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Active control of transition to turbulence in the wake of a cylinder
Aircraft Design 3 (2000) 1}15
Active control of transition to turbulence in the wake of a cylinder Resat S. Keles* Department of Mechanical Engineering, Mason Laboratory, Yale University, New Haven, CT 06520-2159, USA
Abstract This paper presents experimental observations of two-dimensional air #ows with a Reynolds number of 170 passing a stationary circular cylinder and its active control of transition to turbulence. One of the potentials of this research application is in aircraft design. A hot-wire sensor was located in the upper shear layer of the cylinder at about 0.9d streamwise and about 0.8d above the cylinder axis. After the phase of the feedback signal shifted 1803$23 and the ampli"er gain was adjusted, perturbations were imposed at vortex-shedding frequency on the wake of the cylinder on both sides of the wind tunnel. The induced perturbations were signi"cant and the Karman vortex street responded vigorously to the feedback of the signal from the hot-wire sensor in the wake of the cylinder at vortexshedding frequency. Thereafter, the amplitudes of velocity #uctuations were signi"cantly reduced in the Karman vortex street. The Karman vortex street was studied at various locations spanwise to examine the extent of the response of the longitudinal components of velocity #uctuations in the wake. The amplitude of velocity #uctuations was measured with the hot-wire probe positioned at x/d"2 o! the center about 1/2 diameter spanwise in the wake of the cylinder. Finally, the vortex street was studied at various locations to examine variability of the longitudinal components of the velocity #uctuations. The free stream velocity of the wind tunnel maintained uniformly at ; "80.4 cm/s during the experiment. 2000 Published by Elsevier Science Ltd. All rights reserved.
* Corresponding author: Present address: Department of Mathematics, Columbia University, New York, New York 10027. E-mail address: [email protected] (R.S. Keles). A shorter version of this paper is published in the proceedings of the ASME, Fluids Engineering Division, Summer Meeting, Turbulence Modi"cation and Drag Reduction, July 7}11, 1996, San Diego, CA. 1369-8869/00/$ - see front matter 2000 Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 9 - 8 8 6 9 ( 9 9 ) 0 0 0 1 7 - 8
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Nomenclature AR f Re l St u u x y d ; o k z v ¸ = H
aspect ratio ("¸/d) natural vortex-shedding frequency of the cylinder ("50 Hz) Reynolds number based on cylinder diameter (Re"170) kinematic viscosity of air l"k/o ("0.150 cm/s) Strouhal number based on cylinder diameter (St"f d/; ) longitudinal velocity component in the boundary layer longitudinal root mean square (rms) velocity #uctuations distance from center of cylinder in streamwise direction distance from center of cylinder in normal direction diameter of circular cylinder ("3.17 mm) free-stream velocity ("80.4 cm/s) mass density of air ("1.21 kg/m) coe$cient of viscosity ("0.99 N s/m) distance in spanwise direction normal xy plane normal velocity component in the boundary layer distance between end plates of the cylinder width of test section of the wind tunnel ("15.2 cm) height of test section of the wind tunnel ("15.2 cm)
1. Introduction DESPITE Strouhal's observations in 1878, our understanding of the wake behind a cylinder is still incomplete. Signi"cant contributions toward theoretical understanding were made in 1889 by Kirchho! [3] who introduced the idea of free streamlines and by von Karman [4] at beginning of this century. Kirchho! 's [3] model of the #ow with an ideal, inviscid #uid with streamlines was an original contribution to all branches of applied mechanics, #uid mechanics and heat transfer. Although this theoretical understanding is more than a century old, researchers still have to relate the #ow to that of turbulent wakes behind a blu! body. von Karman [4] based his analysis ideally on the stability of the vortex street, using Kircho! 's model. No one has been able to go beyond von Karman's [4] potential #ow analysis for a perfect #uid in the near "eld of the cylinder to provide a complete theory (see von Karman and Rubach [5]). Since the advent of airplane #ight, the skin-friction drag reduction has been a major goal in airplane design with an emphasis on airplane components. The reduction of drag allows airplanes to operate at optimal e$ciency. It results in signi"cant fuel saving, quiet aircraft engines and reduced operating costs. Therefore, implementing a new airplane design a long range of travel is possible with consequent fuel saving. Recently, Bushnell and Heiner [33] and Bushnell [34] reviewed the importance of drag reduction and provided a summary of the current state of research in this area.
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Drag on slender bodies such as aircraft wings consists of viscous drag and form drag. However, for a slender body, form drag is negligible and can be neglected in comparison to viscous drag. Based on this concept many ideas have been developed since 1930 to achieve the goal of drag reduction. Scientists applied these ideas to re-design airfoils and aircraft wings to reduce viscous drag. This technique is known as natural laminar #ow (NLF) control as outlined by Cebeci [38]. The laminar #ow over axisymmetric bodies such as airplane wings adjusts of pressure gradient to achieve such #ow. Later on, supercritical wings were developed to reduce wave drag on airplanes. In addition, manipulations by suction and blowing of the laminar boundary layer helped reduced viscous drag. This paper, however, demonstrates the transition control in the wake of a circular cylinder. The potential application described in this paper includes instabilities control in the laminar boundary layer. The technique of suction and blowing of the boundary layer to airplane wings also applies to control of vortices from the wing. The related problem of drag on blu! bodies is equally important from a practical standpoint because it involves signi"cant fuel consumption in powered vehicles, such as aircraft, automobiles or submarines. Most of the power is spent to overcome drag. This paper presents a design that method reduces drag via control of velocity #uctuations within a boundary layer. The control of velocity #uctuations in the boundary layer is the most recent technological advancement. Understanding the transition point and delaying its onset is a concern of drag research. The problem of drag of blu! bodies is ancient, but it still remains one of the most important in turbulence control.
2. Transition to turbulence in the wake of cylinders The transition occurs over a "nite length along the surface called a transition length. Then, the boundary layer transition occurs when a laminar boundary layer cannot maintain disturbances exerted on it, and breakdowns to form a turbulent boundary layer over the surface. Numerical studies explored the transition in depth by several authors such as Cebeci, and Stewartson [39]. Lord Rayleigh [6,7,9,10] studied stability of certain #uid motions without taking into account viscous a!ects. Also, Orr [8] did study theoretically the stability or instability aspect of perfect and viscous liquid in 1907. However it was Tollmien [11] "rst time theoretically discovered in 1929 and computed instability amplitudes taking into account viscous a!ect of the #uid. Later on Tollmien and Schlichting [13,14] carried out further stability computations. Roshko [1] explained that, in the wake of a vortex-shedding cylinder, transition to turbulence must occur in the shear layer before the vortices fully form and must occur away from the cylinder in the range of Re"150 to 300. Roshko further pointed out that the near wake #ow is independent not only of the free shear stability, but also of the wake dynamics. In a later study, Roshko [2] demonstrated that the near wake of a circular cylinder ranges Re"150, at which point turbulence "rst appears in the vortex formation region, up to Re"150 and 3;10, when transition "nally establishes to the upstream from the separation point. Hama [30] studied the three dimensional vortex pattern behind a circular cylinders in water channel and provided pictures of the three-dimensionality of the wake.
