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## Numerical Modeling Of Air Flow Economics Essay

All types of buildings are subjected to velocity and pressure caused by wind around it. Skyscrapers with the great height are most likely to experience high wind load. There are several methods to analyze the airflow around buildings. But for this dissertation, Computational Fluid Dynamics, StarCd is applied to simulate the velocity and pressure distribution around One Canada Square, London.

This document also presents the influence of using different velocities and turbulent models on single and multiple buildings.

## List of Figures

Figure 1 Flow field around a cubic model from Reference [15] 23

Figure 2 Distribution of mean pressure coefficient (Cp) on a cube from Reference [15] 24

Figure 3 Outline of Geometry 24

Figure 4 2D Pressure distribution at number of iterations=100 25

Figure 5 2D Pressure distribution at number of iterations=200 25

Figure 6 2D Pressure distribution at number of iterations=300 26

Figure 7 2D Pressure distribution at number of iterations=400 26

Figure 8 2D Pressure distribution at number of iterations=500 27

Figure 9 2D Simulation of Pressure Distribution around One Canada Square for Case 1.1 (Table 2) 27

Figure 10 2D Simulation of Pressure Distribution around One Canada Square for Case 1.2 (Table 2) 28

Figure 11 2D Simulation of Pressure Distribution around One Canada Square for Case 1.3 (Table 2) 28

Figure 12 2D Simulation of Pressure Distribution around One Canada Square for Case 2.1 (Table 2) 29

Figure 13 2D Simulation of Pressure Distribution around One Canada Square for Case 2.2 (Table 2) 29

Figure 14 2D Simulation of Pressure Distribution around One Canada Square for Case 2.3 (Table 2) 30

Figure 15 2D Simulation of Pressure Distribution around One Canada Square for Case 2.4 (Table 2) 30

Figure 16 2D Simulation of Pressure Distribution around One Canada Square for Case 2.5 (Table 2) 31

Figure 17 2D Simulation of Pressure Distribution around One Canada Square for Case 3.1 (Table 2) 31

Figure 18 2D Simulation of Pressure Distribution around One Canada Square for Case 4.1 (Table 2) 32

Figure 19 2D Simulation of Pressure Distribution around One Canada Square for Case 4.2 (Table 2) 32

Figure 20 2D Simulation of Pressure Distribution around One Canada Square for Case 4.3 (Table 2) 33

Figure 21 2D Simulation of Pressure Distribution around One Canada Square for Case 4.4 (Table 2) 33

Figure 22 2D Simulation of Pressure Distribution around One Canada Square for Case 5.1 (Table 2) 34

Figure 23 2D Simulation of Pressure Distribution around One Canada Square for Case 5.2 (Table 2) 34

Figure 24 2D Simulation of Pressure Distribution around One Canada Square for Case 6.1 (Table 2) 35

Figure 25 2D Simulation of Pressure Distribution around One Canada Square for Case 6.2 (Table 2) 35

Figure 26 2D Pressure Distribution for Case 1 in Table 6 36

Figure 27 2D Pressure Distribution for Case 2 in Table 6 36

Figure 28 2D Pressure Distribution for Case 3 in Table 6 37

Figure 29 2D Pressure Distribution for Case 4 in Table 6 37

Figure 30 2D Velocity Distribution around One Canada Square at Velocity = 41.16m/s 38

Figure 31 2D Pressure Distribution around One Canada Square at Velocity = 9.39m/s 38

Figure 32 2D Velocity Distribution around One Canada Square at Velocity = 9.39m/s 39

Figure 33 2D Pressure Distribution around One Canada Square at Velocity = 25.275m/s 40

Figure 34 2D Velocity Distribution around One Canada Square at Velocity = 25.275m/s 40

Figure 35 2D Pressure Distribution around Multiple Buildings at Velocity = 41.16m/s 41

Figure 36 2D Velocity Distribution around One Canada Square at Velocity = 41.16m/s 41

Figure 37 2D Pressure Distribution around Multiple buildings at Velocity = 9.39m/s 42

Figure 38 2D Velocity Distribution around Multiple buildings at Velocity = 9.39m/s 42

Figure 39 2D Pressure Distribution around Multiple buildings at Velocity = 25.275m/s 43

Figure 40 2D Velocity Distribution around Multiple buildings at Velocity = 43

Figure 41 2D Pressure Distribution around One Canada Square at Velocity = 41.16m/s using k-ε low Reynolds no 44

