, while Low et al. (1991) used a passive flap to produce Cl E1.05 (see Table 2). Significant lateral force coefficients can be produced by energizing the boundary layer using zero net mass-flux slot blowing (e.g. Amitay et al., 1998; Naim et al., 2007) with Cl E1 (see Table 2). These lateral loads, however, did not show a

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187

Table 2 Summary of typical lateral force and drag force (where reported) coefficients measured on two-dimensional circular cylinders using passive and active means. Investigator

Method

Control parameter

CL

D CD

Low et al. (1991) Naim et al. (2007) Amitay et al. (1998) Naim et al. (2007) Dunham (1968) Low et al. (1991)

Flap/spoiler Passive trip Normal ZMF blowing Tangential ZMF blowing Steady slot blowing Flap plus steady suction

– – Cm ¼0.0006 Cm ¼0.092 Cm ¼0.56 CQ ¼ 0.20

1.05 0.81 0.95 1.25 7.9 5.65

0.95 0.52 0.26 0.6 – 1.3

significant benefit over the DBD plasma actuators employed here. In addition, their net benefit was difficult to assess because the power supplied to the zero mass flux actuators was not reported. In contrast, relatively large lateral force coefficients can be obtained on circular cylinders when subjected to steady slot blowing or surface suction. In the case of steady slot blowing, Cl E7.9 can be obtained with momentum coefficients Cm E0.56. Low et al. (1991) combined a flap with a porous suction surface to produce Cl E5.65 with CQ EQ/dUN ¼ 0.2 where Q is the air volumetric flowrate. From these investigations, it appears that steady slot blowing or porous suction, or a combination of the two, could increase the power coefficient by an order of magnitude. However, the power required to drive these systems, relative to the power gain, would be critical in determining if these methods were aerodynamically viable. Such an assessment is beyond the scope of this paper.

8.2. Effect of system scaling In this section, we consider increasing the power coefficient by increasing the natural frequency or the cylinder diameter. A common method for increasing natural frequency is to add a spring to the system, but this solution is outside of our relatively simple analysis. Consider, however, scaling-up the entire system linearly, namely increasing its dimensions such that the ratios d/L¼0.38 and d/h¼0.74 are maintained constant. We consider here a factor of 10 geometric up-scaling as a basis for our discussion (d¼1.5 m, h¼2.04 m and l ¼2.92 m), resulting in dimensions that are typical of a small kW-rated wind turbine. The motivation for up-scaling the system can be shown by substituting the equation for the system natural frequency of Eq. (2) into the power coefficient expression of Eq. (10). Maintaining geometric similarity d/L¼0.38, the power coefficient can be written as sffiffiffiffiffiffiffiffi gL C P ¼ 0:095C L : U 21

ð28Þ

Assuming no changes to the maximum lateral-force and wind speed, it is evident that the power coefficient increases with L1/2. Hence the 10 fold increase in linear dimensions increases the power coefficient by more than 3, resulting in a maximum Cp E0.13 (see Table 1). Although this is a positive result and serves as a motivator for increasing the diameter in particular, it should be noted that Cp decreases with increasing UN. Furthermore, with this geometric modification alone, the power coefficient still falls far short of values typically encountered on modern wind turbines, of approximately 0.45. Furthermore, although this may seem like an elementary scaling problem, there are a number of important differences that must be taken into account. The first aspect is that the linear approximation detailed in Section 3 will be questionable because the larger dimensions result in Ly_ max =U 1 ¼ 1:7. This will result in a component normal to the lateral-force in the wind direction that will increase the natural damping and thereby act to decrease the idealized power coefficient results expressed in Eq. (10). An additional aspect to consider is the Reynolds number. For example, at a mean wind speed of 5 m/ s, the Reynolds number on the cylinder will be approximately 500 000 and therefore supercritical. With supercritical flows the separation angle moves aft on the cylinder and it is not certain that DBD plasma actuators will have the same effect on the lateral-forces when forcing the fully turbulent separation. This limitation might be overcome by enforcing separation, for example using flaps or spoilers as discussed in Section 8.1, rather than attempting to control turbulent boundary layer separation. Similarly, the combined effect of up-scaling the system as described here, and the introduction of BLC using suction or blowing, may render this concept viable for larger-scale wind energy generation. Finally, it can be seen from Table 2, that passive and active flow control techniques result in changes to the drag coefficient. The variations in drag coefficient could conceivably be exploited by adding a second degree-of-freedom, namely allowing the system to oscillate in the streamwise direction. Hence the periodic variations in the drag force resulting from the actuation could also be used to generate power. Characterization of such a system would require a nonlinear two degree-of-freedom model and such an analysis is beyond the scope of the present paper.

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9. Concluding remarks This paper described a novel approach to wind energy generation by means of flow-control-induced vibrations. The concept was demonstrated experimentally using a one-degree-of-freedom pivoted cylindrical bob, mounted vertically in a wind tunnel. DBD plasma actuators were used to periodically control separation at subcritical Reynolds numbers. The effectiveness of the actuators, together with their energy efficiency at low duty cycles and ease of application, rendered them ideal for the present investigation. The power developed by the system was estimated by means of a linear secondorder model. Static load and flowfield measurements were consistent with published data near the cylinder centerline and the parameters found to be effective in two dimensional geometries were also effective on the low aspect ratio cylinder. Periodic loading of the cylinder was achieved by periodic modulation of the actuator in an open-loop manner. As expected, large amplitude oscillations were observed when the modulation frequency was close to the system natural frequency. In contrast to natural vortex induced vibration, the large amplitude oscillations were achieved by alternating dynamic separation and attachment of the boundary layer. Estimation of the transient loads was performed using a system identification technique and the power generated by the system was estimated on the basis of a piecewise linear model. Although the power coefficients were relatively small compared to conventional wind turbines, increasing the maximum lateral force coefficients, increasing the system natural frequency and increasing the cylinder diameter were identified as methods that could result in improvements. Future research should focus on effective and efficient forms of boundary layer control and system up-scaling. Future research should also consider nonlinear modeling of the system and the effects of Reynolds number because the linear-model assumptions invoked here are violated with up-scaling and the flow over the cylinder will be supercritical.

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