numerical study of wake interaction and its effect on wind

Numerical Study of Wake Interaction and its Effect on Wind Turbine Aerodynamics Based on Actuator

Line Model

Xu Ning1, Yang Huang1, Decheng Wan1*, Changhong Hu2

1State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China

2Research Institute for Applied Mechanics, Kyushu University, Fukuoka, Japan *Corresponding author

ABSTRACT Wake interaction normally occurs in all wind farms and impacts significantly the flow field and performance of downstream wind turbines. The present work aims to study the wind turbine wake interaction phenomenon through the CFD method using LES and actuator line model. The solver used in the present work is developed based on the open source C++ class library OpenFOAM, in which the PISO algorithm is applied to deal with the velocity pressure coupling problem. The simulations which consider uniform inflow condition and six different layouts are implemented to study the evolving process of the interacting wakes. From the numerical result, the interacting region of wakes contains higher level turbulent flow than the single wake. The fully developed turbulence appears the earliest in the case of tandem layout, leading to serious wake meandering in the end of computational domain. The diffusion of turbulence causes the merging of wakes, and thus the velocity is redistributed among the whole wake region. Velocity deficit caused by the wake decreases the convertible wind energy. The turbulent flow and meandering of the wake result in the multi-scale fluctuation of the aero-power curves of wind turbines downstream. KEY WORDS: actuator line model; CFD; wind turbine aerodynamics; wake interaction. INTRODUCTION Benefiting from the rapid development of wind turbine technology in recent years, the number of wind farms putted into operation keeps increasing. As one of the most concerned problems in the wind energy industrial, wake effect occurs widely in all wind farms, which could not only result in a sharp reduce in the total power production but also cause a considerable increase of the fatigue load of wind turbine structure (Vermeer et al., 2003, Troldborg, 2009). The formation of the wake region is due to the basic working principles and characteristics of a wind turbine. When the wind flows to a wind turbine, the blades are pushed by the lift force to rotate around the horizontal low speed shaft. During this process, the wind turbine converts the kinetic energy

of the wind into electrical energy though a generator placed in the nacelle and thus inevitably leaves a meandering tube-shaped region behind the rotor, where the wind speed is slowed down and turbulence level is relatively high (Troldborg et al., 2011). Taking into account the limiting factors such as land cost, topography, transportation, power transmission and etc., all the wind turbines of a wind farm must be placed in a fairly limited area, therefore, power losses caused by wake effects cannot be completely avoided. Since the layout of the turbine array apparently has a vital influence on how serious the wake effect will be, we could find out theoretically a reasonable arrangement and thus reduce the losses as much as possible. In order to achieve this goal, many researchers have made efforts in the study of wind turbine aerodynamics and the development of wake models. Jensen et al. (1986) described a theoretical model to calculate the velocity deficit in the wake for prediction of the total output from the wind farm. The model is based on axisymmetric wake assumption and considers a uniform distribution of velocity across each transverse section downstream. The results show an agreement only with the experimental data in the far wake region, which is enough to give a quite good prediction of the power output because the wind turbines spacing in real wind farms should be a large value because of the less convertible energy and higher turbulence intensity in the near wake. The improved version of Jensen wake model named Park model (Katic, 1987) considering different types of the wake shading and the ground effect is implemented in WAsP (Wind Atlas Analysis and Application Programs), a software for wind resource evaluating (Mortensen, 1997). Similarly based on axisymmetric and self-similar velocity profile assumption, Larsen et al. (1996) proposed an analytical model, in which the velocity deficit and wake width change non-linearly with downstream distance. Models like the above can be collectively referred to as Kinematic Model (Crespo, 1999), in which the velocity deficit profiles are obtained from basic physical principles and assumptions supported by experimental data. Similar work was done by Vermeulen (1980), who used a gaussian profile instead of the uniform type, Kiranoudis and Maroulis (1997) who predict the wind park efficiency according to the parameters of the farm and turbine. Due to its simplicity and agreeable accuracy, kinematic models are widely