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As early as 1959, Tritton [27] discovered that the transition of vortex streets behind cylinders takes place at Re"90 and above. Bloor [24] demonstrated the instability of the #ow in the wake of cylinders of the separated shear layers that lead to transition from Re"200 to 5;10 with "ve di!erent diameters of cylindrical tubes. Bloor veri"ed Roshko's hypothesis of basic change in the #ow occurring at Re"400 when the wake becomes turbulent. Below this number, the transition to turbulence takes place in the fully formed vortex street by irregular three-dimensional low-frequency #uctuations. At the beginning of the transition range about Re"200, the hot-wire traces occasionally showed a slight increase in amplitude and more frequently a drastic change of time traces. For Reynolds numbers above 400, the transition occurs in the separated shear layers before the vortices form. As a consequence, instability occurs and is characterized by Tollmien}Schlichting waves. Bloor [24] provided a photograph of the oscilloscope that displays shedding signals which shows two traces of each hot-wire position. For Reynolds numbers above the stable range as well as low-frequency modulations are associated with three-dimensional e!ects across the span of the cylinder. These e!ects precede the transition to turbulence in the wake of the cylinders. Bloor [24] was able to capture the onset of regular low-frequency modulations within the stable range as well as the appearance of irregular #uctuations in the transition range that leads to a turbulent wake. Her observation that Tollmien}Schlichting waves occur in the wake of cylinders at about Re"200 was a notable conclusion. Schubauer and Skramstad [15] added a #ow diagnostic tool with the use of control disturbances for wall turbulence in order to control laminar boundary-layer #ow. Berger [17] and Wehrmann [18] introduced the concept in free turbulence to control the wake of cylinders. They conducted experiments that suppressed the vortex shedding behind an oval `Bimorph transducera that had a width of 0.69 mm and a length of 1.68 mm. Wehrmann [18] found a suppression range from Re"40 to 80 on an oblong `Bimorph transducera cylinder. Berger [16,17] was able to demonstrate a suppression of the wake behind an oblong Bimorph transducer cylinder with an aspect ratio ¸/d"2.33 from Re"77 to 80. He also con"rmed the existence of transition at `low-speeda, `high modea and at transitional Reynolds numbers in the irregular range. However, he found that in the range of Re"126 to 160, there was a `basic modea that sometimes occurred in the `high-speed mode.a Monkewitz [19] demonstrated theoretically with model feedback the control of global oscillations in a #uid system with a single sensor and actuator. Monkewitz et al. [20] repeated Berger's original experiment and con"rmed the suppression of vortex shedding only at low Reynolds numbers. There is currently much debate concerning whether the closed loop of active control loop is possible only at low Reynolds number but not above transitional or high Reynolds number. At a critical Reynolds number of about 48 to 55, periodic vortex shedding begins in laminar #ow regime. Ffowcs Williams and Zhao [21] were able to demonstrate, with active, control of vortex shedding behind a cylinder with a diameter of 0.6 cm at a speed of 1 m/s and Reynolds number of 400. Roussopoulos [23] repeated Ffowcs Williams and Zhao's experiment and concluded that the feedback control was possible only at a Reynolds number 20% higher than at the critical Reynolds number. He claimed that Ffowcs Williams' active control of vortex shedding of around transitional
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Reynolds number at about 400 was really an active probe when a!ected, and prevented a second sensor from detecting a vortex shedding. He attempted to show this interference of probes was actually claimed to be control of vortex shedding as claimed by them. He visualized the #ow in a water channel and tried to show that there was no control of vortex shedding. Roussopoulos [23] tried to show that their claim of control at a high Reynolds number was an error. However, he could not provide #ow visualization pictures of feedback control even at a low Reynolds number of about Re"55 in his water channel experiment. Until recently, there was no known photograph of #ow visualization by feedback control of vortex shedding from a cylinder, even at low Reynolds number of about 48.5, which is the number when circular cylinders vortex shedding begins. Tao et al. [32] provided visualization photos between Reynolds numbers 48.5 and 51. This range is 18}24% above the onset of Reynolds number at the shedding frequency of about 1.05}1.1 Hz. At x/d"10 and 30 locations a complete elimination of vortex shedding is achieved, and #ow-streak lines are reduced to almost a straight line in the cylinder wake. Recently, Keles and Chen [36] provided an outline on the feedback control of vortex shedding behind a cylinder. Thereafter, Keles [37] demonstrated experimental details of the transition to turbulence in the wake of a circular cylinder at Re"170. In those "ndings by Keles [37] the data in the wake of cylinder "rst time, provides a clear picture of the feedback transition control. The distribution of the amplitude of velocity #uctuation's control was achieved for transitional at about Re"170. Gerrad [25] provided hypotheses on the mechanics of the vortices formation region behind blu! bodies in 1964. The identi"cation of T}S instability waves in the wake of cylinders by Tritton [27] in 1959 and Bloor [24] in 1964 provided an important step to understand the wake #ows at low Reynolds numbers behind circular cylinders. Bloor [24] and Tritton [28] were able to document oscilloscope time traces of velocity #uctuations and show the transition to turbulence at about Re"90 and above at a distance of 40 diameters downstream and at about Re"400 at 3 diameters downstream.
3. Description of the experiment A top view of the experimental setup is shown in Fig. 1. 3.1. Wind tunnel facility Experiments were carried out in a low-turbulence wind tunnel with ="15.2 cm and H"15.2 cm in the test section. The investigation was conducted at a low turbulence level of about 0.03% in the absence of acoustic excitation. A top view of the associated instrumentation is shown in Fig. 1. The wind tunnel a suction type described by Olinger [31] accommodates velocities up to 500 cm/s. The wind tunnel is driven by two vacuum pumps located one #oor below the tunnel assembly. The cylinder is passed through small holes in the cylinder endplates and tunnel walls supported on structure isolated from the tunnel test section. Also the cylinder is passed through a supported thick foam isolated from tunnel which is placed on both sides of the tunnel test section. Additionally
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Fig. 1. Top view of wind tunnel and associated instrumentation.
possible interferences of #oor vibrations, are eliminated by a block of foam placed under heavy stainless-steel supports on both sides of the tunnel's test section. The wind tunnel has an overall contraction ratio of 64 with a section containing three screens between two contraction. The #ow conditions can be varied by adjusting a suction valve as desired. 3.2. Circular cylinder For this experiment, the circular cylinder is made from a polished brass drill rod "tted with two end plates supported on a foam isolated cylinder from end plates holes walls, and is mounted across the wind tunnel test section. An aspect ratio ¸/d"20.5 is used with d"3.17 mm. 3.3. Hot-wire probe The hot wire had a diameter of 0.00508 in and a platinum core. It is formed from a silver-coated wollaston wire. Its coating of a suitable length was removed by process of etching and electrolysis in a drop of nitric acid. The length of the etched portion was about 1.5 mm and the hot wire operated at an overheat ratio of 1.5. In this paper only x/d"2 (near-wake) o!-center data are analyzed with y/d"0.80. The probe was moved in a spanwise direction parallel to the cylinder. A DANTEC constanttemperature hot-wire anemometer (type 55M01 main system with 55M10 standard bridge) and a DANTEC 55D26 signal conditioner with ampli"er were used.The probes signal was high-pass "ltered below 4 kH and low-pass "ltered above 2 Hz.
