Proceedings of Al-Azhar Engineering 9 th International Conference, April, 2007, Cairo, Egypt

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1 Proceedings of Al-Azhar Engineering 9 th International Conference, April, 2007, Cairo, Egypt Characteristics of Wind Forces Acting on Uncommon Tall Buildings Wael M. Elwan, Ahmed F. Abdel Gawad, Salem S. Abdel Aziz, and Hesham E. Abdel Hameed,

2 CHARACTERISTICS OF WIND FORCES ACTING ON UNCOMMON TALL BUILDINGS Wael M. Elwan Demonstrator Ahmed F. Abdel Gawad Assoc. Prof. Member ASME, AIAA, Salem S. Abdel Aziz Assist. Prof. Hesham E. Abdel Hameed Assist. Prof. Mechanical Power Eng. Dept., Faculty of Eng., Zagazig University, Zagazig 44519, Egypt Abstract In the present work, a CFD model was developed to predict the flow characteristics around four different models of uncommon tall buildings. These models simulate typical actual famous tall buildings. Local and total wind forces on tall buildings are investigated in terms of the distribution of force parameters, such as pressure and drag coefficients, at different levels along the height of the building model for different wind directions. Also, the results include the streamline patterns as well as contours of Cp and turbulence kinetic energy. Results demonstrate that both the pressure and drag coefficients, for most of the studied cases, reach their maximum values (corresponding to stagnation) at 0.86 of the height of the building. Then, the values of these two coefficients decrease gradually towards the roof of the building. In the unsteady analysis, it was found that pressure takes a specified period of time to reach the steady state condition. This time period depends on the building configuration and the incoming wind direction. Interesting findings and conclusions are reported. Key Words Tall buildings, Wind force, Computational solution, Unsteady. 1. Introduction For the structure engineering, a tall building can be defined as one whose structure system must be modified to make it sufficiently economic to resist lateral forces from wind or earthquake within the prescribed criteria for strength, shift, and comfort of occupants. As building height increases, the forces of nature begin to dominate the structure system and take on increasing importance in the overall building system. Especially for tall buildings, lateral load effects are quiet variable and increase rapidly with the increase in height. The development of tall buildings along the past time was depending on the big progress and development of the high-strength materials, the new design concepts, the new structural systems and improved construction methods. The tall buildings technology can be thought of as a progressive reduction of material used within the space occupied by the building. There are three types of occupancy considered in the selection of structure type. The following categories can be distinguished as specifically affecting the structural systems of tall buildings structure; the first is residential buildings, including hotels and apartments, the second is commercial and office buildings, the third is mixed occupancy-commercial and residential facilities. Many researchers considered different aspects of tall buildings. Khanduri et al. [1] studied the wind-induced interference effects between two adacent buildings using neural networks. Lakehal [2] studied the effect of boundary layer roughness and the different incidence angles over a building with complex boundaries He used K-ε modeling in his investigation. Li et al. [3] studied the effect of equivalent wind loads and damping characteristics on two tall buildings with 70 and 30 stores, respectively, which are located in the center district of Hong Kong. The 70-store building is 370 m tall and the 30-store building is 120 m tall. They found that, for the 70-store building, the along-wind vibration is dominated by the longitudinal incidence turbulence and the cross-wind motion is mainly caused by the wake excitation. For the 30-store building, the damping characteristics in building are well represented by random factors. Ohba [4] studied the effect of the separation distances between twin high-rise towers on the flow and concentration fields around them. He found that the effect of the up-wind tower is to retard the flow separation on the top and sides of the down-wind tower. Zhou et al. [5 & 6] studied the effect of unfavorable distribution of static equivalent wind loads as well as the