Figure 42 2D Velocity Distribution around One Canada Square at Velocity = 41.16m/s using k-ε low Reynolds no 44

Figure 43 2D Pressure Distribution around One Canada Square at Velocity = 41.16m/s using k-ω high Reynolds no 45

Figure 44 2D Velocity Distribution around One Canada Square at Velocity = 41.16m/s using k-ω high Reynolds no 45

Figure 45 2D Pressure Distribution around One Canada Square at Velocity = 41.16m/s using k-ε RNG 46

Figure 46 2D Velocity Distribution around One Canada Square at Velocity = 41.16m/s using k-ε RNG 46

## 1 INTRODUCTION

Due to the difficulties in experiments and high cost of the experimental methods, it is beneficial to create a numerical simulation of wind flow around buildings. [1] The numerical model test results highlights parameters including pressure, velocity, temperature, etc in various forms. I.e. charts, graph, animation, etc

All computational fluid dynamic codes are widely applicable in analyzing the flow of air around prototype.

For this paper software called Starcd is used to give accurate results of computer simulation. The accuracy of Computational Fluid Dynamic results can be achieved by many factors which will be explained in detail in later chapters.

## 1.1 Background information

In the 18th century the wind had no effect on the skyscrapers. The weight of the masonry bearing wall system was more than enough (i.e. High Gravity forces) to stop the wind action. When the rigid frame structures were introduced the gravity was still greater to resist the wind effect.

In 1950s the lightweight steel frame which was used in the construction of the skyscraper, the gravitational force was no longer the main factor. [2] This is when the importance of investigating the airflow around building started.

## 1.2 One Canada Square

In this dissertation the geometry of the One Canada square (located in urban city London) is adopted to analyze the flow around tall building. The pinnacle at the top of the roof is treated as a rectangular block box to avoid complexity in drawing the structure in Starcd and to make the analysis easier. The tower at Canary wharf is the tallest building in United Kingdom. [3] The height above the level of the ground is 235 m. [4] It is not open to public as it is used for commercial offices. The floor size is about 2601 m2. “The building is designed to sway 13 and three quarter inches in the strongest winds that might occur once every 100 years.” [3] Therefore the extreme weather condition (High wind speed) that has occurred in 100 years should be considered in analyzing the airflow around tall building.

## 1.3 Objectives

The following are the main objectives of this document:

To learn the applications of CFD code known as Starcd.

To choose the appropriate mesh size and domain for the canary wharf region.

To design the 2D models of the existing buildings in Canary wharf.

To carry out a numerical model test of a single building (One Canada Square) under different conditions i.e. High, Low and mean velocity at the inlet.

To carry out a numerical model test of the existing buildings including One Canada Square, Citigroup and HSBC under different conditions i.e. high, low and mean velocity at the inlet.

To calculate the Velocity distribution.

To determine the pressure distribution.

To investigate the influence of using various turbulent models.

To find out the wind flow pattern on the building in order to place the ventilation intakes and exhaust vents.

To create 3D model of Canary Wharf buildings.

To validate the computational fluid dynamics Simulation by comparing different computational grid and domain.

## 1.4 Outline of Dissertation

Chapter 1 briefly describes the importance of applying CFD to wind engineering problems and identifies the objectives of dissertation.

Chapter 2 contains a review of techniques relevant to computer simulation of flow around buildings. Some problems are addressed in techniques used in previous works and new way of resolving it is presented.

Chapter 3 includes technique used in this paper to satisfy the iterative convergence.

## 2 LITERATURE REVIEW

The techniques of Computational Fluid Dynamics are widely applied in subjects of fluid mechanics and wind engineering. E.g. it replaces the wind tunnel techniques in problems which compose of simple geometry such as cube shape. However, according to the fluid dynamics, the flow around cube is still complicated which will be explained later in details. This means that more work is needed to improve the CFD technique in analyzing the flow around models with complex geometries. [5] Due to a lot of researches carried out presently in predicting the flow around structures, CFD has become a powerful tool in predicting the behavior of Structures. [5, 6]

## 2.1 Computational Domain

Domain plays an important part in Computational Fluid Dynamics analysis. Selecting the domain size entirely depends on the region of interest and boundary conditions. [7] In other words the size of domain needs to reach the limit where boundary conditions at the side and upper boundaries will have small affect on the flow field around the structure. [8] However, it should be noted that choosing the large domain size will increase the number of cells. This will require more Central Processing Unit (CPU) time for computational analysis.