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Proceedings of the Twenty-ninth (2019) International Ocean and Polar Engineering ConferenceHonolulu, Hawaii, USA, June 16-21, 2019Copyright © 2019 by the International Society of Offshore and Polar Engineers (ISOPE)ISBN 978-1 880653 85-2; ISSN 1098-6189

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applied in the study of power output prediction and optimized layout of wind farms. For example, Wan et al. (2012) solved the wind farm micro-siting problem by applying a linear wake model in the gaussian particle swarm optimization algorithm. Parada et al. (2017) solved the wind farm layout problem using a similar methodology but with a Gaussian-based wake model. However, the present kinematic models only provide rough approximation of the flow field information and the selection of its parameters relies heavily on the experimental measurements and experience, which limits its universality. Certain researchers tried to build more complicated models to obtain the information of the whole flow field. Ainslie (1988) proposed a numerical model to calculate the flow in wind turbine wake by solving Navier-Stokes (N-S) equations based on the parabolic approximation. Comparing with the experimental results, this model achieved reliable prediction of the flow field in the wake of wind turbines, although also subject to axisymmetric wake assumption. By defining the boundary conditions with the full scale experiments results, Larsen (2009) improved his early version of a wake calculation procedure (Larsen, 1988) which uses Prandtl’s mixing-length theory to deal with the Reynolds stress term. Still, these models can only handle the stationary problems and have difficulty in precisely describing the ground effect and multiple wake situations due to their fundamental assumptions. Responding to the need of a deeper insight of the mechanism of the wake flow (Sørensen, 2002), CFD theory has been largely applied to the research of wind turbine wake aerodynamics. Solving the full N-S equation on the computational mesh including the fairly fine grids near the blade boundary layer will cost unacceptable computational resource, therefore some rotor modeling methods such as actuator disk model (ADM) (Mikkelsen, 2003), actuator line model (ALM) (Troldborg, 2009), in which the blades are represented by a body force, were proposed to reduce the workload in mesh generation and computation. Churchfield et al. (2012) explored the effects of atmospheric stability and surface roughness on the wind turbine dynamics by combining LES and ALM and generating the atmospheric flow environment in a precursor case. This team also simulated the Lillgrund offshore wind plant which contains 48 2.3-MW Siemens turbines, provided much details on the wake development and its effects on the power output of the wind farm and indicated the such a large scale of computation makes it not yet a mature methodology for engineering practice. Furthermore, Draper (2016) simulated a row of the real wind farm based on ALM with coarse resolution mesh to study the interaction between wind turbines. Howland (2016), Ai (2017), respectively discussed how yaw degree and inter-turbine spacing change the characteristic of the wake flow and loads acting on turbines. However, the flow characteristics in the wake region are affected by numerous elements such as wind turbine working status, spacing, atmospheric environment (Keck et al., 2015) and so on, which makes it difficult to have an overall understanding of the mechanism of wake development and its effect on wind turbine aerodynamics. Present researches lack a systematic summary of the quantitative relationship between the wake features and those factors, thus more work should be done for the establishment of an advanced wake model suitable for engineering field. This paper mainly concentrates on the wake merging phenomenon by simulating a three wind turbine wind farm under uniform inflow in which the middle one is placed in various distances away from the straight line connecting the first and last turbine. Detailed information of velocity deficits, turbulence intensity and Reynolds stress in different cross sections downstream is displayed and the effects of the wake interaction on the load and power of turbines are also discussed. NUMERICAL METHODS Actuator Line Model

The actuator line model proposed by Sørensen and Shen (2002) has been widely used in the numerical study of wind turbine aerodynamics. Its main idea is to represent the presence of the real turbine blades by the body force which is computed according to the local flow information and the 2D airfoil data from experimental measurement. Thus this model avoids a large amount of work in computing the flow near the blade boundary layer, meanwhile giving an solution of the flow field with a high accuracy. The lift force and drag force generated by every segment of the blade can be expressed as:

212 l relL C V cdrρ= (1)

212 d relD C V cdrρ= (2)

Where, lC and dC are the lift and drag coefficient as a function of the attack angle α , c is the chord length, dr is the width of blade element,

relV is the local velocity relative to the rotating blade section which can be calculated by eqn. 3 according to the vector relation shown in Fig. 1.