3 effect of mode shape on the long wind responses of tall buildings. Nishimura and Taniike [7] studied the fluctuating force on a stationary circular cylinder in a smooth flow at a subcritical Reynolds number. Linag et al. [8] studied the effect of crosswind forces on rectangular tall buildings and the corresponding RMS lift coefficients and Strouhal number. Gu and Quan [9] studied the cross-wind dynamic response of 15 typical tall building models at high wind frequency. They introduced the resulting coefficients of base moment and shear force. Abdel Gawad [10] proposed a new approach to minimize the wind load on interfering tall buildings. He used numerical computations and optimization techniques to obtain the best locations and heights to get minimum wind loads on the interfering buildings. Fuisawa et al. [11] studied the local wind forces on nine models with different rectangular cross section. They also included the effect of three parameters; elevation, aspect ratio and side ratio. In their work, local wind forces on tall buildings were investigated in terms of mean and RMS force coefficients, span-wise correlations as well as power spectral density and coherence. Li et al. [12] studied the effect of wind on the tallest building in China by a combined wind tunnel and fullscale investigation. They discussed force coefficients and power spectral densities as well as displacement and acceleration responses. The present investigation demonstrates the results of computational analysis of the flow field for four building models. The study is based on three-dimensional, steady and unsteady, incompressible K-ε modeling that was developed by the authors using a commercial code [13]. The results include streamlines, pressure and drag coefficient distributions at different levels along the model height (Z/H = 0.02, 0.25, 0.5, 0.75 and 0.98) in most of the studied cases. Steady computations give the time-averaged values of wind load (drag) coefficients as well as time-averaged patterns of streamlines and contours of Cp and turbulence kinetic energy. These time-averaged values are essential for the design and construction of the tall buildings. The unsteady (time-dependent) computations are intended to simulate the sudden blow of wind. Thus, the time-development of different quantities (e.g., C P and C D ) can be monitored. 2. Governing Equations and K- ε The governing equations for the mean velocity and pressure are the Reynolds averaged Navier- Stokes equations for incompressible flow. The governing equations of flow field as well as standard K- ε model can be written as: ρ U - Mass: + = 0 (1) t x - Momentum: U i 1 P Ui + ( U U i) = - + ( ν - u i u ) t x ρ x x x i 2 u i u = 2 νt Di - Kδi (3) 3 2 C μ K -Turbulent viscosity: νt = (4) ε 1 U U i D i = ( + ) (5) 2 x x i -Turbulence kinetic energy: K νt K + (U K) = [( + ν ) ] u i u D i - ε (6) t x x Prk x -Dissipation rate of turbulence kinetic energy: 2 ε νt ε ε ε + (U ε) = [( + ν) ] + C 1 (- u i u D i) - C 2 (7) t x x Prε x K K Where K is the turbulence kinetic energy, ε is the rate of dissipation of turbulence kinetic energy, and U i is the velocity component in x i -direction. ν is the kinematic viscosity, ν t is the turbulent kinematic viscosity, ρ is the density. Pr k (= 1.0) and Pr ε (= 1.3) are the Prandtl numbers for kinetic (2)

4 energy of turbulence and rate of dissipation, respectively. C μ (= 0.09), C 1 (= 1.44), and C 2 (= 1.92) are numerical constants. δ i is the kronecker delta. 3. Computational Aspects and Boundary Conditions The computational domain is shown in Fig. 1. The computational meshes were based on triangular-shaped elements, Fig. 2. The mesh is very fine next to the solid boundary of the body. The size of the element increases towards the far field away from the solid boundaries. Number of cells is in the range of 180,000. The least y + from the wall for the first node was about 4. Careful consideration was paid to minimize the dependent of solution on the mesh by improving the clustering of cells near solid walls until results are almost constant. The applied boundary conditions are shown in Fig. 1. These boundary conditions can be listed as: (1) The velocity at upstream boundary is uniform, so u=u. (2) The velocity at far boundaries is uniform, so u=u,. (3) The no-slip and no-penetration conditions are used on the surfaces of the building model and the ground, so U i =0. (4) The zero gradient condition is assumed for all variables at downstream boundary, so U i / x = 0. The law of the wall was used as a wall treatment method. 4. Description of Investigated s The CFD model was used to predict the flow characteristics around four different models of uncommon tall buildings. These models simulate typical actual famous tall buildings. The first model is JR CENTRAL TOWER in the form of circular cylinder as shown in Fig. (3-a), which is located in NAGOYA, JAPAN. It has 59 stores in m tall. The second model is GRAHA KUNINGAN in the form of half ellipse as shown in Fig. (3-b), which is located in JAKARTA, INDONESIA. It has 52 stores in 240 m tall. It is investigated for different flow angles (0 o, 45 o, 90 o, and 180 o ). The third model is PLAZA RAKYAT in the form of three main square blocks above each other with different dimensions as shown in Fig. (3-c), which is located in KUALA LUMPUR, MALAYSIA. It has 77 stores in m tall. It is investigated for two flow angles (0 o & 45 o ). The fourth model is BURJ ALARAB in the form of hyperbolic paraboloids as shown in Fig. (3-d), which is located in DUBAI, UNITED ARAB EMIRATES. It has 70 stores in 320 m tall. It is used as a hotel. It is investigated for three flow angles (0 o, 90 o, and 180 o ). To reduce the computational effort (number of cells and overall computer run-time), the computations were carried out for scaled models. The free-stream incoming velocity was kept fixed for all the investigated models. Table (1) shows the details of the investigation parameters for the four models. Table (2) shows the main dimensions of the four models. Table (1) Investigation parameters for the four models. Description Location Scale Re α M1 Circular cylinder Nagoya Japan 1: o M2 Half ellipse Jakarta 1: o, 45 o, 90 o Indonesia & 180 o M3 Blocks Kuala Lumpur Malaysia 1: o & 45 o M4 Hyperbolic Dubai 1: o, 90 o paraboloids United Arab Emirates & 180 o Figs. 4-7 show the cross sections of the four building models; M1, M2, M3, and M4, respectively, for different angles of attack (α). S represents the dimensionless distance along the circumference of the cross-section of the building model.

