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  The Eighth Asia-Pacific Conference on Wind Engineering,December 10–14, 2013, Chennai, India   AERODYNAMIC AND RESPONSE CHARACTERISTICS OF TALL BUILDINGS WITH VARIOUS POLYGON CROSS-SECTIONS Yong Chul, Kim 1 , Eswara Kumar, Bandi 2 , Yukio, Tamura 3 , Akihito, Yoshida 4   1  Research professor, Korea University, Seoul, Korea,  GCOE Associate Professor, Tokyo Polytechnic University, Atsugi, Kanagawa, Japan   2  Ph D Candidate, Tokyo Polytechnic University, Atsugi, Kanagawa, Japan,   3  Professor, Polytechnic University, Atsugi, Kanagawa, Japan,   4  Associate Professor, Tokyo Polytechnic University, Atsugi, Kanagawa, Japan,   ABSTRACT A series of wind tunnel tests were conducted on 13 straight and helical tall buildings with various polygon cross-sections, including triangle, square, pentagon, hexagon, octagon, dodecagon, and circular. The primary purpose of the present study is to investigate the effect of increasing number of side on aerodynamic characteristics for the straight and helical tall buildings. The results show that the overturning moment coefficients and the spectral values decrease with increasing number of side, showing the largest mean and fluctuating overturning moments for the straight triangle model, and the largest spectral values for the straight square model. And the effects of helical shape on the aerodynamic characteristics decrease with increasing the number of side, but large differences were found in the spectral values for the safety level design wind speed, hence the largest maximum displacement. Keywords: Tall buildings, Wind-induced responses, Polygon cross-section, Helical shape Introduction The current tallest building in the world is the 828m-high Burj Khalifa, and the tallest  building in the next decade will be Kingdom Tower (over 1000m), which will be completed in 2018. The current trend of tall building construction, i.e., manhattanization with various  building shapes, requires attention. Their free-wheeling building shapes are expressed by taper, set-back, helical, or changing cross-sections, reflecting architects’ and engineers’ challenging spirits for new forms. These atypical and unconventional building shapes are a resurrection of an old characteristic, but they have the advantage of suppressing across-wind responses, which is a major factor in safety and habitability design of tall buildings. Besides changing building shapes, many current tall buildings have various polygon cross-sections, not being limited to the simple square cross-section. So far, there have been some studies that have investigated the aerodynamic characteristics of tall buildings with various polygon cross-sections. Chien et al. (2010) examined mean drag forces, in terms of shape factors, for 8 kinds of polygon high mast structures using 2-dimensional CFD analyses. In their study, the mean drag force becomes constant for the polygon structures with more than 10-side.Tang et al. (2013) investigated the mean drag forces and wake flows on straight and twisted polygon tall buildings using numerical simulations. They examined the effect of increasing number of sides, rounded corners of square cross-section, and twisting angle of the square cross-section tall building. They used 10 straight tall buildings for various polygon cross-sections, 11 rounded square cross-sections with various fillet radiuses, and 9 twisted tall  buildings with twisting angle up to 180º by the interval of 22.5º. From 2-dimensional numerical simulations, they found that the mean drag force decreases with increasing the side numbers, and the decrease becomes very slow when the number of sides is larger than 14. The mean drag force of 14-side polygon tall building is only 40% of that of a square tall building. And also from the 2-dimensional numerical simulations for various fillet radius r  , the mean Proc. of the 8th Asia-Pacific Conference on Wind Engineering – Nagesh R. Iyer, Prem Krishna, S. Selvi Rajan and P. Harikrishna (eds)  Copyright c  2013 APCWE-VIII. All rights reserved.  Published by   Research Publishing, Singapore. ISBN: 978-981-07-8011-1doi:10.3850/978-981-07-8012-8 079 770  Proc. of the 8th Asia-Pacific Conference on Wind Engineering (APCWE-VIII)   drag force drops quickly until the radius-to-width ratio r  / b  reaches 0.15, and further increase of fillet radius has little influence on the mean drag force. To support above two finding, they showed the width of wake flow, which is almost constant after the case of 14-side polygon tall buildings and after the radius-to-width r  / b  of 0.15. The effect of twisting angle from 0º (Straight) to 180º was examined using the 3-dimensional numerical simulations for tall  buildings with aspect ratio of 5. The mean drag forces increase or decrease depending on twisting angles, and Tang et al. (2013) concluded that the efficiency of aerodynamic modifications is best for the rounded corners, and next is increasing edge numbers, and the next is twisting the building shape. Chien et al. (2010) and Tang et al. (2013) only focused the mean drag force, and only uniform flow was used in their study. So far, some studies on the effect of increasing number of side on aerodynamic characteristics have been conducted, but in the studies only mean drag force has been focused on by the numerical simulations under a uniform flow, no discussions were found on the characteristics of other wind force components and responses using a boundary layer flow. In the present study, the effects of various polygon cross-sections (triangle, square, pentagon, hexagon, octagon, dodecagon, and circular) on aerodynamic characteristics were investigated systematically using pressure measurement results. And for the helical angle of 180º, the aerodynamic characteristics of the helical tall buildings with various number of sides were also investigated. Wind Tunnel Test Table 1 shows the 13 tall building models which were used for wind tunnel tests.   