AIAA-2004-2321

Open-Loop Control of the Disk Wake with Electro-magnetic Actuators

Hiroshi Higuchi* Syracuse University, Syracuse, NY, 13244 U.S.A.

Satoshi Ide†, Jinhao Qiu‡ and Junji Tani§

Tohoku University, Sendai, 980, Japan

ABSTRACT

This experimental investigation addresses the open-loop control of the immediate wake behind a disk in subsonic flow. The disk edge had tabs that were driven radially using electro-magnetic actuators at specified frequency and relative phase. Tabs retracted flush with the disk edge and protruded 2% of the disk diameter when extended. Even with small amplitude of tab motion, significant reduction of the size of the near wake was achieved with both symmetrical and helical modes of excitations. The effective excitation frequency was corresponded to antisymmetric mode at natural frequency. The effects on the base pressure, the shear layer vorticity and turbulence, as well as the mean velocity vector profiles from the PIV measurements are presented.

I. Introduction ake behind some axisymmetric bluff-bodies with continuous surface such as a sphere may be controlled by modifying the boundary-layer transition and separation. For two-dimensional wake, Amitay et al.1 used a

synthetic jet to modify the surface pressure gradient to control flow separation from a circular cylinder. Practical examples of passive controls of the three-dimensional wake include roughness and seams on sports balls (see, e.g., Ref. 2.) Kiura and Higuchi3 examined in detail the effect of the baseball seam on the boundary layer separation as related to the knuckle-ball side-force variations. The boundary layer on the sphere may be actively controlled; Park et al.4 have achieved reduction of reverse flow region behind a sphere with actuators. An alternative to controlling the separating shear layer is a base bleed. Also for a sharp-edged disk, passive control of the disk wake has been established by adding porosity (Cannon5, Higuchi et al.6). However, the solid disk has a fixed separation line, which is not directly affected by the boundary layer manipulation, and thus the flow configuration poses a different challenge. Higuchi and Balligand7,8 demonstrated the establishment of the 3D wake behind a disk started from rest. The onset of the 3D wake structure was enhanced behind polygonal plates such as hexagon9. As for the active control of the disk wake, Berger et al.10 oscillated the disk itself in a nutation mode resulting in an enhanced helical mode. This nutation may be regarded as time-dependent control of separation line. In the present experiment, the disk model is equipped with moveable edge (i.e., tabs) that is oscillated by the electro-magnetic actuators. The aim of the present study was to ascertain whether the already separating shear layer itself may be manipulated in this manner. The multiple actuators can be moved simultaneously or in various sequences at different frequencies. The earlier hot wire results of the present study were first reported by Higuchi et al.11. The present paper integrates and

e earlier findings and includes detailed measurements using the PIV.

W

expands on th

* Professor, Department of Mechanical and Aerospace Engineering, 151 Link Hall, Syracuse, NY 13244, U.S.A, Associate Fellow. † Graduate Student, Institute of Fluid Science, Tohoku University, Sendai, 980, Japan. ‡ Professor, Institute of Fluid Science, Tohoku University, Sendai, 980, Japan. § Professor Emeritus, Institute of Fluid Science, Tohoku University, Sendai, 980, Japan.

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II. Experiment The experiment was conducted in the low speed closed-return wind tunnel with a 0.61mx0.61m test section at

Syracuse University. The disk was 10cm in diameter and 1.5cm in thickness with a beveled edge with downstream face of 9.2cm diameter. Six TDK P1002A electro-magnetic actuators translated 6 equally spaced segments of the disk edge in radial directions at specified frequency and phase. A sketch of the overall model and a photograph showing the actuators within the model are shown in Figs. 1.

The stroke of the actuator was limited to 2 mm, and in the retracted position the moveable segments were flush with the remainder of the disk edge. Analog outputs from a National Instruments D/A signal processor were input to six KEMO #M32 audio power amplifiers. In earlier experiments, a 0.1mm latex film covered the edge of the disk and tabs to maintain smoothly varying geometry. Subsequently the actuators were used without the film because it required more power to the electro-magnet actuator and also because the difference in effects on the flow was negligible. The actuated tab displacement was measured with the laser displacement meter, and the overall operation and phase were checked with a strobe light. Some additional experiment was carried out with the tabs fixed in an extended position as well as in a retracted position.

