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The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan EXPERIMENTAL STUDY ON THE FLOW FIELD BETWEEN TWO SQUARE CYLINDERS IN TANDEM ARRANGEMENT Hiroshi Hasebe1, Kenji Watanabe2, Yuki Watanabe2 and Takashi Nomura3 Research Associate, Department of Civil Engineering, CST, Nihon University Kanda-Surugadai 1-8-14, Chiyoda-ku, Tokyo, 101-8308 Japan [email protected] 2 Undergraduate student, Department of Civil Engineering, CST, Nihon University Kanda-Surugadai 1-8-14, Chiyoda-ku, Tokyo, 101-8308 Japan 3 Professor, Department of Civil Engineering, CST, Nihon University Kanda-Surugadai 1-8-14, Chiyoda-ku, Tokyo, 101-8308 Japan [email protected] 1 ABSTRACT Flow field between two square cylinders in tandem arrangement is investigated. The surface pressure distributions vary considerably between the spacing ratio L/D = 3 and L/D = 4. The velocity between two square cylinders of L/D = 4 is measured by means of a split-fiber probe. The phase-averaging technique is applied to the measured velocity data with reference to the surface pressure of the upstream cylinder. According to the phase-averaged velocity, the flow between two cylinders shows two patterns. One is diagonal flow which intersects diagonally between two cylinders. The other is high curvature flow which varies the flow direction from upward (downward) to downward (upward) between two cylinders. These two flow patterns vary periodically. The Reynolds stress evaluated from the periodical component of the velocity occupies about 80% of the Reynolds stress evaluated from the total fluctuating component of the velocity. Therefore the periodical component of the velocity which is caused by the vortex shedding from the upstream cylinder has a great influence on the property of the turbulent flow structure between two square cylinders. KEYWORDS: SQUARE CYLINDER, TANDEM ARRANGEMENT, SPLIT-FIBER PROBE, PHASE AVERAGE Introduction There are various tandem-arranged structures or structural components which are exposed in wind, for example, the parallel cables of cable-stayed bridges, the twin hanger ropes and the tower of suspension bridges. It is well known that serious vibrations called as “wake galloping” or “wake induced flutter” occur in the parallel cables and twin hanger ropes. Therefore, aerodynamic characteristics of tandem-arranged structures have been studied widely [Shiraishi et al. (1986) and Tokoro et al. (2000)]. However, since it is difficult to measure, only limited information is available on characteristics of the flow field between tandem-arranged structures [Obi et al. (2006)]. In the present study, the flow field between two square cylinders in tandem arrangement is investigated. The surface pressure distributions are measured for four cases of the spacing ratio. The velocity between the two cylinders is measured by means of the splitfiber probe. The phase-averaging technique is applied to the measured velocity data in order to realize flow pattern. In addition, the Reynolds stress between two square cylinders is investigated. The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan 800mm D 9mm 6mm@7 9mm pressure taps U∞ SFP B C F G E H y 400mm A wind 6mm x D 8mm@3 D z 5D L measurement plane y L x Figure 1: Arrangement of two square cylinders Figure 2: Location of pressure taps Experimental setup The experiment is conducted in an open circuit wind tunnel. The test section has a 400mm×400mm square cross section and 800mm long. The turbulent intensity of the free stream velocity is about 1.5%. The test bodies adopted in the present study are two square cylinders with a width D of 60mm, an axial length S of 356mm and two end plates on both sides. As shown in Fig.1, the upstream square cylinder is placed at 5D distance from the entrance of the test section. The downstream square cylinder is located in the streamwise direction. The space between two square cylinders is designated by L. In order to measure the surface pressure, each single square cylinder has 16 pressure taps of 1.3mm diameter at the center of the span. According to [Sakamoto et al. (1987)], 8 or 10 pressure taps are necessary on a single side of the square cylinder. Therefore, 8 pressure taps are allocated on the upper surface of each square cylinder as shown in Fig.2. Considering the symmetry, 4 pressure taps are allocated on the front and rear surface. These pressure taps are connected to a differential pressure transducer (TOA Industry, MP-32). Since the width of test bodies is determined to allocate the sufficient number of pressure taps, the blockage of the present study is 15%, consequently. The velocity measurement between two square cylinders is conducted by means of a split-fiber probe (DANTEC, 55R55). The measuring points are aligned on a plane normal to the cylinder axis. The measurement plane is located at middle of the cylinder span as shown in Fig.1. The pressure and velocity signals are digitized for 30s at the rate of 500Hz. The averaging time for