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Eﬀect of vortices on power output of vertical axis wind turbine (VAWT) a

a,⁎

a

a

T

a

Ammar Naseem , Emad Uddin , Zaib Ali , Jawad Aslam , Samiur Rehman Shah , Muhammad Sajida, Ali Abbas Zaidia, Adeel Javedb, Muhammad Yamin Younisc a

Department of Mechanical Engineering, School of Mechanical and Manufacturing Engineering (SMME), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan US Pakistan Center of Advance Studies in Energy (USPCAS-E), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan c Department of Mechanical Engineering, Mirpur University of Science and Technology (MUST), Mirpur 10250, AJK, Pakistan b

A R T I C LE I N FO

A B S T R A C T

Keywords: VAWT Bluﬀ body CFD Power augmentation

Performance of a vertical axis wind turbines (VAWTs) is a major focus of research these days. The present research focuses on numerical investigate the performance of a VAWT in the presence of upstream bluﬀ bodies and investigate the impact of vortices shed on the VAWT performance. Designing of wind turbine is performed using Multiple Stream Tube Model which uses turbine power, number of turbine blades, aspect ratio and wind speed as parameter. Simulations are done using Reynolds averaged Navier-Stokes equation. Furthermore, VAWT equipped with three NACA 0018 airfoils is used. In this study, single and two upstream bluﬀ bodies are used and the distance of the VAWT relative to a bluﬀ body is changed to 1D, 2D and 3D (where D is the length and width of bluﬀ body) both along and perpendicular to ﬂow direction in order to ﬁnd an optimal location for maximum power. This study shows that the deﬂected wind from the bluﬀ body possess high wind velocity which is 12% higher for single bluﬀ body and 25% higher for two bluﬀ bodies than the free stream wind velocity. Moreover the VAWTs can be deployed downstream of tall urban structures for enhancement of wind turbine power generation.

Introduction Scientist and engineers are developing new methods and technology to eﬃciently harvest energy from the renewable resources. Wind is both clean and free. Vertical axis wind turbines (VAWT) can harvest energy from wind in any direction. This makes them suitable for urban deployment. VAWTs do not require any yaw or pitch mechanism for the rotor and the blades, respectively. Horizontal axis wind turbines face fatigue due to turbulent and gusty winds; however VAWTs have the ability to take advantage of such wind conditions. Strong support structures are not required for VAWTs as the gearbox, generator and other heavy components are mounted on the ground. This makes the replacement of turbine components simple and signiﬁcantly reduces the maintenance costs. A study suggests that arrangement of VAWTs in an array that follows the natural phenomenon of ﬁsh schooling, the land area required for wind farm is reduced signiﬁcantly. This results in increased power per unit area, generated by VAWTs as compared to HAWTs in wind farms [1,2]. The eﬃciency of VAWTs is low as compared to HAWTs as a single blade of the turbine produces maximum torque at a given instance of time in a complete rotation. Other major disadvantage of ⁎

VAWT is the dynamic stall of the blades, as the angle of attack is changing rapidly throughout the rotational cycle of the turbine [3,4]. Turbine eﬃciency is reduced; noise and structural vibrations are induced due to the phenomenon of dynamic stall. Study had been done using ﬂat plate deﬂector behind the wind turbine and eﬀects of unsteady ﬂow ﬂied on the turbine [5], but no study has been performed on the wake of one and two bluﬀ bodies (mimicking the urban environment) in order to investigate the power augmentation and performance of wind turbines. In this study, performance of VAWT is investigated in the downstream region of a bluﬀ body mimicking the urban structures. Wind turbines operate in wind farms which are usually situated in remote areas like coastal areas and open ﬁelds away from the urban environment. This increases transmission and maintenance costs. Urban structures such as tall buildings shed vortices, the eﬀects of these wakes on the turbine performance is investigated. The distance of the turbine from a bluﬀ body (axial and lateral) is varied to ﬁnd out the optimal point where power can be maximized.

Corresponding author. E-mail address: [email protected] (E. Uddin).

https://doi.org/10.1016/j.seta.2019.100586 Received 30 March 2019; Received in revised form 26 October 2019; Accepted 12 November 2019 2213-1388/ © 2019 Elsevier Ltd. All rights reserved.