5 Upstream Symmetry line Downstream z x Ground Building model H M1 6 H M1 20 H M1 D M1 10 H M1 (a) Side view. Upstream Downstream y x Symmetry lines D M1 10 H M1 D M1 20 H M1 10 H M1 (b) Top view. Fig. (1) Computational domain with boundary conditions. (a) First model (M1). (b) Second model (M2). (c) Third model (M3). (d) Fourth model (M4). Fig. (2) Triangular meshing for the four building models.

6 E Fig. (4) Cross-section of model M1. (a) M1 (Circular cylinder). (b) M2 (Half ellipse). (a) α = 0 o. (b) α = 45 o. d M4 (c) M3 (Blocks). (d) M4 (Bur Alarab). Fig. (3) Main dimensions and features of the four models. (c) α = 90 o. (d) α = 180 o. Fig. (5) Cross-section of model M2 for different angles of attack (α).

7 B U S C A U S A B D E C E (a) α = 0 o. (b) α = 45 o. D Fig (6) Cross-section of model M3 for different angles of attack (α). B A U S C U E B A S D E D C (a) α = 0 o. (b) α = 90 o. E U D S C B (c) α = 180 o. Fig (7) Cross-section of model M4 for different angles of attack (α). 5. Results and Discussions 5.1 Steady computations Pressure coefficient Pressure coefficient is determined as Cp = (( P s P P is the free-stream static pressure, ρ is the air density and A 2 U )) where P s is the static pressure, U is the upstream velocity. The maximum )/(0.5 ρ value of Cp is located at Z/H=0.85 for most cases. For the first model (M1), the values of Cp are plotted against θ at different cross-section along the height of the model in Fig. (8). θ is the angle measured from the stagnation point in clockwise direction as shown in Fig. (4). It is seen that the minimum value of Cp = is at θ = 90 o for all levels except at Z/H = 0.98 where Cp = The separation point is at θ = 145 o for all levels except at Z/H = Symmetry of results is clearly achieved. The correspondence between the present prediction of Cp distributions around this model and the well-known results of [11] gives confidence in the present model and the numerical scheme. For the second model (M2), the pressure coefficient Cp is plotted at different incidence angles (0 o, 45 o, 90 o & 180 o ) against the length of the perimeter (S), which is measured from the stagnation point. The first case is shown in Fig. (9-a) with incidence angle α = 0 o. It is found that the minimum value of Cp is at points (B) and (E) at Z/H = 0.75 because the model is symmetric. The second case is shown in Fig. (9-b) with incidence angle α = 45 o. It is seen that the minimum value of Cp is at point (B). The third case is shown in Fig. (9-c) with incidence angle α = 90 o. It is found that the minimum value of Cp is at point (A) at any section except at Z/H = 0.98 where the minimum value of Cp is at point (B). The fourth case is shown in Fig. (9-d) with incidence angle α = 180 o. The minimum value of Cp is at points (B) and (E) because of symmetry. For the third model (M3), the pressure coefficient Cp is plotted at two incidence angles (0 o & 45 o ) against the normalized distance along the perimeter (S) that is measured from the stagnation point. The first case is shown in Fig. (10-a) with incidence angle α = 0 o. It is found that the minimum value of Cp is at points (B) and (E) at Z/H = 0.2 because of symmetry. The second case is shown in Fig. (10-b) with incidence angle α = 45 o. It is found that the minimum value of Cp = is at Z/H = The effect of the elevation height is clearly noticed in this case, Fig. (10-b). For the fourth model (M4), the pressure coefficient Cp is

