interference between stationary and vibrating cylinder...

Interference between stationary and vibrating cylinder wakesW. C. Lai, Y. Zhou, R. M. C. So, and T. Wang Citation: Phys. Fluids 15, 1687 (2003); doi: 10.1063/1.1569918 View online: http://dx.doi.org/10.1063/1.1569918 View Table of Contents: http://pof.aip.org/resource/1/PHFLE6/v15/i6 Published by the American Institute of Physics. Related ArticlesA new unstable mode in the wake of a circular cylinder Phys. Fluids 23, 121701 (2011) Coupling modes of three filaments in side-by-side arrangement Phys. Fluids 23, 111903 (2011) Effect of turbulence on the downstream velocity deficit of a rigid sphere Phys. Fluids 23, 095103 (2011) Numerical investigation of the subcritical effects at the onset of three-dimensionality in the circular cylinder wake Phys. Fluids 23, 094103 (2011) Alternating half-loop shedding in the turbulent wake of a finite surface-mounted square cylinder with a thinboundary layer Phys. Fluids 23, 095101 (2011) Additional information on Phys. FluidsJournal Homepage: http://pof.aip.org/ Journal Information: http://pof.aip.org/about/about_the_journal Top downloads: http://pof.aip.org/features/most_downloaded Information for Authors: http://pof.aip.org/authors

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PHYSICS OF FLUIDS VOLUME 15, NUMBER 6 JUNE 2003

Interference between stationary and vibrating cylinder wakesW. C. Lai, Y. Zhou,a) R. M. C. So, and T. WangDepartment of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom,Kowloon, Hong Kong

~Received 22 March 2002; accepted 5 March 2003; published 5 May 2003!

The flow behind two side-by-side tubes of identical diameter,d, one stationary and the other forcedto oscillate in the lateral direction at an amplitude ofA50.1;0.5d was examined. Two values ofT/d, i.e., 2.2 and 3.5 were investigated, whereT is the cylinder center-to-center spacing. TheReynolds number Re ranges from 150 to about 1000. The effect ofA/d, T/d, and f e / f s , wheref e

is the cylinder oscillating frequency andf s is the vortex shedding frequency of an isolated stationarycylinder, on the vortex shedding and the wake structure was examined. Specific attention was givento the occurrence of lock-in, where vortex shedding from the oscillating cylinder synchronizes withf e . Significant influence of these parameters has been observed on the flow behind the cylinders interms of the predominant vortex patterns and interactions between vortices. It has been found thatthe shedding frequency associated with the oscillating and the stationary cylinder can be modifiedas f e / f s approaches unity. Furthermore, the flow regime may change under the conditions ofT/d52.2 andA/d50.5 from two distinct coupled streets to the combination of one narrow and onewide street. Subsequently, the lock-in state is considerably extended probably because multipledominant frequencies in the asymmetrical flow regime can all be locked in with the structuraloscillation. © 2003 American Institute of Physics.@DOI: 10.1063/1.1569918#

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I. INTRODUCTION

The wake of a vibrating structure has received considable attention in the literature because of its practical signcance. One of the primary concerns is that the vortshedding frequency from a vibrating structure msynchronize with the natural frequencies of the flustructure system, which amplifies structural vibration amptude and leads to a reduced lifespan of the structure or eearly failure. Furthermore, the wake of one or more vibratstructures is of relevance to the prediction of forces on dostream structures.

In their early studies of a single forced oscillating cylider in a cross flow, Bishop and Hassan1 observed that whenthe cylinder oscillating frequencyf e approached the vorteshedding frequencyf s of a stationary cylinder, the two setof forces were synchronized, and the natural sheddingquency was lost, resulting in the so-called lock-in phenoenon. Within the synchronization range, lift and drag forcvaried in phase and amplitude with the imposed frequenKoopmann2 noted that the lock-in range, over which the votex shedding frequency was dictated byf e , was dependenon the amplitude ratioA/d and, to some extent, on the Renolds number Re~based ond and the free stream velocitU`). The vortex shedding frequency could vary up to625%for the same Re~,300!. Griffin et al.3,4 found that thelock-in occurred forf e50.8– 1.2f s . They further observedthat, due to the forced vibration effect, the lateral spacbetween vortices decreased asA/d increased but the longitudinal spacing was unchanged. Williamson and Rosh5

a!Author to whom correspondence should be addressed. [email protected]

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discussed various spatial modes of vortices, generatedvibrating cylinder at differentA/d and f e / f s . Ongorem andRockwell6,7 investigated at variousf e / f s the phase shift, re-covery and mode competition in the near-wake for an oslating cylinder of different cross sections~circular, square,and triangular!. They noted that whenf e / f s'1, the vortexformation timing switched phase by almost 180° over a vnarrow range off e. Numerical studies have also been coducted. For example, using a primitive-variable formulation a spectral element spatial discretization, BlackburnHenderson8 simulated a two-dimensional flow past a circulcylinder that was either stationary or in simple harmoncross-flow oscillation at Re5500, A/d50.25, and f e / f s