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Research background Diﬀerent airfoils have been studied to ﬁnd out their eﬀects on the power output of the VAWT. NACA four digit series airfoils used in aviation industry are the most widely used airfoils in the wind turbine industry as well [6,7]. Usually airfoils having thickness, ranging from 12% to 21%, of their chord length are selected for VAWTs [7,8]. Cambering the airfoils has no signiﬁcant eﬀect on the performance of the VAWT because it causes the tangential force to increase in one half, but it also causes the tangential force to decrease in the other half of the total swept region [9]. Study of the vertical axis H-darrieus wind turbine model in a wind tunnel suggested that the number of blades inﬂuence the rotation of the rotor in a wind turbine. Increasing the number of blades makes it easy for the wind turbine to run at low wind speeds. Three blade conﬁguration is more stable than two and four blade conﬁgurations [10]. The aspect ratio plays an important role in the performance, as well as it controls the power coeﬃcient of the turbine. High aspect ratio VAWT has a lower power coeﬃcient and vice versa [11]. The blades of VAWT produce maximum torque two times in the cycle that is front and back of the wind turbine. VAWTs have sinusoidal power cycle [12]. The straight blade H-darrieus wind turbines have a simple geometry because their blades are neither twisted nor they have yaw mechanism [13]. Bluﬀ bodies are studied for performance enhancement of VAWTs; it is found that if a ﬂat plate deﬂector is placed in the path of the wind perpendicular to the direction of ﬂow it becomes a source of vortex. These vortices increase the wind speeds in the downstream of bluﬀ bodies. If a deﬂector is placed between the wind path and the wind turbine, at a speciﬁc location, the turbine rotational speed increases which in turn increases the power output of the turbine. This deﬂector bluﬀ body acts as an augmentation device which enhances the power coeﬃcient by 33% [14]. The eﬀect of ﬂat plate deﬂector on the VAWT is also studied using CFD analysis. The detailed 3D analysis is done using CFD simulation in order to study the eﬀect of deﬂector plate on the performance of wind turbine. It was found out that with increase in unsteady ﬂow due to deﬂector plate the performance of wind turbine is increased. With addition of ﬂat plate deﬂector the coeﬃcient of torque is increased by 47.10% [5]. VAWT test case Rotor design has been optimized in the past by researchers and industry to improve the performance of the turbines. To predict the performance of the VAWTs many numerical codes have been developed like single streamtube model, multiple streamtube model, double multiple streamtube model, vortex method, actuator cylinder ﬂow model and computational ﬂuid dynamics method [15–19]. The wind turbine for this study has been designed using the methodology proposed by Brusca, Lanzafame and Messina in their research. This methodology has been derived from Multiple Stream Tube Model (MSTM). Fig. 1 shows a ﬂow chart of the turbine design process [11]. The wind turbines are designed considering the wind speed and desired power output. The wind turbine used for this research is a 3 straight bladed H-rotor capable of producing 10 kW at 12 m/s wind speed. Power coeﬃcient and tip speed ratio are plotted against each other as function of solidity of the rotor. Iterative method was used to calculate the turbine design parameters [11]. The power of a Vertical axis wind turbine is given by Eq. (1).

1 P = ρV 32RHCp 2

Fig. 1. Design process ﬂowchart proposed by Brusca [11].

is selected from that plot. These values are then plugged in the power equation (Eq. (1)) and the wind turbine radius is found. The chord length of the airfoil is calculated using Eq. (2).

c= (1)

σCpmax Nb

R

(2)

Reynolds number of the wind turbine is calculated by Eq. (3).

Power, wind speed, number of turbine blades and aspect ratio are taken as inputs. Then a plot is selected for a speciﬁc Reynolds number (Re) and maximum power coeﬃcient, tip speed ratio and blade solidity

Re =

2

cVo λ Cpmax v

(3)

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and ﬂow can only past the building from above. For doing 3D simulations, the computation cost increases exponentially keeping in view the eﬀects of vortices on 3D VAWT needs to be studied as well. However the results were changed by 2% on the top and back of the building due to the 3D eﬀects [21]. Similarly we considered high rise and symmetric building to minimum the eﬀects of ground and 3D vortices respectively.