8 plotted at three incidence angles (0 o, 90 o & 180 o ) against the normalized length of perimeter (S), which is measured from stagnation point. The first case is shown in Fig. (11-a) with incidence angle α = 0 o. It is found that the minimum value of Cp is at points (B) and (E) at Z/H = 0.4. The second case is shown in Fig. (11-b) with incidence angle α = 90 o. It is seen that the minimum value of Cp = -1.4 at point (D) for all levels except at Z/H =0.02 where Cp = The third case is shown in Fig. (11-c) with incidence angle α = 180 o. It is found that the minimum value of Cp = -1.5 for all levels except at Z/H = 0.8 and Z/H = 0.6 where Cp = -1.0 and , respectively. θ (degree) Fig. (8) Distributions of Cp for the first model (M1) at different levels. (a) α = 0 o. (b) α = 45 o. (c) α = 90 o. (d) α = 180 o. Fig. (9) Distributions of Cp for model M2 at different angles of attack.

9 (a) α = 0 o. (b) α = 45 o. Fig. (10) Distributions of Cp for model M3 at different angles of attack. (a) α = 0 o. (b) α = 90 o. Fig. (11) Distributions of Cp for model M4 at different angles of attack Local drag coefficient (C DL ) The distributions of C DL are shown in Fig. (12) for the four building models. The values of the local drag coefficient C DL are shown in tables (3), (4), (5), and (6) for models M1, M2, M3, and M4, respectively. The local drag coefficient is calculated at different levels along the height of the building. It is found that the local drag coefficient for most of the cases increases with Z/H to reach a maximum value at Z/H = Fig. (11-c) Distributions of Cp for model M4 at α = 180 o. Fig. (12-a) Local drag coefficient (C DL ) for model M1 at different height levels.

10 (a) α = 0 o. (b) α = 45 o. (c) α = 90 o. (d) α = 180 o. Fig. (12-b) Local drag coefficient (C DL ) for model M2 with different angles of attack. (a) α = 0 o. (b) α = 45 o. Fig. (12-c) Local drag coefficient (C DL ) for model M3 with different angles of attack. (a) α = 0 o. (b) α = 90 o. (c) α = 180 o. Fig. (12-d) Local drag coefficient (C DL ) for model M4 with different angles of attack.

11 Table (2) Main dimensions for all models. M1 M2 M3 H M1 /D M1 H M2 /R M2 W M2 /R M2 H 4M3 /W 4M3 H 3M3 /W 4M3 H 2M3 /W 4M3 H 1M3 /W 4M3 W 3M3 /W 4M M3 M4 W 2M3 /W 4M3 W 1M3 /W 4M3 H M4 /d M4 W M4 /d M Table (3) Values of C DL for the first model (M1). α M1 Z/H C DL Table (4) Values of C DL for the second model (M2). α 0 o 45 o Z/H C DL α 90 o 180 o Z/H C DL o M2 M2 Table (5) Values of C DL for the third model (M3). α 0 o 45 o Z/H C DL M3 Table (6) Values of C DL for the fourth model (M4). M4 α 0 o 90 o Z/H C DL α M4 180 o Z/H C DL

