Acta Mech Sinica (2005) 21: 336–341DOI 10.1007/s10409-005-0043-9

RESEARCH PAPER

Zhifu Gu · Yan Li

Flow around three rectangular cylinders arranged in connectedand separated Y-shape∗

Received: 20 January 2004 / Accepted: 12 July 2004 / Revised: 3 August 2004 / Published online: 25 July 2005© Springer-Verlag 2005

Abstract Characteristics of cross flow around three rectan-gular cylinders with two aspect ratios of breadth to widtharranged in connected and separated Y-shape at various an-gles of incident flow were studied by means of force measure-ment in a wind tunnel. Flow visualizations with smoke-wiretechnique for typical cases were also given. Different typesof flow patterns were formed for individual models at differ-ent angles of incident flow. From the results of fluctuatingvelocity measurement in the wake, features of vibration weredetermined. It shows that as the wind blows along the lines ofone limb or rectangular cylinder of the model, oscillation isweak, whereas when the wind blows along the bisector linesof two limbs or cylinders, strong vibration is observed. It isassociated with the regular vortex shedding.

Keywords Rectangular cylinders ·Vortex-induced vibration· Flow visualization · Y-shape

1 Introduction

Cross section of buildings or structures often appears in aform of rectangle with different aspect ratios of breadth towidth. They may be aerodynamically unstable under certainconditions, and the phenomenon of galloping may occur [1].As flow passes through a rectangular cylinder, the boundarylayer becomes detached or separated from the rectangularcylinder at some point on its surface. Vortex will form in thewake because of the instability or interaction between theshear layers,and it may lead to vortex-induced vibrations.While numerous investigations were made of the flow past

∗The project supported by the National Natural Science Foundation ofChina (10172008)The English text was polished by Keren Wang

Z. F. Gu (B) · Y. LiDepartment of Mechanics and Engineering Science,Peking University,Beijing 100871,ChinaE-mail: guzf@pku.edu.cn

single obstacles with various shapes, few studies were con-cerned with the wake interference and vortex shedding asso-ciated with complex configurations consisting of multipleobstacles [2].

In engineering practices, there are many examples ofbuildings or structures in Y-shape, which may be regarded asthree identical rectangular cylinders arranged in l20 degreesapart either in a connected or a separated way. Therefore, it isboth an academic and practical issue to gain an understandingof the flow around such special cross section of structures, aswell as their wind loads. Vortex shedding from an H-shapecylinder was studied by Nakagawa [3]. Hayashida and Iwasa[4] studied vortex-induced vibration of eight different kindsof cross section of high-rise building by wind tunnel tests,including Y-shapes. The results show that no peak value canbe found in the spectrum of cross wind force and no influenceon wind direction.

Gu et al.[5,6] studied the wind loads of three rectan-gular cylinders arranged in separated Y-shape in a uniformsmooth flow; different patterns of pressure distributions wereobtained for different aspect ratios of component rectangularcylinders under various angles of incident flow. Gallopingphenomenon was observed in a certain case. Recently, inengineering practice, a strong vibration was reported on aTV tower with its cross section in a separated Y-shape [7].

In this paper, the flow patterns around three rectangularcylinders with two different aspect ratios arranged both inconnected and separated Y-shape were studied. The aerody-namic forces on the models were measured by wind tunneltests in a low (Iu = 0.2%) and high (Iu = 10%) turbu-lent flow. Special attentions were paid to the mechanism offlow-induced vibration.

2 Experimental setup and models

The experiments were conducted in an open-circuit windtunnel with a working section of 6m long, 0.6 m wide and0.6 m high. The maximum velocity of free stream is about36 m/s with a background turbulence intensity of 0.2%. For

Flow around three rectangular cylinders arranged in connected and separated Y-shape 337

Fig. 1 The cross section of models. (a) Connected Y-shape, (b) Separated Y-shape and the locations of wake flow velocity measurement positionS and C

the high-turbulent flow test, a bi-planar turbulence grid madeof rectangular cylinders (30 mm × 30 mm) with a verticaland horizontal mesh width of 0.114 m is installed 1.82 mupstream of the model position to generate uniform high-turbulent flow. The longitudinal turbulence intensity, Iu, atthe model position is then 10% and the longitudinal integralscale of the U-component, Lx , is 75 mm.