Table 1 Design parameters. Parameter

Reference

Value

Power (kW) Airfoil Wind speed (m/s) Air density (Kg/m3) Kinematic air viscosity (m2/s) Rotor aspect ratio (h/R) Number of blades (Nb) Reynolds number (Re) cpmax, σcpmax, λcpmax Rotor radius (m) Airfoil chord length (m) Rotational speed (rad/s)

– [6–8] – At 300 K At 300 K [11] [10] Eq. (3) [11] Eq. (1) Eq. (2) Eq. (4)

10 NACA 0018 12 1.177 1.568 × 10−5 0.6 3 9.57 × 105 0.475, 0.3, 3.01 4 0.4 9.03

Computational domains VAWT rotor domain Based on the geometric data from design process in previous section, a CAD model of the turbine was generated. A ﬂuid domain was created around the turbine. The domain is designed in two parts rotating ﬂuid domain and ﬂuid domain. This domain has been designed to validate the study. The direction of wind ﬂow and rotation of wind turbine along with the dimensions of the validation domain is shown in Fig. 2. This domain was later meshed using ICEM CFD. A very ﬁne mesh was used near the walls of the blades to capture the gradient of the boundary layer. For this purpose an inﬂation layer has been introduced. From theoretical derivations it is found that the dimensionless parameter (y+ ≤ 5) for the viscous sub layer [22,23].

This Re is compared with the original Re selected at the time of selection of the wind turbine power coeﬃcient curves. The error is reduced by repeating the same procedure. Usually after two iterations the solution is converged and the error is reduced. VAWT rotational speed is given by Eq. (4).

ω=

λ Cpmax Vo R

(4)

After following the design processes the design parameters of the turbine are ﬁnalized and shown in Table 1. Fig. 2b shows the design and geometry of the H-Darreus type vertical axis wind turbine.

Single and two building domains Two more computational domains have been designed for this study. These computational domains have single and two buildings as bluﬀ bodies. Fig. 3 and Fig. 4 show the computation domains for both scenarios. The dimensions of the domain are a multiple of urban structure dimension (D = 20 m). The wind ﬂow in the downstream region of urban structures has been considered while selecting the locations of the wind turbine. A total of nine and twelve diﬀerent cases have been formulated for single and double building scenarios. In these cases the wind turbine location have been changed in the × and y directions. Table 2 and Table 3 shows the distances of wind turbine from the urban structure for both scenarios. These locations have been set after detailed analysis the wind ﬂow deﬂected by urban structures. The main strategy behind selecting these locations is to analyze the eﬀects of deﬂected wind ﬂow characteristics on the performance of the wind turbine appropriately. To make this study and comparison simple the wind turbine locations are related to urban structure dimension D. Starting from 0D and 1D in x and y directions respectively, with the increment of 1. The ﬂow characteristics

Aerodynamic evaluation with CFD A comprehensive aerodynamic evaluation of the wind turbine has been conducted using ANSYS FLUENT and Qblade. The computational machine used for this study had two physical processors (6 cores each) and 16 GBs of RAM. Qblade is an open source software developed at TU Berlin for analysis of wind turbines speciﬁcally [20]. In this study the ﬂow is considered incompressible. To analyze the turbulence in the ﬂow many diﬀerent models are derived from navier-stokes equations. In this study Reynolds Averaged Navier-Stokes equations (RANS) have been used to model the wakes generated in the ﬂow by VAWT blades and the urban structures. In actual 3D simulation, the 3D eﬀects like 3D vortices, ground effects and ﬂow blockage also aﬀects the ﬂow. In 2D simulation the ﬂow cannot go around the sides of the building. Full blockage can be seen

Fig. 2. Computational domain (validation). 3

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Fig. 3. Computational domain (single urban structure).

study. Upstream ﬂow is considered laminar. After interaction with the urban structure and wind turbine blades, the ﬂow is considered turbulent. To model the rotation of the wind turbine, a moving reference frame has to be incorporated in the domain. Rotating cell zone capabilities of the numerical solver have been used to visualize the VAWT rotating motion. The numerical solver used for this study can solve the problems using either relative velocity or the absolute velocity as dependent variables. For this particular study relative velocity is considered as dependent variable.

have no signiﬁcant variation, if the distances between two consecutive wind turbine locations are reduced. If the distances are increased, the wind turbine performance cannot be analyzed appropriately as it will skip some of the key locations at which the wind ﬂow characteristics have been altered due to deﬂection. These ﬂow characteristics are discussed in detail in the next sections. Boundary conditions In this study the ﬂow is considered incompressible. The upstream wind velocity has been varied from 3 m/s to 12 m/s with an increment of 1 m/s. The rotational velocity of the wind turbine has been calculated using Eq. (4). These rotational velocities have been shown in the Table 4. A 300 K ambient temperature has been considered for this