12 From tables 3-6, it is clear that the values of C DL depend on the combined effect of three parameters. These parameters include: (i) the angle of attack (α), (ii) the elevation level (Z/H), and (iii) the shape and geometry of the building Total drag coefficient (C D ) The values of the total drag coefficient (C D ) for the different building models are shown in table 7. Values of C D were calculated by numerical integration of the local drag coefficients (C DL ) that were reported in tables 3-6. Table (7) Values of total drag coefficient (C D ) for different cases. M1 M2 M3 M4 α 0 o 0 o 45 o 90 o 180 o 0 o 45 o 0 o 90 o 180 o C D As can be seen in table 7, the minimum value of C D is naturally found for the first model (M1). The maximum value of C D is found for the second model (M2) at α = 180 o. For the fourth model, values of C D are almost constant for the three tested angles of 0 o, 90 o & 180 o Validation As mentioned in section 5.1.1, the good agreement between the present prediction of Cp distributions around model M1 and the results of [11], Fig. (8), gives confidence in the present CFD model. Also, a good agreement between the present C P distributions around model M2 and the results of [2] at α = 0 o, Fig. (9-a), is clearly noticed. Moreover, from table 7, the C D values of 1.1 and 0.83 for model M3 at α = 0 o and 45 o compares very well to the values of 1.07 and 0.81, respectively, that were reported in [14]. Thus, the results of the present model for different cases can be accepted with great deal of confidence Local and total side force coefficients The coefficient of local side force (C FSL ) equals zero for all cases (because of stream-wise symmetry) except for two cases of the second model (M2) with incidence angles (45 o & 90 o ). Side force (F s ) acts positively in the y-direction, i.e., in the cross-wise direction of the building model. The values of the local and total side force coefficients are shown in table (8) for these two cases. Table (8) The values of C FSL and C FS for model M2. M2 α 45 o 90 o Z/H C FSL C FS C FS is found by numerical integration of values of C FSL along the height of the building model. Table 8 shows that the maximum value of C FS of 0.71 is obtained at α = 90 o Streamline patterns and wake length The streamline patterns of some cases are shown in Fig. (13). The wake length is recorded for all cases with respect to the building height as L/H, where L is the wake length and H is the building height. It is found that the wake length for all cases decreases gradually with Z/H to reach the minimum value at the roof of the building. The maximum and the minimum values of the wake length for all cases are found at Z/H = 0.02 and 0.98, respectively. The values of L/H for all cases are shown in tables 9-12.

13 Table (9) The values of L/H for model M1. M1 α Z/H L/H Table (10) The values of L/H for model M2. M2 α 0 o 45 o Z/H L/H M2 α 90 o 180 o Z/H L/H Table (11) The values of L/H for model M3. M3 α 0 o 45 o Z/H L/H o Table (12) The values of L/H for model M4. M4 α 0 o 90 o 180 o Z/H L/H (i) Z/H = (ii) Z/H = 0.5. (iii) Z/H = Fig. (13-a) Streamline patterns for model M1 at different height levels.

14 (i) Z/H = (ii) Z/H = 0.5. (i) Z/H = (ii) Z/H = 0.5. Fig. (13-b) Streamline patterns for model M2 at two height levels, α = 0 o. Fig. (13-c) Streamline patterns for model M2 at two height levels, α = 45 o. (i) Z/H = (ii) Z/H = 0.5. (i) Z/H = (ii) Z/H = 0.5. Fig. (13-d) Streamline patterns for model M2 at two height levels, α = 90 o. Fig. (13-e) Streamline patterns for model M2 at two height levels, α = 180 o. (i) Z/H = (ii) Z/H = 0.5. (i) Z/H = (ii) Z/H = 0.5. Fig. (13-f) Streamline patterns for model M3 at two height levels, α = 45 o. Fig. (13-g) Streamline patterns for model M4 at two height levels, α = 90 o. 5.2 Unsteady computations Drag and side force coefficients In unsteady analysis, it was found that pressure takes a specified period of time to reach the steady state condition. This time period depends on the building configuration and angle of attack as shown in table (13). The dimensionless time T is defined as T = (( U t )/ H), where U is the upstream velocity (m/s), t is the time in seconds, and H is the building model height (m). Values of total drag coefficient (C D ) decrease with time for all cases as shown in the Fig. (14). The coefficients of side force (C FS ) equal zero for all cases except the two cases of the second model (M2) with incidence angles 45 o and 90 o. The values of the total side force coefficient (C FS ) vary with time depending on the angle of attack, Fig. 15. Fig. (14) Change of values of C D with time. Fig. (15) Change of values of C FS with time.