For this reason, the size of the domain recommended by Hall can be used as initial approach towards the accuracy of results .i.e. the size of the domain should be minimum 5H from the domain edge to any side of the building, where H is height of the building. [9]

In case of a single building, the distance for the inlet, top and lateral boundary of the domain needs to be 5H away from building. The outlet boundary has to be minimum 15 times the height of the building away from the leeward side of the building. This will allow the fully developed flow after the fluid past an obstacle.

For multiple buildings, the height of the tallest building, Hmax is used in place of the height of a single building.

The blockage ratio for both single and multiple buildings should be less than 3%. [7] For wind tunnel blockage ratio of 5% is preferred. The blockage ratio is defined as the maximum cross-sectional area of the building divided by the cross-sectional area of inlet. [10]

## 2.2 Computational Grid

The main factor in achieving accuracy of computational results is to use an appropriate mesh or grid for the specific model and computational domain. It is mainly dependent on the boundary conditions applied to the numerical simulation of airflow around building. [11] Mesh generation can take 70 to 90% of time spent on the analysis of any model. [12] Therefore it is crucial to discuss the size and shape of cell separately:

2.2.1 Cell size

One of the main issues in defining the computational grid is the resolution of cell. A lot of research is carried out in working out the standard cell size for different models. So far no single conclusion can be made as it is affected by boundary conditions and various parameters. For example High Reynolds number will require smaller cell sizes or large no of cells in domain compare to low Reynolds number. Therefore it is known that the smaller the cell size, the better the solution accuracy. [11] In addition the grid size needs to be small enough to display some important physical phenomena e.g. free shear layer, vortex shedding, etc. However, the problem arises when too small cell size is used because it takes great amount of time to iterate the unknowns in Computational Fluid Dynamic Codes.

In order to more detailed information quickly in CFD, a mesh refinement is applied to certain regions. This will require experience in wind engineering field and CFD codes. [7]

However, the mesh divisions used in SHUZO MURKAMI and AKASHI MOCHIDA research indicates that the mesh refinement is required near the model. It was concluded that the mesh refinement of H/24 near the wall region gave less truncation errors near the windward and leeward corners. [8]

2.2.2 Cell Shape

The shape of the mesh should be used in a way so that the errors like truncation errors can be minimized to certain extent. This is possible by using a well known hexahedral cell that reduces the errors compare to tetrahedral grid and also shows good iterative convergence. But tetrahedral shape can be improved to give satisfactory computational results by combining it with the prismatic grid. The improvement was introduced due to the fact that the gridlines on the wall should be 90 degrees. [7] This makes the shape of grid complex compare to hexahedral cell.

## 2.3 Airflow around building

In past the air flow around a building is studied by many researchers. Model like cuboids has been an alternative to represent the buildings. It is found that the flow around building is usually turbulent in nature. [13] Turbulent flow is proved to be complicated in its characteristics because of phenomena like vortex shedding, free shear layer, reattachment, recirculation, stagnation, separation, etc [14, 15]. Therefore to know the pattern of the airflow around a building, it is necessary to describe it with the help of typical diagram shown in Figure 1. The diagram shows the flow around a cube model in place of a building. [14]

## 2.4 Turbulence models

In order to compare different turbulence models, numerical model tests were carried out on using various turbulence models to analyze and compare the airflow around a cube with respect to the wind tunnel experiment. The turbulence models included k-ε, ASM and Large Eddy simulation. Under similar boundary conditions and the numerical method, it was concluded that the outcome of all turbulence models were accurate in mean velocity compared to wind tunnel data. But in terms of pressure distribution the high difference (percentage error>50%) was seen at the upstream corner for k-ε model compare to wind tunnel results. See Figure 2. At this point the other two turbulence models proved to be consistent with the wind tunnel experiment results. I.e. the separation at the frontal roof corner was small. Details of numerical methods, model equations, mesh arrangements and boundary conditions used can be found in reference 14 and 16. [14, 16]

## 2.5 Velocity of wind

Wind is split into two components .i.e. Static and dynamic. [2] The mean velocity of wind generally increases with the increase in height of the building. [2, 17] The rate of change in mean velocity is a function of ground roughness. If the roughness of the ground increases, then the altitude or the height of the maximum velocity will also be increased. At high altitude the roughness of the ground will have no effect on the velocity. [2]

