Journal of Engineering and Applied Science (JEAS), Faculty of Engineering, Cairo University, Egypt, Vol. 55, No. 6, pp. 493-512, December, 2008

Investigation of the Aerodynamic Effect of the Interfering Gap between Uncommon Towers

W. M. Elwan, A. F. Abdel Gawad, H. E. Abdel Hameed,

and S. S. Abdel Aziz,  

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INVESTIGATION OF THE AERODYNAMIC EFFECT OF THE INTERFERING GAP BETWEEN UNCOMMON TOWERS

WAEL M. ELWAN1, AHMED F. ABDEL GAWAD2,

HESHAM E. ABDEL HAMEED3, AND SALEM S. ABDEL AZIZ4

ABSTRACT

A computational model and an experimental work were developed to study the aerodynamic effect of the gap between uncommon towers. The gap between the buildings has a significant effect on the flow characteristics around the buildings. The investigation covers two main interference cases. The first case concerns two similar towers. The second case deals with two different interfering towers. The computations were performed using a suitable steady incompressible turbulence model. The experiments were carried out using an open-circuit suck-down wind tunnel. Scaled-models of the towers were constructed and equipped with measuring facility. The results demonstrate the distributions of the pressure and load coefficients, at various elevations along the height of the tower model. The effect of changing the value of the gap is carefully considered. Moreover, results show different streamline patterns. Validity of using artificial neural networks to predict the values of load coefficient is tested. Results show that a good architecture of neural networks helps greatly in tuning the target predictions. KEYWORDS: Towers, Wind Load, Building Interference, Gap.

1. INTRODUCTION

Due to the rapid development of modern cities, the available spaces to construct

new buildings diminish. Therefore, the price of these spaces rises considerably. This

situation becomes harsher in the crowded downtown of the cities. Moreover, the

complexity of modern life leads to the need of gathering various human activities in a

single place. Thus, residential, commercial, official, and recreational activities may be

located in the same spot. Towers (tall buildings) are the optimum solution for such a

case.

However, the forces of nature begin to dominate the structure system as its height

________________________________________________________________________________________

1 Demonstrator, Mech. Power Eng. Dept., Faculty of Eng., Zagazig Univ., Egypt. 2 Associate Prof., Mech. Power Eng. Dept., Faculty of Eng., Zagazig Univ., Egypt, Member ASME & AIAA. 3 Associate Prof., Mech. Power Eng. Dept., Faculty of Eng., Zagazig Univ., Egypt. 4 Assistant Prof., Mech. Power Eng. Dept., Faculty of Eng., Zagazig Univ., Egypt.

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increases. Strong winds and earthquakes are the principal sources of lateral forces on

towers. The response of the tower to these lateral forces depends on its aeroelastic

properties. Unexpected structure response harms the comfortability of the residents. In

addition, the flow pattern around the tower influences its ventilation and air

conditioning. In recent designs, towers take uncommon shapes for architecture and

aerodynamic reasons. There is an obvious shortage in the aerodynamic studies of these

uncommon-shaped towers. Such studies enlighten to designers the expected local and

total wind loadings on towers. It becomes more important to investigate the flow field

when two towers are constructed near each other. The interference between the two

towers generates a complex flow field around them. Thus, comprehensive study is

needed to demonstrate the complex effect of both the gap between the towers and their

shapes. Many investigators studied the flow field around buildings especially towers

from various views.

Some investigations covered the dynamic wind loads on towers. The effect of

equivalent wind loads and damping characteristics on two tall buildings were

examined [1]. The two buildings are located in the center district of Hong Kong. The

study showed that the along-wind vibration is dominated by the longitudinal incidence

turbulence. However, the cross-wind response is mainly caused by the wake

excitation. Other investigations [2&3] covered the effect of unfavorable distribution of

static equivalent wind loads as well as the effect of wind mode shape on the long

responses of tall buildings. The effect of cross-wind forces on rectangular tall

buildings as well as the corresponding root-mean-square (RMS) lift coefficients were

carefully demonstrated [4]. A further step was carried out in [5] where the cross-wind

dynamic response of 15 typical tower models at high wind frequency were studied.

The resulting coefficients of base moment and shear force were clearly introduced.

