EXPERIMENTAL STUDY ON THE FLOW FIELD BETWEEN TWO SQUARE CYLINDERS IN TANDEM ARRANGEMENT

Transcription

1 The Seventh sa-pacfc Conference on Wnd Engneerng, November 8-1, 9, Tape, Tawan EXPERIMENTL STUDY ON THE FLOW FIELD ETWEEN TWO SQURE CYLINDERS IN TNDEM RRNGEMENT Hrosh Hasebe 1, Kenj Watanabe, Yuk Watanabe and Takash Nomura 3 1 Research ssocate, Department of Cvl Engneerng, CST, Nhon Unversty Kanda-Surugada , Chyoda-ku, Tokyo, Japan hasebe@cvl.cst.nhon-u.ac.jp Undergraduate student, Department of Cvl Engneerng, CST, Nhon Unversty Kanda-Surugada , Chyoda-ku, Tokyo, Japan 3 Professor, Department of Cvl Engneerng, CST, Nhon Unversty Kanda-Surugada , Chyoda-ku, Tokyo, Japan nomura@cvl.cst.nhon-u.ac.jp STRCT Flow feld between two square cylnders n tandem arrangement s nvestgated. The surface pressure dstrbutons vary consderably between the spacng rato L/D = 3 and L/D = 4. The velocty between two square cylnders of L/D = 4 s measured by means of a splt-fber probe. The phase-averagng technque s appled to the measured velocty data wth reference to the surface pressure of the upstream cylnder. ccordng to the phase-averaged velocty, the flow between two cylnders shows two patterns. One s dagonal flow whch ntersects dagonally between two cylnders. The other s hgh curvature flow whch vares the flow drecton from upward (downward) to downward (upward) between two cylnders. These two flow patterns vary perodcally. The Reynolds stress evaluated from the perodcal component of the velocty occupes about 8% of the Reynolds stress evaluated from the total fluctuatng component of the velocty. Therefore the perodcal component of the velocty whch s caused by the vortex sheddng from the upstream cylnder has a great nfluence on the property of the turbulent flow structure between two square cylnders. KEYWORDS: SQURE CYLINDER, TNDEM RRNGEMENT, SPLIT-FIER PROE, PHSE VERGE Introducton There are varous tandem-arranged structures or structural components whch are exposed n wnd, for example, the parallel cables of cable-stayed brdges, the twn hanger ropes and the tower of suspenson brdges. It s well known that serous vbratons called as wake gallopng or wake nduced flutter occur n the parallel cables and twn hanger ropes. Therefore, aerodynamc characterstcs of tandem-arranged structures have been studed wdely [Shrash et al. (1986) and Tokoro et al. ()]. However, snce t s dffcult to measure, only lmted nformaton s avalable on characterstcs of the flow feld between tandem-arranged structures [Ob et al. (6)]. In the present study, the flow feld between two square cylnders n tandem arrangement s nvestgated. The surface pressure dstrbutons are measured for four cases of the spacng rato. The velocty between the two cylnders s measured by means of the spltfber probe. The phase-averagng technque s appled to the measured velocty data n order to realze flow pattern. In addton, the Reynolds stress between two square cylnders s nvestgated.