( )22rel zV V r Vθ= + Ω − (3)

The zV , Vθ and Ω are the axial velocity, tangential velocity and rotor speed respectively.

Fig. 1 Cross-sectional aero foil element (Sørensen and Shen, 2002) Then the body force f can be calculated as:

( ) ( )21,2 rel l L d Df L D V c C e C eρ= = +

(5)

In order to avoid the singular behavior, the so-called Gaussian smooth distribution of the body force computed above is implemented along the blade in the following way:

( )2

2 3 2

1 exp df f dε ε εη ηε π ε

= ⊗ = −

, (6)

The distributed force fε is obtained by taking the convolution of f and

εη . εη is the regularization kernel, distributing the body force f to the mesh grids near the blade elements according to ε , a parameter to adjust the concentration of the regularized load, and d, which represents the distance between the grid points and the points at the i’th actuator line.

Governing Equation In this paper, the large eddy simulation (LES) method is used since it shows better performance in dealing with the large-scale unsteady anisotropy turbulence appearing in the turbine wake (Jimenez, 2007). The governing equation can be written as:

21i ji i

j i i j

u uu upt x x x x

υρ

∂∂ ∂∂+ = − +∂ ∂ ∂ ∂ ∂

(7)

484

0i

i

ux

∂ =∂

(8)

Considering ( )i j i j i j i ju u u u u u u u= + − , we call the term ( )i j i ju u u u− − subgrid stress and then the eqn. 7 becomes following form:

2 ( )1i j i j i ji i

j i j j j

u u u u u uu upt x x x x x

υρ

∂ ∂ −∂ ∂∂+ = − + −∂ ∂ ∂ ∂ ∂ ∂

(9)

Because of the existence of the ij i j i ju u u uτ = − , the Smargorinsky eddy viscosity model (eqn. 10) is introduced to close the governing equations of LES as following:

123ij t ij kk ijSτ υ τ δ= + (10)

Where ijS is the resolved strain-rate tensor, and subgrid viscosity 2 1/2( ) ( )t S ij ijC S Sυ = Δ , where Δ is filter length scale and the Smargorinsky

constant = 0.16sC .

SIMULATION SETUP All the wind turbine used in the present study are the NREL 5MW baseline wind turbines (Jonkman, 2009) and the gross properties are listed in the Table 1. Table 1. Gross properties of NREL-5MW Turbine

Rating 5 MW Rotor Orientation, Configuration Upwind, 3 Blades Rotor Diameter, Hub Diameter 126 m, 3 m Hub Height 90 m Cut-in, Rated, Cut-out Wind Speed 3 m/s, 11.4 m/s, 25 m/s Cut-in, Rated Rotor Speed 6.9 rpm, 12.1 rpm Overhang, Shaft Tilt, Precone Angles 5 m, 5°, 2.5°

Six cases are set up and computed, and among them four cases each includes three turbines, and the rest two cases, as references of comparison, include one and two turbines respectively. In three-turbine cases, T1, T3 are subject to a tandem type layout. T2 is placed between them but with a lateral distance from the horizontal shaft line of T1 and T3. More details of these cases and the arrangement of the corresponding wind farms are shown in Table 2 and Fig. 2. All the sizes associated with the case arrangement are represented by dimensionless distance based on the rotor diameter D equal to 126 m. The domain length xL (flow direction) is set to 17D and the domain height zL equals to 3.2D. It should be noted that the width of the domain yL varies from case to case. As shown in the Fig. 2, yΔ , the distance between the horizontal shaft line of T2 and that of T1 and T3 in three-turbine cases is set to different values. Therefore adjustment of