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Fig. 2. Top view of wind tunnel-measuring locations and end plates.
Fig. 3. Top view of wind tunnel active control system (ACS).
3.4. End plates A top view of the wind tunnel and the end plates are shown in Fig. 2. The cylinder was "tted with two end plates to make the #ow two dimensional and to avoid the in#uence of the boundary layers along the wind tunnel walls. The end plates were made 7}10 times greater than the diameter of the cylinder as prescribed by Stansby [29] and Nishioka and Sato [35] as well as by Ramberg [26]. 3.5. Active control system (ACS) A schematic of the active control system (ACS) is shown in Fig. 3. This active loop consists of: (a) a feedback hot-wire probe; (b) a DISA 55M10 constant-temperature anemometer; (c) a DISA 55D26 signal conditioner with low- and high-pass "lter and ampli"er unit; (d) a narrow band-pass "lter; (e) a phase changer capable of changing the signal phase continually from !3603 to 03 and from 03 to #3603; (f ) a two-channel Panasonic audio power ampli"er with 110 W per channel;
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and (g) 203.2 mm loudspeakers securely attached to the front side of the wind tunnel 500 mm downstream from the cylinder centerline.
4. Details of experiment Initially, the wake pro"les compared in prior readings were taken to see whether or not there was a possible in#uence between the feedback and the measurement hot wire or the second hot wire. However, placements of the feedback hot wire about half to two diameters in the upper shear layer next to the second hot wire did not alter the measurements taken with the second hot wire. On the basis of this, the active control was activated and measurements were taken by the second hot-wire probe in the cylinder wake. A second hot-wire probe was used to investigate the wake while the feedback hot wire was used. The feedback signal drove loud speakers to impose perturbations on the wake. The Reynolds number based on the cylinder diameter and free-stream velocity were estimated to be 170 throughout this investigation. All measurements were taken under this #ow condition. The hot-wire signal fed to an oscilloscope to monitor velocity #uctuations in the wake of the cylinder. The signal from the feedback hot-wire probe at a location in the upper shear layer of about 0.9d streamwise and about 0.8d above the cylinder axis in the wake of the cylinder was then bandpassed, "ltered, phase-shifted, and fed into the audio power ampli"er to drive the loudspeakers. The feedback signal phase-shifted at about 1803$23 and the gain was adjusted to drive the loudspeakers. Perturbations imposed to the wake "eld of the cylinder through a 40 mm hole in diameter. Only one channel of the power ampli"er was used to provide 19.25 watts to drive the loudspeakers. The signal detected by the hot wire was processed by the signal analyzer which gave the power spectrum of the velocity #uctuations at the fundamental vortex-shedding frequency at f"50 Hz. Following the imposed perturbations, the amplitude of velocity #uctuations reduced in the Karman vortex street at the probe. It was observed how active forcing e!ectively reduced the amplitudes of velocity #uctuations to about 56 and 58% of their natural shedding values at z"0.2d and 0.09d, respectively. When the active control system turned o!, the shedding from the cylinder and velocity #uctuations returned to natural values in about 30 s. The reduction of the longitudinal velocity #uctuation was observed on the voltmeter and recorded. A dramatic reduction in the power spectra of the vortex-shedding frequency was also observed at "rst harmonics, especially at the frequency of 50 Hz with active control on. For comparison purposes, the oscilloscope time traces were plotted separately at each location on the same plot. It is important to note that a small feedback signal from the cylinder wake was capable of controlling large velocity #uctuations and reduced amplitudes of longitudinal velocity #uctuations in the boundary layer at the fundamental vortex-shedding frequency.
5. Results and discussion At Re"170, the wake of the cylinder responded dramatically to the active forcing of the Karman vortex street. This response was studied to determine the longitudinal component of the
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Fig. 4. Longitudinal velocity #uctuation versus spanwise locations.
#uctuations with the hot-wire probe positioned at various streamwise stations x/d"2 (near wake) o!-center and at about 1/2 diameter spanwise in the wake of the cylinder. The three-dimensional development of the #ow was examined by investigating spanwise variability of the longitudinal component of the velocity #uctuations in the wake of the cylinder. Fig. 4 shows the distribution of longitudinal velocity #uctuations versus spanwise diameters in the near wake x/d"2. The measurements were obtained at 14 di!erent locations in the wake of the cylinder. The plot shows that the velocity #uctuations are uniform in the wake of a natural state except a small kink. In the control state, the plot shows more uniformity spanwise with small-scale velocity #uctuations. Fig. 5 shows the variation of the spectral peak level in the near wake at a diameter x/d"2 behind the cylinder. The plot shows a relatively uniform 7.8 dB reduction in spectral peak level at a distance z/d"0.09 and across the wake of the cylinder. Similarly, 7.33 dB reduction in spectral peak level at a distance z/d"0.2. It indicates that the control becomes weak toward one end plate. Fig. 6 shows the ratio of velocity #uctuations (u /u ) versus various spanwise diameter locations in the near wake at the streamwise station x/d"2. The e!ect of control in the near wake shows non-uniformity at a point z"0.254 mm (spanwise). No signi"cant wake oscillation can be seen which is indicative of rolled-up vortices due to shear-layer-induced isolation of the wake behind the cylinder. Fig. 7 shows turbulence intensity versus spanwise locations in the near wake of the streamwise station at x/d"2. Measurements were taken spanwise behind the cylinder from z"12.7 mm to 16.25 mm, approximately one diameter spanwise across the wake. Under the natural and controlled conditions, it appears that the distribution of velocity #uctuations does not vary signi"cantly in the wake of the cylinder.
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Fig. 5. Spectral peak level versus spanwise locations.
Fig. 6. (u /u ) versus various spanwise locations.
5.1. Interpretations of the oscilloscope time traces and power spectra During this investigation, instantaneous pictures of the #ow were recorded by plots of oscilloscope time traces. Instability waves were found at the streamwise station at a diameter x"2d, which was a remarkable occurrence. This was interpreted as a natural transition that occurs in the separated boundary layer in the near wake of the cylinder.
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Fig. 7. Turbulence intensity versus spanwise locations.
When the active control was turned on and a single frequency is introduced into the wake, about 1803 phase shifted, a dramatic change in the time traces of the velocity #uctuations occurred. Oscilloscope time traces of velocity #uctuations near the transition are shown in Figs. 8 and 9. Comparison of time traces from these "gures show that (a) for natural conditions and (b) for control conditions, time traces are considerably #attened. The velocity #uctuations initially are regular and periodic and persist, with control these are #attened. This change is interpreted that transition has been to a large extent controlled, or resulted in a transition delay. Fig. 8 shows intermittent velocity #uctuations between the two modes. Fluctuations vary from irregular jumps to a slightly regular mode, an irregular state and "nally back to an almost regular mode. Periodic #uctuations between the two modes are apparent. At control conditions, #uctuations are #attened indicating that velocity #uctuations are controlled except for a few spikes spanwise at z/d"0.09. In Fig. 9 the #uctuation's periodicity was more pronounced. A slow irregularity at two wavelengths is followed by a large irregularity at eight wavelengths and a small irregularity from nine wavelengths. Periodicity is apparent. At control conditions #uctuations #attened indicating that the velocity #uctuations were well controlled spanwise at z/d"0.2. Figs. 10 and 11 show the power spectra of velocity #uctuations measured with an HP frequency analyzer in a band of 0}400 Hz, subdivided in 40 intervals of 3.8194 Hz for natural and controlled conditions. Fig. 10 shows that the spectra was reduced by 7.57 dB, indicating a reduction of velocity #uctuations. Similarly, Fig. 11 shows a reduction 7.33 dB, that also indicates a reduction of velocity #uctuations. This study supports Tritton's [7,19] discovery, that transition could occur in the wake at Reynolds number 90 and above. During this investigation, oscilloscope time traces were similar to those found by Bloor in the range of Re"150 to 300 (i.e. transitional range). There is an instability
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Fig. 8. Oscilloscope time traces of velocity #uctuations near the transition at a diameter z/d"0.09: (a) natural time traces; (b) controlled time traces.