The effect of wind on the tallest building in China was studied [6] by a combined wind

tunnel and full-scale investigation. The force coefficients and power spectral densities

as well as displacement and acceleration responses were discussed. A group of

researchers considered the interference between buildings especially towers. The effect

of the separation distance between two identical (twin) high-rise towers on the flow

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field around them was demonstrated [7]. It was found that the upwind tower retards

the flow separation on the top and sides of the downwind tower. A new approach to

minimize the wind load on interfering towers was proposed [8]. Computational and

optimization techniques were used to find the best locations and heights to minimize

wind loads on the interfering buildings. Many researchers also adopted application of

artificial neural network (ANN). The wind-induced interference effects between two

adjacent buildings were studied [9] using neural networks. The numerical results,

based on k-ε turbulence modeling, were used [10] to train a feed-forward, multi-layer,

back-propagation artificial neural network. ANN was used to predict the values of the

drag coefficient on an isolated building. Moreover, three-layer, time delay, back-

propagation ANN was utilized [11&12] to interpolate wind-induced pressure time-

series on a model of a low-rise building.

The present investigation demonstrates the computational predictions and

experimental results of the flow field around two interfering towers. The

computational investigation is based on three-dimensional, steady, incompressible k-ε

modeling. The authors used a commercial code [13] to develop the computational

model. The experimental study was carried out using a suck-down type wind tunnel.

Suitable models of the towers were constructed and tested. The results include

streamline patterns and distributions of pressure and load coefficients. The results are

recorded at different levels along the model height for various gap ratios.

2. DESCRIPTION OF INVESTIGATED MODELS

Two models were selected to study the interference of twin and mixed models.

The first model is GRAHA KUNINGAN, which is located in Jakarta, Indonesia. It is in

the form of half-ellipse and has 52 stores in 240 m-tall. The second model is BURJ AL-

ARAB, which is located in Dubai, United Arab Emirates. It is in the form of hyperbolic

paraboloids and has 70 stores in 320 m-tall. The configurations of the two models and

the interference arrangements are shown in Fig. 1. S is the dimensionless distance

along the circumference of the cross-section of the building model. Table 1 shows the

main dimensional ratios of the two models.

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3. COMPUTATIONAL INVESTIGATION

3.1 Governing Equations and K-ε Model

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:

- Mass: 0j

j

Ux

∂=

∂ (1)

- Momentum: )(1ji

j

i

jiij

j

uuxU

xxPUU

x−

∂∂

∂∂

+∂∂

−=∂∂ υ

ρ (2)

Where, i j t ij ij2 u u 2 D - K3

ν δ− = & 1 )2

jiij

j i

U UD ( x x

∂∂= +

∂ ∂

-Turbulent viscosity: 2

t

C Kμνε

= (3)

-Turbulence kinetic energy (K): ευυ

−−∂∂

+∂∂

=∂∂

ijjijk

t

jj

j

DuuxK

xKU

x])

Pr[()( (4)

-Dissipation rate (ε): K

CDuuK

Cxx

Ux ijji

jk

t

jj

j

2

21 )(])Pr

[()( εεευυ

ε −−+∂∂

+∂∂

=∂∂ (5)

Where, K is the turbulence kinetic energy, ε is the rate of dissipation of

turbulence kinetic energy, and Ui is the velocity component in xi-direction. ν is the

kinematic viscosity, νt is the turbulent kinematic viscosity, ρ is the density. Prk (= 1.0)

and Prε (= 1.3) are the Prandtl numbers for kinetic energy of turbulence and rate of

dissipation, respectively. Cμ (= 0.09), C1 (= 1.44), and C2 (= 1.92) are numerical

constants. δij is the kronecker delta.

Fig. 1a Cross-section of twin models. Fig. 1b Schematic diagram of twin models.

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Fig. 1c Cross-section of mixed modelswith half-ellipse in front (case 1).

Fig. 1d Schematic diagram of mixed models With half-ellipse in front (case 1).

Fig. 1e Cross-section of mixed models with Burj Al-Arab in front (case 2).

Fig. 1f Schematic diagram of mixed models With Burj Al-Arab in front (case 2).