50.875– 0.975. They showed that the change in phasevortex shedding is associated with a change in sign of mchanical energy transfer between the cylinder and the flo

Previous studies have greatly improved our understaing of the flow behind a vibrating cylinder. In engineerinhowever, we are frequently faced with the problem of mtiple vibrating cylinders instead of an isolated one. Numous investigations have been conducted to understandcylinder wake in the presence of a neighboring cylinder. Inow well known that, when the cylinder center-to-censpacing ratioT/d is greater than 2, two distinct vortex streeoccur behind the cylinders. The two streets are predonantly in antiphase mode.9 Nevertheless, the in-phase vortestreets are also observed form time to time.10–12The criticalpoints, such as vortex centers and the saddle points,13 of thetwo in-phase streets are antisymmetrical about the flow cterline, but symmetrical for the antiphase case. At 1.5&T/d&2.0, the gap flow between the cylinders is deflected, foring one narrow and one wide wake.10,14 The deflected gapil:

7 © 2003 American Institute of Physics

icense or copyright; see http://pof.aip.org/about/rights_and_permissions

1688 Phys. Fluids, Vol. 15, No. 6, June 2003 Lai et al.

FIG. 1. ~a! Schematic diagram of the water tunnel.~b!Cylinder arrangement in the test section.

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flow may change over intermittently from one side to anotand is bi-stable. For very small spacing ratio, i.e.,T/d,1.2, vortices are alternately shed from the free-streamonly of the two cylinders, generating one single vortex streMahir and Rockwell15 investigated the wake of two side-byside cylinders (T/d53.0), both forced to vibrate laterally. Inthe lock-in state, they observed a variety of flow patterwhich depended on the phase relationship between thevibrating cylinders. The power spectral density function cresponding to the flow patterns was nevertheless almossame. However, information on the flow when the neighbing cylinder is vibrating is scarce.

This work aims to investigate interference between ationary and a vibrating cylinder wake based on particle iage velocimetry~PIV!, hot wires, and laser-induced fluorecence~LIF! flow visualization measurements. Great attentwas given to the occurrence of lock-in. Various parametincluding A/d, T/d, and f e / f s , are investigated of their influence on the flow behind the cylinders in terms of the pdominant vortex patterns, shedding frequencies and intetions between vortices.

II. EXPERIMENTAL DETAILS

A. Flow visualization in a water tunnel

Experiments were carried out in a water tunnel withsquare working section~0.15 m30.15 m! of 0.5 m long. Thewater tunnel is a recirculating single reservoir [email protected]~a!#. A centrifugal pump delivers water from the reservoirthe tunnel contraction. A honeycomb is used to removelarge-scale irregularities prior to the contraction. The flospeed, controlled by a regulator valve, is up to a maximumabout 0.32 m/s in the working section. The working sectis made up of four 20 mm thick Perspex panels.

Two side-by-side acrylic circular tubes of an identicdiameter d50.01 m, were horizontally mounted 0.20downstream of the exit plane of the tunnel contraction a


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placed symmetrically about the midplane of the working stion @Fig. 1~b!#. The cylinders were cantilevered; there was1 mm or so clearance between the cylinder free end andtunnel wall. The resulting blockage was about 13%. The retively high blockage may postpone the near-wake instabito a higher Re and further lead to the wake narrowing asubsequently rising Strouhal number,16 which are not the fo-cus of the present investigation. Therefore, no correctionmade for the blockage effect. The upper cylinder oscillavertically at A/d50.1 and 0.5, respectively. The oscillatiowas provided by a dc motor through a cam-linkage systeThe oscillation frequency,f e , was measured by a tachomet~accuracy:65%! and confirmed by counting cylinder oscilation when playing back the real-time indexed video recoThe f e / f s investigated varied between 0.74 and 1.44. In tpaper,f s denotes the vortex shedding frequency of a sinstationary cylinder~measured in the same tunnel!, while f s1

and f s2 are the vortex shedding frequencies of the oscillatand the stationary cylinder, respectively.

Two transverse spacing ratios were used, i.e.,T/d53.50 and 2.20, respectively. For stationary cylinders, thdistinct flow regimes occur, depending on theT/d value.9–12

Two distinct and coupled streets occur atT/d>2; a bi-stableasymmetrical flow is observed for 1.5&T/d&2. It is inter-esting to see how the coupling is affected when one cylinoscillates and thusT/d53.5 was selected. It is equally inteesting to see whether the flow regime could be changbecause of the cylinder oscillation, from two distinct couplstreets to the asymmetrical flow regime. Therefore,T/d52.2 was also investigated.