2 The Seventh sa-pacfc Conference on Wnd Engneerng, November 8-1, 9, Tape, Tawan wnd D SFP 8mm 4mm U pressure taps y x 9mm 6mm C F D E 8mm@3 6mm@7 9mm G H D 5D Fgure 1: rrangement of two square cylnders L z measurement plane y x L Fgure : Locaton of pressure taps Expermental setup The experment s conducted n an open crcut wnd tunnel. The test secton has a 4mm 4mm square cross secton and 8mm long. The turbulent ntensty of the free stream velocty s about 1.5%. The test bodes adopted n the present study are two square cylnders wth a wdth D of 6mm, an axal length S of 356mm and two end plates on both sdes. s shown n Fg.1, the upstream square cylnder s placed at 5D dstance from the entrance of the test secton. The downstream square cylnder s located n the streamwse drecton. The space between two square cylnders s desgnated by L. In order to measure the surface pressure, each sngle square cylnder has 16 pressure taps of 1.3mm dameter at the center of the span. ccordng to [Sakamoto et al. (1987)], 8 or 1 pressure taps are necessary on a sngle sde of the square cylnder. Therefore, 8 pressure taps are allocated on the upper surface of each square cylnder as shown n Fg.. Consderng the symmetry, 4 pressure taps are allocated on the front and rear surface. These pressure taps are connected to a dfferental pressure transducer (TO Industry, MP-3). Snce the wdth of test bodes s determned to allocate the suffcent number of pressure taps, the blockage of the present study s 15%, consequently. The velocty measurement between two square cylnders s conducted by means of a splt-fber probe (DNTEC, 55R55). The measurng ponts are algned on a plane normal to the cylnder axs. The measurement plane s located at mddle of the cylnder span as shown n Fg.1. The pressure and velocty sgnals are dgtzed for 3s at the rate of 5Hz. The averagng tme for the tme-average of the measured data s 3s. For the pressure measurement, the free stream velocty s set to 1.m/s (Re = 5,). On the other hands, for the velocty measurement, the free stream velocty s decreased to 6.m/s (Re = 5,) snce the output voltage from a splt-fber probe exceeds the range whch can be measured. Surface pressure dstrbuton correspondng to the spacng rato The surface pressure measurement s conducted at four cases of the spacng ratos (L/D =, 3, 4 and 5). Fgures 3 and 4 show the dstrbutons of tme-averaged surface pressure coeffcent C P and fluctuatng pressure coeffcent C P, respectvely. The surface pressure dstrbutons of L/D = 4 and 5 dffer consderably from those of L/D = and 3; wth regard to the tme-averaged pressure, the downstream cylnder reveals completely dfferent dstrbutons; the fluctuatng pressures of L/D = 4 and 5 are magnfed consderably. For L/D = and 3, on the upper surface of the downstream square cylnder (surface F- G), the recover of the pressure lke reattachment-type rectangular cylnder are observed. For L/D = 4 and 5, on the front surface of the downstream square cylnder (surface E-F), tmeaveraged pressure coeffcents becomes approxmately zero. s shown n Fg.5, for L/D =, only the negatve pressure s measured at the center of the front surface of the downstream sq-

3 The Seventh sa-pacfc Conference on Wnd Engneerng, November 8-1, 9, Tape, Tawan C P L/D= L/D=3 L/D=4 L/D=5 C D E F G H Poston Fgure 3: Dstrbutons of the tme-mean pressure coeffcent C P L/D= L/D=3 L/D=4 L/D=5 C D E F G H Poston Fgure 4: Dstrbutons of the fluctuatng pressure coeffcent pressure (Pa) tme (s) L/D = 4 L/D = Fgure 5: Tme hstory of the surface pressures at pont E n Fg. uare cylnder (pont E). On the contrary, for L/D = 4, the surface pressure at pont E fluctuates between postve and negatve values. s a result, tme-averaged pressure becomes approxmately zero. From the observaton of the pressure fluctuaton, t s nferred that the vortex emanated from the upstream square cylnder mpnges to the front surface of the downstream square cylnder. Consderable change of the dstrbuton of the surface pressure between L/D = 3 and 4 s n accordance wth the expermenttal work by [Sakamoto et al. (1987)]. [Lu et al. ()] show that the flow pattern changes between L/D = 3 and 4 by the flow vsualzaton. However, the Reynolds number of ther expermental work s,7 whch s smaller than that of the present study (Re = 5,). In addton, they dd not measure the velocty between the two square cylnders n detal. In the present study, for the purpose of the detaled nvestgaton of the flow feld between the two square cylnders, the velocty s measured at densely dstrbuted locatons between the two square cylnders. Treatment of outputs from a splt-fber probe Snce the dstrbutons of the surface pressure suggest the exstence of the fluctuatng flow between the two square cylnders n case of L/D = 4 and 5, the measurement of the velocty between the two square cylnders wth the spacng rato L/D = 4 s conducted by means of a splt-fber probe. The locatons of 7 measurement ponts are shown n Fg. 6. t each pont, the velocty components wth respect to the x-axs (U) and the y-axs (V) are measured. In order to measure the velocty near the square cylnders, a splt-fber probe s set n the plane as parallel to the axs of the cylnder (z drecton) as shown n Fg.1. For the measurement of the velocty component V, the splt-fber probe s set as orthogonal to the y- axs as shown n Fg.7. For the measurement of the velocty component U, the splt-fber probe s rotated 9 around z-axs. The sensor of the splt-fber probe s wrapped around a quartz core, and then, the flmlke sensor s splt nto two sensors as shown n Fg.7. Therefore the splt-fber probe provdes