Fig. 1 Main configurations of the two models and interference arrangements.

Table 1. Main dimensional ratios of two models.

Model D1/W1 H1/W1 W2/D2 H2/D2 Half-ellipse 3.17 7 ----- -----

Hyperbolic paraboloids ----- ----- 1.2 6.0 3.2 Computational Aspects and Boundary Conditions

To reduce the computational effort (number of cells and overall computer run-

time), the computations were carried out for scaled models. The upstream velocity was

kept fixed for all the investigated models. Table 2 shows more details about the two

computational models.

Table 2. Computational parameters of the two models.

Model Scale Re = (U∞D /υ)

Half-ellipse 1:955 3.18×104

Hyperbolic-paraboloids 1:1000 4.7 × 104

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The computational domain and boundary conditions are shown in Fig. 2. 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 models and the ground,

so Ui=0. (4) the zero gradient condition is assumed for all variables at downstream

boundary, so ∂Ui/∂x = 0. The law of the wall was used as a wall treatment method. The

computational meshes were constructed using triangular-shaped elements, Fig. 3. The

mesh is very fine next to the solid boundary of the building. The size of the element

increases towards the far field away from the solid boundaries. The investigation was

carried out using a different number of cells, namely: 150,000, 200,000, 250,000, and

300,000. It was found that the number of cells in the range of 250,000 gives the best

results in comparison to the experimental findings. So, there is no need to increase the

number of cells above 250,000. The least y+ from the wall for the first node was about

5. 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.

4. OUTLINE OF EXPERIMENTAL STUDY

4.1 Wind Tunnel and Models

The experiments were carried out in the open section of a delivery wind tunnel

that is located in the Fluid Mechanics Lab., Faculty of Eng., Zagazig Univ., Fig. 4-a.

The wind tunnel has a cross-section of 0.5 × 0.5 m2. To compare with the numerical

predictions, the up-stream velocity (U∞) was kept at 14 m/s. Three scaled models were

fabricated from Plexiglas. Two similar models were constructed to resemble the half-

ellipse tower. A single model was fabricated to resemble the hyperbolic-paraboloids

tower. The model is fixed on a suitable turning table, see Fig. 4-b. Each of the two

models was equipped with 50 taps. The taps are distributed at 5 levels (0.02, 0.25, 0.5,

0.75, 0.98 H) such that 10 taps are located at each level. The taps were connected

sequentially to an electrical analog micro-manometer that gives readings in

millimeters-water. Its calibration shows accuracy ± 2 % .

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(a) Side view.

(b) Top view. Fig. 2 Computational domain with boundary conditions.

(a) Twin models. (b) Mixed models.

Fig. 3 Triangular meshing for the twin and mixed tower models.

Fig. 4-a Elevation section of the wind tunnel arrangement.

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Fig. 4-b Photograph of tower models in the wind tunnel. Fig.5 Mean velocity profile

ahead of the upwind tower.Fig. 4 Experimental facility.

4.2 Experimental Conditions

The dimensionless gap (Gt = L/H1) between the twin (similar) models was set as

0.5, 1.0, 1.5, 3.0, and 4.5. For the mixed models, the dimensionless gap (Gm = L/Hm)

was set as 0.5, 1.0, 3.5, and 4.5. Where, L is the distance between the two buildings.

H1 is the height of the twin models. Hm is the mean value of the heights of the mixed

models, Hm = (H1 +H2)/2. The velocity profile ahead of the upwind building (at x/H1 =

5) is shown in Fig. 5. The velocity profile obeys the power law: α

1

u Z=U H∞

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟

⎝ ⎠ ⎝ ⎠.

Where, u is the velocity at height Z. α is the exponent of the velocity profile, which

was 0.125 for this case. A Pitot-Static tube of 5 mm-outer diameter was used to

measure this mean velocity profile.

5. RESULTS AND DISCUSSIONS

5.1 Pressure Coefficient

The pressure coefficient is calculated from the relation: Cp = (( ∞− PPs )/(0.5 ρ 2∞U )).

Where, Ps is the static pressure, ∞P is the free-stream static pressure, ρ is the air

density, and ∞U is the upstream velocity.