The cylinders have an aspect ratio of 15. For a stationcylinder, an aspect ratio of 27 or larger is needed to avoidend effects.17 However, an oscillating cylinder may reorganize the vortex shedding process to enhance significantlytwo dimensionality. Griffin18observed that, when the oscillation amplitude was greater than 0.01–0.02d, the correlationcoefficient,rp , between spanwise fluctuating pressures


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1689Phys. Fluids, Vol. 15, No. 6, June 2003 Interference between stationary and vibrating cylinder wakes

creased greatly, compared with a stationary cylinder. Forample, given a threshold ofrp50.5, the spanwise correlatiolength was about 1d at A/d50.025, 6d at A/d50.075 and10d at A/d50.125. ForA/d50.5, the correlation length isestimated to be over 40d based on an extrapolation of thdata. It may be thus inferred that the end effect of the oslating cylinder is negligible. Section III will show that vorteshedding from the stationary cylinder is also reorganizedthe neighboring oscillating flow, which enhanced the twdimensionality of the flow, implying a small end effect fothe stationary cylinder.

For each cylinder, dye~Rhodamine 6G 99%!, which hada faint red color and became metallic green when excitedlaser, was introduced through two injection pinholes atmidspan of the cylinder. The pinholes were located arou90° away, clockwise and anticlockwise, respectively, frothe leading stagnation point. A thin laser sheet, which wgenerated by laser beam sweeping, provided illuminavertically at the midplane of the working section. A SpectPhysics Stabilite 2017 argon ion laser with a maximupower output of 4 watts was used to generate the laser beA digital video camera recorder~SONY DCR-PC100E! wasused to record, at a framing rate of 25 frames per seconddye-marked vortex streets. Flow-visualization was carrout in the range of Re5150–1000 over 0<x/d<8. At largerRe andx/d, the dye diffused too rapidly to be an effectivmarker of vortices.

B. Experiments in a wind tunnel

Wind tunnel and cylinder assembly:The wind tunnelwas described in detail by Zhouet al.19 It has a square working section~0.6 m30.6 m! of 2.4 m in length. The viewwindow of the working section is made of optical glassorder to maximize the signal-to-noise ratio in PIV measuments. The wind speed in the working section is adjustain the range of 0–50 m/s. The cylinder assembly wassigned similarly to that used for the LIF measurements inwater tunnel. Two aluminum alloy cylinders ofd50.015 mwere cantilever-supported symmetrically about the midplof the working section. Their transverse spacing was adjable in the range ofT/d52 – 4.5. The length of both cylinders inside the tunnel was 0.35 m, thus resulting in a bloage of 1.25% and an aspect ratio of about 23. A 0.15 m lsection from the free end of each cylinder was replaced btransparent acrylic tube in order to allow the laser sheeshine through, thus minimizing the shadow effects in the Pmeasurement. One microcomputer-controlled dc motor stem was used to drive the upper cylinder to oscillateA/d50.1– 0.5, andf e / f s'0.5– 1.3. The first-mode naturafrequency of each cylinder was about 272 Hz, a factor oftimes the maximumf e(524 Hz!. To minimize the reflectionnoise generated by the laser sheet shining on the cylindthe surface of both cylinders were painted black excep0.02 m long section at 0.12 m from the free end onacrylic section. Measurements were conducted atU`51.17m/s ~Re51150!. In the free stream, the longitudinal turbulence intensity was measured to be approximately 0.4%.

PIV measurements:A Dantec standard PIV2100 syste


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was used. Flow was seeded by the smoke of a particlearound 1mm in diameter, which was generated from Parafoil. Illumination was provided in the plane of mean she0.13 m from the cylinder free end, by two New Wave stadard pulsed laser sources of a wavelength of 532 nm, ehaving a maximum energy output of 120 mJ. Digital particimages were taken using one CCD camera~HiSense type 13,gain34, double frames, 128031024 pixels!. A Dantec Flow-Map Processor~PIV2100 type! was used to synchronizimage-taking and illumination. Each image covered an aof 129 mm3102 mm or 8.6d36.8d of the flow field. Thelongitudinal and lateral image magnifications were identici.e., 0.1 mm/pixel. Each laser pulse lasted for 0.01ms. Theinterval between two successive pulses was typically 50ms.Thus, a particle would only travel 0.059 mm~0.59 pixels or0.004d! at U`51.17 m/s. An optical filter was used to allowonly the green wavelength~532 nm!, generated by the laseto pass. Since both cylinders were included in the PIV iages, which could cause errors in deriving velocities arouthe cylinders, they were masked using a built-in maskfunction in the Dantec PIV2001 system before calculationparticle velocities. In image processing, 32332 rectangularinterrogation areas were used, each including 32 pix~'0.2d! with 25% overlap with other areas in both the logitudinal and lateral directions. The ensuing in-plane velocvector field consisted of 53342 vectors. The same number ospanwise vorticity component,vz, were approximately de-rived based on particle velocities. The spatial resolutionvorticity estimate was about 2.43 mm or 0.16d.