Fig. 9. Oscilloscope time traces of velocity #uctuations near the transition at a diameter z/d"0.2: (a) natural time traces; (b) controlled time traces.
in the laminar region. That instability is ampli"ed so that it leads to transition to turbulence in separated layers. We interpret that the disturbances exist preceding boundary layer with local ampli"cations occurring before the separation point and the geometry of the cylinder surface. The growth of a velocity #uctuations randomness are ampli"ed in the transition process, on one side, and reduction of regularity on the other side.
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Fig. 10. Power spectra of velocity #uctuations at a spanwise distance z/d"0.09: (a) (*) natural power spectrum; (b) (2) controlled power spectrum.
Fig. 11. Power spectra of velocity #uctuations at a spanwise distance z/d"0.2: (a) (*) natural power spectrum; (b) (2) controlled power spectrum.
6. Conclusions We examined active control of transition to turbulence behind a cylinder in a wind tunnel at the transitional Reynolds number 170. We conclude the following:
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1. Local wake control was achieved under transitional #ow conditions. 2. Reductions in the amplitude of #uctuation's spanwise behind the cylinder are reasonably uniform. The pattern shows no signi"cant spanwise variation of velocity #uctuations behind the cylinder under active control. 3. Signi"cant reductions of the amplitude of the velocity #uctuations in the Karman vortex street were observed when the active control was turned on. The beginning of the transition point was changed. When the active control was turned o!, velocity #uctuations regained their amplitudes and the natural vortex shedding from the cylinder returned to the original condition within 30 s. 4. We have demonstrated that it is possible to reduce amplitude of velocity #uctuations in the wake of the cylinder in transitional #ow conditions. Acknowledgements The author would like to take this opportunity to acknowledge Anurag Juneja for his assistance with the plot, and Dr. Anil Suri of Harvard University for engaging in helpful and critical discussions with me during the course of this research. References [1] Roshko A. On the development of wakes from vortex streets. NACA Technical Report No. 1191, 1954, p. 25. [2] Roshko, A. Some observations on transition and re-attachment of a free shear layer in incompressible #ow, in: Charwat et al., editors. Proceedings of 1965 Heat Transfer and Fluid Mechanics Institute. Held at the University of California at Los Angeles, June 21}23, 1965. Stanford: Stanford University Press, 1965, pp. 157}67. [3] Kirchho! G. Zur Theorie freier Flussigkeitsstrathlen. Crelle's Jour fur Maths 1889;70:289}98. [4] von Karman. Th Nachr Ger Wiss Gottingen 1911;509, 547 [in German]. [5] von Karman Th, Rubach H. Uber den Mechanismus des #ussigkeits und luftwiderstandes (On the mechanism of #uid resistance). Phys Zeitschr Bd 13 Heft 2 1912;49}59. [6] Lord Rayleigh. On the stability or instability of certain #uid motions. Proceedings of London Mathematical Society 1887;11:57. [7] Lord Rayleigh. Proceedings of London Mathematical Society 1895;19:27. [8] Orr W.McF. The stability or instability of steady motions of a perfect liquid and of viscous liquid, Part II. A viscous liquid. Proceedings of the Royal Irish Academy, Part I, 1907;27:69,124}8. [9] Lord Rayleigh. On the stability of the laminar motion of an inviscid #uid. Philosophy Magazine 6 1913;26:1001. [10] Lord Rayleigh. On the stability of three-dimensional distribution of viscous #uid between parallel walls. Proceedings of the Royal Society of London A 1933;142:621. [11] Tollmien W. Uber die Eutstehung der Turbulenz, Mitteing. Nachr Ges Wiss Gottingen Math Phys k l 1929; 21}44. [13] Schlichting H. Amplitudenverteilung und Energiebilanz der kleinen Storungen bei der Plattenstromung. Nachr Ger Wiss Gottingen Math Phys klasse, Fachgruppe I, 1:1935;47}78. [14] Schlichting H. Boundary layer theory. New York: McGraw-Hill, 1980. [15] Schubauer GB, Skramstad HK. Laminar boundary layer oscillations and transition on a #at plate. NACA TR 907 (April 1949, Advance Con"dential Report). [16] Berger E. Transition of the laminar vortex #ow to the turbulent state of the Karman vortex street behind an oscillating cylinder at low Reynolds number. Jahrbuc der Wissenschaftlichen Gesellschaft fur Lft- und Raumfahrt, 1964, p. 165. [17] Berger E. Suppression of vortex shedding and turbulence behind oscillating cylinders. Physics of Fluids, 1967;10(Suppl S):191}3.
