WATER TUNNEL EXPERIMENTAL INVESTIGATION ON THE DRAG REDUCTION CHARACTERISTICS OF THE TRAVELING WAVY

65Available online at www.sciencedirect.com中ScienceDirect+JIIDJoumal of HydrodynamicsELSEVIER201 1,23(1 ):65-70www. sciencedirect.com/science/journal/10016058DOI: 10.1016/S1001-658(10)60089-3WATER TUNNEL EXPERIMENTAL INVESTIGATION ON THE DRAGREDUCTION CHARACTERISTICS OF THE TRAVELING WAVY WALL°YAO YanDepartment of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240, ChinaBejjing Electromechanic Engineering Institute, Beijing 100074, China, E -mail: yaoyanyy@163.comLU Chuan-jingDepartment of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240. ChinaState Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200030, ChinaSI TingDepartment of moder Mechanics, University of Science and Technology of China, Hefei 230027, ChinaZHU KunBeijing Electromechanic Engineering Institute, Beijig 100074, China(Received June 3, 2010, Revised December 25, 2010)Abstract: Drag reduction experiment of the traveling wavy wall at high Reynolds number is conducted. A suit of traveling wavywall device is developed. The drag forces of the traveling wavy wall with various wave speeds (c ) are measured under different(U ) in the KI5 cavitation water tunnel and are compared with that of the flat plate. The results show that the meandrag force of the traveling wavy wall have decreased and then increased with oscillation frequency increasing at the same flow speed.Under different flow speeds, when traveling wave wall reached to the minimum of drag force, the corresponding the ratio of the wallmotion phase speed c to flow speed U，c1U is slightly different. W ithin the parameters of the experiment, when c/U reachesa cetain value, the drag force of the traveling wavy wall can be less than that of the flat plate. The drag reduction can be up to 42%.Furthermore, as the value of c/U increases, the traveling wavy wall can restrain the separation and improve the quality of flowfield.Key words: flow control, drag reduction, traveling wavy wall, water tunnel testIntroductiondolphin'4. Then, much work has been performed toIt has been believed for a long time thatexplore. this problem. Important contributions byswimming velocities attained by fish are remarkablyLighthil3.4I and Wul5.6 have shed light on the inviscidhigh in relation to their available muscle power". Fishhydrodynamics of fish-like propulsion.swimming can be very instructive in disclosingIt has been proposed that the travelling wavemechanisms of unsteady flow control, which wasmotions result in reducing drag force and increasingraised first in the relation to swimming of live fish.propulsive efficiency by restraining separation'-9.Gray observed that an actively swimming dolphinExperiments were undertaken to investigate viscousonly consumes one seventh of the energy needed tolow past a travelling wavy wall. Taneda andtow a rigid body at the same speed, and suggested thatTomonarilol observed that the boundary layersubstantial drag reduction must occur in the liveseparates at the_ back of the wave crest for thetravel中国煤化工smaller than theexterrMYHlary layer does notsepar;C N M H Gbeing larger than* Biography: YAO Yan (1978-), Female, Ph. D. Candidate,the extemal flow velocity. Kena!" investigated theEngineer66effect of a travelling wavy wall on flow behaviour.cylinders by a number of windpipes. When the airNumerical simulations' have been carried out forcylinder is working, air is compressed into one gateviscous flow over a fixed wavy surface and confirmedand extruded from the other gate of the air cylinder.the previous experimental measurements.Either in or out is decided by the signals of theIn this article, a suit of traveling wavy wallelectromagnetic valve. When the valve is opened, thedevice based on the air cylinders with high frequencypole is moving upwards, while when the valve isis developed and the characteristics of drag reductionclosed, the pole is moving downwards. The controlat high Reynolds number are experimentallycircuit system can set the frequencies and switches ofinvestigated. The drag forces of the traveling wavyseven electromagnetic valves.wall with various wave speeds c are measured underEach air cylinders was with a successive phasedifferent free-stream flow velocities (U) in the K15difference of 90, and the wave was propagated in thewater tunnel and are compared with the drag force ofstreamwise direction. The motion equation of thethe flat plate, which is also calculated according to thetraveling wavy is described in the followingboundary layer theory. The theoretical predictionindicates that the flow in the experiment becomesy= asin(x-c)|turbulent,and the experimental method isdemonstrated to be valid. When the value of Streaches a certain value, it is also shown that the dragwhere a，a and C stand for the amplitude,force of the traveling wavy wall can be less than thatwavelength and phase speed of the traveling wavyof the flat plate. There are drag reduction methodswall, x，y for the displacement in the horizontalsimilar to the traveling wavy wall. Cai et al.l4)analyzed the mechanism of drag reducing