Grid generation and independence Grid independence study has been carried out on six grids of

Fig. 4. Computational domain (two urban structures). 4

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Table 2 Wind turbine locations for single urban structure. Location 1

2

3

4

5

6

7

8

9

X = 1D Y = 0D

X = 2D Y = 0D

X = 3D Y = 0D

X = 1D Y = 1D

X = 2D Y = 1D

X = 3D Y = 1D

X = 1D Y = 2D

X = 2D Y = 2D

X = 3D Y = 2D

diﬀerent resolutions. Number of cells, corresponding to each grid resolution, has been compared with the coeﬃcient of lift generated on each blade of the wind turbine. Initially a coarse grid of 70 k cells has been generated, the cell count has been approximately doubled for each new grid resolution until an optimum grid resolution has been obtained. The grid independence study is shown in Fig. 5. The grid independence study suggested that coeﬃcient of lift has no signiﬁcant change when the grid resolution is in between 1 and 2 Million cells. Thus, the domains have been meshed according to the results of the grid independence test. The optimum grid resolution was 0.9 Million cells. The optimum grid is shown in Fig. 6. The ﬁgure shows the stationary domain has structured mesh, rotating domain has unstructured mesh and there is an inﬂation layer of 20 layers with the initial layer height of 2 × 10−5 m and the growth rate of 1.2. The optimum mesh has average skewness 0.12 and average orthogonal quality 0.96.

Table 4 Simulation conditions for free stream velocity and rotational velocity. Index

Wind Speed(m/s)

Rotational velocity (rad/s)

1 2 3 4 5 6 7 8 9 10

3 4 5 6 7 8 9 10 11 12

2.2575 3.01 3.7625 4.515 5.2675 6.02 6.7725 7.525 8.2775 9.03

comparison with numerical solver software and Qblade software. The analytical results for turbine power are calculated using Eq. (1) for wind velocity changing from 3 m/s to 12 m/s (rest of variables in Eq. (1) remain same). For numerical solver software the computational domain for the validation study is shown in Fig. 2. The torque on each blade is calculated using Eq. (5). For the calculation of coeﬃcient of moment Cm of each blade the turbine rotor is rotated for 10 revolutions and Cm is obtained by numerical solver. Cm from numerical solver is averaged for last 2 revolutions of turbine rotor for removing any transient eﬀects. After obtaining torque, power on each blade is calculated using Eq. (6).

Turbulence model In this study SST k-ω turbulence model is used. This model uses k-ω model at the walls and switches to k-ε model in the free stream away from the walls. By switching to k-ε model it averts the high sensitivity to free stream turbulence properties faced by k-ω model [24,25]. This model is based on the Reynolds Averaged Navier-Stokes equations (RANS).

τ=

Yplus of the model

1 ρCm Vo2 HS 2

(5) (6)

P = τω

Yplus is the non-dimensional number, which is used to describe the coarseness and ﬁneness of the mesh. For speciﬁc turbulence, model diﬀerent value yplus is used depending upon the Reynold’s number. There are restriction of choosing reasonable overall y plus wall function for speciﬁc turbulence model. Generally, for SST k-ω turbulence model y plus value is taken to be ≤1. In the Table 5 the values for the y plus of each blade is shown along with contours in Fig. 7.

For obtaining total wind power, power on all blades is summed up. In case of Qblade, total wind power is directly obtained by selecting the studied parameters and wind turbine. The power obtained by experiments, analytical model (Eq. (1)), numerical solver software and Qblade is compared in Fig. 8. It can be seen that the power output from the numerical solver follows the same trend as of experimental and Qblade data for diﬀerent wind velocities. At low wind velocities, the diﬀerence is very small for diﬀerent approaches. However, at high wind velocities the diﬀerence of wind power increases but the overall trend remains same.