4 The Seventh sa-pacfc Conference on Wnd Engneerng, November 8-1, 9, Tape, Tawan Reference pressure pont (Pont R) Measurement pont 3mm Pont P 6mm y wnd x 8mm@6 6mm mm mm@7 mm Fgure 6: Locaton of the velocty measurement ponts z y splt x V 1 CH I V CH II Fgure 7: Head of a splt-fber probe velocty (m/s) CH I CH II velocty (m/s) tme (s) tme (s) Fgure 8: Measured data at pont P by a splt-fber probe Fgure 9: Combned velocty data two output sgnals. For example, when the flow comes from V 1 drecton ndcated n Fg.7, the output of channel I sensor becomes larger than that of channel II sensor. Fgure 8 shows outputs from the two sensors of a splt-fber probe when the velocty component V s measured at pont P ndcated n Fg.6. Snce t s nferred that the perodcal vortex sheddng occurs, outputs from two sensors ncrease alternately. These two sgnals should be combned nto one velocty sgnal. The result n Fg.8 shows that when the output from one sensor becomes large, the output from the other sensor becomes almost zero. Moreover, the rounded two sensors of the splt-fber probe are facng to the opposte drectons. Therefore, n the present study, the followng relaton s employed to combne the two sgnals: V ( ) ( ) V V V = V V < V (1) where V 1 and V are the velocty components measured by the two sensors, respectvely. Phase averagng technque ccordng to [Hussan et al. (197)], the nstantaneous velocty u s decomposed nto the followng three components: u = U + u + u = u + u c r r () where U s the tme-mean component, u c s the perodcal component wth zero mean and u = U + u c s the phase-averaged component. Snce u c and u r s the random component. ( )

5 The Seventh sa-pacfc Conference on Wnd Engneerng, November 8-1, 9, Tape, Tawan velocty (m/s) measured flterd sampled Fourer spectrum (m/s) tme (s) frequency (Hz) (a): Tme hstory of the velocty at pont P n Fg.6 (b): Fourer spectrum of the measured velocty at pont P n Fg.6 - measured flterd sampled pressure (Pa) tme (s) Fourer spectrum (Pa) frequency (Hz) (c): Tme hstory of the surface pressure at pont R n Fg.6 (d): Fourer spectrum of the measured surface pressure at pont R n Fg.6 Fgure 1: Process of the phase average u r are zero mean components, the tme averagng technque to measured velocty data can not reveal the pattern of the fluctuatng flow between two square cylnders. Therefore, n order to obtan the phase-averaged velocty u, the phase averagng technque [Lyn et al. (1994) and Perrn et al. (7)] s appled to the present measured velocty data. The phase averagng technque needs the referental sgnal to defne the flow phase. In the present study, the surface pressure of the upstream cylnder, of whch the locaton s shown n Fg.6, s used as the reference sgnal. The process to compute the phase-averaged velocty conssts of the followng three procedures: 1) Smultaneous measurement of velocty and pressure The velocty and the surface pressure are measured smultaneously. Typcal result of measured data, velocty component V whch s measured at pont P ndcated n Fg.6, surface pressure whch s measured at the pont R n Fg.6 and ther Fourer spectrums are shown n Fgs.1 (a)-(d). To remove the random component u r from the measured data, the data s fltered by a low-pass flter. s shown n Fgs.1 (b) and (d), Fourer spectrums of the