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[18] Wehrmann OH. Reduction of velocity #uctuations in a Karman vortex street. Physics of Fluids 1965;8:760}1. [19] Monkewitz, P. Feedback control of global oscillations in #uid systems, AIAA 2nd Shear Flow Conference, March 13, 16, 1989, Tempe, AZ. AIAA-89-0991, 1989, p. 19. [20] Monkewitz P, Berger E, Schumm M. The non-linear stability of spatially inhomogeneous shear #ows, including the e!ect of feedback. European Journal Mechanics B 1991;10:295}300. [21] Williams, Ffowcs JE, Zhao B. The active control of vortex shedding. Journal of Fluids and Structures 1989;3:115}22. [23] Roussopoulos K. Feedback control of vortex shedding at low Reynolds number. Journal of Fluid Mechanics 1993;248:267}96. [24] Bloor MS. The transition to turbulence in the wake of a circular cylinder. Journal of Fluid Mechanics 1964;19:290}304. [25] Gerrad JH. The mechanics of the formation region of vortices behind blu! bodies. Journal of Fluid Mechanics 1964;19:290}304. [26] Ramberg SE. The e!ects of yaw and "nite length upon the vortex wakes of stationary and vibrating circular cylinders. Journal of Fluid Mechanics 1983;128:81. [27] Tritton DJ. Experiments on the #ow past a circular cylinder at low Reynolds number. Journal of Fluid Mechanics 1959;6:547}67. [28] Tritton DJ. A note on vortex streets behind circular cylinders at low Reynolds numbers. Journal of Fluid Mechanics 1971;45:203}5. [29] Stansby PK. The e!ects of end plates on the base pressure coe$cients of a circular cylinder. Aeronautical Sciences 1974;78:36}7. [30] Hama FR. Three dimensional vortex pattern behind a circular cylinder. Journal of Aeronautical Sciences 1957;24:156}8. [31] Olinger D. Universality in the wake of circular cylinder. Ph.D. thesis, Yale University (December 1990). [32] Tao JS, Huang XY, Chan WK. A #ow visualization study on feedback control of vortex shedding from a circular cylinder. Journal of #uids and structures 1996;10:965}70. [33] Bushnell DM, Heiner JN (Editors) Viscous Drag Reduction in Boundary Layers. Progress in Aeronautics and Astronautics. Vol. 123, AIAA, Washington, D.C. 1990. [34] Bushnell DM. Panel Summary. High Speed transition experiments. In the Instability and Transition. M.Y. Hussaini, R.G. Voigt (Editors) Workshop, May 15}June 9, 1989. Hampton, Virginia. Springer-Verlag. Vol. 1, pp. 43}44. [35] Nishioka M, Sato H. Measurements of velocity distributions in the wake of a circular cylinder at low Reynolds numbers. Journal of Fluid Mechanics 65:97}112. [36] Keles R, Chen L. Feedback control of vortex shedding in the wake of a circular cylinder. American Physical Society, The 48th Annual Meeting of the Division of Fluid Dynamics, November 19}21, 1995, Irvine, CA. [37] Keles R. Transition to Turbulence in the Wake of a Cylinder (Abstract). ASME Symposium on Drag Reduction and Turbulence Modi"cation, ASME Proceedings of the Fluids Engineering, Summer Meeting, July 7}11, 1996, San Diego, CA. pp. 69}76. [38] Cebeci T, Stewartson K. On the stability and transition of three-dimensional #ows. AIAA Jour. 1980;18:398}405. [39] Cebeci T. Application of CFD to reduction of skin friction drag. D.M Bushnell, and J.N. Heiner (Editors) Viscous Drag Reduction in Boundary Layers. Progress in Aeronautics and Astronautics. Vol. 123. AIAA, Washington, D.C. 1990.
Active control of transition to turbulence in the wake of a cylinder Resat S. Keles* Department of Mechanical Engineering, Mason Laboratory, Yale University, New Haven, CT 06520-2159, USA
Abstract This paper presents experimental observations of two-dimensional air #ows with a Reynolds number of 170 passing a stationary circular cylinder and its active control of transition to turbulence. One of the potentials of this research application is in aircraft design. A hot-wire sensor was located in the upper shear layer of the cylinder at about 0.9d streamwise and about 0.8d above the cylinder axis. After the phase of the feedback signal shifted 1803$23 and the ampli"er gain was adjusted, perturbations were imposed at vortex-shedding frequency on the wake of the cylinder on both sides of the wind tunnel. The induced perturbations were signi"cant and the Karman vortex street responded vigorously to the feedback of the signal from the hot-wire sensor in the wake of the cylinder at vortexshedding frequency. Thereafter, the amplitudes of velocity #uctuations were signi"cantly reduced in the Karman vortex street. The Karman vortex street was studied at various locations spanwise to examine the extent of the response of the longitudinal components of velocity #uctuations in the wake. The amplitude of velocity #uctuations was measured with the hot-wire probe positioned at x/d"2 o! the center about 1/2 diameter spanwise in the wake of the cylinder. Finally, the vortex street was studied at various locations to examine variability of the longitudinal components of the velocity #uctuations. The free stream velocity of the wind tunnel maintained uniformly at ; "80.4 cm/s during the experiment. 2000 Published by Elsevier Science Ltd. All rights reserved.
* Corresponding author: Present address: Department of Mathematics, Columbia University, New York, New York 10027. E-mail address: [email protected] (R.S. Keles). A shorter version of this paper is published in the proceedings of the ASME, Fluids Engineering Division, Summer Meeting, Turbulence Modi"cation and Drag Reduction, July 7}11, 1996, San Diego, CA. 1369-8869/00/$ - see front matter 2000 Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 9 - 8 8 6 9 ( 9 9 ) 0 0 0 1 7 - 8
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Nomenclature AR f Re l St u u x y d ; o k z v ¸ = H
aspect ratio ("¸/d) natural vortex-shedding frequency of the cylinder ("50 Hz) Reynolds number based on cylinder diameter (Re"170) kinematic viscosity of air l"k/o ("0.150 cm/s) Strouhal number based on cylinder diameter (St"f d/; ) longitudinal velocity component in the boundary layer longitudinal root mean square (rms) velocity #uctuations distance from center of cylinder in streamwise direction distance from center of cylinder in normal direction diameter of circular cylinder ("3.17 mm) free-stream velocity ("80.4 cm/s) mass density of air ("1.21 kg/m) coe$cient of viscosity ("0.99 N s/m) distance in spanwise direction normal xy plane normal velocity component in the boundary layer distance between end plates of the cylinder width of test section of the wind tunnel ("15.2 cm) height of test section of the wind tunnel ("15.2 cm)
1. Introduction DESPITE Strouhal's observations in 1878, our understanding of the wake behind a cylinder is still incomplete. Signi"cant contributions toward theoretical understanding were made in 1889 by Kirchho! [3] who introduced the idea of free streamlines and by von Karman [4] at beginning of this century. Kirchho! 's [3] model of the #ow with an ideal, inviscid #uid with streamlines was an original contribution to all branches of applied mechanics, #uid mechanics and heat transfer. Although this theoretical understanding is more than a century old, researchers still have to relate the #ow to that of turbulent wakes behind a blu! body. von Karman [4] based his analysis ideally on the stability of the vortex street, using Kircho! 's model. No one has been able to go beyond von Karman's [4] potential #ow analysis for a perfect #uid in the near "eld of the cylinder to provide a complete theory (see von Karman and Rubach [5]). Since the advent of airplane #ight, the skin-friction drag reduction has been a major goal in airplane design with an emphasis on airplane components. The reduction of drag allows airplanes to operate at optimal e$ciency. It results in signi"cant fuel saving, quiet aircraft engines and reduced operating costs. Therefore, implementing a new airplane design a long range of travel is possible with consequent fuel saving. Recently, Bushnell and Heiner [33] and Bushnell [34] reviewed the importance of drag reduction and provided a summary of the current state of research in this area.
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Drag on slender bodies such as aircraft wings consists of viscous drag and form drag. However, for a slender body, form drag is negligible and can be neglected in comparison to viscous drag. Based on this concept many ideas have been developed since 1930 to achieve the goal of drag reduction. Scientists applied these ideas to re-design airfoils and aircraft wings to reduce viscous drag. This technique is known as natural laminar #ow (NLF) control as outlined by Cebeci [38]. The laminar #ow over axisymmetric bodies such as airplane wings adjusts of pressure gradient to achieve such #ow. Later on, supercritical wings were developed to reduce wave drag on airplanes. In addition, manipulations by suction and blowing of the laminar boundary layer helped reduced viscous drag. This paper, however, demonstrates the transition control in the wake of a circular cylinder. The potential application described in this paper includes instabilities control in the laminar boundary layer. The technique of suction and blowing of the boundary layer to airplane wings also applies to control of vortices from the wing. The related problem of drag on blu! bodies is equally important from a practical standpoint because it involves signi"cant fuel consumption in powered vehicles, such as aircraft, automobiles or submarines. Most of the power is spent to overcome drag. This paper presents a design that method reduces drag via control of velocity #uctuations within a boundary layer. The control of velocity #uctuations in the boundary layer is the most recent technological advancement. Understanding the transition point and delaying its onset is a concern of drag research. The problem of drag of blu! bodies is ancient, but it still remains one of the most important in turbulence control.