the time-average of the measured data is 30s. For the pressure measurement, the free stream velocity is set to 12.0m/s (Re = 50,000). On the other hands, for the velocity measurement, the free stream velocity is decreased to 6.0m/s (Re = 25,000) since the output voltage from a split-fiber probe exceeds the range which can be measured. Surface pressure distribution corresponding to the spacing ratio The surface pressure measurement is conducted at four cases of the spacing ratios (L/D = 2, 3, 4 and 5). Figures 3 and 4 show the distributions of time-averaged surface pressure j , respectively. The surface pressure coefficient CP and fluctuating pressure coefficient C P distributions of L/D = 4 and 5 differ considerably from those of L/D = 2 and 3; with regard to the time-averaged pressure, the downstream cylinder reveals completely different distributions; the fluctuating pressures of L/D = 4 and 5 are magnified considerably. For L/D = 2 and 3, on the upper surface of the downstream square cylinder (surface FG), the recover of the pressure like reattachment-type rectangular cylinder are observed. For L/D = 4 and 5, on the front surface of the downstream square cylinder (surface E-F), timeaveraged pressure coefficients becomes approximately zero. As shown in Fig.5, for L/D = 2, only the negative pressure is measured at the center of the front surface of the downstream sq- The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan 2 2 1.5 L/D=2 L/D=3 L/D=4 L/D=5 1 0.5 CP L/D=2 L/D=3 L/D=4 L/D=5 1.5 j C P 0 1 -0.5 -1 0.5 -1.5 -2 A B C D E F G H Position Figure 3: Distributions of the time-mean pressure coefficient 0 A B C D E F G H Position Figure 4: Distributions of the fluctuating pressure coefficient uare cylinder (point E). On the contrary, for L/D = 4, the surface pressure at point E 200 L/D = 4 fluctuates between positive and negative values. As a result, time-averaged pressure 100 becomes approximately zero. From the 0 observation of the pressure fluctuation, it is inferred that the vortex emanated from the -100 upstream square cylinder impinges to the L/D = 2 -200 front surface of the downstream square cylinder. -300 29.5 29.6 29.7 29.8 29.9 30 Considerable change of the distritime (s) bution of the surface pressure between L/D = Figure 5: Time history of the surface 3 and 4 is in accordance with the experimentpressures at point E in Fig.2 tal work by [Sakamoto et al. (1987)]. [Liu et al. (2002)] show that the flow pattern changes between L/D = 3 and 4 by the flow visualization. However, the Reynolds number of their experimental work is 2,700 which is smaller than that of the present study (Re = 25,000). In addition, they did not measure the velocity between the two square cylinders in detail. In the present study, for the purpose of the detailed investigation of the flow field between the two square cylinders, the velocity is measured at densely distributed locations between the two square cylinders. pressure (Pa) 300 Treatment of outputs from a split-fiber probe Since the distributions of the surface pressure suggest the existence of the fluctuating flow between the two square cylinders in case of L/D = 4 and 5, the measurement of the velocity between the two square cylinders with the spacing ratio L/D = 4 is conducted by means of a split-fiber probe. The locations of 72 measurement points are shown in Fig. 6. At each point, the velocity components with respect to the x-axis (U) and the y-axis (V) are measured. In order to measure the velocity near the square cylinders, a split-fiber probe is set in the plane as parallel to the axis of the cylinder (z direction) as shown in Fig.1. For the measurement of the velocity component V, the split-fiber probe is set as orthogonal to the yaxis as shown in Fig.7. For the measurement of the velocity component U, the split-fiber probe is rotated 90° around z-axis. The sensor of the split-fiber probe is wrapped around a quartz core, and then, the filmlike sensor is split into two sensors as shown in Fig.7. Therefore the split-fiber probe provides The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan Reference pressure point (Point R) Measurement point 30mm Point P 6mm y wind V2 split x 8mm@6 z CH II y CH I 6mm x V1 20mm 20mm@7 20mm Figure 7: Head of a split-fiber probe Figure 6: Location of the velocity measurement points velocity (m/s) velocity (m/s) CH I CH II 8 6 4 2 0 29.5 29.6 29.7 29.8 29.9 30 8 6 4 2 0 -2 -4 -6 -8 29.5 time (s) 29.6 29.7 29.8 29.9 30 time (s) Figure 9: Combined velocity data Figure 8: Measured data at point P by a split-fiber probe two output signals. For example, when the flow comes from V1 direction indicated in Fig.7, the output of channel I sensor becomes larger than that of channel II sensor. Figure 8 shows outputs from the two sensors of a split-fiber probe when the velocity component V is measured at point P indicated in Fig.6. Since it is inferred that the periodical vortex shedding occurs, outputs from two sensors increase alternately. These two signals should be combined into one velocity signal. The result in Fig.