6 The Seventh sa-pacfc Conference on Wnd Engneerng, November 8-1, 9, Tape, Tawan measured velocty and the surface pressure have same peak-frequency at 1.8Hz ( S =.18) whch s n accordance wth the Strouhal number of the sngle square cylnder [Lyn et al. (1995)]. Therefore, the cut-off frequency of the low-pass fler s set at 3Hz whch s twce hgh frequency of the vortex sheddng from the upstream cylnder. ) Subdvson of the measured data To defne the phase, the measured data s dvded nto a seres of sngle cycle perods. The perod s defned as the nterval between peaks of the pressure sgnal whch are shown n Fg.1(c) by crcle symbols. 3) Extracton of data at same phase From every dvded data, veloctes at the same phase are extracted and averaged. In the present study, each perod s dvded nto phases. s a result, the phase-averaged velocty u s obtaned. In Fg.1(a), crcle symbols ndcate the extracted velocty data at phase φ=. Phase-averaged velocty between two square cylnders n tandem arrangement The dstrbutons of the phase-averaged velocty vectors and the streamlnes are shown n Fg.11(a)-(h). t phases ( ) φ= φ=φ π and φ= 1, large vortces as large as the square cylnder are observed behnd the upstream cylnder ndcated as n Fg.11(a) and as n Fg.11(e) respectvely. The advectve speed of the vortex s about.6m/s calculated from the locaton of the vortex center at every phase. It s about 4% of the nflow velocty (6.m/s). t phases φ= 3and5, snce the vortex emanated from the lower sde of the upstream cylnder has passed the regon between two cylnders, the upward flow s formed almost of all the regon between two cylnders. t phases φ= 8 and 1, rollng t (a) : φ = (e) : φ= 1 (b) : φ= 3 (f) : φ= 13 (c) : φ= 5 (g) : φ= 15 (d) : φ= 8 (h) : φ= 18 Fgure 11: Phase-averaged velocty vector and streamlne

7 The Seventh sa-pacfc Conference on Wnd Engneerng, November 8-1, 9, Tape, Tawan (a) u Un (b) v Un Fgure 1: Dstrbuton of normal components of the Reynolds stress (a) uc Un.1 (b) vc Un Fgure 13: Dstrbuton of normal components of the Reynolds stress evaluated from the perodcal component of the velocty up from the upper sde of the upstream cylnder forms the downward flow behnd the upstream cylnder. On the other hands, the vortex emanated from the lower sde of the upstream cylnder forms the upward flow n front of the downstream cylnder. Therefore, hgh curvature of the streamlne exsts between two cylnders at these phases. s shown n Fgs.11(e)-(h), at phases from φ= 1 to 18, the flow patterns are symmetrc to the flow at phases from φ= to8 wth respect to the vertcal axs through both centers of the two cylnders. Dstrbuton of the Reynolds stress Snce the fluctuatng component of the velocty u s calculated as u = u U, where u s the nstantaneous velocty, U s the tme-averaged component, the Reynolds stress uu j can be nvestgated. The fluctuatng component of the velocty u s further decomposed to the perodcal component u c and the random component u r as u = u c + u r. Therefore, the Reynolds stress calculated from the perodcal component u c and the Reynolds stress calculated from the random component u r can be evaluated. In ths chapter, we dscuss that how these components contrbute to the total Reynolds stress uu j. Fgures 1(a) and (b) show contours of the Reynolds stress uu j. Snce the smultaneous measurement of the velocty components U and V s not conducted, only the normal components of the Reynolds stress u and v are nvestgated. u and v are nondmensonalzed by square of the nflow velocty U n (=6.m/s). s shown n Fg.1(a), the dstrbuton of u component has two peaks near the tralng edges of the upstream cylnder. On the other hands, the dstrbuton of v component has one peak behnd the upstream cylnder. The locaton of the peak of the v component s further from the upstream cylnder than that of the u component. Snce the perodcal component of the velocty u c s evaluated as u c = u U, the Reynolds stress calculated from the perodcal component u c u c j can be evaluated. Fgs.13(a) and (b) show the normal components of the Reynolds stress calculated by the perodcal component of the velocty u c and v c. In comparson wth Fgs.1(a), (b) and Fgs.13(a), (b),