yL according to yΔ is made to ensure the enough domain width for computing the expanded wake in each case. The specific domain width for each case is defined by setting both lΔ and rΔ (the lateral distance between the sidewall and the shaft line of its nearest turbine) equal to 2D. T1 is placed 1D downstream to the inlet plane and the streamwise distance between each turbine is 5D. Thus a distance of 6D is left between the wind turbine T3 and the outlet plane. The case 5 and case 6 are set as comparative simulation cases, removing both T2, T3 and only T2 respectively. Other conditions in comparative cases such as inflow condition, grid resolution, locations of turbines remain the same as those in three-turbine cases. The low speed shaft of all turbines are

placed in the height of 90m according to the designed hub height.

(a) Cross section of T1, T3 and T2

(b) Vertical section Fig. 2 wind farm layout Since the ALM is used instead of the real physical blade model, all computations in the present work are implemented in Cartesian domain, as the Fig. 3 shows. The computational domain is divided into three regions (marked as Ⅰ, Ⅱ and Ⅲ) with serially increased grid resolutions. The side lengths of grid cells in each region are 8m, 4m and 2m respectively, ended with a total mesh being 16~18 million for each case. All turbines are placed in the region Ⅲ which covers the space starting from 0.5D ahead of T1 to the outlet plane, so that the detailed information of the wind turbine wake especially the wake merging procedure can be captured.

(a) Grid in lengthwise section

(b) Grid in cross section Fig. 3 the grid in lengthwise section and cross section Uniform inflow condition with a velocity of 11.4m/s is applied to all simulation cases. Free-slip constraint is imposed at the top boundary

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which prohibits the outflow of the air but allows the velocity parallel to the upper plane. The bottom is considered as the ground surface, so the wall condition is imposed on it. The left and right side boundary are set

to symmetry, which means 0yV = and 0x zV Vy y

∂ ∂= =∂ ∂ . At the outlet

plane the zero-gradient condition is applied, implying

0yx zVV Vx x x

∂∂ ∂= = =∂ ∂ ∂

. The computation duration is 320s. Since the

time that the wind needs to flow from the inlet plane to the outlet plane

0

126 17m 18811.4m/s

xLt sV

×= = ≈ , the flow after 200s is considered to reach a

quasi-static state, so all the averaging process mentioned below uses flow information from 200s to 320s. The principle for choosing time step is that the displacement of the blade tip point in one time step should be less than the side length of a grid cell, i.e.

2m 0.02512.1/60 2 63m/stip

t sV πΔΔ < = =

× × . Thus the time step tΔ is set

to 0.02s. Table 2. simulation cases setup

Case Number yΔ Remark 1 0D

D=126 m

2 0.25D 3 0.5D 4 0.75D 5 - 6 -

RESULT AND DISSCUSION Aerodynamic Power Output Different layout of wind farm could result in significant influence on the power output of wind turbines in it. Fig. 4 shows the average power output of each turbine in every case. T1 is the most upstream wind turbine, which always works under rated conditions, so obviously the power output of T1 for each case keeps the same 5.1MW. T2, T3 are located 5D and 10D downstream T1 respectively. There exists a lateral distance yΔ between the shaft line of T1 and that of T2, while T3 is placed straight behind T1. In this way, T2 suffers from different degrees of wake effect from T1 and T3 is affected by the mixed wakes of both T1 and T2. In case 1, where three turbines are arranged in a straight line ( 0yΔ = ), the loss of power output caused by wake effect is the largest, so the average aerodynamic powers of T2 and T3 are only 42.4% and 29.3% of T1.

Fig. 4 Average power output of turbines in different cases

It is clearly seen form the result of the other three-turbine cases that the total power output of the wind farm increases as the yΔ grows. For T2, increasing yΔ means that the area of the wake shadow ahead its rotor from the upstream wind turbine T1 reduces and thus more undisturbed wind resource can be converted, while the working condition for T3 is relatively complicated, because all the airflow ahead its rotor is the result of the mixed and developed wakes of both T1 and T2. Thus when

yΔ is small, the wakes of T1 and T2 still fully merge and the velocity deficit in the far wake remains in a high level. As a result, the power output of T3 in case 2 only increases by 4%, compared with case 1.