15 Table (13) Values of dimensionless time required to reach steady state. M1 M2 M3 M4 α 0 o 0 o 45 o 90 o 180 o 0 o 45 o 0 o 90 o 180 o T Contours of Cp and turbulence kinetic energy Generally, values of the pressure coefficient (Cp) decrease with time in the region in front of the building and increase in the wake region for all cases as shown in the Figs The patterns of the dimensionless turbulence kinetic energy (K n ) contours change with time (T) depending on the building configuration as shown in Figs until steady state patterns are achieved. The region where change of K n is seen extends further downstream the building as we approach the ground. 6. Conclusions In the present work, a CFD model was developed to predict the flow characteristics around four different models of uncommon tall buildings. These models simulate typical actual famous tall buildings. Local and total wind forces on tall buildings are investigated in terms of the distribution of force parameters, such as pressure and drag coefficients, at different levels along the height of the model for different angles of attack. Many interesting remarks and observations can be recorded as follows: (1) The present predictions compare very well to the results of other authors. This gives confidence in the present CFD model. (2) Pressure and drag coefficients, for most of the studied cases, reach their maximum values (corresponding to stagnation) at 0.86 of the height of the building model. Then, the values of these two coefficients decrease gradually towards the roof of the building. (3) Considerable amount of side force is generated due to the stream-wise wind on the building model if there is no stream-wise symmetry. (4) The wake length behind the building model, for all the studied cases, decrease with height to reach the minimum value at Z/H = (5) The minimum and maximum values of wake length (L/H) are found for the second model (Half ellipse) depending on the flow angle of attack. (6) In the unsteady analysis, it was found that pressure takes a specified period of time to reach the steady state condition. This time period depends on the building configuration and the incoming flow angle. (7) In the unsteady analysis, it is seen that the drag coefficients decrease with time to reach the steady state values that depend on the building configuration and the flow angle. (8) Generally, the region, where change of K n is seen, extends further downstream the building as we approach the ground. References [1] A. C. Khanduri, C. Bedard, and T. Stathopoulos, ling Wind-Induced Interference Effects Using Back propagation Neural Networks, J. Wind Eng. & Ind. Aerod., 72, 1997, pp [2] D. Lakehal, Application of the k-ε to Flow over a Building Placed in Different Roughness Sublayers, J. Wind Eng. & Ind. Aerod., 73, 1998, pp [3] Q. S. Li, J. Q. Fang, A. P. Jeary, and C. K. Wong, Full Scale Measurements of Wind Effects on Tall Buildings, J. Wind Eng. & Ind. Aerod., 74 & 76, 1998, pp [4] M. Ohba, Experimental Study of Effects of Separation Distance between Twin High-Rise Tower s on Gaseous Diffusion behind the Downwind Tower, J. Wind Eng. & Ind. Aerod., 77 & 78, 1998, pp [5] Y. Zhou, M. Gu, and H. Xiang, Along Wind Static Equivalent Wind Loads and Response of Tall Buildings. Part I: Unfavorable Distributions of Static Equivalent Wind Loads, J. Wind Eng. & Ind. Aerod., 79, 1999, pp [6] Y. Zhou, M. Gu, and H. Xiang, Along Wind Static Equivalent Wind Loads and Response of Tall Buildings. Part II: Effects of Mode Shape, J. Wind & Ind. Aerod., 79, 1999, pp [7] H. Nishimura, Y. Taniike, Aerodynamic Characteristics of Fluctuating Forces on a Circular Cylinder, J. Wind Eng. & Ind. Aerod., 89, 2001, pp