Hot wire and laser vibrometer measurement:The domi-nant frequencies behind the two cylinders were measuusing two hot wires. They were placed atx52d downstreamof the cylinders and symmetrically about the centerline, iat y562.6 (T/d52.2) or 63.25 (T/d53.5). Constant-temperature circuits were used for the operation of thewires. The displacement of the upper oscillating cylinder wmeasured simultaneously with the flow using a Polytecries 3000 dual beam laser vibrometer.20 Signals from the hotwires and laser vibrometer were offset, amplified and thdigitized using a 16 channel~12 bit! analog/digital board anda personal computer at a sampling frequencyf sampling53.5kHz per channel. The typical duration of each record wabout 20 s.

III. RESULTS AND DISCUSSION

A. Vortex shedding frequencies

In the case of an isolated cylinder, the lock-in phenoenon occurred for the range off e / f s'0.7– 1.1 at A/d'0.7; this range narrows asA/d reduces.15 When two inlinecylinders were both forced to oscillate laterally in phasvortex shedding from both cylinders was locked in with ocillation and thef e / f s range, where lock-in occurred, waalmost the same as its single counterpart; however, if thecylinders oscillated in antiphase, the range was redusignificantly.21 When two side-by-side cylinders were bo


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forced to oscillate laterally, the lock-in range off e / f s wasnarrower, particularly at relatively largeA/d, than that of asingle cylinder and shifted to a higherf e / f s .15 It is of inter-est to explore whether vortex shedding from a stationaryinder could be locked in when the cylinder interacts withneighboring oscillating cylinder.

Figure 2 illustrates the power spectral density functioEu andEY , of the hot wire and displacement signals. Nothat the displacement signal,Y, monitored the motion of theupper oscillating cylinder, while hot wires 1 and 2 measuthe wake of the upper oscillating and lower stationary cylder, respectively. AtT/d53.5 andA/d50.5 @Fig. 2~a!#, bothEY andEu from hot wire 1 display a pronounced peak atidentical frequencyf * 5 f d/U` , i.e., f s1* 5 f e* 50.19 (f e / f s

50.95), indicating the lock-in between vortex sheddifrom the upper cylinder and structural oscillation. Unleotherwise stated, the asterisk denotes normalization byd andU` in this paper.Eu from hot wire 2 also displays a peakf s2* 5 f e* . Apparently, vortex shedding from the lower cylinder was modified by the neighboring synchronizationtween f s1* and f e* , its frequency,f s2* , being thus locked inwith f e* . As A/d is reduced to 0.1, vortex shedding from thupper cylinder is again locked in with structural oscillatioi.e., f s1* 5 f e* @Fig. 2~b!, T/d53.5, f e / f s50.85]. So is vortexshedding from the lower cylinder, resulting inf s2* 5 f e*5 f s1* . Similar observations were made whenT/d is reducedto 2.2 @Figs. 2~c! and 2~d!#.

Figure 3 comparesf s2* and f s1* with f e for different T/dandA/d as f e / f s varies. It is evident that in all cases, witf e / f s approaching 1, bothf s2* and f s1* have been modifiedand eventually collapse withf e* . The three frequencies remain synchronized for a range off e / f s , and f s2* and f s1* willthen be decoupled fromf e* as f e / f s exceeds 1 appreciablyIn general, vortex shedding from the stationary cylindercomes locked in withf e* later than that from the oscillating

FIG. 2. Power spectral density functions:EY of the displacement signal othe oscillating cylinder,Eu obtained atx/d52 and 1.5d laterally from theoscillating~hot wire 1! and the stationary cylinder axis~hot wire 2!, respec-tively, towards the free stream.~a! T/d53.5, A/d50.5, f e / f s50.95; ~b!3.5, 0.1, 0.85;~c! 2.2, 0.5, 1.15;~d! 2.2, 0.1, 0.85. Re51150.


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cylinder but decoupled earlier. As expected, the synchrontion range off e / f s dwindles for smallerA/d and depends onT/d. Note that atT/d52.2 andA/d50.5, the lock-in rangeof f e / f s is especially wide for oscillating cylinder, starting toccur at f e / f s'0.5. In contrast, the lock-in starts atf e / f s

'0.8 for other cases.At T/d52.2 andA/d50.5, the smallest center-to-cent

cylinder spacing is 1.7. It is well known that for two sideby-side stationary cylinders ofT/d<2.0, the gap flow be-tween the cylinders is deflected, forming one narrow andwide wake, which are characterized by two dominant fquencies, i.e.,f * '0.3 and 0.1.9,10,12 The hot wire spectra~not shown!, presently measured in the shear layers aroutwo stationary cylinders ofT/d51.7, displayed two peaks af * '0.1 and 0.3. Thus, it seems plausible that the upperinder oscillation at a largeA/d ~50.5! may have excited theshear layer instability atf * '0.1, resulting in an early lock-in, as illustrated in Fig. 4. For the same token, the upcylinder oscillation will probably excite the shear layer i

FIG. 3. The vortex shedding frequencies,f s1* ~hot wire 1! and f s2* ~hot wire2!, asf e / f s varies:~a! T/d53.5,A/d50.5; ~b! 3.5, 0.1;~c! 2.2, 0.5;~d! 2.2,0.1.