8 The Seventh sa-pacfc Conference on Wnd Engneerng, November 8-1, 9, Tape, Tawan dstrbutons of u c and v c are qute smlar to those of u and v. Ther peaks appear at the same locatons. The peak values u c and v c occupy about 8% to that of u and v, respectvely. Therefore, the perodcal component of the velocty whch s occurred by the vortex sheddng from the upstream cylnder has a great nfluence on the property of the turbulent flow structure between two square cylnders. Concluson In the present study, for the purpose of the nvestgaton of the flow feld between two square cylnders n tandem arrangement, the measurement of the surface pressure and the measurement of the velocty between two square cylnders are conducted. s a result, the surface pressure dstrbutons vary consderably between the spacng rato L/D = 3 and L/D = 4 n accordance wth the expermental work by [Sakamoto et al. (1987)]. For L/D = 4, accordng to the phase-averaged velocty, the flow feld between two cylnders shows two patterns. One s the dagonal flow whch ntersects between two cylnders. The other s hgh curvature flow whch forms the upward (downward) flow behnd the upstream cylnder and the downward (upward) flow n front of the downstream cylnder. For L/D = 4, these flow patterns vary perodcally between two square cylnders n tandem arrangement. etween two square cylnders, the Reynolds stress evaluated from the perodcal component of the velocty occupes about 8% to the total Reynolds stress whch s evaluated from the fluctuatng component. Therefore, the perodcal component of the velocty has a great nfluence on the property of the turbulent flow structure between two square cylnders. Reference Hussan,. K. M. F. and Reynolds, W. (197), The mechancs of an organzed wave n turbulent shear flow, Journal of Flud Mechancs, 41, Lu, C. H. and Chen, J. M. (), Observatons of hysteress n flow around two square cylnders n a tandem arrangement, Journal of Wnd Engneerng and Industral erodynamcs, 9, Lyn, D.. and Rod, W. (1994), The flappng shear layer formed by flow separaton from the forward corner of a square cylnder, Journal of Flud Mechancs, 67, Lyn, D.., Enav, S., Rod, W. and Park, J.-H. (1995), laser-doppler velocmetry study of ensembleaveraged characterstcs of the turbulent near wake of a square cylnder, Journal of Flud Mechancs, 34, Ob, S. and Toka, N. (6), The pressure-velocty correlaton n oscllatory turbulent flow between a par of bluff bodes, Internatonal Journal of Heat and Flud Flow, 7, Perrn, R., Cd, S., Cazn, S., Sevran,., raza, M., Morade, F. and Harran, G. (7), Phase-averaged measurements of the turbulence propertes n the near wake of a crcular cylnder at hgh Reynolds number by C-PIV and 3C-PIV, Experments n Fluds, 4, Sakamoto, H., Hanu, H. and Obata, Y. (1987), Fluctuatng force actng on two square prsms n a tandem arrangement, Journal of Wnd Engneerng and Industral erodynamcs, 6, Shrash, N., Matsumoto, M. and Shrato, H. (1986), On aerodynamc nstabltes of tandem structures, Journal of Wnd Engneerng and Industral erodynamcs, 3, Tokoro, S., Komatsu, H., Nakasu, M., Mzuguch, K. and Kasuga,. (), study on wake-gallopng employng full aeroelastc twn cable model, Journal of Wnd Engneerng and Industral erodynamcs, 88, 47-61