Fig. 5 Time history curves of aerodynamic power of turbines in case 1




The time history curves of power output of each wind turbine in case 1~4 are displayed in Fig. 5~8, which show the stability of the aerodynamic powers of turbines in different positions. To ensure that

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the wake is already developed completely, only the data from 200s to 320s is used. Running under uniform inflow of 11.4m/s, T1 provides the power output near the rated value with almost negligible fluctuation, while affected by the influence of wake effect, the power outputs of T1 and T2 experience a sharp drop and meanwhile strong fluctuations. However, it is worth noting that, as the yΔ increases, the aerodynamic power curves of T2 and T3 show different fluctuation characteristics. When T2 is placed straight behind T1 in case 1, the only factor that disturbs the power output stability is the turbulence in the wake of T1, so the power curve of T2 shows random fluctuations with relatively small amplitude. It is seen in the Fig. 6~8 that the fluctuation amplitude of the power output of T2 raises rapidly as yΔ approaches 0.5, and then reduces again. Furthermore, a periodic oscillation can be clearly seen in case 3 and case 4. The cause of these phenomena is that the main factor causing the power instability of T2 is no longer the turbulence in the wake but the special distribution of incoming flow velocity ahead of the rotor of T2. When 0 1D y D< Δ < , the T2 is partly shadowed by the wake of T1, where the wind velocity is low and disturbed, while the other part experiences the uniform and laminar inflow. Every time the blade moves from the shadowed region to the uniform inflow region, the power output will see a sharp rise, and vice versa. Compared with T2, T3 is completely covered by the mixed wake from upstream wind turbines. In the first case, where all turbines are tandem arranged, the power output curve of T3 not only shows local random oscillations as that of T2, but also displays a wave-shaped curve as a whole with long period and large amplitude up to over 0.5MW. The former is due to the high level turbulent flow in the wake while the latter reflects the large-scale movement of the entire turbine wake, which is usually called wake meandering (España, 2009). As clearly shown in Fig. 6~8, the amplitudes of both small-scale random oscillation and large-scale heave of the T3 power output go down as T2 deviates the horizontal shaft line of T1 and T3, which indicates the lateral position of T2 has a significant impact on the power output stability of T3. Moreover, the result also points out that in the uniform inflow condition the tandem type of layout arouses the largest scale wake meandering and the turbulence in the mixed wake reaches the highest level. Wake Characteristics The wake behavior in a wind farm determines the aerodynamic environment of the downstream wind turbines and hence affects their power output and service life. Fig. 9~14 display the speed at hub height for case 1~6. In case 5, there is only one wind turbine T1, which is placed in the most upstream position, and thus the behavior of a single wake from the rear of the rotor to 16D downstream position can be distinctly seen. As the tip vortices shed from the blades, the shear layer is formed and thickens continuously under the action of the turbulence in the wake as the flow moves downstream. According to Crespo (1999), the shear layer will reach the wake axis at a certain distance downstream, which marks the start of the far wake region. On the basis of his definition, the end of the near wake region in is at about 5D downstream the rotor, where the high speed flow behind the root just fully diffuses. Because the turbine works under uniform inflow, all the turbulent flow in the wake is stimulated by the turbine itself, so the diffusion and momentum exchange process in the wake is not as intense as those in the atmospheric environment. This explains the relatively long near wake region compared with the usual length reported in the work of other researchers (Sanderse, 2011). Furthermore, starting from 10D downstream, the wake begins to meander and the radius and center position of the wake cross section change continuously. The same observation was made in the work of Bingöl (2007).

