Spring-Supported Cylinder Wake Control · I. Introduction FLUID ‘ owing over ... an...

AIAA JOURNAL

Vol 41 No 8 August 2003

Spring-Supported Cylinder Wake Control

M M Zhangcurren Y Zhoudagger and L ChengDagger

Hong Kong Polytechnic University Kowloon Hong Kong Peoplersquos Republic of China

A novel technique is proposed for the vortex control in the wake of a freely vibrating bluff body The essenceof the technique is to create a local perturbation on the surface of the body using piezoelectric actuators thusmodifying interactions between the ow and the structure A square cylinder exibly supported on springs at bothends was placed in a uniform ow and allowed to vibrate laterally Three actuators were embedded underneathone side parallel to the ow of the cylinder They were simultaneouslyactivated by a sinusoidal wave thus causingthe cylinder surface to oscillate Measurements were conducted at the synchronization condition when the vortexshedding frequency fs coincided with the natural frequency of the uid-structure system As the perturbationfrequency fp of the actuators falls in the synchronization range both particle image velocimetry and laser-induced uorescence ow visualization captured dramatically enhanced vortices shed from the cylinder The circulation ofthese enhanced vortices doubled On the other hand when fp was shifted away from the synchronization the vortexcirculation dropped by about 50 The spectral analysis of the structural displacement signal Y and hot-wiresignal u points to the fact that the perturbation has altered uid-structure interactions the spectral phase AacuteYu atfs between uid excitation and structural vibration changing from 0 to iexclfrac14 namely from reinforcing each otherto dissipating each other The perturbation effect on the drag coef cient and the cross ow distribution of Reynoldsstresses is also investigated

I Introduction

F LUID owing over a bluff body is a common occurrenceExamples include ow past heat exchangers offshore struc-

tures power transmission lines and high-rise buildings When theReynoldsnumberRe exceedsa criticalvaluethe boundarylayerwillseparate from the body to form an unsteady ow pattern that is astaggered vortex street In engineering the unsteady ow patternaround the body often needs altering either cancelled for exampleto suppress ow-induced vibration or reinforced such as for trans-port enhancement in heat-transfer applications The vortex controlproblem has therefore attracted a great deal of interest in the past

The vortex control strategy can be passive or active A passivemethod requires no energy input thus having the advantage of be-ing easier to implement less expensive in cost and more stablePrevious passive approaches frequently rely on adding surface pro-trusionsshroudsor near-wakestabilizersto the structuresto modifyvortex shedding The methods have proved successful particularlyin offshore explorations and marine hydraulics

The activecontrolstrategycanbe separatedintoopen-and closed-loop control A closed-loop active control system uses actuatorsdriven by external energy sources through a feedback-signal con-trolled electronic system The action of the actuators alters uidor structural dynamics or interactions between the two nonlineardynamical systems thus counteracting the effect of the ow in-stability Berger1 was probably the rst to introduce the feedbackcontrol to suppress the wake instability He used a hot-wire signalobtained in the wake to actuate a bimorph cylinder and reportedthe possibilityof avoiding vortex shedding at a low Reynolds num-ber Re acute U1h=ordm D 80 where U1 is the freestreamvelocityh is thecharacteristicheightof the cylinderand ordm is the kinematicviscosityWarui and Fujisawa2 managed to reduce the vortex strength usingelectromagnetic actuators installed at both ends of a circular cylin-

Received 20 August 2002 revision received 13 December 2002acceptedfor publication 23 February 2003 Copyright cdeg 2003 by the American In-stitute of Aeronautics and Astronautics Inc All rights reserved Copies ofthis paper may be made for personal or internal use on condition that thecopier pay the $1000 per-copy fee to the Copyright Clearance Center Inc222 Rosewood Drive Danvers MA 01923 include the code 0001-145203$1000 in correspondence with the CCC

currenPhD Candidate Department of Mechanical Engineering Hung HomdaggerAssociate Professor Department of Mechanical Engineering Hung

HomDaggerProfessor Department of Mechanical Engineering Hung Hom

der to createa lateraloscillationwhichwas controlledby a feedbackhot-wire signal from the turbulent wake (Re D 67 pound 103) Fujisawaet al3 and Fujisawa and Nakabayashi4 introduced a rotational os-cillation and used different feedback control algorithms to reduceeffectivelyvelocity uctuations and drag force (Re D 2 pound 104) Thecylinder was activated by the hot-wire feedback signal from uctu-ating velocities in the wake Using a similar oscillation methodTokumaru and Dimotakis5 managed to attenuate both vortexstrength and drag force (Re D 15 pound 104) Shiels and Leonard6

investigated numerically the physics underlying Tokumaru andDimotakisrsquos observation and concluded that rotational oscillationtriggeredmultiplevorticitystructureswhich lead to a time-averagedseparationdelayand subsequentlydrag reductionBaz and Ro7 usedan electromagnetic actuator installed inside a cylinder to exert aforce on the cylinder The actuator was driven by a feedback hot-wire signal measured in the wake thus increasing damping to thecylinderand effectivelyreducingthe vortex-inducedvibrationat theoccurrenceof resonancewhen the vortexsheddingfrequency fs co-incided with the natural frequency f 0

n of the system One commonfeature in these investigations is to alter the structural dynamicssubsequently in uencing the ow eld