2. Transition to turbulence in the wake of cylinders The transition occurs over a "nite length along the surface called a transition length. Then, the boundary layer transition occurs when a laminar boundary layer cannot maintain disturbances exerted on it, and breakdowns to form a turbulent boundary layer over the surface. Numerical studies explored the transition in depth by several authors such as Cebeci, and Stewartson [39]. Lord Rayleigh [6,7,9,10] studied stability of certain #uid motions without taking into account viscous a!ects. Also, Orr [8] did study theoretically the stability or instability aspect of perfect and viscous liquid in 1907. However it was Tollmien [11] "rst time theoretically discovered in 1929 and computed instability amplitudes taking into account viscous a!ect of the #uid. Later on Tollmien and Schlichting [13,14] carried out further stability computations. Roshko [1] explained that, in the wake of a vortex-shedding cylinder, transition to turbulence must occur in the shear layer before the vortices fully form and must occur away from the cylinder in the range of Re"150 to 300. Roshko further pointed out that the near wake #ow is independent not only of the free shear stability, but also of the wake dynamics. In a later study, Roshko [2] demonstrated that the near wake of a circular cylinder ranges Re"150, at which point turbulence "rst appears in the vortex formation region, up to Re"150 and 3;10, when transition "nally establishes to the upstream from the separation point. Hama [30] studied the three dimensional vortex pattern behind a circular cylinders in water channel and provided pictures of the three-dimensionality of the wake.
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As early as 1959, Tritton [27] discovered that the transition of vortex streets behind cylinders takes place at Re"90 and above. Bloor [24] demonstrated the instability of the #ow in the wake of cylinders of the separated shear layers that lead to transition from Re"200 to 5;10 with "ve di!erent diameters of cylindrical tubes. Bloor veri"ed Roshko's hypothesis of basic change in the #ow occurring at Re"400 when the wake becomes turbulent. Below this number, the transition to turbulence takes place in the fully formed vortex street by irregular three-dimensional low-frequency #uctuations. At the beginning of the transition range about Re"200, the hot-wire traces occasionally showed a slight increase in amplitude and more frequently a drastic change of time traces. For Reynolds numbers above 400, the transition occurs in the separated shear layers before the vortices form. As a consequence, instability occurs and is characterized by Tollmien}Schlichting waves. Bloor [24] provided a photograph of the oscilloscope that displays shedding signals which shows two traces of each hot-wire position. For Reynolds numbers above the stable range as well as low-frequency modulations are associated with three-dimensional e!ects across the span of the cylinder. These e!ects precede the transition to turbulence in the wake of the cylinders. Bloor [24] was able to capture the onset of regular low-frequency modulations within the stable range as well as the appearance of irregular #uctuations in the transition range that leads to a turbulent wake. Her observation that Tollmien}Schlichting waves occur in the wake of cylinders at about Re"200 was a notable conclusion. Schubauer and Skramstad [15] added a #ow diagnostic tool with the use of control disturbances for wall turbulence in order to control laminar boundary-layer #ow. Berger [17] and Wehrmann [18] introduced the concept in free turbulence to control the wake of cylinders. They conducted experiments that suppressed the vortex shedding behind an oval `Bimorph transducera that had a width of 0.69 mm and a length of 1.68 mm. Wehrmann [18] found a suppression range from Re"40 to 80 on an oblong `Bimorph transducera cylinder. Berger [16,17] was able to demonstrate a suppression of the wake behind an oblong Bimorph transducer cylinder with an aspect ratio ¸/d"2.33 from Re"77 to 80. He also con"rmed the existence of transition at `low-speeda, `high modea and at transitional Reynolds numbers in the irregular range. However, he found that in the range of Re"126 to 160, there was a `basic modea that sometimes occurred in the `high-speed mode.a Monkewitz [19] demonstrated theoretically with model feedback the control of global oscillations in a #uid system with a single sensor and actuator. Monkewitz et al. [20] repeated Berger's original experiment and con"rmed the suppression of vortex shedding only at low Reynolds numbers. There is currently much debate concerning whether the closed loop of active control loop is possible only at low Reynolds number but not above transitional or high Reynolds number. At a critical Reynolds number of about 48 to 55, periodic vortex shedding begins in laminar #ow regime. Ffowcs Williams and Zhao [21] were able to demonstrate, with active, control of vortex shedding behind a cylinder with a diameter of 0.6 cm at a speed of 1 m/s and Reynolds number of 400. Roussopoulos [23] repeated Ffowcs Williams and Zhao's experiment and concluded that the feedback control was possible only at a Reynolds number 20% higher than at the critical Reynolds number. He claimed that Ffowcs Williams' active control of vortex shedding of around transitional
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Reynolds number at about 400 was really an active probe when a!ected, and prevented a second sensor from detecting a vortex shedding. He attempted to show this interference of probes was actually claimed to be control of vortex shedding as claimed by them. He visualized the #ow in a water channel and tried to show that there was no control of vortex shedding. Roussopoulos [23] tried to show that their claim of control at a high Reynolds number was an error. However, he could not provide #ow visualization pictures of feedback control even at a low Reynolds number of about Re"55 in his water channel experiment. Until recently, there was no known photograph of #ow visualization by feedback control of vortex shedding from a cylinder, even at low Reynolds number of about 48.5, which is the number when circular cylinders vortex shedding begins. Tao et al. [32] provided visualization photos between Reynolds numbers 48.5 and 51. This range is 18}24% above the onset of Reynolds number at the shedding frequency of about 1.05}1.1 Hz. At x/d"10 and 30 locations a complete elimination of vortex shedding is achieved, and #ow-streak lines are reduced to almost a straight line in the cylinder wake. Recently, Keles and Chen [36] provided an outline on the feedback control of vortex shedding behind a cylinder. Thereafter, Keles [37] demonstrated experimental details of the transition to turbulence in the wake of a circular cylinder at Re"170. In those "ndings by Keles [37] the data in the wake of cylinder "rst time, provides a clear picture of the feedback transition control. The distribution of the amplitude of velocity #uctuation's control was achieved for transitional at about Re"170. Gerrad [25] provided hypotheses on the mechanics of the vortices formation region behind blu! bodies in 1964. The identi"cation of T}S instability waves in the wake of cylinders by Tritton [27] in 1959 and Bloor [24] in 1964 provided an important step to understand the wake #ows at low Reynolds numbers behind circular cylinders. Bloor [24] and Tritton [28] were able to document oscilloscope time traces of velocity #uctuations and show the transition to turbulence at about Re"90 and above at a distance of 40 diameters downstream and at about Re"400 at 3 diameters downstream.