Fig. 9 Wind speed at hub height for case 1 in axial direction





Fig. 14 Wind speed at hub height for case 6 in axial direction Tandem layout could maximize the wake effect and make the wakes of all three turbines fully merge. The existence of T2 in case 1 accelerates the formation of the meandering of wake ahead of T3. As a result, the most active large scale movement of the wake appears, presented in Fig. 9, which explains why the power output of T3 in case 1 has more severe instability than that in case 6. The interaction process of the wakes of turbines in stagger arrangement is depicted in Fig. 10~12. Partly shadowed by the wake of T1, the near wake region of T2 shows highly asymmetric velocity deficit distribution. As the wake flow goes downstream, the momentum is redistributed under the diffusion of

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turbulence and the wakes of both T1 and T2 will merge into one unity within different distances according to the value of . In this way, the radius of the whole wake region expands. The larger the yΔ is, the larger the range of the wake region and the smaller the velocity deficit is. The newly formed wake needs more time (distance) to fully develop, so the wake meandering movement in case 2 only shows up at almost the end of the domain, and cannot be clearly detected in case 3 and 4. The velocity deficit distributions at hub height in different downstream sections for case 1 to case 4 are shown in Fig. 15~18, and the data in case 5 and case 6 are also illustrated as reference. Compared with the result in case 5, the velocity deficit 7D and 9D downstream T1 (i.e. 2D and 4D downstream T2) for case 1 to case 4 aggravates unsurprisingly as T2 comes in. The wake effect in case 1 is the most serious as a result of tandem layout and in Fig. 15 the M-shaped augmented part of the velocity deficit caused by T2 is clearly seen. Especially in case 4, where the low speed shaft axis of T2 is thoroughly out of the wake region of T1, the flow passing through the hub of T2 (because only the blades are mimicked in the present actuator line model) is not disturbed by the turbulence in the wake of T1, so there is a apparent valley in the velocity deficit distribution of the wake behind T2. In position 9D downstream of T1, the velocity deficit in the wake is redistributed to some degree. Nearly all the sharpness in the curves is smoothed under the influence of turbulence. The total velocity deficit of T1 and T2 is no longer subject to a simple superimpose principle but reforms a larger wake region as a entire entity, marking the merging of the wakes.

Fig. 15 Velocity deficit at hub height in 7D downstream position




However, in Fig. 17 no obvious increase of the velocity deficit is seen from the comparison between case 1~4 and case 6, which indicates the existence of T2 has quite limited impact on the velocity deficit in the near wake region of T3. There are mainly two reasons accounting for this phenomenon. Firstly, T2 works under the wake effect of T1, making the energy convertible for it is reduced to a low level. The second is that the relatively high turbulence level in the region behind T2 accelerates the recovery procedure and makes up partly the velocity deficit brought by T2. Besides, the increasing lateral distance of the arrangement of T2 weakens its effect on T3 especially in case 4. Moreover, an interesting phenomenon appears in position 14D downstream of T1, which is, the velocity deficit in three-turbine case is even less than that in case 6. Although the total aerodynamic power for three-turbine cases is apparently higher than that in case 6, the wind speed in the 14D downstream position in case 1 and case 2 is larger. The only explanation for this is the faster recovery speed due to the fully developed turbulent flow in the far wake region of the last turbine T3. The higher turbulence level the wake flow contains, the faster the wind speed recovery process is. Furthermore, we cannot distinct the wakes caused respectively by three turbines in different positions in the end of the domain, as shown in Fig. 18. The velocity deficit is completely redistributed in a expanded wake region with a diameter more than two times larger than the rotor diameter. This is also a result of the entrainment and diffusion effect of the high level turbulent flow in the merged wake. To illustrate the development process of the turbulent flow and the

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contribution of the turbine rotor in it, the turbulence intensity field images for case 1~4 is plotted in Fig. 19~22 (the first row represents case 1 and case2 and the second row represents case 3 and case 4). Here the turbulence Intensity only considers the flow speed in x-direction, and its expression formula is demonstrated as following:

Standard DeviatioTim

n oe Aver g

f a ed

xx

x

x

x

V VV

TIV

σ= = (11)