Another approachis to use acousticexcitation to control the ow- eld Ffowcs-Williams and Zhao8 used a hot-wire signal to providea feedback control into a loudspeaker mounted on the wind-tunnelwall The acoustic excitation from the loudspeaker suppressed vor-tex shedding from a cylinder (Re D 4 pound 102) Roussopoulos9 revis-ited the investigationand concludedthat the onsetReynoldsnumberfor vortex shedding could be increased by 20 as a result of thecontrol Lewit10 used a feedback hot-wire signal to activate soundwaves inside a circular tube The sound waves interacted with owthrough two rows of holes arranged at sect90 deg away from theforward stagnation line of the tube respectively so that the soundwaves through the two rows of holes were in antiphase thus sup-pressingvortexsheddingfrom the tube up to Re D 104 Huang11 alsointroduced sound again generated inside a cylinder and activatedby a feedback hot-wire signal from the wake into ow through athin slit on the cylinder surface He found that the shear ow nearthe slit was modi ed so that vortexsheddingcould be suppressedupto a Reynolds-number range between 4 pound 103 and 13 pound 104 BothLewit and Huang applied a high level of acoustic excitation (morethan 120 dB) in order to produce suf cient control effects Thismight not be a feasible solution when noise is a concern

In contrastwith the closed-loopcontrol an open-loopcontrol in-jects energy to the system without a feedback loop Williams et al12

1500

ZHANG ZHOU AND CHENG 1501

introducedsymmetric and antisymmetric acoustic excitationsinto awater ow (Re D 470) at a frequencyof about 2 fs through two rowsof holes located at sect45 deg respectively away from the forwardstagnation line of the cylinder He observed a modi ed behaviorof fs and the ow structure Using acoustic waves emitted from aslot on the surface of a cylinder Hsiao and Shyu13 demonstratedthat a local perturbation near the shear-layer instability frequencyand around the ow separation point caused an increase in lift buta reduction in drag and the vortex scale In both investigations theacoustic excitation did not have any apparent relationshipwith vor-tex shedding

The paper proposes an alternative to the existing open-loop con-trol methods A novel techniquebased on piezoelectric actuators isinvestigatedWhen placed within an electric eld the piezoelectriceffect results in a strain in the material Conventional piezoelectricwafers can only generatevery small deformationThe piezoceramicactuator presently investigated overcomes this obstacle by embed-ding a piezoelectric layer on the surface of a curved metallic thinplate Because of its special fabrication process and the effect ofcurvature a relatively large displacement can be achieved This ac-tuator is further characterized by a light weight and is capable ofgenerating large forces over a wide range of frequenciesWhen theactuator is used to create a perturbation on the surface of a bluffbody uid dynamics or interactionsbetween uid and structurecanbe altered thus modifying vortex sheddingThis technique is foundto be particularly effective for the control of vortices from a freelyvibrating structure in response to ow excitation especially whenresonance occurs Flow measurements using a laser-induced uo-rescence (LIF) techniqueparticle image velocimetry (PIV) and hotwire indicate that the vortex strength can be drastically reduced orincreaseddependingon the perturbationfrequencyThe correspond-ing variationin thecross owdistributionof Reynoldsstresses is alsomeasured using a two-component laser Doppler anemometer

II Experimental DetailsA Wind Tunnel and Test Cylinder

Experimentswere conductedin a closed-circuitwind tunnel witha square working section (06 pound 06 m) of 24-m length The windspeed of the working section is up to 50 ms The streamwise meanvelocityuniformityis about01and the turbulenceintensityis lessthan 04 More details of the tunnel were given in Zhou et al14 Analuminum alloy square cylinder of side h D 00152 m was mountedhorizontally in the midplane 02 m downstreamof the exit plane ofthe contraction and spanned the full width of the working sectionresulting in a blockage of about 253 The cylinder supportedon springs at both ends was allowed to vibrate laterally (Fig 1)Measurements were carried out on the resonance condition of the uid-structuresystem that is fs frac14 f 0

n (D30 Hz) The correspondingreduced velocity Ur acuteU1= f 0

nh was about 78 Re was 35 pound 103and the maximum displacementof cylinderYmax was about 12 mmor 008h

B Actuators and Their InstallationPiezoelectric actuators presently used were prestressed and

curved they consist of a number of composite laminates whichhave different thermal expansion coef cients and deform out-of-plane under an applied voltage Three actuators were embedded inseries in a slot on one side of the cylinder to support a thin plasticplate of 3 mm thick which was installed ush with the top cylindersurface(Fig 2) To minimize the asymmetryof the dynamicsystemthe opposite side of the cylinder was identically constructedbut noactuators were installed The length of the plastic plate was 049m that is two-thirds of the cylinder length The gap between theplastic plate and cylinder was very small about 01 mm and welllubricated The plate ushes with cylinder surface thus not chang-ing the cross section of the cylinder The actuators were activatedby a signal generated from a signal generator and ampli ed by adual-channel piezodriver ampli er (Trek PZD 700) Driven by theactuators this plate would oscillate to create the local perturbationof the cylinder surface

Fig 1 Experimental setup

Fig 2 Installation of actuators in the square cylinder model Thedrawing is not scaled to the actual size