FIG. 4. Power spectral density functionsEY of the displacement signal othe oscillating cylinder,Eu obtained atx/d52 and 1.5d laterally from theoscillating~hot wire 1! and the stationary cylinder axis~hot wire 2!, respec-tively, towards the free stream,T/d52.2,A/d50.5, f e / f s50.55. Re51150.


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and f s1* remain synchronized withf e* at the upperf e / f s . Itmay be concluded that atT/d52.2 the oscillation of onecylinder, particularly at a large amplitude, acts to reducefective spacing between cylinders so that the asymmetrflow behind two side-by-side cylinders may occur aboT/d52. The asymmetrical flow regime is characterizeddominant vortex frequenciesf * '0.3 and 0.1, respectivelyConsequently, lock-in may be inclined to occur near thtwo frequencies in addition tof * '0.2, leading to a rela-tively wide lock-in range off e / f s .

Vortex frequencies were also estimated by playing brecorded data from the LIF flow visualization and counticonsecutive vortices~about 100 pairs! at x/d'2 for a certainperiod. The measurement uncertainty was estimated toabout 2%. The results~not shown! are essentially consistenwith the above observations from spectral analysis.

B. Typical flow structures

At T/d53.5, interference between the two streetspears relatively small in the immediate vicinity, perhapsto x/d'5, of the cylinders. This is illustrated in Fig. 5, whethe two vortex streets behind one oscillating and one statary cylinder @Fig. 5~a!# are compared with that behindsingle oscillating @Fig. 5~b!# or stationary [email protected]~c!#. The upper street@Fig. 5~a!# behind the oscillating cyl-inder appears rather similar to that@Fig. 5~b!# behind thesingle oscillating cylinder, and the lower street in the newake of the stationary cylinder resembles that@Fig. 5~c!#behind the single stationary cylinder. The similarity disapears forx/d>5 as the two streets grow and their interfeence intensifies, which grossly increases the three dimsionality of the flow.

The two streets behind the cylinders, shown in Fig.are symmetrical about the flow centerline or in the antiphmode, irrespective of the vibration amplitude of the uppcylinder, as in the stationary cylinder case.9,10,12 But the in-phase streets are also observed from time to time and ca

FIG. 5. Comparison between vortex streets behind two cylinders and tbehind an isolated cylinder:~a! T/d53.5, A/d50.5, f e / f s50.83; ~b! anisolated vibrating cylinder,A/d50.5, f e / f s50.83; ~c! an isolated stationarycylinder. Re5150.


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stable. Furthermore, the oscillation of the upper cylindtends to increase the wake width asA/d increases. Note thathe lateral spacing between vortices generated by the olating cylinder will decrease asA/d increases.3,4 The flowstructures in Figs. 6~b! and 6~c! are closely similar to thosewhen both cylinders were forced to oscillate at a phase sof 0° and 95° observed by Mahir and Rockwell.15

As T/d reduces to 2.2@Figs. 6~d!–6~f!#, the interactionbetween the two streets is expected to intensify, especfor large A/d. For stationary cylinders@Fig. 6~d!#, two dis-tinct streets are evident and predominantly symmetrabout the flow centerline. Present data also show the ocrence of in-phase streets~not shown!, as previouslyreported.10 The two configurations for vortex streets are oserved when the upper cylinder oscillates. The effect of cinder oscillation is dependent on the configurations of vorstreets. For vortex streets in the antiphase mode, the osction acts to intensify the vortex interaction and to destabilthe two streets. Consequently, the two streets breaksooner, in particular at smallT/d @compare Figs. 6~d!, 6~f!with Figs. 6~b! and 6~c!#. On the other hand, the two streein phase typically start to merge into one at a downstredistance close to the cylinders~see the following section formore details!. The above typical flow structures were alsobserved for a higher Re~up to 1000 in the present LIF flowvisualization data! in the turbulent flow regime~not shown!,indicating an independence of Re in the range examined

One vortex street in Figs. 6~e! and 6~f! appears rathernarrow, compared with the other. This is more evidentA/d50.5 @Fig. 6~f!#, in support of the earlier proposition thathe cylinder oscillation could reduce effective spacing btween cylinders, thus causing the formation of one narrand one wide wake even atT/d52.2.

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FIG. 6. Vortex streets behind two cylinders at different vibration amplitu~a! T/d53.5,A/d50, f e / f s50; ~b! 3.5, 0.1, 1.28;~c! 3.5, 0.5, 1.22;~d! 2.2,0, 0; ~e! 2.2, 0.1, 1.22;~f! 2.2, 0.5, 1.28. Re5150, f s15 f s2 .