effect byand vertical direction, and t for the time.coupling flexible tubes with turbulent flow based onThe wave length was 0.48 m, amplitude wasexperimental examination.50 mm. and the oscillation frequency could be variedintherange0Hzto7Hz.The experimental device was supported by a1. Experimental apparatus and methodssemi-mode balance in the test section. Although theThe experiment is conducted in KI5 cavitationbalance is designed to measure five components of thewater tunnel of Shanghai Ship and Shipping Researchload, the drag force in the horizontal direction isInstitute (SSSRI), which is a square water tunnel withespecially concerned in order to obtain the drag of themaximum speed up to 12 m/s. Size of the test sectiontraveling wavy wall. The whole model was placed in ais 0.6 mx 0.6 m x 2.6 m. And the non-uniformity ofwater tank, which connected with the floor of the testwater velocity less than 1%， instability of watersection (see Fig.1).velocity less than 1%.Figure 1 show the experimental model used inthe water tunnel. The experimental apparatus togenerate the wave motion included flexible plate,allof_seven air cylinders, seven metal knightheads, seven三; Bgend Feribleplatleelectro-magnetic valves, a control circuit, fixedsupports and so on. A flexible plate (0.92 mx 0.2 m x0.0004 m) was used as the test plate. It was connectedElectromagneticto the poles of seven air cylinders (ISO standard,Airylindorortworking medium is compressed air) by seven metalWaurtankknightheads. The pole of the air cylinder is movingwith a reciprocating motion, whose equation i. Balancedescribed approximately byy= Asin(ft+中)(1)Fig.1 Sketch of experimental model setup systemIn this experiment, how to measure the drag ofwhere A is the reciprocating movement distance ofhe flexible plate separately is a difcult problem. Inthe pole, f the frequency and φ the phase of theorder to prevent the influence of the resistance of theair cylinder.devic中国煤化ied on the balance,Each air cylinders was spaced at 0.12 m intervalsandaIsisting of organicin the streamwise direction. Seven electromagneticglasseTH.CNMHGnelasshowedinvalves controlled by a control circuit system are fixedFig.21比1unl uI uIc uI ICIIC cqupment is designedon the support and connected one by one with the airto be triangle shape, the upper surface of which is67plane and with the same height as the forehead of theThe experimental data are collected by a dataflexible plate. Note that the oriented equipmentacquisition system. Collecting a data point costs 0.02 s.surrounding the experimental device is not linked withThen in each case we spend more than 20 s to collectit but has a lttle spacing. Then the measured force in1 000 data points for analyzing.the streamwise direction is mainly the drag force ofthe flexible plate.2. Results and discussionsIn the experiment the flat plate and travelingwavy wall with fourteen oscillation frequencies wereperformed. The flat plate was shaped by placing thepoles of seven air cylinders at their center position,and then the flexible plate had the same height as theoriented equipment. The drag forces of the flat platewere firstly measured to compare with the resultspredicted by the boundary layer theory. Then the dragforces of the traveling wavy wall with differentoscillation frequencies controlled in the range of0 Hz- 7 Hz were measured. A typical traveling wavy walland flat plate is shown in Fig.3. In the experiment, thefree-stream flow velocities were up to 0 m/s- 3.5 m/s.As the value of Reynolds number is too high, the flowis demonstrated to be turbulent.Fig.2 Photo of the experimental model in the water tunnel2.1 Drag forces of the flat plateAs known, the flow will change from laminar toturbulent as the value of Re increases. The classicalview of the critical Reynolds number is believed in therangeof3x10’to3x10°.Theflowcanbeconsidered to be laminar below the value of3 x 10while the flow is turbulent above the value of3x 10.The altermative flow mode can be identified forspecified situations when the value of Re lies in therangeof3 x 105 to3 x 10. Then the drag force ofaflat plate F， with length L and width W in asteady flow with velocity U can be predictedaccording to the boundary layer theoryl"s, whichgivesF, =0.664pW (vU'L)" for laminar flow(3)andF, =0.037pW(vU9IL*)'3 for turbulent flow (4)where p and v stand for the density and dynamicviscosity of the flow, respectively.6)The size of the flat plate is L= 0.96m，W=0.2m，For U=1m/s ，the value ofRe=pUL/μ is equal to 9.49 x 10. The measuredforces中国煤化工for laminar andturbulg.4, which showsthat thTHC N M H Gd agreement withthat of the turbulent mode. On the one hand, the resultFig3 Configuration of experimental modelsindicates that the flow has already turned into68turbulent state. On the other hand, the method of then increases as the value of f increases in the rangemeasuring the drag force is demonstrated to be valid.of0.5 Hz- 7 Hz for the same value of U . The effectof the St on the drag force is presented in Fig.6,which shows that as the value of St increases, the drag3.5甘Exprimentforce trends to decrease and then increase. The.0 