Given a constant voltage the deformation of actuators and sub-sequently the perturbation displacement Yp of the upper cylindersurface can vary with the perturbation frequency f p In the presentinvestigation a constant rms voltage (1414 V) was imposed on theactuators At this voltage the Y curren

prms iexcl f currenp relationship (Fig 3) was

rst quanti ed under no ow condition where f currenp D f ph=U1 and

the rms value of the perturbation displacement Y currenprms D Yprms=h

Unless otherwise stated the asterisk denotes normalization by U1and h in this paper Yprms exhibits a peak over a small range of f curren

p The occurrence of the peak can be speci ed and is presently setover the range of f curren

p D 01 raquo 013 This range once set is not ad-justable for the same actuatorsThe maximum Yprms was 0319 mm(or 0021 h at f curren

p D 013

C Flow eld MeasurementsThe velocity eldwas measuredusinga DantecstandardPIV2100

systembeforeand after theperturbationFlow was seededby smokewhichwas generatedfromparaf n oil of a particlesize around1 sup1min diameter Flow was illuminated in the plane of mean shearby twonew wave standardpulsed laser sources of a wavelength of 532 nmeach having a maximum energy output of 120 mJ Digital particleimages were taken using one charge-coupleddevice (CCD) camera(HiSense Type 13 gainpound 4 double frames 1280pound 1024 pixels)A

1502 ZHANG ZHOU AND CHENG

Fig 3 Dependence of the perturbation amplitude on the perturbationfrequency under a constant voltage (no ow)

Dantec FlowMap Processor (PIV2100 type) was used to synchro-nize image taking and illumination A wide-angle lens was used sothat each image covered an area of 150 pound 120 mm of the ow eldthat is x=h frac14 08 raquo 108 and y=h frac14 iexcl27 raquo 52 the x and y coor-dinates and their origin are de ned in Fig 1 The longitudinal andlateral image magni cations were identical that is 012 mmpixelEach laser pulse lasted 001 sup1s The interval between two succes-sive pulses was typically 50 sup1s Thus a particle would only travel0179 mm (153 pixels or 00118h at U1 D 3576 ms which wasused for measurementsAn optical lter was used to allow only thegreen light (wavelengthD 532 nm) generated by a laser source topass In the image processing 32 pound 32 rectangular interrogationar-eas were used Each interrogationarea included 32 pixels (frac14025hwith 25 overlap with other areas in either the longitudinal or lat-eral direction The ensuing in-plane velocity vector eld consistedof 53 pound 42 vectors Spanwise vorticity component z was approxi-mately obtained based on particle velocities using a central differ-ence scheme The spatial resolution of vorticity estimate dependson grid spacing about 29 mm or 019h

The LIF measurementwas conductedusingthe ow-visualizationfunction of the PIV system The same smoke as used in thePIV measurement was introduced through eight injection pinholes(diameterD 1 mm) symmetricallydistributedat the midspan of theleading side (normal to the ow direction)of the cylinderThe CCDcamera was used on the single-exposuremode A wide-angle lenswas also used to enlarge the view eld so that each image coveredan area of approximately 165 pound 125 mm or x=h frac14 033 raquo 112 andy=h frac14 iexcl41 raquo 41 in the ow eld The recording interval betweensuccessiveimageswas 0143s Other con gurationparametersweresimilar to the PIV measurement

D Cylinder Displacement and FluctuatingFlow Velocity Measurements

A Polytec Series 3000 dual beam laser vibrometer15 and a 5-sup1mtungstenhotwire wereused to measuresimultaneouslythestructuraldisplacement and ow velocity respectively The hot wire placedat x=h D 2 and y=h D 15 was operated at an overheat ratio of 18with a constant temperatureanemometerSignals fromboth the laservibrometer and the hot wire were conditionedand digitized using a12-bit AD board at a sampling frequency of 35 kHz per channelThe duration of each record was about 20 s

The mean NU and NV and uctuatingvelocities u and v along the xand y directionrespectivelyin the wake (x=h D 3 raquo 25) were mea-sured using a two-component laser Doppler anemometer (LDA)system (Dantec Model 58N40 with an enhanced ow velocity anal-yser signal processor) The measuring volume has a minor axis of118 mm and a major axis of 248 mm Thus the measured meanvelocity was estimated to have an error of less than 3 and thecorresponding error for the measured rms values u rms and vrms wasless than 10 The seeding was provided by smoke the same asused in the PIV and LIF measurements

III Perturbation EffectsA Impaired Vortex Strength

Figure 4 shows the photograph taken using the LIF techniquewhen the uid-structuresystem was under the resonance conditionthat is f curren

s D f0currenn D 013 (Re D 35 pound 103 Ur D 78 without any ex-

ternalperturbationThe solid square in the gure indicatesthe cylin-der position The Karman vortex street is evident The isocontour(Fig 5) of the normalized spanwise vorticity curren

z D zh=U1 fromthe PIV measurement show a similar ow pattern The uncertaintyof the vorticity measurement was estimated to be about 9