16 [8] S. Linag, S. Liu, Q. S. LLi, L. Zhng, M. Gu, Mathematical of a Crosswind Dynamic Loads on Rectangular Tall Buildings, J. Wind Eng. & Ind. Aerod., 90, 2002, pp [9] M. Gu, Y. Quan, Across-wind Loads of Typical Tall Buildings, J. Wind Eng. & Ind. Aerod., 92, 2004, pp [10] Ahmed F. Abdel Gawad, A New Approach to Minimize the Wind Load on Interfering Tall Buildings Based on Numerical and Optimization Techniques, Proceedings of Al-Azhar Engineering 8th International Conference, December, 2004, Cairo, Egypt. [11] N. Fuisawa, Y. Asano, C. Arakawa, T. Hashimoto, Computational and Experimental Study on Flow around a Rotationally Oscillating Circular in a Uniform Flow, J. Wind Eng. & Ind. Aerod., 93, 2005, pp [12] Q. S. Li, J. Y. Fu, Y. Q. Xiao, Z. N. Li, Z. H. Ni, Z. N. Xie, M. Gu, Wind Tunnel and Full-scale Study of Wind Effects on China s Tallest Building, J. Wind Eng. & Ind. Aerod., 28, 2006, pp [13] Fluent 6.0 User s Guide, Fluent Inc., USA, 2001 [14] F. M. White, Fluid Mechanics, McGraw-Hill Companies, Inc., Nomenclature A p2 : 2-D stream-wise proected area. A p3 : 3-D stream-wise proected area. A ps2 : 2-D cross-wise proected area. A ps3 : 3-D cross-wise proected area. C 1, C 2 and C μ : numerical constants of turbulence model. 2 C D : Total drag coefficient =Total drag force/( 0.5 ρ U A p3 ). 2 C DL : Local drag coefficient = local drag force/( 0.5 ρ U A p2 ). 2 C FS : Total coefficient of side force = F S /( 0.5 ρ U A ps3 ). 2 C FSL : Local coefficient of side force = F SL /( 0.5 ρ U A ps2 ). 2 Cp : Pressure coefficient = (P s P )/( 0.5 ρ U ). D : Diameter of the first building model (M1). F SL : Local side (cross-wise) force in y-direction. F S : Total side (cross-wise) force in y-direction. H : Height of the building model. L : Length of wake behind the building model. K : turbulence kinetic energy. 2 K n : normalized turbulence kinetic energy ( = K / U ). P s = P : Static pressure. P : Free-stream static pressure. Pr : Prandtl number for flow. Pr k and Pr ε : Prandtl numbers for turbulence kinetic energy and rate of dissipation, respectively. Re : Reynolds number (=U H/ν) S : Dimensionless normalized distance along the circumference of the cross-section of the building model. T : Dimensionless time = (( U t )/ H) t : time. U i : velocity component in x i -direction. U : Free-stream incoming (upstream) velocity. u : streamwise velocity component. x, y, z : Three-dimensional Cartesian coordinates. y + y τw : dimensionless distance normal to wall = ν ρ. Z : Distance along the building model height starting from the ground level. W : Width of the building model. d : depth of the fourth building model (M4).

17 Greek α : Flow angle of attack (incidence angle). δ i : kronecker delta. ε : rate of dissipation of turbulence kinetic energy. ν : kinematic viscosity. ν t : turbulent kinematic viscosity. ρ : Fluid density. θ : Orientation angle measured in clockwise-direction from the stagnation location for the first building model (M1). τ w : wall shear stress. Abbreviations 2-D : Two-dimensional. 3-D : Three-dimensional. CFD : Computational Fluid Dynamics. RMS : Root-mean-square. T = 9.4 (Steady State). T = 0.4. T = 9.4 (Steady State). Fig. (16) Cp contours for model M1 at two height levels. T = 13.7 (Steady State). T = T = 13.7 (Steady State). Fig. (17-a) Cp contours for model M2 at two height levels, α = 0 o.

18 T = 18.0 (Steady State). T = T = 18.0 (Steady State). Fig. (17-b) Cp contours for model M2 at two height levels, α = 45 o. T = 11.0 (Steady State). T = T = 11.0 (Steady State). Fig. (17-c) Cp contours for model M2 at two height levels, α = 90 o. T = 14.6 (Steady State). T = T = 14.6 (Steady State). Fig. (17-d) Cp contours for model M2 at two height levels, α = 180 o. T = 7.0 (Steady State). T = T = 7.0 (Steady State). Fig. (18-a) Cp contours for model M3 at two height levels, α = 0 o.

19 T = 8.6 (Steady State). T = T = 8.6 (Steady State). Fig. (18-b) Cp contours for model M3 at two height levels, α = 45 o. T = (Steady State). T = T = (Steady State). Fig. (19-a) Cp contours for model M4 at two height levels, α = 0 o. T = (Steady State). T = T = (Steady State). Fig. (19-b) Cp contours for model M4 at two height levels, α = 90 o. T = 13.7 (Steady State). T = T = (Steady State). Fig. (20-a) Dimensionless turbulence kinetic energy (K n ) contours for model M2 at two height levels, α = 0 o.

20 T = 11.0 (Steady State). T = T = 11.0 (Steady State). Fig. (20-b) Dimensionless turbulence kinetic energy (K n ) contours for model M2 at two height levels, α = 90 o. T = 7.0 (Steady State). T = T = 7.0 (Steady State). Fig. (21-a) Dimensionless turbulence kinetic energy (K n ) contours for model M3 at two height levels, α = 0 o. T = 8.6 (Steady State). T = T = 8.6 (Steady State). Fig. (21-b) Dimensionless turbulence kinetic energy (K n ) contours for model M3 at two height levels, α = 45 o.