Two aspect ratios of breadth l to width b, i.e. l/b = 3.0and 1.4, for the rectangular cylinders, were chosen to con-struct two connected and separated Y-shape models, respec-tively. As a frequent reference will be made to the individualmodel, the connected models of l/b = 3.0 and 1.4 are labeledas LC and SC, and the separated models of l/b = 3.0 and 1.4are labeled as LS and SS, respectively. For the same reason,the individual limb of the connected model or the cylinder ofthe separated model is denoted as A, B and C, respectively,as shown in Fig. 1 together with the definition of length D/2and β.

The models are made of Plexiglas and placed horizontallyin the middle of the test-section between end plates. The nat-ural frequencies of LC, LS and SC, SS are 43 Hz and 54 Hz,respectively, with a damping ratio of 0.022, which is close tothat in an actual structure. The loads on the models are mea-sured with strain gauges in one particular direction enablinga separate measurement of drag and lift forces. Two identicalstrain gauges are placed on each surface of a flat profile withrectangular cross section, which is mounted on one side ina stiff support. On the other side of this profile, the modelis clamped, leading to dominant deformations and, conse-quently, strains in the strain gauges, if forces perpendicularto the profile are exerted on the model. The strain gauges areinterconnected in half-Wheatstone bridge in order to guaran-tee a linear bridge output. The signals from the strain gaugesthrough a low pass filter are amplified by a DC amplifier(6M72). The drag and lift coefficients, denoted by CD andCL, are defined conventionally and made dimensionless bythe characteristic length D. In order to obtain the specificproperty of wake fluctuating velocity, a constant tempera-ture hot-wire anemometer (TSI model 1050) is used. Twohot-wire probes are placed at the two positions downstreamof the model, located on one side (position S) and on thecenterline (position C) in the wake, respectively (see Fig. 1).

The flow visualization experiment was performed in thesame wind tunnel. The smoke-wire technique was employed.

One of the four wires was placed in the front of the modeland the remaining three were located behind the model. Thepictures were taken with a time-delay, between the genera-tion of smoke and the flash of camera, of 80 milliseconds.The Reynolds numbers (Re), which is based on the lengthof D in the flow visualization, are l.3×104 and 7.8×103 formodels l/b = 3.0 and 1.4, respectively. In the force measure-ment experiments, the Reynolds numbers are in the rangeof 4.8×104 to 1.4×105. It is believed that the aerodynamiccharacteristics of a rectangular-cylinder type object, such asvortex shedding frequency, separation points, shear layersand wake structures, are similar in the region of subcriticalReynolds numbers.

3 Results and discussion

3.1 Flow visualization

The pictures of flow around the connected models at β = 0◦,30◦ and 60◦ are shown in Fig. 2. For LC model at β = 0◦,no evident vortex structure can be observed. The separatedshear layers from the leading edges of the windward surfaceof limb A reattach on the limbs B and C, and then re-sep-arate. The angles of re-separated shear layers are big, as aresult, a wide wake, somewhat like a “dead water region”,forms behind the model. Since the two shear-layers deviatefrom each other, also because of their self-stability in nature,no regular vortex forms in the near wake flow region. Thisphenomenon is verified by the results of the fluctuating forcemeasurement on the model and the velocity measurement inthe near wake, and will be discussed later on. However, alarge size vortex could form in a far wake behind the modelbecause of the instability of wake structure.

At β = 30◦, the separated shear layer generated from thedownside of limb A passes over limb C, which is entirelysubmerged in the wake. A big separating area forms and cre-ates a significant suction on the downside of the model. It isconfirmed by the results of force measurement. On the otherhand, a shear layer forms on limb B. Vortex forms due to theinteraction between the two shear layers. Peak-values can befound in the power spectra of both the lift force on the modeland the velocity in the wake. It suggests that a vortex-induced

338 Z.F. Gu & Y. Li

Fig. 2 Photographs of flow visualization for the connected models at three typical angles of incident flow

Fig. 3 Photographs of flow visualization for the separated models at three typical angles of incident flow

vibration occurs, though it is rather weak, which will be dis-cussed in a later section.

At β = 60◦, the flow separates from both sharp edgesof limbs A and B. The wake flow region formed is ratherbroad. Symmetrical reversed flows are established in thewake regions between limbs B & C and limbs A & C, respec-tively. The power spectra of both the force and the velocityshow that a strong peak-value appears at the same frequency.It means that two individual symmetrical vortices are formedbehind the model and the strong vortex-induced vibration isfound. However, it is interesting that no peak value can bedetected in the power spectrum of velocity at the centerlineof the wake (position C, now located behind limb C). It sug-gests that there is no significant interference between the twovortices because of the existence of limb C, which functionsas a split plate in the wake.