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5.1.1 Twin Models On the windward face, Cp increases with the building height (Z/H1). CP is

calculated at different levels (not shown) along the building height and found that the

maximum values are at (Z/H) = 0.86 and 0.98 for the upwind and downwind models,

respectively . In Figs. 6 and 7, Cp is plotted for different gap ratios (Gt) against the

length of the perimeter (S). S is measured from the stagnation point. For the upwind

model, Fig. 6, values of Cp increase with Gt on the leeward face. For the downwind

model, Fig. 7, values of Cp increase with Gt on both the windward and leeward faces.

There is no effect of the upwind model on the downwind model when Gt reaches 4.5

(not shown). Generally, the computational predictions compare very well to the

experimental findings.

(6a) Z/H = 0.5.

(6b) Z/H = 0.98.

Fig. 6 Cp distributions for the upwind model of twin models at different gap ratios.

Computational Experimental

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(7a ) Z/H = 0.5.

(7b) Z/H = 0.98. Fig. 7 Cp distributions for the downwind model of twin models at different gap ratios.

5.1.2 Mixed Models

Figures 8 and 9 show the distributions of Cp for case 1, when the upwind model is

the half-ellipse. On the leeward face of the upwind model, Cp increases with Gm,

Fig. 8. The values of Cp increase with Gm on the downwind model especially on the

windward face. There is no effect of the upwind model on the downwind model when

Gm reaches 4.5 (not shown). For case 2, when the upwind model is Burj Al-Arab, Cp

values decrease with Gm in the leeward face of this model. Cp values increase on both

the windward and leeward faces of the downwind model, Figs. 10 and 11. There is no

effect of the upwind model on the downwind model when Gm reaches 3.5 (not shown).

(8a) Z/H = 0.5.

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(8b) Z/H = 0.98. Fig. 8 Cp distributions for the upwind model (half-ellipse) of mixed models at different

gap ratios.

(9a) Z/H = 0.5.

(9b) Z/H = 0.98. Fig. 9 Cp distributions for the downwind model (Burj Al-Arab) of mixed models at

different gap ratios.

(10a) Z/H = 0.5.

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(10b) Z/H = 0.98. Fig. 10 Cp distributions for the upwind model (Burj Al-Arab) of mixed models at

different gap ratios.

(11a) Z/H = 0.5.

(11b) Z/H = 0.98.

Fig. 11 Cp distributions for the downwind model (half-ellipse) of mixed models at different gap ratios.

5.2 Local Load Coefficient (CLL)

CLL is the local drag coefficient at different levels along the building height. Fig.

12 shows the variations of CLL with height (Z/H). For most cases, CLL increases with Z

to reach a maximum value at Z/H = 0.86 and 0.98 for the upwind and downwind

models, respectively. For most cases, at different height levels, values of CLL decrease

with gap ratio for the upwind model. For the downwind model, CLL increases with the

gap ratio. From Fig. 12, it is obvious that the variation of CLL depends on the effect of

three parameters. These parameters are: (i) the gap between models, (ii) the height

ratio (Z/H), and (iii) the shape and configuration of the model.

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(i) Upwind model

(Twin models). (ii) Downwind model

(Twin models). (iii) Upwind model-case 1

(half-ellipse).

(iv) Downwind model- case 1 (Burj Al-Arab).

(v) Upwind model-case 2 (Burj Al-Arab).

(vi) Downwind model- case 2 (half-ellipse).

Fig. 12 Local load coefficient (CLL) at different height levels.

5.3 Total Load Coefficient (CLt)

CLt is the total drag coefficient on the building. Table 3 demonstrates the values

of the total load coefficient (CLt) for the twin and mixed cases. These values of CLt

were calculated by numerical integration of the local load coefficients (CLL) that were

presented in Fig. 12. The negative value that appears in table 3a is a result of

completely containing the downwind model in the wake of the upwind model.

Table 3a. Values of total load coefficient (CLt) for twin models.

Model Position Upwind Downwind Gt 0.50 1.00 1.50 0.50 1.00 1.50 CLt 0.93 0.93 0.93 -0.06 0.13 0.17

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Table 3b. Values of total load coefficient (CLt) for mixed models.