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 split-fiber probe are facing to the opposite directions. Therefore, in the present study, the following relation is employed to combine the two signals: ⎧⎪ V1 V =⎨ ⎪⎩−V2 (V (V 1 ≥ V2 1 < V2 ) ) (1) where V1 and V2 are the velocity components measured by the two sensors, respectively. Phase averaging technique According to [Hussain et al. (1970)], the instantaneous velocity ui is decomposed into the following three components: ui = U i + uci + ur′ i = ui + ur′ i (2) where U i is the time-mean component, uc i is the periodical component ‘with zero mean’ and ur′ i is the random component. ui = U i + uc i is the phase-averaged component. Since uc i and ( ) The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan measured filterd sampled 4 Fourier spectrum (m/s) 8 velocity (m/s) 6 4 2 0 -2 -4 -6 -8 29.5 3.5 3 2.5 2 1.5 1 0.5 0 29.6 29.7 29.8 29.9 0 30 50 100 time (s) 200 250 frequency (Hz) (a): Time history of the velocity at point P in Fig.6 (b): Fourier spectrum of the measured velocity at point P in Fig.6 measured filterd sampled 0 150 20 Fourier spectrum (Pa) pressure (Pa) -20 -40 -60 -80 -100 -120 -140 29.5 15 10 5 0 29.6 29.7 29.8 29.9 30 time (s) (c): Time history of the surface pressure at point R in Fig.6 0 50 100 150 200 250 frequency (Hz) (d): Fourier spectrum of the measured surface pressure at point R in Fig.6 Figure 10: Process of the phase average ur′ i are zero mean components, the time averaging technique to measured velocity data can not reveal the pattern of the fluctuating flow between two square cylinders. Therefore, in order to obtain the phase-averaged velocity ui , the phase averaging technique [Lyn et al. (1994) and Perrin et al. (2007)] is applied to the present measured velocity data. The phase averaging technique needs the referential signal to define the flow phase. In the present study, the surface pressure of the upstream cylinder, of which the location is shown in Fig.6, is used as the reference signal. The process to compute the phase-averaged velocity consists of the following three procedures: 1) Simultaneous measurement of velocity and pressure The velocity and the surface pressure are measured simultaneously. Typical result of measured data, velocity component V which is measured at point P indicated in Fig.6, surface pressure which is measured at the point R in Fig.6 and their Fourier spectrums are shown in Figs.10 (a)-(d). To remove the random component ur′ i from the measured data, the data is filtered by a low-pass filter. As shown in Figs.10 (b) and (d), Fourier spectrums of the The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan measured velocity and the surface pressure have same peak-frequency at 12.8Hz ( St = 0.128 ) which is in accordance with the Strouhal number of the single square cylinder [Lyn et al. (1995)]. Therefore, the cut-off frequency of the low-pass filer is set at 30Hz which is twice high frequency of the vortex shedding from the upstream cylinder. 2) Subdivision of the measured data To define the phase, the measured data is divided into a series of single cycle periods. The period is defined as the interval between peaks of the pressure signal which are shown in Fig.10(c) by circle symbols. 3) Extraction of data at same phase From every divided data, velocities at the same phase are extracted and averaged. In the present study, each period is divided into 20 phases. As a result, the phase-averaged velocity ui is obtained. In Fig.10(a), circle symbols indicate the extracted velocity data at phase φ = 0 . Phase-averaged velocity between two square cylinders in tandem arrangement The distributions of the phase-averaged velocity vectors and the streamlines are shown in Fig.11(a)-(h). At phases φ = 0 φ = φ 2π and φ = 10 20 , large vortices as large as the square cylinder are observed behind the upstream cylinder indicated as “A” in Fig.11(a) and as “B” in Fig.11(e) respectively. The advective speed of the vortex is about 2.6m/s calculated from the location of the vortex center at every phase. It is about 40% of the inflow velocity (6.0m/s). At phases φ = 3 20 and 5 20 , since the vortex “B” emanated from the lower side of the upstream cylinder has passed the region between two cylinders, the upward flow is formed almost of all the region between two cylinders. At phases φ = 8 20 and 10 20 , rolling ( ) A B A B (a) : φ = 0 (e) : φ = 10 20 A B (b) : φ = 3 20 (f) : φ = 13 20 A B (c) : φ = 5 20 (g) : φ = 15 20 A B (d) : φ = 8 20 (h) : φ = 18 20 Figure 11: Phase-averaged velocity vector and streamline The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan 0.35 0.45 0.10 0.05 0.10 0.25 0.15 (a) u ′ U 2 (b) v′2 U in2 2 in Figure 12: Distribution of normal components of the Reynolds stress 0.30 0.35 0.05 0.05 0.20 0.10 (a) u U 2 c 2 in (b) vc2 U in2 Figure 13: Distribution of normal components of the Reynolds stress evaluated from the periodical component of the velocity up from