The flow around SC model at β = 0◦ seems somewhatunstable compared with that of LC model. The two shearlayers separated from limbs B and C are relatively closer,therefore, the interference between the two shear layers hap-pens not far away in the wake. At β = 30◦, the interactionof the shear layers is stronger than that of LC model and

vortex forms close to the model. The separating angles ofshear layers from both limbs A and B are small at β = 60◦,the reversed flows are found close to the back of limbs A andB. Limb C now is no longer acting as a split plate becauseof its shortness in breadth, and a full interaction between thetwo shear layers occurs just behind the cylinder.

Figure 3 shows the flow visualization of the separatedY-shape models. For the LS model at β = 0◦, the flow is sep-arated from the leading edges of cylinder A and then passesthrough the gap between cylinders B and C, the wake struc-ture is disturbed and the “dead water region” no longer exists.On the other hand, the oncoming flow can reach cylindersB and C directly, and forms two separate shear layers. Thewake region is relatively narrower than that in the LC model.The wake is unstable because of the gap-flow, which is, inturn, unstable and sensitive to the angular change of incidentflow and usually switches to one side. At β = 30◦, the sepa-rated shear layer from the downside of cylinder A is curvedand rolled up, the oncoming flow can reach the tip of cyl-inder C and then separates. An upward gap flow forms andstrongly interferes with the separated flow from the upsideof the model. At β = 60◦, compared with the case of LC, the

Flow around three rectangular cylinders arranged in connected and separated Y-shape 339

Fig. 4 The variations in time-mean lift force coefficients CL for both connected and separated Y-shape models (LC, SC, LS and SS) with theincident flow angle of β in (a) low (Iu = 0.2%) and (b) high (Iu = 10%) turbulent flow

Fig. 5 For model SC, (a) the time-mean lift coefficients CL versus β at different Reynolds numbers and (b) the fluctuating lift coefficients CLrmsat various flow conditions

separated shear layers from cylinders A and B are concaveand the wake structure with the two individual symmetricalvortices are destroyed because of the gap flow.

For the SS model at β = 0◦ the strong gap flow plays animportant role in the wake structure. At β = 30◦ cylinder Cis immersed in the wake and the reversed flow can be foundclose to the back of cylinder B. At β = 60◦ the gap flowsinteract strongly with the shear layers separated from cylin-ders A and C. The power spectra of both fluctuating force onthe model and velocity in the wake have significant peak val-ues at the same frequency (see Fig. 6). It suggests that ratherstrong vortex shedding occurs in the wake.

Compared with that of the connected model, the flowpattern of the separated Y-shape model is more complicatedbecause of the interference of gap flow and the shear layersin the wake.

3.2 Time-mean and fluctuating lift force

Figure 4 shows the variation in time-mean lift force coeffi-cients CL for both connected and separated Y-shape modelswith the incident flow angle β in low (Iu = 0.2%) and high(Iu = 10%) turbulent flow, respectively.

For the connected models (LC, SC) in the low turbu-lent flow, the lift forces CL increase (in absolute value, thesame below) rapidly and reach their maximum values atβ = 10◦, and then decrease steadily as β increases.As for the

separated models, they show some complicated features, suchas, the CL variations for models LS and SS are quite differentbecause of the difference in aspect ratios of the componentcylinders. For SS model, as β increases from 10◦ to 20◦, CL

decreases greatly. In the previous study [5], the results ofpressure distributions on the surfaces of individual cylindershow that the main cause of reduction in CL for the wholemodel comes from cylinder B. The aerodynamic force actingon cylinder B changes its direction at β between 10◦ and 20◦,which causes aerodynamic instability and a serious vibrationat a certain oncoming flow velocity. For the LS model, themaximum value of CL occurs at β = 30◦. The lift forces, ingeneral, are smaller compared with those of connected one.The effect of high turbulence in the oncoming flow changesthe β value for the maximum CL of LC from 10◦ to 20◦, andthe variations of lift force with β for other models becomemore gradual.

In order to determine the effect of flow conditions on theaerodynamic force of the models, such as Reynolds num-ber, turbulence intensity in oncoming flow, some results formodel SC, as a typical case, are presented and discussed.Figure 5 shows the time-mean lift coefficients, CL for theSC model versus β at three different Re and the fluctuatinglift coefficients, CLrms under various flow conditions. It showsthat there is no significant changes in the time-mean lift forceacting on such model in the Reynolds numbers tested.