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tion were corroborated by vorticity contours,vz*5vzd/U` , deduced from PIV measurements. Figure 7 illutrates the antiphase vortex streets at differentT/d and A/d( f e / f s51). In all cases, thevz* contours display essentialltwo vortex streets approximately symmetrical~not in termsof the sign ofvz* ) about y/d50, but symmetry does noappear evident forx/d>5. On the other hand, the flow visualization photographs indicate that symmetry persists up tleast aboutx/d'8 for T/d53.5, though not for the case oT/d52.2. At T/d52.2, strong interactions between the twstreets quickly destroys the symmetry perhaps even bex/d55. Disparity in the streamwise extent of symmetryT/d53.5 could be partially ascribed to different Reynolnumbers between the LIF photographs~Fig. 6, Re5150! andPIV data~Fig. 7, Re51150!. It is worthwhile remarking thatthe two streets atT/d52.2 measured by PIV were morlikely to be in-phased than antiphased, which is not quunderstood at this stage. The comparison between flow valization and PIV measurements suggests that the streakpresently measured reflect reliably the flow structure innear wake, at least up tox/d55. Therefore, the followingdiscussion of vortex interactions in the near wake willconducted largely based on the flow visualization data, wa caveat that the streak lines may not follow vortices entirwhen far away from the point where dye was released.22

C. Change in the phase relation between the twostreets

It is of fundamental interest to understand why the tstreets may change from antiphase to in-phase. For two sby-side cylinders of relatively large spacing, i.e.,T/d.2,two distinct coupled vortex streets occur.23 Based on flow-visualization data at Re5100–200, Williamson11 demon-

FIG. 7. Instantaneous vorticity contoursvz* 5vzd/U` obtained for the PIVmeasurement:~a! T/d53.5, A/d50.5, the contour increment50.3; ~b! 3.5,0.1, 0.5;~c! 2.2, 0.5, 0.5;~d! 2.2, 0.1, 0.5. Re51150, f e / f s51.


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strated that the two streets may occur in phase or intiphase. The in-phase streets eventually merged downstrto form a single street, while the in-antiphase streetsmained distinct farther downstream. He observed a predonant antiphase vortex shedding for 2,T/d,6. However, itis not clear what triggers the transition of the two vortstreets from antiphase to in-phase or vice versa.

Figure 8 presents sequential photographs for Re5150and A/d50.1. The real time index is indicated by the firtwo numbers on the lower left-hand corner in the phographs and the sequential order is given by the third numThe vortex formation from the two cylinders is initially symmetric @Fig. 8~a!#. One gap vortexA generated by the oscillating cylinder approaches the opposite-signed vortexB,which was shed from the free-stream side of this cylinderis apparent thatA and B are engaged in a pairing proce@Figs. 8~a!–8~d!#. Similarly, the following cross-stream vortices C and D also approach each other@Figs. 8~d!–8~g!#.The pair of counter-rotating vortices at close proximitylikely to generate a low-pressure region between them.low-pressure region is responsible for drawing in the g

FIG. 8. Sequential photographs of flow visualization: the occurrence ofpairing vortices followed by the merging of two cross-stream vortices sfrom the vibrating cylinder with the inner vortex from the stationary cylider. Meanwhile, symmetrical vortex shedding changes to the antisymmcal one. T/d52.2, the upper cylinder is vibrating atA/d50.1, f e / f s

5 f s1 / f s5 f s2 / f s51.22, Re5150.


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vortex E shed for the lower stationary cylinder, which lagbehindA, thus resulting in the amalgamation of vorticesC,D, andE @Figs. 8~d!–8g!#. Note that the amalgamation of ththree vortices acts to slow down vortexF and subsequentlyG and H @Figs. 8~d!–8~g!#. Eventually, the antisymmetricavortex formation emerges@Fig. 8~h!# as a result of vortexinteractions.

The antisymmetrical vortex shedding did not last loand would soon revert to the symmetrical vortex formatioSequential photographs~Fig. 9! following those in Fig. 8indicate that vorticesA and B appear pairing@Figs. 9~d!–9~h!#. Due to the low-pressure region formed between theA and B manage to pinch fluid from vortexF in the lowerstreet, but they fail to draw in vortexF. Apparently,F travelsat an appreciably slower velocity. Meanwhile, vorticesE andF behind the stationary cylinder appear approaching eother, though not pairing up. This may again produce a lopressure region between them. Consequently, fluid in theper street is assimilated to vortexE @Figs. 9~b!–9~h!#. Thisprocess is associated with a slowdown of the subsequenttices ~e.g., vorticesF and G!, thus leading to asymmetrivortex shedding@Fig. 9~h!#.

FIG. 9. Sequential photographs of flow visualization: the merging of tcross-stream vortices shed from the vibrating cylinder with the inner vofrom the stationary cylinder. Meanwhile, antisymmetrical vortex sheddchanges to the symmetrical one.T/d52.2, the upper cylinder is vibrating aA/d50.1, f e / f s5 f s1 / f s5 f s2 / f s51.22, Re5150.