3. Description of the experiment A top view of the experimental setup is shown in Fig. 1. 3.1. Wind tunnel facility Experiments were carried out in a low-turbulence wind tunnel with ="15.2 cm and H"15.2 cm in the test section. The investigation was conducted at a low turbulence level of about 0.03% in the absence of acoustic excitation. A top view of the associated instrumentation is shown in Fig. 1. The wind tunnel a suction type described by Olinger [31] accommodates velocities up to 500 cm/s. The wind tunnel is driven by two vacuum pumps located one #oor below the tunnel assembly. The cylinder is passed through small holes in the cylinder endplates and tunnel walls supported on structure isolated from the tunnel test section. Also the cylinder is passed through a supported thick foam isolated from tunnel which is placed on both sides of the tunnel test section. Additionally
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Fig. 1. Top view of wind tunnel and associated instrumentation.
possible interferences of #oor vibrations, are eliminated by a block of foam placed under heavy stainless-steel supports on both sides of the tunnel's test section. The wind tunnel has an overall contraction ratio of 64 with a section containing three screens between two contraction. The #ow conditions can be varied by adjusting a suction valve as desired. 3.2. Circular cylinder For this experiment, the circular cylinder is made from a polished brass drill rod "tted with two end plates supported on a foam isolated cylinder from end plates holes walls, and is mounted across the wind tunnel test section. An aspect ratio ¸/d"20.5 is used with d"3.17 mm. 3.3. Hot-wire probe The hot wire had a diameter of 0.00508 in and a platinum core. It is formed from a silver-coated wollaston wire. Its coating of a suitable length was removed by process of etching and electrolysis in a drop of nitric acid. The length of the etched portion was about 1.5 mm and the hot wire operated at an overheat ratio of 1.5. In this paper only x/d"2 (near-wake) o!-center data are analyzed with y/d"0.80. The probe was moved in a spanwise direction parallel to the cylinder. A DANTEC constanttemperature hot-wire anemometer (type 55M01 main system with 55M10 standard bridge) and a DANTEC 55D26 signal conditioner with ampli"er were used.The probes signal was high-pass "ltered below 4 kH and low-pass "ltered above 2 Hz.
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Fig. 2. Top view of wind tunnel-measuring locations and end plates.
Fig. 3. Top view of wind tunnel active control system (ACS).
3.4. End plates A top view of the wind tunnel and the end plates are shown in Fig. 2. The cylinder was "tted with two end plates to make the #ow two dimensional and to avoid the in#uence of the boundary layers along the wind tunnel walls. The end plates were made 7}10 times greater than the diameter of the cylinder as prescribed by Stansby [29] and Nishioka and Sato [35] as well as by Ramberg [26]. 3.5. Active control system (ACS) A schematic of the active control system (ACS) is shown in Fig. 3. This active loop consists of: (a) a feedback hot-wire probe; (b) a DISA 55M10 constant-temperature anemometer; (c) a DISA 55D26 signal conditioner with low- and high-pass "lter and ampli"er unit; (d) a narrow band-pass "lter; (e) a phase changer capable of changing the signal phase continually from !3603 to 03 and from 03 to #3603; (f ) a two-channel Panasonic audio power ampli"er with 110 W per channel;
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and (g) 203.2 mm loudspeakers securely attached to the front side of the wind tunnel 500 mm downstream from the cylinder centerline.
4. Details of experiment Initially, the wake pro"les compared in prior readings were taken to see whether or not there was a possible in#uence between the feedback and the measurement hot wire or the second hot wire. However, placements of the feedback hot wire about half to two diameters in the upper shear layer next to the second hot wire did not alter the measurements taken with the second hot wire. On the basis of this, the active control was activated and measurements were taken by the second hot-wire probe in the cylinder wake. A second hot-wire probe was used to investigate the wake while the feedback hot wire was used. The feedback signal drove loud speakers to impose perturbations on the wake. The Reynolds number based on the cylinder diameter and free-stream velocity were estimated to be 170 throughout this investigation. All measurements were taken under this #ow condition. The hot-wire signal fed to an oscilloscope to monitor velocity #uctuations in the wake of the cylinder. The signal from the feedback hot-wire probe at a location in the upper shear layer of about 0.9d streamwise and about 0.8d above the cylinder axis in the wake of the cylinder was then bandpassed, "ltered, phase-shifted, and fed into the audio power ampli"er to drive the loudspeakers. The feedback signal phase-shifted at about 1803$23 and the gain was adjusted to drive the loudspeakers. Perturbations imposed to the wake "eld of the cylinder through a 40 mm hole in diameter. Only one channel of the power ampli"er was used to provide 19.25 watts to drive the loudspeakers. The signal detected by the hot wire was processed by the signal analyzer which gave the power spectrum of the velocity #uctuations at the fundamental vortex-shedding frequency at f"50 Hz. Following the imposed perturbations, the amplitude of velocity #uctuations reduced in the Karman vortex street at the probe. It was observed how active forcing e!ectively reduced the amplitudes of velocity #uctuations to about 56 and 58% of their natural shedding values at z"0.2d and 0.09d, respectively. When the active control system turned o!, the shedding from the cylinder and velocity #uctuations returned to natural values in about 30 s. The reduction of the longitudinal velocity #uctuation was observed on the voltmeter and recorded. A dramatic reduction in the power spectra of the vortex-shedding frequency was also observed at "rst harmonics, especially at the frequency of 50 Hz with active control on. For comparison purposes, the oscilloscope time traces were plotted separately at each location on the same plot. It is important to note that a small feedback signal from the cylinder wake was capable of controlling large velocity #uctuations and reduced amplitudes of longitudinal velocity #uctuations in the boundary layer at the fundamental vortex-shedding frequency.
5. Results and discussion At Re"170, the wake of the cylinder responded dramatically to the active forcing of the Karman vortex street. This response was studied to determine the longitudinal component of the
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Fig. 4. Longitudinal velocity #uctuation versus spanwise locations.
#uctuations with the hot-wire probe positioned at various streamwise stations x/d"2 (near wake) o!-center and at about 1/2 diameter spanwise in the wake of the cylinder. The three-dimensional development of the #ow was examined by investigating spanwise variability of the longitudinal component of the velocity #uctuations in the wake of the cylinder. Fig. 4 shows the distribution of longitudinal velocity #uctuations versus spanwise diameters in the near wake x/d"2. The measurements were obtained at 14 di!erent locations in the wake of the cylinder. The plot shows that the velocity #uctuations are uniform in the wake of a natural state except a small kink. In the control state, the plot shows more uniformity spanwise with small-scale velocity #uctuations. Fig. 5 shows the variation of the spectral peak level in the near wake at a diameter x/d"2 behind the cylinder. The plot shows a relatively uniform 7.8 dB reduction in spectral peak level at a distance z/d"0.09 and across the wake of the cylinder. Similarly, 7.33 dB reduction in spectral peak level at a distance z/d"0.2. It indicates that the control becomes weak toward one end plate. Fig. 6 shows the ratio of velocity #uctuations (u /u ) versus various spanwise diameter locations in the near wake at the streamwise station x/d"2. The e!ect of control in the near wake shows non-uniformity at a point z"0.254 mm (spanwise). No signi"cant wake oscillation can be seen which is indicative of rolled-up vortices due to shear-layer-induced isolation of the wake behind the cylinder. Fig. 7 shows turbulence intensity versus spanwise locations in the near wake of the streamwise station at x/d"2. Measurements were taken spanwise behind the cylinder from z"12.7 mm to 16.25 mm, approximately one diameter spanwise across the wake. Under the natural and controlled conditions, it appears that the distribution of velocity #uctuations does not vary signi"cantly in the wake of the cylinder.