Model Position Upwind Downwind Upwind Downwind Model Shape Half-ellipse Burj Al-Arab Burj Al-Arab Half-ellipse

Gm 0.50 1.00 0.50 1.00 0.50 1.00 0.50 1.00 CLt 1.03 0.93 0.14 0.20 0.95 0.88 0.28 0.28

5.4 Streamline Patterns and Recirculation Zones

The computational streamline patterns of the different investigated cases are

shown in Figs. 13-16. The vertical center-planes of streamline patterns are shown in

Figs. 13 and 15. It is obvious that the streamline patterns and vortical formations

behind towers change dramatically with the gap ratio. The downwind tower is entirely

contained in the wake of the upwind tower. Generally, the recirculation zone of the

isolated model is larger than the recirculation zone of the downwind model of twin

models. In most cases, the recirculation zone behind the upwind model increases with

the gap ratio. However, the gap ratio has a minor effect on the recirculation zone

behind the downwind model.

Isolated model. Twin models, Gt=0.5. Twin models, Gt=1.0. Twin models, Gt=1.5.

Fig. 13 Streamline patterns at vertical center plane.

(i) Z/H = 0.02. (ii) Z/H = 0.5. (iii) Z/H = 0.98. Fig. 14a Streamline patterns for twin models at three height levels (Gt=0.5).

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Case 1 (Gm=0.5). Case 1 (Gm=1.0). Case 2 (Gm=0.5). Case 2 (Gm=1.0).

Fig. 15 Streamline patterns of the vertical center-plane for mixed models.

Fig. 16a Case 1, Gm=0.5.

Fig. 16b Case1, Gm=1.0.

Fig. 16c Case 2, Gm=0.5.

Fig. 16d Case 2, Gm=1.0.

(i) Z/H = 0.02.

(ii) Z/H = 0.5.

(iii) Z/H = 0.98. Fig. 16 Streamline patterns for mixed models at three height levels.

(i) Z/H = 0.02. (ii) Z/H = 0.5. (i) Z/H = 0.98. Fig. 14b Streamline patterns for twin models at three height levels (Gt=1.5).

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5.5 Predictions of Artificial Neural Network (ANN)

An artificial neural network (ANN) is a computational tool, which is used to

predict the values of the local load coefficient (CLL). The neural network Toolbox of

the Matlab 7 package was chosen to train ANN. Each ANN consists of three or more

layers, including an input layer, an output layer, and a number of hidden layers. The

input layer is connected to the hidden layer by the weights as shown in Fig. 17.

Fig. 17 Artificial neural network (ANN) with a backpropagation learning rule.

Fig. 18 Results of the testing of the five ANNs for CLL.

Table 4. Details of ANNs to predict the values of CLL.

ANN To predict values of CLL for: Number of neurons (S1) ANN-1 ANN-2 ANN-3 ANN-4 ANN-5

Upwind model - twin models. Downwind model – twin models. Upwind model – mixed models (cases 1 & 2). Downwind model – mixed models (case 1). Downwind model – mixed models (case 2).

200 200 800 400 400

Five ANNs were used to predict the values of CLL as shown in table 4. Each

network has three input vectors (W/H, G=L/H & Z/H) and one output vector (CLL).

Many testing cases were operated to get the optimum transfer function and number of

neurons (S1) for the hidden layer. The transfer function "purelin" was used for the

output layer. Fig. 18 shows comparisons between the numerical and ANN predictions.

The results indicate that ANN predictions are very acceptable as shown in table 5.

Thus, a well-trained ANN can be used to predict the values of local load coefficient of

interfering towers.