Figure 1(a). Disk model (Front diameter100mm and rear 92mm)

Figure 1(b). Interior of the diskshowing 6 electro-magnetic actuators

The experiment was carried out in the Reynolds number range between 34,000 and 84,000 based on the disk

diameter. The main part of the results presented below corresponded to a Reynolds number of 67,000 with the nominal free stream velocity 10 m/s. The Reynolds number effect in the present range was minor. The disk was aligned carefully with respect to the free stream direction to assure the good wake axisymmetry. The model was originally supported by piano wires with electrical leads extending from the settling chamber of the wind tunnel, but the support was modified to a streamlined cantilever support upstream of the model for ease of alignment and electrical connection without leaving significant disturbance in the flow.

The velocity measurement was carried out using a DANTEC 2-component Particle Image Velocimetry (PIV) system with a 200mJ double-cavity Nd:YAG laser. Olive oil-based seeding was introduced near the downstream diffuser from a Luskin nozzle seeder. Particle diameter was 5µm in average. The base pressure was monitored using a pressure tap at the center of the base plate connected to a Barotron capacitance-type pressure transducer. Constant-temperature anemometers were also used in the hot-wire measurement to monitor the velocity time histories.

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III. Results Behind the non-actuated stationary disk, the wake exhibited a spectral peak at the Strouhal number 0.15, which

approximately corresponded to the established value for a primary helical structure behind a disk. The number was slightly higher than 0.135 for thin disks reported by Berger et al10 in air and by Balligand8 in water, and the discrepancy is likely due to the geometric difference such as thickness. Though the analysis was for two-dimensional cylinders, Roshko’s analysis correlated the wake width with the shedding frequencies behind various cylinders12.

Phase π/3

Type 0 Type 1 Type 2x+

Type 2x- Type 3 Type 4+-

Phase 2π/3Phase π Phase π/3

Figure 2. Schematic of tab actuation

In the experiment, tabs were actuated nominally at x1, x2, x3 of the above frequency corresponding to m=1

fundamental frequency (e.g., 15Hz, 30 Hz and 45 Hz at 10m/s.) In some cases, the actuation frequency was varied at a finer increment. Figure 4 shows schematically all modes of actuation tested. Most of the experiments, however, were conducted with radially symmetric mode (T1 in the figure) or helical mode (T2),as well as the stationary mode as a control. These modes are termed for the time being T0: no actuation, T1: axisymmetric actuation (m=0 mode), T2: neighboring actuators moving in sequence with π/3 phase in clockwise (-) or counterclockwise (+) direction viewed from downstream (m=1 mode). No clear distinction in results was seen between the - and + cases during the test.

A. Base Pressure The time-averaged base pressure was measured on the rear wall at the center of the disk under various tab

actuation (see Fig. 2). When the base pressure was normalized with the natural wake value (pressure coefficient, Cp=-0.49), its dependency on the excitation frequency is clear as shown in Fig.3. The helical mode of actuation is the most effective at a frequency corresponding to the natural shedding frequency. The direction of helical actuation did not change the results. Berger et al10 observed that the wake was most responsive to the frequency slightly higher than that of the natural frequency, but at present the change was not discernible within the present frequency sweep increment shown.

For the radially symmetric excitation (T1), the change in pressure occurs at twice the frequency of the natural wake, but it is less effective than the helical excitation (T2). In other modes of excitation, the change was almost below the uncertainty of the experiment. Note that the observed decreased base pressure corresponds to the increased drag coefficient as will be further discussed. The base pressure was also monitored when the tabs were held fully extended in a stationary state, but there was no discernible difference from the stationary disk with tabs retracted flush with the disk edge.

B. Velocity Vector Field The velocity field in the immediate wake region was measured with the PIV system. Figure 4(a) shows the

instantaneous velocity vector behind a stationary disk. Aside from some spurious velocity correlations in the original data form, roll-ups of large vortical structure can be clearly seen. Figures 4(b) is a snapshot of the velocity vector field with symmetrical tab actuation. Compared to the natural wake case, the large scale vortices are brought toward

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the center line behind the disk. The instantaneous vorticity plots indicated strong vorticity layer from the disk edge curved toward the rear stagnation point with actuators on.