t十Turbulent flow theoryminimum value of the drag force occurs at different古Laminar flow theoaySt and the values of the drag force at the same St5have only a lttle difference for different flowvelocities. Note that the drag forces of the travelingstwavy wall are all statistical average values in theexperiment.0叶1020 253.0▲U-20m/sU ms'▼U=25msFig.4 Drag force F, of flat plate versus the flow velocity U2.2 Drag force of the traveling wary wallExcept for the Reynolds number Re= pUL1μ,the main controllable parameters in the experiment isthe Strouhal number St =c/U. In the present work,the amplitude a and wave length n of the travelingwave keeps constant and their ratio a/n is equal to0.104. The phase speed c of the traveling wavy wall isFig.5 Drag force F, of traveling wavy wall versus thedetermined by the oscilation frequency of the airoscillation frequency fcylinder. A list of values of St corresponding todifferent frequency f and flow speed U is givenin Table 1. Under different oscillation frequencyf =0.5Hz-7Hz, the corTesponding phase speed十U=15m's- + U-2.0m'sc= hy reaches 0.24 m/s - 3.36 m/s..平- U-25msTable 1 The Strouhal number St versus frequency fand flow velocity UU (m/s)1.52.f= 0.5 Hz0.24 0.160.080.032f=1Hz .0.48 0.32).160.06420 25 30f=2Hz0.96 0.640.320.128f=3Hz1.440.960.480.192Fig.6 Drag force F, of traveling wavy wall versusthe Stf=4Hz1.92 1.280.640.2562.3 Comparisons and discussionsf=5Hz2.41.60.8The drag forces of the flat plate and the travelingf=6 Hz2.88 1.920.384wavy wall were measured experimentally. The resultsf=7Hz3.36 2.241.120.448are presented in Table 2 once more. It can be seen thatas the flow velocity increases, the difference betweenThe measured drag force F, of traveling wavythe flat plate and the traveling wavy wall trends todistinct. In the case of the lower flow velocity, thewall versus the oscillation frequency f is plotted intrave中国煤化工; reduction, and asFig.5. It is shown that the drag force always increasesthe vE:tion efeet will beas the flow velocity U increases for the sameweakYHCNMHGit,thebestdragosillation frequency f , and basically decreases andreduction state corresponds to the different oscillation69frequencies. In this experiment, the effect of dragflows over a smooth flexible wall undergoingreduction was most obviousat f = 3Hz-4 Hz .streamwise traveling-wave transverse motions. TheThe tendeney in Fig.6 also indicates that the dragReynolds number based on the free-stream velocityforce of the traveling wavy wall first decreases andU and the experimental length L is 0(10*).then increases as the value of St increases.By varying the ratio of the traveling wave phaseGenerally, higher St is advantageous for dragspeed c relative to the extemal stream velocity U ,itreduction. In this situation, the traveling wavy wallis found that the wall oscillations can be optimized toindeed plays a role in reducing the drag force.achieve separation suppression and turbulencereduction, to reduce drag force.Table 2 Drag force of the fnat plate and traveling wavy wallAt the same flow speed U , with the oscillation(unit: N)frequency f increasing, the drag force of traveling∪FlatTraveling wavy wallwavy wall having decreased then increases That is toplasay, as c/U increases, the drag force of traveling2.5Hz 3Hz 3.5Hz 4Hz 4.5 Hz .wavy wall is generally reduced. At different flowspeed, when the traveling wavy wall to reach to1.50.8471 0.7147 0.6335 0.6054 0.4884 0.5977minimal drag force, the corresponding c/U values2.01.4104 1.26741.1758 1.0556 1.0451 1.3147are also different.Compared with the flat plate， experimental2.52.3147 2.7712 2.4466 2.1001 2.3782 2.4205measurement results show the traveling wavy indeedplay the role of drag reduction, for example ,whenThe mechanism of drag reduction of travelingthe wall motion phase speed c= 1.92 m/s and waterwavy wall has been investigated. Shen et al.81 showedflow speed U=1.5m/s, c1U=1.26 m/s, the dragnumerically that as c/U increases from zero, theseparation bubble moves further upstream and awayreduction is about 42%.When c/U increases from zero, experimentalfrom the wall. Above a threshold value of c/U=1,separation is eliminated. Triantafyllou et al.(] showedstudies showed that the traveling wavy wall employsnumerically and experimentally that the travelingmechanisms of separation elimination, turbulencewavy wall employs mechanisms of separationreduction.elimination，turbulence reduction. However， theReynolds numbers are relatively low in the previousReferencesexperiments because of the unattainably highfrequency.[1] NORRIS K. s. Whales, dolphins, and porpoises[M].In this article, the experiments at high ReynoldsBerkeley, CA, USA: University of California Press,number were performed by the special technique1966, 410.using air cylinders. There are some difficulties in the[2 ]Gray J. Studies in animal locomotion[]. Journal ofExperimental Biology, 1936, 13: 192-199.process. Firstly, the frequency of the air cylinder3] LIGHTHILL M. J. Aquatic animal propulsion of highdetermines the phase speed of the traveling wavy wall,hydromechanical efficiency[J]. 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