Oncea perturbationwas introducedat f currenp D 01 howeverthe ow

structurechangeddrasticallyas shown in Fig 6 The Karman vortexstreet appears to be breakingup and greatly impaired irrespectiveofthe phase of the cylinder oscillation The quantitative informationon the impaired vortex street can be gained from the contour of curren

z

(Fig 7) The magnitude jcurrenz maxj of the maximum curren

z drops by about46 Furthermore the size of vortices also shrinks signi cantlyThe circulation around a vortex can be estimated by the followingnumerical integration16

0

U1hD

X

i j

iexclcurren

z

centi j

1A

h2(1)

where currenz i j is spanwise vorticity over area 1A D 1x1y with 1x

and 1y being the integral step along the x and y directions re-spectively Integration was conducted over an area enclosed by thecutoff level jcurren

zcj D 04 about 10 of jcurrenz maxj as used by Sumner

Fig 4 Typical photograph from LIF measurements of unperturbedvortex shedding ( f curren

p = 0 Ur = 78 Re = 35 poundpound 103) Flow is right to left

Fig 5 The isocontour of spanwise vorticity currenz = zhU1 from PIV

measurements of unperturbed vortex shedding ( f currenp = 0 Ur = 78 Re =

35 poundpound 103 ) the contour increment centcurrenz = 04 the cutoff level jjcurren

zcjj =04 Flow is right to left


Fig 6 TypicalphotographfromLIF measurements of impaired vortexshedding ( f curren

p = 01 is beyond the synchronization range Ur = 78 Re =35 poundpound 103 ) Flow is right to left

Fig 7 The isocontour of spanwise vorticity currenz = zh U1 from PIV

measurements of impaired vortex shedding ( f currenp = 01 is beyond the syn-

chronization range Ur = 78 Re = 35 poundpound 103 ) the contour incrementcentcurren

z = 04 the cutoff level jjcurrenzcjj = 04 Flow is right to left

et al17 The error associated with the 0 estimate is about 15 Thedecrease in 0 exceeds 50 compared with the case without pertur-bation (Fig 5)

B Enhanced Vortex StrengthAs the perturbationfrequencywas increased to f curren

p D 013 whichcoincided with the natural frequency of the uid-cylinder systemthe vortex shedding (Fig 8) was enhanced The vortices appearbetter organizedand larger in size when comparedwith that withoutperturbation (Fig 4) This is more evident in the contour of curren

z

(Fig 9) The magnitude of the maximum currenz experiences a jump

of 38 the size enclosed by jcurrenzcj D 04 increases drastically (that

is Fig 5) Accordingly a conservative estimate of 0 (part of thearea enclosed by jcurren

zcj D 04 was outside the PIV image) doublesthat in Fig 5 Consideringa relatively small perturbationamplitudeYprms=h D 2 (Ymax=h D 8) the variation in the vortex street isastonishing implying a great change in uid-structure interactionsduring the vortex shedding process

The surface perturbation was imposed only on the upper side ofthe squarecylinderbut both sides of the wake centerline(Figs 6ndash9)appear equally affected The observation suggests that the localperturbation has changed the global interaction between uid andstructure

IV Perturbed Fluid-Structure InteractionsIt has been seen from Sec III that f curren

p is crucial in how the per-turbation would in uence the near wake and implicitly the uid-

Fig 8 Typical photograph from LIF measurements of enhanced vor-tex shedding ( f curren

p = 013 is within the synchronization range Ur = 78Re = 35 poundpound 103) Flow is right to left

Fig 9 Isocontour of spanwise vorticity currenz = zh U1 from the PIV

measurements of enhanced vortex shedding ( f currenp = 013 is within the

synchronizationrange Ur = 78 Re = 35 poundpound 103) the contour incrementcentcurren


structure interaction To thoroughly understand the f currenp effect on

uid-structure interactions when synchronization ( f currens D f

0currenn oc-

curs the structural oscillation and streamwise uctuating ow ve-locitywere simultaneouslymeasuredusing the laser vibrometeranda single hot wire (hot wire was located at x=h D 2 and y=h D 15)respectivelyas f curren

p varied from 0 to 034Figures 10a and 10b display the power spectral density func-

tions EY and Eu of Y and u respectively The spectrum of uc-tuation reg (reg represents either Y or u has been normalized sothat

R 10

Ereg f d f D 1 At f currenp D 0 a pronounced peak occurs at

f currens D 013 in both EY and Eu the number (091 in EY and 059

in Eu near the peak indicating the peak magnitude at f currens The sec-

ond harmonic is also evident at f curren D 026 Once the perturbationis introduced both EY and Eu show an additional spike at f curren

p Forf curren

p middot 01 the peak value at f currens is attenuated for both EY and Eu

The attenuation effect is most signi cant at f currenp D 01 where the

peak value in EY and Eu is only 25 and 40 respectively of itscounterpart at f curren

p D 0 The result is consistent with the LIF andPIV measurements (Figs 6 and 7) Note that the peak at the sec-ond harmonic is also appreciably reduced As f curren

p exceeds 013 butnot beyond the second harmonic 026 of f curren

s the peak at f currens in EY

and Eu is more pronounced than at f currenp D 0 the maximum occurs at

f currenp D 013 where f curren

p D f currens D f

0currenn and the peak value in both EY and

Eu are more than twice the value at f currenp D 0 agreeable with the LIF

and PIV data (Figs 8 and 9) But once f currenp reaches 03 and beyond

the peak value drops below that at f currenp D 0 Evidently the in uence

of the perturbationdependson the interrelationshipbetween f currenp and

f currens or f

0currenn


a) b)