Figure 3. Base pressure at various actuator excitations

(a) Stationary disk (no excitation) Figure 4. Instantaneous velo

The instantaneous velocity vector fields were ensemble-averag5. The flowfield near the rear stagnation region representing a sareduced-size figures Figs. 5 (a-c), a part of Fig. 2c is reproduced inthe axisymmetric vortex centered near one diameter downstream omodel caused low velocity data immediately below the disk butresults. Zero velocity lines in Fig. 5(d) indicate that the rear stagnupstream by the helical excitation at 30Hz. It is to be noted tunaffected up to 1 diameter downstream of the wake.

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(b) Symmetrical excitation at 30Hz.

city vector field

ed, and the mean velocity fields are shown in Fig. ddle point was clearly depicted. To supplement Fig. 5(e). In addition to the rear stagnation point, f the disk is visible. The shadow cast by the disk

deemed non-critical for present interpretation of ation point of the natural wake is shifted furthest hat the wake width or shear layer curvature is

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(a) Sationary disk (b) Helical excitation 30Hz

(c) Symmetric excitation 30Hz

(e) Close-up of Fig. (c)

Figure 5. Mean

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(d) Comparison of zero velocity (u=0) line

velocity fields

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C. Velocity Fluctuations and Time-Series Analysis

The time-series analysis of the velocity fluctuations was performed with the hot wire data. These particular experiments were conducted earlier in an open test section of the Low Turbulence Wind Tunnel with 0.81m cross section at Tohoku University11. The hot-wire measurements were repeated in the Syracuse tunnel and the overall results remained the same.

The power spectrum density of the axial velocity fluctuation was measured as the hot-wire probe was placed at X/D=2 and traversed in the radial direction. The fundamental frequency corresponding to St=0.15 (15Hz) as noted earlier was evident in the natural wake. With axisymmetric tab excitation (T1), the spectral peak was significantly reduced at 15Hz excitation (Fig. 6a), increased significantly in a wider radial range at twice the natural frequency (30Hz) (Fig. 6b), then reduced when the frequency was tripled (not shown). The helical tab excitation, on the other hand, increased the spectral peak over a wide radial range at 15Hz (Fig. 6c), but significantly reduced at 30 Hz (Fig. 6d) and a moderate spectral peak was observed at the triple frequency. It is to be noted that the excitation mode and frequency reduced or enhanced the fundamental frequency peak, but that it did not alter the peak frequency, indicating the lock-in condition. The actual waveform of the tab movement was closer to a rounded triangular wave rather than being purely sinusoidal, involving harmonics, but the enhancement and suppression of turbulence by the axisymmetric and helical excitations appear to be consistent. The similarity between Fig. 6(b) and (c) indicates that the axisymmetric excitation at the double frequency was effectively generating subharmonic helical forcing of the wake.

(a) Symmetric excitation at 15Hz (b) Symmetric excitation at 30Hz

(c) Helical excitation at 15Hz (d) Helical excitation at 30HzFig. 6 Power spectral density at X/D= 2D, 0<r/D<1.5 Re=66,000

The space-time cross-correlations at X=2D between the two opposite radial positions were surveyed. Anti-symmetric wake oscillations were observed at helical excitation at 15Hz, but the correlation diminished at higher frequencies. With the axisymmetric excitation at 30Hz, the anti-phase cross-correlation was observed. In order to examine the time relationship between the excitation and the velocity fluctuation in the shear layer of the wake, the actuator motion and the hot-wire signal in the wake were cross-correlated. With the symmetric excitations the high

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correlation areas corresponded to the tab actuation frequency and were limited in the radial region directly downstream of the tabs. The helical excitation at 15Hz showed strong correlation region across the wake, indicating enhancement of large-scale helical vortex structures. Note that these lock-in frequencies were overshadowed by the fundamental frequency in the overall power spectra as shown in Fig.6. Siegel13 applied controlled suction and injection at the blunt tail of the sting model in water and surveyed the wake response in detail. When the forcing frequency was scanned, the results at Reynolds number 1500 indicated the maximum spectral peak at the natural frequency as well as lock-in frequency to the forcing.

IV. Discussion of Results and Concluding Remarks In a review on bluff-body wakes and cavity flows, Wu14 contrasted the free separation from the continuously

curved body that is sensitive to Reynolds number and state of the boundary layer with the separation from the sharp corner that has the fixed separation like the present disk. Different types of flow control are applicable in these cases. For example, the drag reduction on the sphere was achieved by the boundary layer manipulation with reduced recirculation region4, while the uniform forcing of the separated shear layer resulted in the increased drag15. In the present study on the disk wake, the forcing reduced the recirculation region with decreased base pressure and increased drag. Figure 7(a) is the streamwise velocity along the wake center line with forcings. Here major changes are seen after one diameter downstream of the disk. Here, as also noted by Siegel13 and Kim and Durbin15, the symmetric excitation at twice the natural frequency is actually forcing the wake in a higher mode at a half frequency.