## 2.6 Pressure distribution on building

Pressure distribution on building can be described by pressure Coefficient, Cp. It is the dynamic pressure on surface of building divided by the dynamic pressure in undisturbed flow at the reference height. Pressure coefficient is derived from the Bernoulli’s equation shown below:

Pstat+(1/2)ρairV2=k [18]

Where:

Pstat = Static pressure (pa)

Ρair = Density of air (pa)

V = Velocity (m/s)

k = Constant (no unit)

This is further simplified for the incompressible and steady flow as follow:

Cp=1-(Vsurf/Vref)2

Where:

Vsurf = Velocity on surface (m/s)

Vref = Velocity at reference height (m/s)

When Cp = 0 -the pressure at the point will be the free stream pressure.

= 1 -the pressure is stagnation pressure at a stagnation point. [19]

Typical mean pressure distribution on a cube produced by atmospheric boundary layer is shown in Figure 2. The negative values of Cp represent the suction pressure which is at the top and leeward side of a cube where the direction of wind will be perpendicular and away from the model. The positive mean pressure coefficient on the windward side of cubic model indicates the wind going into the model at an angle of 90˚. [20]

Wind pressure is affected by the following:

1) Shape of the building, 2) Density and velocity of air, and 3) Angle of approaching wind. [17]

However the main concern here is the effect of variations in velocity of air.

## 2.7 Wind tunnel experiments

2.7.1 Burj Dubai

The construction of the tallest Burj Dubai is one of the most challenging in mitigating motion of structure caused by wind.

Before the construction of the Burj Dubai, the first isolated scale model was tested in a wind tunnel and after the results were evaluated. The geometry was then modified to reduce the wind effect at a height where it sways. Final shape was then verified by using a large scale model of 1:50 and high Reynolds number. Computational Fluid Dynamic simulation was attempted to observe the velocity of wind in the local area. [21]

2.7.2 Famen Temple

The wind tunnel experiments were also conducted on famen temple to get the pressure and velocity distribution on its surface. The dimensions of the tower shaped building that were scaled to a ratio of 1:200 were 147m high and 50m wide. Geometrical similarity is essential in wind tunnel experiments as the size of the wind tunnel is limited. The scaled model was placed on a plate that rotates about an axis to analyze the influence of approaching wind at different angles to the building. The following were used to determine velocity and pressure distribution: Pitot tube anemometer, microbarovario-graph and hot wire anemometer. [22]

## 2.8 Summary and findings of Literature Review

From review of the literature it is found that the techniques of CFD have been used in wide range of problems associated with evaluating wind flow around obstructions. One of the main turbulence models that can be applied to many problems was Two Model equation k-ε.

In the view of limitations in the computer hardware and computational time, the domain and grid sizes were kept to a limit to get the efficient results as possible.

The results will be more accurate in this dissertation as the components of computer that will be used for simulation are more advanced compare to past projects. Non uniform meshes and small mesh refinement (H/24) were used to reduce duration of computer analysis. Therefore it is decided that the uniform grid and mesh refinement will be applied in order to get efficient results.

Different cases will be investigated in selecting the domain and mesh. In addition independent tests on grid size and domain will be carried out to save time.

The characteristics of turbulent flow suggested should be taken into account when comparing the simulation of flow using various cases.

It is also found that pressure coefficient should be determined on the building surface for the calculation pressure distribution. Standard k-ε model gives efficient results for velocity distribution but overestimates the pressure at the frontal corner. The review briefly outlines the need of considering the effect of different velocities.

Current projects show the importance of investigating the flow around a single building because it helps the designers to minimize the impact of wind load by changing model shape.

Another interesting point that should be noted is analyzing the influence of incoming flow that approaches from different angles to the prototype. In real life the direction of approaching wind is always unpredictable.