Fig 10 At variousperturbation frequency f currenp a) power spectra of cylinder displacement Y and b) uctuating ow velocity u The hot wire was located

at xh = 2 yh = 15

Fig 11 Effect of the perturbation frequency on the spectral coherenceCohYu at fcurren

s frac14 013between the Y and u signalsThe hot wire was locatedat xh = 2 yh = 15

The spectral coherence between Y and u calculated byCohYu D Co2

Yu C Q2Yu=EY Eu providesa measure of the degree of

correlationbetween the Fourier componentsof Y and u where CoYu

and QYu are the cospectrumand quadraturespectrum of Y and u re-spectively Here the cross spectrum is computed from the Fouriertransform of the correlation Y t C iquestut (see Zhang et al18 formore details) Figure 11 presents CohYu at fs as f curren

p varies The per-turbation causes an increase in CohYu at fs compared with that at

f currenp D 0 for 01 lt f curren

p middot 026 and otherwisea decreaseThe enhancedCohYu range can result from synchronizationbetween vortex shed-ding and induced vibration Based on experimental data Gowda19

suggested that for bluff bodies with xed separation points thesynchronizationphenomenon began at fs frac14 08 f 0

n and ended whenfs frac14 2 f 0

n This corresponds presently to a frequency range of f currenp D

011 raquo 026 coinciding well with the range of enhanced CohYuTo gain a better insight into the relationship between the Y and

u signalsCoYu is examined in Fig 12 A strong peak occurs at f currens

which is negativefor 0 lt f currenp middot 01 positivefor 01 lt f curren

p middot 026 andnegative again for f curren

p gt 026 The peak indicates a good correlationbetween Y and u at f curren

s whereas the positive and negative signs cor-respondto in phasedand antiphasedY and u at f curren

s respectivelyTheaverage phase shift between Y and u can be quanti ed by the spec-tral phaseangle (Fig 13) de ned by AacuteYu[acute taniexcl1QYu=CoYu] Thisangle is zero at f curren

p D 0 close to iexclfrac14 for 0 lt f currenp middot 01 and uctuating

about zero for f currenp gt 01

An interpretation is now proposed for the enhancement and im-pairmentof vortexsheddingAs f curren

p fallswithin thepossiblesynchro-nization range the perturbation will not break the synchronizationbetween vortex shedding and structural vibration instead the per-turbation is more likely to increase the strength of synchronizationor resonance Notably at f curren

p D 013 where f 0n D fs D f p CohYu at

fs reaches the maximum090Howeverwhen f currenp is beyondthe syn-

chronization range the perturbation changes the phase relationshipbetween synchronizing structural oscillation and vortex sheddingfrom zero to near iexclfrac14 This implies an alteration in the nature of


Fig 12 Cospectrum between the Y and u signals at various perturba-tion frequency fcurren

p The hot wire was located at xh = 2 yh = 15

Fig 13 Effect of the perturbation frequency on the phase shift AacuteYuat f curren

s frac14 013 between the Y and u signals The hot wire was located atxh = 2 yh = 15

uid-structureinteractionsthe in-phased uid excitationand struc-tural oscillation turning into antiphased interactions against eachother which dissipate each other in energy and result in drasticweakening vortex shedding and structural oscillation

It is pertinent to comment that CohYu at fs drops to the minimumat f curren

p D 01and reachesthemaximumat f currenp D 013The perturbation

effect is dependent on Yprms as well as f currenp The Yprms peak is

presently set at f currenp D 01 raquo 013 (Fig 3) This might explain why

a)

b)

c)

d)

Fig 14 Cross ow distribution of mean velocity Reynolds stresses atxh = 3 a) U

curren b) u2

curren c) v2

currenand d) uvcurren

the perturbation effect is particularlyeminent in this f currenp range The

small Yprms for f currenp D 002 raquo 007 and f curren

p cedil 026 is at least partiallyresponsible for the relatively weak perturbation effect over thesefrequencies (Fig 11)

V Downstream Evolution of Perturbed FlowIt might be of fundamental interest to estimate how far down-

stream of the cylinder the perturbation effect could persist This isinvestigated by examining the cross ow distribution of mean ve-locity U

currenand Reynolds stresses u2

curren v2

curren and uvcurren obtained from

the LDA measurementFigure 14 presents a comparison in Ucurren u2

curren

v2curren and uvcurren at x=h D 3 between the cases without perturbationand

the impaired ( f currenp = 01) or enhanced vortex street ( f curren

p D 013) Forf curren

p D 01 the maximum of Ucurren u2

curren v2

curren and uvcurren at x=h D 3 shows

a considerable decrease down to 85 85 88 and 78 of that un-perturbed respectively On the other hand for f curren

p D 013 the fourquantities increaseby 16 13 10 and 22 respectivelyThe resultsare in line with the LIF and PIV measurements The perturbationon the upper side of the cylinder has the equal effect on either sideof the wake centerline as qualitatively seen from the vortex street(Figs 6ndash9) The difference is still discernible at x=h D 20 but van-ishes at x=h D 25 (not shown)