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It is interesting to note that the pairing of two vorticesthe amalgamation of three vortices leads to the formationa single vortex street downstream, which is probably asymetrical. The observation bears resemblance to that betwo stationary cylinders. In the asymmetrical flow regimi.e., T/d51.5– 2.0, where a combination of one wide aone narrow wake occurs, Zhouet al.12 showed the amalgamation of the two cross-stream vortices in the narrow wawith the gap vortex in the wide wake. Subsequently the tstreets merge into one. The resemblance further supportearlier suggestion that the vibration of one cylinder couinduce the change of the flow regime from two distinct votex streets to one wide and one narrow street at aT/d valuegreater than 2.0.

One remark could be made on the vortex interactionfect on the convection velocity of vortices. In order to higlight this point, a few photographs in Fig. 8 are replottedFig. 10. Evidently, the low-pressure region between pairvorticesC andD draws in and hence slows downE. On theother hand,B may have been accelerated due to pairingAandB. Consequently,B andE were traveled at different velocities. In contrast, the gap vortices, sayA andB in Fig. 11,do not show appreciable difference in their convection velity when the vortex pairing or amalgamation is absent. Zhet al.19 measured the turbulent wake (x/d510– 40) behindtwo side-by-side cylinders (T/d51.5 and 3.0! using a three-wire probe ~one cold wire plus one X wire!. The phase-averaged sectional streamlines and vorticity contoursT/d51.5 showed two rows of vortices, asymmetrically aranged about the flow centerline. The average convecvelocity, estimated atx/d510, differed by about 10% between the two rows of vortices. It was, however, not quclear what was responsible for this difference. The presobservation~Figs. 10 and 11! suggests that the interactiobetween vortices could be partially responsible.

IV. CONCLUSION

The effect of a neighboring vibrating cylinder on a cicular cylinder wake has been investigated using particleage velocimetry, hot wires, and laser-induced fluorescetechniques. The dependence of the flow structure and voshedding frequencies onf e / f s , T/d, andA/d is examined.The following conclusions could be drawn.

~1! For T/d53.5, the vortex shedding frequencyf s1 of theforced oscillating cylinder can be locked on with thvibration frequencyf e , i.e.,f s15 f e , the same as in thecase of an isolated cylinder.3,4 The f e / f s range oflock-on is comparable with that for a single cylinder blarger than that for two oscillating side-by-sidcylinders.15 At the lock-in state, the vortex shedding frequencyf s2 of the stationary cylinder may also be modfied, resulting inf e5 f s15 f s2 . In general, vortex shedding for the stationary cylinder becomes locked in wf e* later than that from the oscillating cylinder but dcoupled earlier.

~2! When T/d reduces to 2.2, thef e / f s range of lock-onincreases very significantly atA/d50.5. The cylinderoscillation at such large amplitude acts to reduce eff

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tive spacing between cylinders and to change the flregime from two distinct vortex streets to one wide aone narrow street. The lock-in of the multiple instabilifrequencies in the asymmetrical flow regime with toscillation frequency is probably responsible for the etended lock-in.

FIG. 10. Sequential photographs of flow visualization: vortex interactleads to a difference in the convection velocity between the inner vortshed from the two cylinders.T/d52.2, the upper cylinder is vibrating aA/d50.1, f e / f s5 f s1 / f s5 f s2 / f s51.22, Re5150.


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~3! At T/d52.2, the two streets do not seem to be stablea result of the oscillating cylinder. The oscillation effedepends on the mode of vortex streets. For in-antiphmode streets, the cross-stream inner vortices intestrongly and consequently break up quickly. A sing

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FIG. 11. Sequential photographs of flow visualization: the same convtion velocity for the inner vortices shed from the two cylinders.T/d53.5,the upper cylinder is vibrating atA/d50.5, f e / f s5 f s1 / f s5 f s2 /f s

51.22, Re5150.


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street probably emerges further downstream. Forphase mode streets, the two cross-stream vortices bethe oscillating cylinder tend to pair. The pairing vorticare likely to induce a low-pressure region between thethus drawing in the gap vortex generated by the statiary cylinder. The amalgamation of the three vorticleads to the formation of a single vortex street dowstream, which is probably asymmetrical. The observatis consistent with the occurrence of the asymmetriflow regime, which has been extended beyond thatthe stationary cylinders because of the oscillation of ocylinder.

~4! The amalgamation of the gap vortex shed from the stionary cylinder with two cross-stream vortices genated by the oscillating cylinder acts to slow down tsubsequent vortices shed from the stationary cylindera result, the in-antiphase vortex formation changes toin-phase formation. Similar vortex interaction is assoated with the variation from the in-phase vortex formtion to the in-antiphase streets.