The decreased base pressure was in agreement with the reduced recirculation region as shown in Fig. 3 and Fig. 5(d). Siegel’s direct drag force measurements indicated that the drag increased through the helical-mode forcing within the frequency range tested, and the increase was nearly 40% of the natural wake13. Berger et al.10 measured the line corresponding to u=0 in the recirculation bubble using a pulsed wire. The rear stagnation point behind a stationary disk was approximately at 2.5 diameters downstream whereas the disk vibration in a nutation mode at the frequency near the natural helical modemoved the rear stagnation point to approximately 1.4 diameters downstream. Their findings agree with the trend found in the present PIV velocity field maps, though the change is not as dramatic as in Berger et al.’s case. The wake width did not show significant change with forcing in both studies. They also found the peak pressure fluctuation within the shear layer that moved upstream with excitation.

The present tab excitation resulted in decreased base pressurestationary extended tab did not alter the wake. When stationary flapat the edge, the wake turbulence was clearly modified generatinfluence the wake. Thus it was the tab movements that enhancstagnation point upstream and reduced the recirculaton bubble in the

Many analytical works were carried out to solve the 2-dimenusing complex variables. They are not directly applicable for the axworks to extend the analysis to axisymmetric cases14.

It is noted that the smaller recirculation region with forcing is amay be attributed to the larger vorticity along the shear layer. T

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Figure 7 (b) Mean vorticity with helical excitation at 30Hz, (unit 1/s)

Figure 7 (a) Streamwise velocity alongthe centerline

(Fig. 3), i.e., increased drag. Incidentally, the s as long as 15% of the disk diameter were fixed ing sufficiently strong longitudinal vortices to ed the shear layer vortices and shifted the rear immediate wake. sional wake and cavity problems, for example, isymmetric geometries, and Wu reviews several

ssociated with larger shear layer curvature. This hough Batchelor16 meant it for the laminar 2-

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Dimensional wake, the concept should apply to turbulent wakes in the time-averaged sense. As the rear stagnation point moves upstream, the streamline curvature increases and thus the strength of the shear layer vorticity. Note that the wake width remained nearly constant but the wake length changed with the present tab actuation. When the disk was impulsively started in another experiment, the resulting vortex strength gave rise to an extremely high drag, and as the circulation reached the maximum value, the vortex started to shed with a steady-state drag value8,17. The time-dependent vorticity field was integrated to render the drag time-history that agreed with the measured drag. It may be simplistic but one may consider a standing axisymmetric vortex in the recirculation region and estimate its strength that controls the flowfield in the immediate wake. However, the time averaged vorticity plots show shorter vorticity layer with forcing (Fig.7b), and the steady state argument is likely to pose a limitation explaining the flowfield.

Axial vibration of the disk in Berger et al’s experiment as well as in Canon’s experiment did not produce significant coherence or lock-in phenomena in the wake. This may be partly due to the relatively low excitation frequency compared to the axisymmetric instability mode. The present as well as past experiments on the disk applied non-dimensional frequency (St) of approximately unity. Though the present actuator was limited in low frequency mechanical excitation, it would be of interest to observe the effect of the higher frequency forcings. Glezer’s group1 has found effective control of the 2D separated flow at an order of magnitude higher.

It is evident that more precise feedback control of the wake structure would be desirable. For a 2-dimensional wake in a low speed water channel, Siegel et al.18 have successfully implemented a proportional feedback control. The wake behind a disk, however, poses an additional challenge due to multi-mode three-dimensional wake movement. In order to decrease the drag and suppress the helical mode vortices, an alternative flow sensing and control will be required. An active separation control over a wing is concurrently conducted at Syracuse University. The PIV velocity field is used to ascertain and implement the low-dimensional model of flow control19. A real-time control of the airfoil flow separation has been demonstrated. The similar methodology is expected to help in constructing the control strategy of the present disk wake.

Acknowledgments Authors wish to acknowledge following undergraduate students, Messrs. Gerald Gandlin, Kazumasa Sanada and

Eric Turluer for their assistance during the earlier phase of experiment. Acknowledgement is also due Prof. Kenjiro Kamijo for arranging his then undergraduate student, Satoshi Ide’s participation in the present project at Syracuse University.