## 3.1 Assumptions

The following are the main assumptions for the computer analysis in this paper:

Steady flow

Isothermal-Temperature is constant inside the domain

No-slip condition

Fluid (Air) is incompressible

Turbulent flow

## 3.2 Examining Iterative Convergence

After doing the tutorials it was decided to find the no of iterations that will give efficient results. The number of iterations can also be seen as the factor affecting the accuracy of results. However it is known from general knowledge that the more no of iteration are chosen, the higher the accuracy in getting the solution is achieved. As the main concern of this document is achieving the accuracy, the multiple of 100 iterations were tried unless the results were similar. The boundary conditions and extent of domain were kept similar to analyze the effect of iterations only. Extreme weather condition .i.e. high velocity of 41.16m/s was also used in all iterations. [23] It can be seen from Figure 4 to 8 that the variations in pressure and velocity distribution occur by changing the iterations. At case 5 (no of iteration = 500), it was observed that increasing the iteration had no effect on the results as the maximum no of iteration (431 Iteration) was reached shown in Figure 8. Therefore the no of iterations was chosen to be 1000 for the analysis of flow around building as this will be enough to achieve iterative convergence. [24]

## 3.3 Independent tests on domain

Initially it was decided to find the appropriate domain for the canary wharf area in order to meet the objectives of the project. In independent tests on the domain, only the size of the domain is changed (Details are shown in Table 2). The first attempt included LW, LH and LL equal 5 times the height of the building, as it is suggested earlier in literature review, where LW is the distance between the windward side of the building to inlet boundary of the domain, LH is the distance between the height of the building to top boundary of the domain and LL is the distance between the Leeward side of the building to outlet boundary of the domain.

The test was conducted in an extreme weather condition i.e. velocity = 41.16m/s using computer simulation. The standard k-ε high Reynolds no was selected as it is mostly applicable to many problems. Mesh was further divided into four on a region near the wall and roof of building. At this stage the grid size was guesstimated to be 23.5m in vertical axis and 28m in horizontal axis for domain.

It can be seen in Figure 9 that the pressures near the top of wall boundary is not constant. The values of pressure are represented by a unique color in pressure distribution visualization. Therefore the LH was increased until the pressure near the wall becomes stable (See Figure 10 and 11). Figure 11 show the pressure is constant near the top wall boundary.

Other simulations were carried out where LW and LL were increased by adding 2H to previous cases except the last case 6.2. Case 6.1 and 6.2 covers the largest region for which the domain is about 50H in horizontal direction and 64 in vertical direction.

Similar method was adopted i.e. adding distance to LH to get the constant pressure near the wall boundary.

The values of pressure at a specific point for final cases (Case 1.3, 2.5……) were compared relative to the last case 6.2 in Table 3.

It can be predicted in terms of percentage difference in pressure that the domain suitable for canary wharf should be from Case 4.4.

The results show that the length of the domain should be increased by the same amount as initial step in getting the constant pressure of the layer near the top wall boundary. I.e. horizontal length of domain (Ld) should be approximately equal to the vertical length of the domain (Hd).

## 3.4 Independent tests on cell sizes

Due to the limitation of computational hardware and time it is crucial to analyze the grid size using small domain. Apart from the size of domain, rest of the method

(k-ε model) and conditions (velocity = 41.16) were kept similar to independent test on domain. The size of the domain was about 2H in vertical and horizontal direction. (See Table 4 and 5 for more details on input data). No visualization was done for choosing the grid size. The pressure distribution values were calculated at a specific point (Vertex).

Overall seven cases were done by changing the cell sizes of domain shown in Table 4. After seventh case the software stopped responding which was due to hardware capacity.

Percentage difference was calculated for each case relative to Case 7. (See Table 5) The results table 5 shows that the change in pressure distribution at case 3 and 4 is close compare to others. In addition Case 7 has fine cell size compare to other cases is also close to case no 4 in terms of pressure distribution indicating case 4 to be the best choice.

However it should be noted that the domain used for case 7 is pretty small. The large grid size should be chosen for the ease of analysis where the domain will be large. Also the present hardware capacity would not tolerate such small grid sizes with large domain. For this reason cell size of Case no 3 should be fine enough to get satisfying results.

## 3.5 Test on different domain using grid size of Case 3 in Table 4

Another test was done to see the effect of domain on pressure distribution using a chosen grid size. The data used is given in Table 6 and the results are shown in Table 7. Now it can be clearly seen from the results table that the increase in domain will cause great change in pressure parameters which makes it difficult to choose the domain for investigating the flow around building.

## 3.6 Conclusions

It was concluded that the cell size and domain of case 4 in Table 7 should be good enough to complete the remaining objectives. The domain and cell size might not be appropriate. This is due to the limitations in hardware. In addition it consumes a vast majority of time during analysis. The software was not responding after the limits of domain and cell sizes were reached. More advanced techniques of reducing the computational time is needed to overcome this issue.

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