~5! Two symmetrically formed gap vortices may have beconvected at different velocity. The convection velocof the gap vortex shed from the stationary cylinder wreduced due to the amalgamation of this vortex with tcross-stream vortices generated by the oscillating cyder. On the other hand, the gap vortex shed fromoscillating cylinder could be accelerated in the processpairing with the cross-stream outer vortex.

ACKNOWLEDGMENT

The authors wish to acknowledge support given to thby the Central Research Grant of The Hong Kong Polytenic University through Grant No. G-W009.

1R. E. D. Bishop and A. Y. Hassan, ‘‘The lift and drag forces on a circucylinder oscillating in a flowing fluid,’’ Proc. R. Soc. London, Ser. A277,51 ~1964!.

2G. H. Koopmann, ‘‘The vortex wakes of vibrating cylinders at low Renolds numbers,’’ J. Fluid Mech.28, 501 ~1967!.

3O. M. Griffin and C. W. Votaw, ‘‘The vortex street in the wake ofvibrating cylinder,’’ J. Fluid Mech.55, 31 ~1972!.

4O. M. Griffin and S. E. Ramberg, ‘‘The vortex street in the wake ofvibrating cylinder,’’ J. Fluid Mech.66, 553 ~1974!.


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,-

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--

se

--

n

s

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-

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5C. H. K. Williamson and A. Roshko, ‘‘Vortex formation in the wake of aoscillating cylinder,’’ J. Fluids Struct.2, 355 ~1988!.

6A. Ongoren and D. Rockwell, ‘‘Flow structure from an oscillating cylinder. Part I: Mechanisms of phase shift and recovery in the near wakeFluid Mech.191, 197 ~1988!.

7A. Ongoren and D. Rockwell, ‘‘Flow structure from an oscillating cylinder. Part II: Mode competition in the near wake,’’ J. Fluid Mech.191, 225~1988!.

8H. M. Blackburn and R. D. Henderson, ‘‘A study of two-dimensional flopast an oscillating cylinder,’’ J. Fluid Mech.385, 255 ~1999!.

9S. Ishigai, E. Nishikawa, K. Nishmura, and K. Cho, ‘‘Experimental stuon structure of gas flow in the tube banks with tube axes normal to fl~Part 1, Karman vortex flow around two tubes at various spacings!,’’ Bull.JSME15, 949 ~1972!.

10P. W. Bearman and A. J. Wadcock, ‘‘The interaction between a paircircular cylinders normal to a stream,’’ J. Fluid Mech.61, 499 ~1973!.

11C. H. K. Williamson, ‘‘Evolution of a single wake behind a pair of blubodies,’’ J. Fluid Mech.159, 1 ~1985!.

12Y. Zhou, Z. J. Wang, R. M. C. So, S. J. Xu, and W. Jin, ‘‘Free vibratioof two side-by-side cylinders in a cross flow,’’ J. Fluid Mech.443, 197~2001!.

13Y. Zhou and R. A. Antonia, ‘‘Critical points in a turbulent near-wake,’’Fluid Mech.275, 59 ~1994!.

14D. Sumner, S. S. T. Wong, S. J. Price, and M. P. Paidoussis, ‘‘Fluidhaviour of side-by-side circular cylinders in steady cross-flow,’’ J. FluStruct.13, 309 ~1999!.

15N. Mahir and D. Rockwell, ‘‘Vortex formation from a forced system otwo cylinders: Part II: Side-by-side arrangement,’’ J. Fluids Struct.10, 491~1996!.

16M. M. Zdravkovich,Flow Around Circular Cylinders~Oxford UniversityPress, Oxford, 1997!, Vol. 1, pp. 38 and 192.

17R. King, ‘‘A review of vortex shedding research and its applicationOcean Eng.4, 141 ~1977!.

18O. M. Griffin, ‘‘OTEC cold water pipe design for problems causedvortex-excited oscillation,’’ NRL Memorandum Report 4157, Naval Rsearch Laboratory, Washington, DC, 1980.

19Y. Zhou, H. J. Zhang, and M. W. Yiu, ‘‘The turbulent wake of two sideby-side circular cylinders,’’ J. Fluid Mech.458, 303 ~2002!.

20Y. Zhou, R. M. C. So, W. Jin, H. G. Xu, and P. K. C. Chan, ‘‘Dynamstrain measurements of a circular cylinder in a cross flow using a fiBragg grating sensor,’’ Exp. Fluids27, 359 ~1999!.

21N. Mahir and D. Rockwell, ‘‘Vortex formation from a forced system otwo cylinders: Part I: tandem arrangement,’’ J. Fluids Struct.10, 473~1996!.

22J. N. Cimbala, H. M. Nagib, and A. Roshko, ‘‘Large structure in the fwakes of two-dimensional bluff bodies,’’ J. Fluid Mech.190, 265 ~1988!.

23L. Landweber, ‘‘Flow about a pair of adjacent, parallel cylinders normaa stream,’’ D. W. Taylor Model Basin, Department of Navy, Report485,Washington, DC, 1942.


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