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Table 5. Results of the testing values of ANN. Position of model

L / H

Z / H Numerical

Results (CLL)ANN

Results (CLL)

% error

Twin model (Upwind model)

0.5 0.02 0.628 0.57 9.23 1.0 0.25 0.66 0.62 6.0 1.0 0.75 1.34 1.22 8.9 1.5 0.98 0.76 0.8 5.26

Twin model (Downwind model)

0.5 0.5 -0.083 -0.08 3.6 1.0 0.25 0.049 0.047 4.0 1.0 0.86 0.13 0.14 7.6 1.5 0.98 0.45 0.42 6.66

Mixed (Upwind)

0.25 0.25 0.916 0.92 0.43 0.5 0.75 1.259 1.12 11.0 1.0 0.5 0.923 0.96 4.0 0.5 0.02 0.79 0.76 3.7 0.5 0.25 0.85 0.83 2.35

Mixed ( Downwind Burj Al-

arab)- Case 1

0.5 0.98 0.374 0.35 6.4 1.0 0.02 0.13 0.135 3.8

Mixed ( Downwind Half

ellipse)- Case 2

0.5 0.98 1.28 1.2 6.25 1.0 0.02 0.02 0.019 5.0 1.0 0.25 0.034 0.032 5.8

6. CONCLUSIONS

In the present investigation, a computational model and an experimental work

were utilized to study the flow characteristics of interfering towers. The investigation

covers the interference between twin and mixed uncommon tall buildings. Local and

total wind loads are investigated in terms of the distributions of force parameters.

These parameters, such as pressure and load coefficients, were recorded at different

levels of the model height for various gap distances between the models. Also, the

results include the distribution of Cp as well as the streamline patterns. Many

interesting remarks and observations can be recorded as follows:

(1) For twin models, gap ratio (Gt) has almost no effect on Cp values of the windward

face of the upwind model. However, values of Cp increase with Gt. Also, for the

downwind model, values of Cp increase on both the windward and leeward faces

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with Gt. There is no effect of the upwind model on the downwind model when Gt

reaches 4.5.

(2) For mixed models, the effect of the gap ratio depends on the shape and geometry

of the upwind model. For case 1, when the upwind model is the half-ellipse,

values of Cp do not change with Gm on the windward face of the upwind model.

However, Gm increases the values of Cp on the leeward face of the upwind model.

For the downwind model (Burj Al-Arab), Cp values increase on the windward face

and decrease on the leeward face with Gm. For case 2, when the upwind model is

Burj Al-Arab, Cp values decrease on the leeward face of this model with Gm. For

the downwind model (half-ellipse), Cp values increase on both the windward and

leeward faces with Gm.

(3) For most cases, the local load coefficient (CLL) increases with Z/H to reach

maximum values at Z/H = 0.86 and 0.98 for the upwind and downwind models,

respectively. Generally, CLL decreases with the gap ratio for the upwind model

and increases with the gap ratio for the downwind model.

(4) Values of CLt for the downwind model are much smaller than that of the upwind

model. The reason is that the downwind model lies completely or partially in the

wake of the upwind model.

(5) The values of CLt on the downwind model may be positive or negative depending

on the values of the towers heights and the gap ratio.

(6) Generally, the computational predictions compare very well to the experimental

findings.

(7) A well-trained neural network is capable of predicting the values of the local load

coefficient. Thus, lots of investigation effort and time are saved.

REFERENCES

1.Li , Q. S., Fang , J. Q., Jeary , A. P., and Wong , C. K., “Full Scale Measurements of Wind Effects on Tall Buildings”, J. Wind Eng. & Ind. Aerod., 74 & 76, pp.741-750, 1998.

2.Zhou, Y., Gu , M., and Xiang, H., “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, pp.151-158, 1999.

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3.Zhou, Y., Gu, M., and Xiang, H., “Along Wind Static Equivalent Wind Loads and Response of Tall Buildings. Part II: Effects of Mode Shape”, J. Wind & Ind. Aerod., 79, pp.151-158, 1999.

4.Linag, S., Liu, S., LLi, Q. S., Zhng, L., Gu, M., “Mathematical Model of a Crosswind Dynamic Loads on Rectangular Tall Buildings”, J. Wind Eng. & Ind. Aerod., 90, pp.1757-1770, 2002.

5.Gu, M., Quan, Y., “Across-wind Loads of Typical Tall Buildings”, J. Wind Eng. & Ind. Aerod., 92, pp.1147-1165, 2004.

6.Li, Q. S., Fu, J. Y., Xiao, Y. Q., Li, Z. N., Ni, Z. H., Xie, Z. N., Gu, M., “Wind Tunnel and Full-scale Study of Wind Effects on China’s Tallest Building”, J. Wind Eng. & Ind. Aerod., 28, pp.555-566, 2006.