the upper side of the upstream cylinder forms the downward flow behind the upstream cylinder. On the other hands, the vortex “A” emanated from the lower side of the upstream cylinder forms the upward flow in front of the downstream cylinder. Therefore, high curvature of the streamline exists between two cylinders at these phases. As shown in Figs.11(e)-(h), at phases from φ = 10 20 to 18 20 , the flow patterns are symmetric to the flow at phases from φ = 0 to 8 20 with respect to the vertical axis through both centers of the two cylinders. Distribution of the Reynolds stress Since the fluctuating component of the velocity ui′ is calculated as ui′ = ui − U i , where ui is the instantaneous velocity, U i is the time-averaged component, the Reynolds stress ui′u ′j can be investigated. The fluctuating component of the velocity ui′ is further decomposed to the periodical component uc i and the random component ur′ i as ui′ = uc i + ur′ i . Therefore, the Reynolds stress calculated from the periodical component uc i and the Reynolds stress calculated from the random component ur′ i can be evaluated. In this chapter, we discuss that how these components contribute to the total Reynolds stress ui′u ′j . Figures 12(a) and (b) show contours of the Reynolds stress ui′u ′j . Since the simultaneous measurement of the velocity components U and V is not conducted, only the normal components of the Reynolds stress u ′2 and v′2 are investigated. u ′2 and v′2 are nondimensionalized by square of the inflow velocity Uin (=6.0m/s). As shown in Fig.12(a), the distribution of u ′2 component has two peaks near the trailing edges of the upstream cylinder. On the other hands, the distribution of v′2 component has one peak behind the upstream cylinder. The location of the peak of the v′2 component is further from the upstream cylinder than that of the u′2 component. Since the periodical component of the velocity uc i is evaluated as uc i = ui − U i , the Reynolds stress calculated from the periodical component uc i uc j can be evaluated. Figs.13(a) and (b) show the normal components of the Reynolds stress calculated by the periodical component of the velocity uc2 and vc2 . In comparison with Figs.12(a), (b) and Figs.13(a), (b), The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan distributions of uc2 and vc2 are quite similar to those of u′2 and v′2 . Their peaks appear at the same locations. The peak values uc2 and vc2 occupy about 80% to that of u ′2 and v′2 , respectively. Therefore, the periodical component of the velocity which is occurred by the vortex shedding from the upstream cylinder has a great influence on the property of the turbulent flow structure between two square cylinders. Conclusion In the present study, for the purpose of the investigation of the flow field between two square cylinders in tandem arrangement, the measurement of the surface pressure and the measurement of the velocity between two square cylinders are conducted. As a result, the surface pressure distributions vary considerably between the spacing ratio L/D = 3 and L/D = 4 in accordance with the experimental work by [Sakamoto et al. (1987)]. For L/D = 4, according to the phase-averaged velocity, the flow field between two cylinders shows two patterns. One is the diagonal flow which intersects between two cylinders. The other is high curvature flow which forms the upward (downward) flow behind the upstream cylinder and the downward (upward) flow in front of the downstream cylinder. For L/D = 4, these flow patterns vary periodically between two square cylinders in tandem arrangement. Between two square cylinders, the Reynolds stress evaluated from the periodical component of the velocity occupies about 80% to the total Reynolds stress which is evaluated from the fluctuating component. Therefore, the periodical component of the velocity has a great influence on the property of the turbulent flow structure between two square cylinders. 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(2006), “The pressure-velocity correlation in oscillatory turbulent flow between a pair of bluff bodies”, International Journal of Heat and Fluid Flow, 27, 768-776 Perrin, R., Cid, S., Cazin, S., Sevrain, A., Braza, M., Moradei, F. and Harran, G. (2007), “Phase-averaged measurements of the turbulence properties in the near wake of a circular cylinder at high Reynolds number by 2C-PIV and 3C-PIV”, Experiments in Fluids, 42, 93-109 Sakamoto, H., Haniu, H. and Obata, Y. (1987), “Fluctuating force acting on two square prisms in a tandem arrangement”, Journal of Wind Engineering and Industrial Aerodynamics, 26, 85-103 Shiraishi, N., Matsumoto, M. and Shirato, H. (1986), “On aerodynamic instabilities of tandem structures”, Journal of Wind Engineering and Industrial Aerodynamics, 23, 437-447 Tokoro, S., Komatsu, H., Nakasu, M., Mizuguchi, K. and Kasuga, A. (2000), “A study on wake-galloping employing full aeroelastic twin cable model”, Journal of Wind Engineering and Industrial Aerodynamics, 88, 247-261