Table 1: Tall building models with various polygon cross-sections Straight models TR SQ PE HE OC DO CI Helical models TR-180H SQ-180H PE-180H HE-180H OC-180H DO-180H Considering the results of Tanaka et al. (2012) on the effect of helical angles of square section tall buildings, a helical angle of 180º was used in the present study. Equilateral cross-sections 771  Proc. of the 8th Asia-Pacific Conference on Wind Engineering (APCWE-VIII)   were used and the cross-sectional area of all building models was set the same. The model height was  H  =400m in common, giving the same total volume for all building models. The  profiles of mean wind speed and turbulence intensity are plotted in Fig. 1. The experiments were conducted under urban area flow (power-law index,   = 0.27) for various wind directions. The wind speed at the model height was about U   H   = 12 m/s, and the turbulence intensity was about  I  uH   = 11%. Fig. 2 shows the coordinate system used in the study; structural axes,  M   X   and  M  Y  , not wind axes,  M   D  and  M   L , were used. Wind direction of 0º is defined when wind is normal to one side of cross-section, and the considered wind directions are different depending on building models.   A length scale of 1/1000 and a time scale of 1/167 were assumed. There were more than 200 pressure taps and all the pressures were measured simultaneously with a sampling frequency of 781 Hz, and a low pass-filter with a cut-off frequency of 300 Hz was cascaded in each data acquisition channel to eliminate aliasing effects. The measuring time was adjusted such that 33 samples were obtained, which one sample corresponds to 10-minute sample in full time scale. The Reynolds number which is defined by the width of square model and wind speed at model height was about  Re  = 4.2×10 4 , and as the number of side increases, the Reynolds number effect becomes significant, but in the present study the only a Reynolds number in subcritical range was considered. (a) mean wind speed (b) turbulenc intensity Fig. 1 Profiles of incident flow Fig. 2 Coordinate system Results and Discussion Considering the tributary area of each pressure tap, the time series of overturning moments (o.t.m.) were obtained, and using Eqs. (1) ~ (3), o.t.m. coefficients were calculated. C   MX   =  M   X  /( q  H   BHH  ) (1); C   MY   =  M  Y  /( q  H   BHH  ) (2); C   MZ   =  M   Z  /( q  H   BHB ) (3) where,  M   X  ,  M  Y  , and  M   Z  : overturning moment about  X  -, Y  -, and  Z  -direction; q  H  : velocity pressure defined at model height;  B : width of the square model(representative width);  H  : model height  Mean and fluctuating overturning moment coefficients  M   X   Y  M  Y    Wind       U  h   ;    z  0.27    I  u,h  ;  z  -0.32 772  Proc. of the 8th Asia-Pacific Conference on Wind Engineering (APCWE-VIII)   (a)   Straight models (b)   Helical models Fig. 3 Variation of mean overturning moment coefficients in  X  -direction. Fig. 3 shows the variations of mean o.t.m. coefficients for  X  -direction  MX  C  . Fig. 3(a) is for the straight models, and Fig. 3(b) is for the helical models. The dotted line indicates the mean o.t.m. coefficient of circular model (CI). For all models, mean coefficients decrease with wind directions, showing their largest absolute values near the wind direction of     = 90º ~ 100º. And it seems that the mean coefficients of the models with larger number of sides are smaller. One characteristic point is that the variations of mean coefficients near the wind directions of     = 0º. Only for the straight triangle (TR) and square (SQ) models in Fig. 3(a) show clear positive slope ( 0 > θ  d C d   MX  ) near the small wind directions, meaning a possibility of occurrence of instability vibrations. For the straight octagon (OC) model, a positive slope is observed, but the slope is very small and can be ignored. Fig. 4 shows the variations of fluctuating o.t.m. coefficients on wind directions for  X  -direction  MX  C  ′ . The largest value is found for the straight square (SQ) model near the wind direction of     = 0º, and decrease with increasing wind directions. The difference among models is not clear, but the smaller value seems to be found for the models with larger number of sides, showing slightly larger values than that of the circular (CI) model.   The largest absolute mean and fluctuating o.t.m. coefficients were obtained for the considered wind directions and the variations on number of side are shown in Fig. 5. For the coefficients for  X  - and Y  -directions, C   MX   becomes C   MY   and C   MY   becomes C   MX   depending on the wind directions, thus larger absolute mean and fluctuating coefficients were selected regardless of wind directions. Open symbols indicate the straight models, and solid symbols indicate the helical models. And circle indicates the coefficients for  X  - and Y  -directions, and  X   M  Y   M   Z  X   M  Y   M   Z  773
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