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Fig. 5. Spectral peak level versus spanwise locations.
Fig. 6. (u /u ) versus various spanwise locations.
5.1. Interpretations of the oscilloscope time traces and power spectra During this investigation, instantaneous pictures of the #ow were recorded by plots of oscilloscope time traces. Instability waves were found at the streamwise station at a diameter x"2d, which was a remarkable occurrence. This was interpreted as a natural transition that occurs in the separated boundary layer in the near wake of the cylinder.
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Fig. 7. Turbulence intensity versus spanwise locations.
When the active control was turned on and a single frequency is introduced into the wake, about 1803 phase shifted, a dramatic change in the time traces of the velocity #uctuations occurred. Oscilloscope time traces of velocity #uctuations near the transition are shown in Figs. 8 and 9. Comparison of time traces from these "gures show that (a) for natural conditions and (b) for control conditions, time traces are considerably #attened. The velocity #uctuations initially are regular and periodic and persist, with control these are #attened. This change is interpreted that transition has been to a large extent controlled, or resulted in a transition delay. Fig. 8 shows intermittent velocity #uctuations between the two modes. Fluctuations vary from irregular jumps to a slightly regular mode, an irregular state and "nally back to an almost regular mode. Periodic #uctuations between the two modes are apparent. At control conditions, #uctuations are #attened indicating that velocity #uctuations are controlled except for a few spikes spanwise at z/d"0.09. In Fig. 9 the #uctuation's periodicity was more pronounced. A slow irregularity at two wavelengths is followed by a large irregularity at eight wavelengths and a small irregularity from nine wavelengths. Periodicity is apparent. At control conditions #uctuations #attened indicating that the velocity #uctuations were well controlled spanwise at z/d"0.2. Figs. 10 and 11 show the power spectra of velocity #uctuations measured with an HP frequency analyzer in a band of 0}400 Hz, subdivided in 40 intervals of 3.8194 Hz for natural and controlled conditions. Fig. 10 shows that the spectra was reduced by 7.57 dB, indicating a reduction of velocity #uctuations. Similarly, Fig. 11 shows a reduction 7.33 dB, that also indicates a reduction of velocity #uctuations. This study supports Tritton's [7,19] discovery, that transition could occur in the wake at Reynolds number 90 and above. During this investigation, oscilloscope time traces were similar to those found by Bloor in the range of Re"150 to 300 (i.e. transitional range). There is an instability
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Fig. 8. Oscilloscope time traces of velocity #uctuations near the transition at a diameter z/d"0.09: (a) natural time traces; (b) controlled time traces.
Fig. 9. Oscilloscope time traces of velocity #uctuations near the transition at a diameter z/d"0.2: (a) natural time traces; (b) controlled time traces.
in the laminar region. That instability is ampli"ed so that it leads to transition to turbulence in separated layers. We interpret that the disturbances exist preceding boundary layer with local ampli"cations occurring before the separation point and the geometry of the cylinder surface. The growth of a velocity #uctuations randomness are ampli"ed in the transition process, on one side, and reduction of regularity on the other side.
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Fig. 10. Power spectra of velocity #uctuations at a spanwise distance z/d"0.09: (a) (*) natural power spectrum; (b) (2) controlled power spectrum.
Fig. 11. Power spectra of velocity #uctuations at a spanwise distance z/d"0.2: (a) (*) natural power spectrum; (b) (2) controlled power spectrum.
6. Conclusions We examined active control of transition to turbulence behind a cylinder in a wind tunnel at the transitional Reynolds number 170. We conclude the following:
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1. Local wake control was achieved under transitional #ow conditions. 2. Reductions in the amplitude of #uctuation's spanwise behind the cylinder are reasonably uniform. The pattern shows no signi"cant spanwise variation of velocity #uctuations behind the cylinder under active control. 3. Signi"cant reductions of the amplitude of the velocity #uctuations in the Karman vortex street were observed when the active control was turned on. The beginning of the transition point was changed. When the active control was turned o!, velocity #uctuations regained their amplitudes and the natural vortex shedding from the cylinder returned to the original condition within 30 s. 4. We have demonstrated that it is possible to reduce amplitude of velocity #uctuations in the wake of the cylinder in transitional #ow conditions. Acknowledgements The author would like to take this opportunity to acknowledge Anurag Juneja for his assistance with the plot, and Dr. Anil Suri of Harvard University for engaging in helpful and critical discussions with me during the course of this research. References [1] Roshko A. On the development of wakes from vortex streets. NACA Technical Report No. 1191, 1954, p. 25. [2] Roshko, A. Some observations on transition and re-attachment of a free shear layer in incompressible #ow, in: Charwat et al., editors. Proceedings of 1965 Heat Transfer and Fluid Mechanics Institute. Held at the University of California at Los Angeles, June 21}23, 1965. Stanford: Stanford University Press, 1965, pp. 157}67. [3] Kirchho! G. Zur Theorie freier Flussigkeitsstrathlen. Crelle's Jour fur Maths 1889;70:289}98. [4] von Karman. Th Nachr Ger Wiss Gottingen 1911;509, 547 [in German]. [5] von Karman Th, Rubach H. Uber den Mechanismus des #ussigkeits und luftwiderstandes (On the mechanism of #uid resistance). Phys Zeitschr Bd 13 Heft 2 1912;49}59. [6] Lord Rayleigh. On the stability or instability of certain #uid motions. Proceedings of London Mathematical Society 1887;11:57. [7] Lord Rayleigh. Proceedings of London Mathematical Society 1895;19:27. [8] Orr W.McF. The stability or instability of steady motions of a perfect liquid and of viscous liquid, Part II. A viscous liquid. Proceedings of the Royal Irish Academy, Part I, 1907;27:69,124}8. [9] Lord Rayleigh. On the stability of the laminar motion of an inviscid #uid. Philosophy Magazine 6 1913;26:1001. [10] Lord Rayleigh. On the stability of three-dimensional distribution of viscous #uid between parallel walls. Proceedings of the Royal Society of London A 1933;142:621. [11] Tollmien W. Uber die Eutstehung der Turbulenz, Mitteing. Nachr Ges Wiss Gottingen Math Phys k l 1929; 21}44. [13] Schlichting H. Amplitudenverteilung und Energiebilanz der kleinen Storungen bei der Plattenstromung. Nachr Ger Wiss Gottingen Math Phys klasse, Fachgruppe I, 1:1935;47}78. [14] Schlichting H. Boundary layer theory. New York: McGraw-Hill, 1980. [15] Schubauer GB, Skramstad HK. Laminar boundary layer oscillations and transition on a #at plate. NACA TR 907 (April 1949, Advance Con"dential Report). [16] Berger E. Transition of the laminar vortex #ow to the turbulent state of the Karman vortex street behind an oscillating cylinder at low Reynolds number. Jahrbuc der Wissenschaftlichen Gesellschaft fur Lft- und Raumfahrt, 1964, p. 165. [17] Berger E. Suppression of vortex shedding and turbulence behind oscillating cylinders. Physics of Fluids, 1967;10(Suppl S):191}3.
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