Results and discussion Validation In this paper, the studied cases are validated by comparing the power output obtained from the experimental data, analytical calculations, numerical solver software and Qblade software. The experimental results are obtained from the study of Aeolos V-10kKw wind turbine in real environment. Although, Aeolos V-10KW wind turbine has diﬀerent aspect ratio than the studied wind turbine but it shows the same performance trend at diﬀerent wind speeds and can be used for qualitative

Urban environment performance The performance of the wind turbine has been investigated in two diﬀerent scenarios. A single building and two buildings have been considered as two urban scenarios in this study. These two scenarios were tested to visualize the vortex shedding of the buildings and their eﬀect on the velocity magnitude around them. Vortex shed from urban

Table 3 Wind turbine locations for two urban structures. Location 1

2

3

4

5

6

7

8

9

10

11

12

X = 1D Y = 0D

X = 2D Y = 0D

X = 3D Y = 0D

X = 1D Y = 1D

X = 2D Y = 1D

X = 3D Y = 1D

X = 1D Y = 2D

X = 2D Y = 2D

X = 3D Y = 2D

X = 1D Y = 3D

X = 2D Y = 3D

X = 3D Y = 3D

5

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Table 5 Y plus value of the blades. Blades

Y plus values

Blade 1 Blade 2 Blade 3

0.93818104 0.67257905 0.65848517

been placed in the downstream region of the urban structure. These probes helped to analyze the ﬂow characteristics of the wind in the downstream region. The output of these probes have been recorded and averaged over the complete cycle of 20.16 s. It has been established that, wind speed is augmented after deﬂection from the urban structures. This fact has been conﬁrmed from previous research work [14]. Keeping the results of this analysis 9 and 12 locations have been picked for the analysis of wind turbines. Single building In the case of single urban structure as wind deﬂection device, Fig. 11 shows the wind characteristics. After 5.4 s a deﬂected wave is forming near the building walls shown in Fig. 11(a). This wave will augment the wind speed in the downstream region. Fig. 11(b,c,d & e) show that the defected wave is passing through the wind turbine locations. At these instances, it is found that the wind speed at locations 2,4,5,7 and 8 has been augmented initially, but later wind speed diminishes at locations 2 and 4. Similarly, Fig. 11 also suggests that the wind speed at locations 1, 2, 3, 5, 6 and 9 falls below the free stream wind velocity. The Fig. 9 shows the interaction of vortices generated by the bluﬀ body on the turbine blades. This means that the urban structure has favorable and adverse eﬀects on the downstream wind speeds. This trend of wind speed augmentation and diminution at deferent locations has been shown in the graph in Fig. 10. Fig. 5. Grid independence.

Two building In the case of two buildings, the wakes produced by deﬂection of wind from both the buildings eﬀect each other. This leads to both augmentation and diminution of wind speed in the downstream region. Fig. 13 shows the wind characteristics in the in upstream and downstream regions of the urban structures. The ﬁgure suggests that the urban structures have a favorable eﬀect on the downstream wind

structures require 20.16 s to complete one cycle. This complete vortex cycle is shown in the ﬁgures for both the scenarios. The ﬁgures show the augmentation in the free stream velocity after deﬂection by an urban structure. Before analyzing the wind turbine performance in this scenario, various velocity magnitude probes have

Fig. 6. Optimum grid resolution (1.2 million cells). 6

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Fig. 7. Yplus contours on every blade.

even falls below the free stream wind speed. This trend of wind speed augmentation and diminution at deferent locations has been shown in the graph in Fig. 12. Velocity magnitudes calculated by the simulation software are shown in Fig. 10. These ﬁgures show the behavior of ﬂow for one complete cycle for both the scenarios. The results shown in the ﬁgures are at free stream velocity of 6 m/s. The time required for one complete cycle at this free stream velocity is approximately 20.20 s.

speeds. In Fig. 13(a), deﬂected wave is shown forming near the walls of buildings. In this case two diﬀerent deﬂected waves have been observed. One of these waves is formed by the combined deﬂection of both the urban structures. Fig. 13(b, c, d, e & f) show that the deﬂected waves are passing through the wind turbine locations. At these instances, the wind speed at locations 1, 2, 3, 6, 7 and 8 augments initially, but later it diminished at locations 1,2,6,8 and 9. Similarly, Fig. 13 also suggests that the urban structures have an adverse eﬀect on the wind speed at locations 1, 2, 3, 4, 5, 6, 7, 8 and 9. The wind speed

Fig. 8. Power comparison (validation). 7

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Fig. 9. Vorticity contours in the wake of square building.

Results

and 3D). These locations yield the Cm enhancement from 8% to 56%.