One remark is caused by the perturbation effect on the drag co-ef cient CD which can be estimated based on U

curren u2

curren and v2

curren

(Ref 20) that is

CD D 2

Z 1

iexcl1

U

U1

sup3U1 iexcl U

U1

acuted

sup3y

h

acuteC2

Z 1

iexcl1

sup3v2 iexcl u2

U 21

acuted

sup3y

h

acute

(2)


Without perturbation CD is 188 falling in the range (17 raquo 20)reported previously21iexcl23 CD dropped marginally about 5 for thecase of impaired vortex shedding ( f curren

p D 01) but jumped by 17when vortex shedding was enhanced ( f curren

p D 013)

VI ConclusionsPiezoceramic actuators have been deployed to generate a pertur-

bationof controllablefrequencyand amplitudeon a squarecylinderThe perturbationcan be used for the effectivecontrolof vortexshed-ding from a bluff body in a cross ow Investigation is conductedwhen a square cylinder and ow system experiences resonanceleading to the following conclusions

1)When theperturbationfrequency f currenp is outsidethe synchroniza-

tion rangeof the uid-cylindersystem the uid-structureinteractionhasbeen alteredso thatvortexsheddingandstructuraloscillationareanti-phasedThe spectral coherence at fs drops from 066 ( f curren

p D 0)to 015 ( f curren

p D 01) Correspondingly the vortex strength (circula-tion) reduces by 50 The drag coef cient CD decreases slightlyonly 5

2) When f currenp falls within the synchronization range of the uid-

cylinder system vortex shedding and structural oscillation remainsynchronized As a matter of fact the spectral coherence at fs in-creases substantiallyfrom 066 at f curren

p D 0 to 090 at f currenp D 013 As a

result the vortex strength exceeds twice that at f currenp D 0 There is an

increase of 17 in CD 3) The perturbation also alters considerably the cross ow distri-

bution of Ucurren u2

curren v2

curren and uvcurren The maximumU

curren u2

curren v2

curren and uvcurren

values at x=h D 3 drop by 146 152 121 and 220 respectivelyinthe attenuatedvortex-sheddingcase and increaseby 162130946and 217 respectivelyin the enhancedvortex-sheddingcase Theperturbation effect persists up to x=h frac14 25

AcknowledgmentThe authors acknowledge support given to them by the Central

Research Grant of the Hong Kong Polytechnic University throughGrant G-W108

References1Berger E ldquoSuppression of Vortex Shedding and Turbulence Behind

Oscillating Cylindersrdquo Physics of Fluids Vol 10 1967 pp 191ndash1932Warui H M and Fujisawa N ldquoFeedback Control of Vortex Shedding

from a Circular Cylinderby Cross-FlowCylinderOscillationsrdquo Experimentsin Fluids Vol 21 1996 pp 49ndash56

3Fujisawa N Kawajiand Y and Ikemoto K ldquoFeedback Controlof Vor-tex Shedding from a Circular Cylinder by Rotational Oscillationsrdquo Journalof Fluids and Structures Vol 15 2001 pp 23ndash37

4Fujisawa N and Nakabayashi T ldquoNeural Network Control of VortexSheddingfrom a Circular CylinderUsing RotationalFeedback OscillationsrdquoJournal of Fluids and Structures Vol 16 2002 pp 113ndash119

5Tokumaru P T and Dimotakis P E ldquoRotary Oscillation Control of aCylinder Wakerdquo Journal of Fluid Mechanics Vol 224 1991 pp 77ndash90

6Shiels D and Leonard A ldquoInvestigation of a Drag Reduction on a Cir-cular Cylinder in Rotary Oscillationrdquo Journal of Fluid Mechanics Vol 4312001 pp 297ndash322

7Baz A and Ro J ldquoActive Control of Flow-Induced Vibrations of aFlexible Cylinder Using Direct Velocity Feedbackrdquo Journal of Sound andVibration Vol 146 1991 pp 33ndash45

8Ffowcs-Williams J E and Zhao B C ldquoThe Active Control of VortexSheddingrdquo Journal of Fluids and Structures Vol 3 1989 pp 115ndash122

9Roussopoulos K ldquoFeedback Control of Vortex Shedding at LowReynolds Numbersrdquo Journal of Fluid Mechanics Vol 248 1993pp 267ndash296

10Lewit M ldquoActive Control of Dipole Sound from Cylindersrdquo Proceed-ings of DAGArsquo92 1992

11Huang X Y ldquoFeedback Control of Vortex Shedding from a CircularCylinderrdquo Experiments in Fluids Vol 20 1996 pp 218ndash224

12Williams D R Mansy H and Amato C ldquoThe Response and Sym-metry Properties of a Cylindrical Wake Subjected to Localized Surface Ex-citationrdquo Journal of Fluid Mechanics Vol 234 1992 pp 71ndash96

13Hsiao F B and Shyu J Y ldquoIn uence of Internal Acoustic Excitationupon Flow Passing a Circular Cylinderrdquo Journal of Fluids and StructuresVol 5 1991 pp 427ndash442

14Zhou Y Zhang H J and Liu M W ldquoThe Turbulent Wake of TwoSide-by-Side Circular Cylindersrdquo Journal of Fluid Mechanics Vol 4582002 pp 303ndash332