For low turbulent flow, the values of CLrms are small for βbetween 0◦ and 30◦ and for different Re. The trend of increase

340 Z.F. Gu & Y. Li

Fig. 6 Power spectra of (a) lift force on the model and (b) wake velocity at location S for model SS (Re = 8.6×104, Iu = 0.2%) at β = 0◦, 30◦and 60◦, respectively

Fig. 7 Power spectra of lift force on the model, wake velocity at position S and C of model SC (Re = 8.6 × 104, Iu = 0.2%) at β = 60◦

of CLrms begins as β > 30◦, especially after β > 50◦. Thevalue of CLrms increases rapidly with the increase in Re atβ = 60◦ and reaches 0.26 at Re = 8.6 × 104, which cor-responds to the reduced velocity Ur = 5.47. (Ur = U/f D,where U and f are the velocity of free stream and the vortexshedding frequency, respectively.) It is shown that vortex-induced vibration occurs. On the other hand, the effect of highturbulence in the oncoming flow causes CLrms to increase formost wind directions, however, the values of CLrms decreaseat β = 50◦ and increase again at β = 60◦ . The value ofCLrms is always bigger than those obtained in low turbulentflow at the same reduced velocity.

3.3 Power spectra of lift force and wake velocity

Figure 6 shows the power spectra of the non-dimensional liftforce on the model and fluctuating velocity in the wake atposition S for the separated model SS at β = 0◦, 30◦ and60◦, respectively, in low turbulent flow, where SF (f ) andSU(f ) are power spectrum intensities of lift force and wakevelocity, SFmax and SUmax are the maximum values of SF (f )and SU(f ) in each particular case.

At β = 0◦, several peak-values can be identified in thepower spectrum of lift force on the model although theyare rather weak, which corresponds to the frequency of vor-tex shedding (47 Hz), the natural frequencies of the model(54 Hz) and the multiple frequency of vortex shedding (94 Hz),respectively, whereas, no evident peak values can be identified

in the power spectrum of wake velocity. Therefore, the flow-induced vibration is quite weak in this case. However, atβ = 30◦ a little stronger peak values can be found at the samefrequency both in the power spectra of lift force and wakevelocity. It could be assumed that the regular vortex sheddinghas happened in the wake. At β = 60◦ much stronger nar-row peak-values are obtained in both the power spectra of liftforce and wake velocity at the same frequency. There is nosignificant difference in this phenomenon for the other two(LC and SC) models. As for the LS model, there is no evidentpeak-value found in both the power spectra of lift force andwake velocity at β = 60◦. It could be explained that it is thegap-flow, which destroys the regular vortex forming in thenear wake of the model. It is believed, however, that vortexcould be formed though not regularly but with rather weakintensity in the wake far away behind the model.

Figure 7 shows the power spectra of the lift force on themodel and the wake velocity at positions S and C of SCmodel at three different velocities of the oncoming flow. Thefrequencies of peak-values are the same in both spectra of liftforce and velocity at position S under the same velocity. Thecorresponding Strouhal number St (St = f D/U , where f isthe frequency of vortex shedding) is 0.145. The peak-valuesof power spectrum of velocity at twice the frequencies areobtained at position C. It suggests that the vortices shed fromcylinders A and B alternatively. It should be noted here thatthe St values are different for different models, as well as forthe different angles of incident flow. For models LC and SC,St is equal to 0.14 and 0.124, respectively, at = 60◦.

Flow around three rectangular cylinders arranged in connected and separated Y-shape 341

4 Conclusions

The main results of this study may be summarized as follows:

(1) As the wind blows along the lines of one limb or cylinder,the separated shear layers are far apart from each other,and the wake structures are relatively stable. Therefore,the interference between the two shear layers is very weakand no regular vortex is formed in the near wake behindthe models. The bigger the aspect ratio of the model, themore stable the separated shear layers and the wake struc-ture will be. The oscillations of the models are weak.

(2) As the angle of incident flow increases, the wake struc-tures become unstable. The regular vortices form in thenear wake at β = 30◦. The strong vortices that induce thevibration appear mostly at β = 60◦.

(3) Effects of turbulence intensity in the oncoming flow some-what reduce the time-mean lift force, but could increasethe fluctuating lift force notably in most cases.

(4) The effects of Reynolds number on time-mean force arevery limited whereas the effect of reduced velocity onfluctuating force is significant because of the vortex-induced vibration.

(5) Because of the existence of gap flow, the flow aroundseparated Y-shape models is more complicated. The flow

patterns and the features of vibration depend critically onthe aspect ratios of the component rectangular cylindersand the angle of incident flow.

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