Wind turbine performance has analyzed for both scenarios. Location of wind turbine was changed as shown in the schematics (Fig. 3 & Fig. 4). The coeﬃcient of moments calculated at diﬀerent locations were compared with the results in free stream. Results mentioned in Table 6 and Table 7 shows that coeﬃcient of moment is eﬀected by the vortex shedding of buildings. The coeﬃcient of moment is enhanced up to 24% and 56% in case of a single building and two buildings side by side used as a deﬂection obstacles respectively. In case of single building used as deﬂector the suitable turbine locations are X = (2D and 3D) at Y = 1D and X = (1D, 2D and 3D) at Y = 2D. The Cm enhancement on these locations vary from 10% to 24%. In case of two buildings side by side used as deﬂectors the suitable locations are X = 3D at Y = 0D and X = (1D, 2D and 3D) at Y = (2D

Conclusion In this study, the performance of an H-rotor vertical axis wind turbine was investigated in an urban environment. The study was conducted by varying the location of the wind turbine in the downstream region of urban scenarios. Two urban scenarios considered were single building and two buildings side by side. The characteristics of wind ﬂow were analyzed and simulated. Details if the simulation setup has been described in the study. Velocity magnitude for urban scenarios and coeﬃcient of moment and power for VAWT were calculated for this study. The VAWT performance in free stream was validated from experimental data literature and analytical calculation. The study shows a potential in power augmentation when used at

Fig. 10. Wind velocities at diﬀerent wind turbine locations (single urban structure). 8

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Fig. 11. Velocity contours (single urban structure).

Fig. 12. Wind velocities at diﬀerent wind turbine locations (two urban structures). 9

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Fig. 13. Velocity contours (Double urban structure).

locations in both urban scenarios, the high wind velocity enhances the torque generated on the turbine blades, which subsequently increases the power output of the VAWT. If the turbine is located in other locations, the wind speed reduces which decreases the power output of the VAWT signiﬁcantly. The average Cm was increased by 24% and 56% for single building and two buildings side by side respectively. From this study, it is found that the VAWTs can be deployed in the downstream of buildings for enhancement of generated power. For future, this phenomenon may be validated experimentally. More parameters of the buildings such as aspect ratio, diﬀerent shapes and height needed to explore in the future.

speciﬁc location in the downstream region of buildings (33°38′12.5″N 72°59′23.8″E). The buildings act as deﬂectors and subsequently augment the wind turbine power. The deﬂected wind from the buildings, near the wake region, possesses high wind velocity. This wind velocity is 12% and 25% higher than the free stream wind velocity in case of single building and two buildings side by side respectively. As the power possessed by wind is directly proportional to the cube of upstream velocity, this high velocity wind enhances the rotor RPM and turbine power output. According to the simulation results, the power of the VAWT is dependent on its location in the downstream of building. At optimum

Table 6 Comparison of turbine Cm calculated at diﬀerent locations and in free stream (single building). Bare turbine

Averaged Cm Change (%)

1.78 –

Location 1

2

3

4

5

6

7

8

9

X = 1D Y = 0D

X = 2D Y = 0D

X = 3D Y = 0D

X = 1D Y = 1D

X = 2D Y = 1D

X = 3D Y = 1D

X = 1D Y = 2D

X = 2D Y = 2D

X = 3D Y = 2D

1.57 −12

1.41 −21

1.36 −24

1.67 −06

1.96 10

2.05 15

2.21 24

2.00 12

1.96 10

10

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Table 7 Comparison of turbine Cm calculated at diﬀerent locations and in free stream (two buildings side by side). Bare Turbine

Averaged Cm Change (%)

1.78 –

Location 1 X = 1D Y = 0D

2 X = 2D Y = 0D

3 X = 3D Y = 0D

4 X = 1D Y = 1D

5 X = 2D Y = 1D

6 X = 3D Y = 1D

7 X = 1D Y = 2D

8 X = 2D Y = 2D

9 X = 3D Y = 2D

10 X = 1D Y = 3D

11 X = 2D Y = 3D

12 X = 3D Y = 3D

1.75 −02

1.59 −11

2.18 22

1.53 −14

1.33 −25

1.06 −40

2.78 56

2.27 27

1.93 08

2.44 37

2.40 34

2.34 32

Declaration of Competing Interest

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