15ZhouY So R M C Jin W Xu H G and Chan P K C ldquoDynamicStrain Measurements of a Circular Cylinder in a Cross Flow Using a FibreBragg Grating Sensorrdquo Experiments in Fluids Vol 27 1999 pp 359ndash367

16Cantwell B and Coles D ldquoAn Experimental Study of Entrainmentand Transport in the Turbulent Near Wake of a Circular Cylinderrdquo Journalof Fluid Mechanics Vol 136 1983 pp 321ndash374

17Sumner D Price S J and PaDaggerdoussisM P ldquoFlow-Pattern Identi ca-tion for Two Staggered Circular Cylinders in Cross-Flowrdquo Journal of FluidMechanics Vol 411 2000 pp 263ndash303

18Zhang H J Zhou Y and Antonia R A ldquoLongitudinal and Span-wise Structures in a Turbulent Wakerdquo Physics of Fluids Vol 12 2000pp 2954ndash2964

19Gowda B H L ldquoSome Measurements on the Phenomenon of VortexSheddingand Induced Vibrations of Circular Cylindersrdquo Deutsche Luft-undRaumfahrt Forschungsbericht No 75-01 1975

20AntoniaR A and Rajagopalan S ldquoA Comment on the DeterminationofDrag of a Circular CylinderrdquoAIAA Journal Vol 28 1990pp 1833ndash1835

21Knisely C W ldquoStrouhal Numbers of Rectangular Cylinders atIncidencemdashA Review and New Datardquo Journal of Fluids and StructuresVol 4 1990 pp 371ndash393

22ZhouY and AntoniaR A ldquoEffect of Initial Conditionson Vortices ina TurbulentNear Wakerdquo AIAA Journal Vol 32 No 6 1994pp 1207ndash1213

23Lee B E ldquoThe Effect of Turbulence on the Surface Pressure Field ofa Square Prismrdquo Journal of Fluid Mechanics Vol 69 1975 pp 263ndash282

W J DahmAssociate Editor


introducedsymmetric and antisymmetric acoustic excitationsinto awater ow (Re D 470) at a frequencyof about 2 fs through two rowsof holes located at sect45 deg respectively away from the forwardstagnation line of the cylinder He observed a modi ed behaviorof fs and the ow structure Using acoustic waves emitted from aslot on the surface of a cylinder Hsiao and Shyu13 demonstratedthat a local perturbation near the shear-layer instability frequencyand around the ow separation point caused an increase in lift buta reduction in drag and the vortex scale In both investigations theacoustic excitation did not have any apparent relationshipwith vor-tex shedding

The paper proposes an alternative to the existing open-loop con-trol methods A novel techniquebased on piezoelectric actuators isinvestigatedWhen placed within an electric eld the piezoelectriceffect results in a strain in the material Conventional piezoelectricwafers can only generatevery small deformationThe piezoceramicactuator presently investigated overcomes this obstacle by embed-ding a piezoelectric layer on the surface of a curved metallic thinplate Because of its special fabrication process and the effect ofcurvature a relatively large displacement can be achieved This ac-tuator is further characterized by a light weight and is capable ofgenerating large forces over a wide range of frequenciesWhen theactuator is used to create a perturbation on the surface of a bluffbody uid dynamics or interactionsbetween uid and structurecanbe altered thus modifying vortex sheddingThis technique is foundto be particularly effective for the control of vortices from a freelyvibrating structure in response to ow excitation especially whenresonance occurs Flow measurements using a laser-induced uo-rescence (LIF) techniqueparticle image velocimetry (PIV) and hotwire indicate that the vortex strength can be drastically reduced orincreaseddependingon the perturbationfrequencyThe correspond-ing variationin thecross owdistributionof Reynoldsstresses is alsomeasured using a two-component laser Doppler anemometer

II Experimental DetailsA Wind Tunnel and Test Cylinder

Experimentswere conductedin a closed-circuitwind tunnel witha square working section (06 pound 06 m) of 24-m length The windspeed of the working section is up to 50 ms The streamwise meanvelocityuniformityis about01and the turbulenceintensityis lessthan 04 More details of the tunnel were given in Zhou et al14 Analuminum alloy square cylinder of side h D 00152 m was mountedhorizontally in the midplane 02 m downstreamof the exit plane ofthe contraction and spanned the full width of the working sectionresulting in a blockage of about 253 The cylinder supportedon springs at both ends was allowed to vibrate laterally (Fig 1)Measurements were carried out on the resonance condition of the uid-structuresystem that is fs frac14 f 0

n (D30 Hz) The correspondingreduced velocity Ur acuteU1= f 0

nh was about 78 Re was 35 pound 103and the maximum displacementof cylinderYmax was about 12 mmor 008h

B Actuators and Their InstallationPiezoelectric actuators presently used were prestressed and

curved they consist of a number of composite laminates whichhave different thermal expansion coef cients and deform out-of-plane under an applied voltage Three actuators were embedded inseries in a slot on one side of the cylinder to support a thin plasticplate of 3 mm thick which was installed ush with the top cylindersurface(Fig 2) To minimize the asymmetryof the dynamicsystemthe opposite side of the cylinder was identically constructedbut noactuators were installed The length of the plastic plate was 049m that is two-thirds of the cylinder length The gap between theplastic plate and cylinder was very small about 01 mm and welllubricated The plate ushes with cylinder surface thus not chang-ing the cross section of the cylinder The actuators were activatedby a signal generated from a signal generator and ampli ed by adual-channel piezodriver ampli er (Trek PZD 700) Driven by theactuators this plate would oscillate to create the local perturbationof the cylinder surface