7.Ohba, M., “Experimental Study of Effects of Separation Distance between Twin High-Rise Tower Models on Gaseous Diffusion behind the Downwind Tower Model” , J. Wind Eng. & Ind. Aerod., 77 & 78, pp.555-566, 1998.

8.Abdel Gawad, A. F., “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, Cairo, Egypt, 24-27 December, 2004.

9.Khanduri, A. C., Bedard, C., and Stathopoulos, T., "Modeling Wind-Induced Interference Effects Using Back-propagation Neural Networks", J. Wind Eng. & Ind. Aerod., 72, pp.71-79, 1997.

10.Abdel Gawad, A. F., "Numerical and Neural Study of the Turbulent Flow around Sharp-Edged Bodies", Proceedings of 2002 Joint US ASME-European Fluids Engineering Division Summer Meeting, Montreal, Canada, July 14-18, 2002.

11.Chen, Y., Kopp, G. A., and Surry, D., "Interpolating of Wind-Induced Pressure Time Series with An Artificial Neural Network", J. Wind Eng. & Ind. Aerod., 90, pp.589-615, 2002.

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13.“Fluent 6.0 User’s Guide”, www.fluentusers.com, Fluent Inc., USA, 2001. LIST OF SYMBOLS

Ap2 = 2-D stream-wise projected area. Ap3 = 3-D stream-wise projected area. C1, C2 and Cμ = numerical constants of turbulence model. CLL = local load coefficient = local load force/( 2

p20.5 U Aρ ∞ ). CLt = total load coefficient = total load force/( 2

p30.5 U Aρ ∞ ). Cp = pressure coefficient = (Ps – P∞)/( 20.5 Uρ ∞ ). D = tower depth in stream-wise direction. G = dimensionless gap = gap ratio = L/H. H = tower height. H1 = height of the twin models.

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Z = Distance along the model height starting from the ground level. Subscripts: m = mixed. t = twin. w = wall. ∞ = upstream/free-stream flow. Abbreviations: 2-D = two-dimensional. 3-D = three-dimensional. ANN= Artificial Neural Network RMS = Root-Mean-Square. Greek: α = power coefficient. δij = kronecker delta. ε = rate of dissipation of turbulence kinetic energy. ν = kinematic viscosity. νt = turbulent kinematic viscosity. ρ = fluid density. τw = wall shear stress

H2 = height of Burj Al-Arab model. Hm = average height of mixed models

= (H1+H2)/2. K = turbulence kinetic energy. L = distance between models. Ps = P = static pressure. P∞ = free-stream static pressure. Pr = Prandtl number for flow. Prk and Prε = Prandtl numbers for turbulence kinetic energy and rate of dissipation, respectively. Re = Reynolds number = U∞ D/ν. S = dimensionless normalized distance

along the circumference of the cross-section of the building model.

S1 = number of neurons for the hidden layer.

Ui = velocity component in xi-direction. U∞ = free-stream incoming (upstream)

velocity. u = stream-wise velocity component. W = tower width in cross-wise direction. x, y, z = three-dimensional Cartesian

coordinates. y+ = dimensionless distance normal to wall =

wy τν ρ

.

حسابية ومعملية للتأثير اإليرودينامى لثغرة التداخل بين أبراج غير تقليديةدراسة

علـى باالعتمـاد دينامى المتبادل بين أبراج متداخلة وغير تقليدية الشـكل بالتأثير اإليرو يهتم البحث

حيث تم عرض تأثير ثغرة التداخل بين البرجين علـى . النمذجة الحسابية والمعملية لبرجين عالميين مشهورين

ضـمن برنـامج k-εاستخدام نموذج اضـطراب الحسابات ب إجراءوتم . كل منهماأحمال الرياح على أسطح

اسـتخدام تـم و. استخدام نفق هوائى لتحقيق الدراسة الحسابية باالستعانة بالنتـائج المعمليـة و. ى معتمدتجار

مجموعـة ظهـرت و. للتنبؤ بقيم معامل الحمل الموضعى للرياح على البرجين االصطناعيةالشبكات العصبية

.مفيدة من النتائج واإلستنتاجات