Fig. 19 Turbulence intensity in 7D downstream position



Fig. 22 Turbulence intensity in 14D downstream position Form Fig. 19, the turbulent flow stimulated by the tip and root vortex shed from the turbine rotor is clearly presented. The region where

wakes of different turbines interact with each other contains higher level turbulent flow and thus compared with other cases, the wake flow in case 1 becomes fully developed turbulence the earliest and shows the highest level of turbulence intensity in 7D downstream position. It is also worth mentioning that the vortex patterns seen from case 3 and 4 are not two perfectly circle but with a certain degree of deformation in the interaction region. The reason for this phenomenon is the Counterclockwise rotation of the wake caused by the torque implemented to the air by the rotor. When two rotational vortex structure in the wake encounter, the original movement track is interrupted and the two wake flow begin to merge. As a result, the distribution of turbulence intensity in 9D downstream position, shown in Fig. 20, becomes more uniform to some degree than that in 7D downstream position. When the third turbine comes in, the turbulence in the wake jumps to a higher level. As displayed in Fig. 21 (noticed that the max value of the color legend changes from 0.20 to 0.40), the wake expands and turbulence further diffuses, which accounts for the acceleration of velocity recovery process mentioned before. As the flow move to the 14D downstream position, wakes of all the turbines merge and reform a large wake region where the turbulence intensity is relatively uniform and the velocity deficit tends to obey the gaussian distribution as presented in Fig. 18. CONCLUSIONS In this paper, a set of numerical simulations of aerodynamic characteristics and wakes of wind farms under uniform inflow containing NREL 5WM wind turbines in various arrangement are implemented based on the LES and actuator line model. The wake interaction and merging phenomenon and its effect on the power output of downstream turbines are carefully analyzed. Multiple wakes interaction is complex non-linear process, resulting in significant changes in aerodynamic environment and wake development of downstream wind turbines. From the view of power output, the power curves of turbines operating in wake region shows both small-scale and large-scale oscillations. The former is caused by the turbulence flow in the wake and the latter is due to the so called wake meandering movement. Thus the stability is seriously damaged, which reduces the quality of the power produced and makes grid integrating harder. Besides, the blades of partly shadowed turbines like T2 in case 2~4 work in periodically changing inflow condition and this is the main reason for the fluctuation of its aerodynamic power. From the perspective of wake evolution, the numerical result indicates that the velocity deficit in the wake intersection area are not subject to a simple linear superposition principle. That’s why wake models based on momentum theory and linear sum rule could not provide accurate prediction of velocity distribution in the interacting wake region. Furthermore, the turbulent flow in the wake plays an important role in the wake merging process. Turbulence intensity images clearly shows that the turbine operating in the wake further stimulates higher level turbulence. Moreover, the rotation movement of the turbine wake facilitates the wake interaction, makes the vortex structure breaks earlier and accelerates the turbulence development. For the perspective of the future work, although plenty of work focusing on the simulation of wind farms has been done based on LES and actuator line model, simulations of real scale large wind farm comprised of hundreds of wind turbines under various inflow conditions especially the atmospheric boundary layer flow are still difficult due to the current limited computation capacity. Additionally, as the most commonly used control operation, yaw and pitch degree also impact significantly on the performance of a wind farm. Therefore, simulations of typical arranged wind farm with complex inflow conditions should be done in the future work to achieve systematic

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analysis of the wake effects and the mature methodology to realize wake collaboration. ACKNOWLEDGEMENTS This work is supported by the National Natural Science Foundation of China (51879159, 51490675, 11432009, 51579145), Chang Jiang Scholars Program (T2014099), Shanghai Excellent Academic Leaders Program (17XD1402300), Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning (2013022), Innovative Special Project of Numerical Tank of Ministry of Industry and Information Technology of China (2016-23/09) and Lloyd’s Register Foundation for doctoral student, to which the authors are most grateful. REFERENCES Ai, Y., Wan, D., & Hu, C. (2017, July). Effects of Inter-Turbines

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