Fig 1 Experimental setup

Fig 2 Installation of actuators in the square cylinder model Thedrawing is not scaled to the actual size

Given a constant voltage the deformation of actuators and sub-sequently the perturbation displacement Yp of the upper cylindersurface can vary with the perturbation frequency f p In the presentinvestigation a constant rms voltage (1414 V) was imposed on theactuators At this voltage the Y curren

prms iexcl f currenp relationship (Fig 3) was

rst quanti ed under no ow condition where f currenp D f ph=U1 and

the rms value of the perturbation displacement Y currenprms D Yprms=h

Unless otherwise stated the asterisk denotes normalization by U1and h in this paper Yprms exhibits a peak over a small range of f curren

p The occurrence of the peak can be speci ed and is presently setover the range of f curren

p D 01 raquo 013 This range once set is not ad-justable for the same actuatorsThe maximum Yprms was 0319 mm(or 0021 h at f curren

p D 013

C Flow eld MeasurementsThe velocity eldwas measuredusinga DantecstandardPIV2100

systembeforeand after theperturbationFlow was seededby smokewhichwas generatedfromparaf n oil of a particlesize around1 sup1min diameter Flow was illuminated in the plane of mean shearby twonew wave standardpulsed laser sources of a wavelength of 532 nmeach having a maximum energy output of 120 mJ Digital particleimages were taken using one charge-coupleddevice (CCD) camera(HiSense Type 13 gainpound 4 double frames 1280pound 1024 pixels)A















z



0

U1hD

X

i j

iexclcurren

z

centi j

1A

h2(1)




















z
















0currenn oc-




R 10





p Forf curren









p D f currens D f






f currens or f

0currenn


a) b)


at xh = 2 yh = 15





































a)

b)

c)

d)


curren b) u2

curren c) v2








curren v2



curren





curren v2





curren u2

curren and v2

curren

(Ref 20) that is

CD D 2

Z 1

iexcl1

U

U1

sup3U1 iexcl U

U1

acuted

sup3y

h

acuteC2

Z 1

iexcl1

sup3v2 iexcl u2

U 21

acuted

sup3y

h

acute

(2)




p D 013)













curren v2


curren u2

curren v2

curren and uvcurren











































z



0

U1hD

X

i j

iexclcurren

z

centi j

1A

h2(1)




















z
















0currenn oc-




R 10





p Forf curren









p D f currens D f






f currens or f

0currenn


a) b)


at xh = 2 yh = 15





































a)

b)

c)

d)


curren b) u2

curren c) v2








curren v2



curren





curren v2





curren u2

curren and v2

curren

(Ref 20) that is

CD D 2

Z 1

iexcl1

U

U1

sup3U1 iexcl U

U1

acuted

sup3y

h

acuteC2

Z 1

iexcl1

sup3v2 iexcl u2

U 21

acuted

sup3y

h

acute

(2)




p D 013)













curren v2


curren u2

curren v2

curren and uvcurren







































z
















0currenn oc-




R 10





p Forf curren









p D f currens D f






f currens or f

0currenn


a) b)


at xh = 2 yh = 15





































a)

b)

c)

d)


curren b) u2

curren c) v2








curren v2



curren





curren v2





curren u2

curren and v2

curren

(Ref 20) that is

CD D 2

Z 1

iexcl1

U

U1

sup3U1 iexcl U

U1

acuted

sup3y

h

acuteC2

Z 1

iexcl1

sup3v2 iexcl u2

U 21

acuted

sup3y

h

acute

(2)




p D 013)













curren v2


curren u2

curren v2

curren and uvcurren






























a) b)


at xh = 2 yh = 15





































a)

b)

c)

d)


curren b) u2

curren c) v2








curren v2



curren





curren v2





curren u2

curren and v2

curren

(Ref 20) that is

CD D 2

Z 1

iexcl1

U

U1

sup3U1 iexcl U

U1

acuted

sup3y

h

acuteC2

Z 1

iexcl1

sup3v2 iexcl u2

U 21

acuted

sup3y

h

acute

(2)




p D 013)













curren v2


curren u2

curren v2

curren and uvcurren







































a)

b)

c)

d)


curren b) u2

curren c) v2








curren v2



curren





curren v2





curren u2

curren and v2

curren

(Ref 20) that is

CD D 2

Z 1

iexcl1

U

U1

sup3U1 iexcl U

U1

acuted

sup3y

h

acuteC2

Z 1

iexcl1

sup3v2 iexcl u2

U 21

acuted

sup3y

h

acute

(2)




p D 013)













curren v2


curren u2

curren v2

curren and uvcurren
































p D 013)













curren v2


curren u2

curren v2

curren and uvcurren





























Spring-Supported Cylinder Wake Control · I. Introduction FLUID ‘ owing over ... an...

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Transcript of Spring-Supported Cylinder Wake Control · I. Introduction FLUID ‘ owing over ... an...