References 1Amitay, M., Honohan, A.M., and Glezer, A., “Flow Control on a Two-Dimensional Circular Cylinder,” Third International

Symposium on Turbulence and Shear Flow Phenomena, Sendai, Japan , 2003. 2Mehta, R. D., " Aerodynamics of Sports Balls" Annual Review of Fluid Mechanics, Vol. 17, pp. 151-189, 1985. 3Kiura, T. and Higuchi, H.,"Knuckleball Aerodynamics: Passive Alteration of Three-Dimensional Wake-Structure

Interactions, " IUTAM Symposium on Bluff Body Wakes and Vortex-Induced Vibrations, Marseille, France, 1998. 4Park, J., Choi, H. and Jeon, W.,"Active Control of Flow over a Sphere for Drag Reduction using Electro-magnetic

Actuators," IUTAM Symposium on Bluff-Body Wake, Marseille, France, 1998 5Cannon, S., C., "Large -scale Structures and the Spatial Evolution of Wakes behind Axisymmetric Bluff Bodies," Ph.D.

dissertation, University of Arizona, 1991. 6Higuchi, H., Anderson, R.W., and Zhang, J., "Three-Dimensional Wake Formations Behind Regular Polygonal Plates, "

AIAA Journal, Vol. 34, No. 6, pp. 1138-1145, June 1996. 7Higuchi, H. and Balligand, H.,"Circulation Time-history and Onset of Three-dimensional Vortex Shedding in the Wake

behind a Disk,” Proceedings, Second International Symposium on Turbulence and Shear Flow Phenomena, Stockholm, Vol. 1, pp. 301-306, 2001. 8Balligand, H. "Unsteady Wake Structure Behind a Solid Disk," Ph. D. Thesis, Syracuse University, Syracuse, NY, 2000.

9Higuchi, H., Zhang, J., Furuya, S. and Muzas, B.K., "Immediate and Near Wake Flow Patterns Behind Slotted Disks" AIAA Journal Vol. 36, No. 9, pp. 1626-1634, September 1998. 10Berger, E. Scholz, D. and Schumm, M.,"Coherent Vortex Structures in the Wake of a Sphere and a Circular Disk at Rest and

under Forced Vibrations", Journal of Fluids and Structures, Vol. 4, pp. 231-257, 1990. 11Higuchi, H., Qiu, J., Gandelin, G., and Tani, J., “Control of the Wake behind a Disk using Electro-magnetic Actuators,”

Proceedings of the 3rd International Symposium on Turbulence and Shear Flow Phenomena, June 25-27, Sendai, Japan, Vol. 2, pp. 555-560, 2003. 12Roshko, A., "On the Wake and Drag of Bluff Bodies, " J. Aeronautical Sciences, pp. 124-132, 1955.

13Siegel, S. "Experimental Investigation of the Wake behind an Axisymmetric Bluff Body," Ph. D. Thesis, University of Arizona, AZ, 1999. 14Wu, T. Y., “Cavity and Wake Flows,” Annual Review of Fluid Mechanics, Vol. 4, pp. 243-284, 1972.

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15Kim, H.-J. and Durbin, P.A., “Observation of the Frequencies in a Sphere Wake and of Drag Increase by Acoustic Excitation,” Physics of fluids, Vol. 31, pp. 3260-3265, 1988. 16Bathelor, G.K., “A Proposal Concerning Laminar Wakes Behind Bluff Bodies at Large Reynolds Number,” Journal of Fluid

Mechanics, Vol. 1, pp. 388-398, 1956. 17Higuchi, H., Balligand, H. and Strickland, J. H., "Numerical and Experimental Investigations of the Flow Over a Disk

Undergoing Unsteady Motion," J. of Fluids and Structures, Vol. 10, pp. 705-719, 1996. 18Siegel, S., Cohen, K., McLaughlin , T., “Feedback Control of a Circular Cylinder Wake in a Water Tunnel Experiment”

AIAA 2004-0580, Reno, NV, Jan. 2004. 19Glauser, M., Higuchi, H., Young, M., Hunter, D., and Carlson, H., “Feedback Control of Separated Flows,” AIAA-2004-2521,

2nd Flow Control Conference, Portland, Oregon, 28 June-1 July 2004

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