J. Wind Eng. Ind. Aerodyn. 117 (2013) 11–17

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Journal of Wind Engineeringand Industrial Aerodynamics

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Numerical study on the horizontal axis turbines arrangement in a windfarm: Effect of separation distance on the turbine aerodynamicpower output

Nak Joon Choi a, Sang Hyun Namb, Jong Hyun Jeong b, Kyung Chun Kim c,n

a Graduate School of Mechanical Engineering, Pusan National University, Busan 609-735, Republic of Koreab CFD Business Unit, DNDE Inc., Busan 612-021, Republic of Koreac School of Mechanical Engineering, Pusan National University, Busan 609-735, Republic of Korea

a r t i c l e i n f o

Article history:Received 2 October 2012Received in revised form14 February 2013Accepted 7 April 2013Available online 7 May 2013

Keywords:Wind farmCFDWakePower outputSeparation distanceInteraction

05/$ - see front matter & 2013 Elsevier Ltd. Ax.doi.org/10.1016/j.jweia.2013.04.005

esponding author. Tel.: +82 51 510 2324; fax:ail address: kckim@pusan.ac.kr (K. Chun Kim)

a b s t r a c t

This paper presents the results of a computational fluid dynamics (CFD) study of a wind farm with twosets of 2 MW class wind turbines. CFD analysis was calculated by using the commercial multi-purposeCFD solver ANSYS CFX. Blade design and modeling were based on blade element momentum theory. Therotational phase of two wind turbine rotors was synchronized, and the distance between the two windturbines was changed from three to seven times of the rotor diameter. The tilting angle of the 2 MW classwind turbine was set to 51. A complete wind farm mesh is generated including the rotor, nacelle andtower. The results showed that there was a power output difference due to the wake effect between twowind turbines. The power output of the downstream wind turbine was changed with respect to theseparation distance between wind turbines. The optimal compromise between wind farm constructioncost, annual energy production and wind turbine lifetime as a function of separation distance is crucial.These CFD results can be applied to wind farm layout design, site evaluation and power outputprediction.

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1. Introduction

Wind energy is a promising renewable energy resource to helpovercome global warming and environmental pollution from theuse of fossil fuel (Kiranoudis et al., 2001). Wind farms composed oflarge capacity wind turbines will become a main electrical energysource (Abderrazzaq and Hahn., 2006; Abderrazzaq., 2004). Aswind turbines become larger, wind farm layout design becomesmore important (Gonzalez et al., 2010). Among several wind farmlayout design factors, wind turbine arrangement according toseparation distance is one of the most critical factors for poweroutput, annual energy production, availability, and lifetime of thewind turbine. Therefore, during wind farm layout design, separa-tion distance and interaction between wind turbines must becarefully considered because they are directly connected to theinitial investment cost, payback period and economic efficiency.

To study aerodynamic power output of the 2 MW class windturbine according to separation distance, an experimental methodis unrealistic because of the high cost required and length of timeinvolved. The computational fluid dynamics (CFD) approach can be

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successfully applied with minimum cost and time compared to theexperimental method (Christiane Montavon and Jones, 2009).Before computer resources reached an adequate level, it was onlypossible to analyze a wind farm with an actuator disk, momentumsource, and rather coarse elements, as used in previous wind farmCFD study results with various limitations (Sten et al., 2004). Dueto the rapid development of computer resources, it is now possibleto analyze an entire wind farm and evaluate sites with a full three-dimensional (3-D) wind turbine model, as used in this wind farmCFD analysis. To the best of knowledge, no research has beenreported in the literature that describes a CFD wind farm analysisusing a full wind turbine model. The electrical power output of ahorizontal axis wind turbine is proportional to the square of therotor diameter and the cube of the wind speed. This behaviorreflects a tendency toward larger scale wind turbines. The elec-trical power output of a wind turbine at the generator terminal canbe written as

Pgen ¼12ρAV3ηCp; ð1Þ

where Pgen is the electrical power output (W), ρ is the air density(kg/m3), A is the rotor swept area (m2), V is the wind speed (m/s), ηis the overall efficiency and Cp is the power coefficient.

Fig. 1. 2 MW class wind turbine, front view (left) and side view (right).

N.J. Choi et al. / J. Wind Eng. Ind. Aerodyn. 117 (2013) 11–1712

The power coefficient can be written as

Cp ¼P

ð1=2ÞρAV3 ; ð2Þ

where P is the aerodynamic power output (hereafter called “poweroutput”).

The power coefficients of each wind turbine are not the samedue to different power outputs resulting from different incidentwind speeds. For a wind farm, the annual energy production isvery important because it is directly connected to income from thesale of electricity. It is also affected by other factors such asseparation distance and interaction. The annual energy productionAEP can be written as

AEP ¼ 24� 365� Nf l∑½PVpðV Þ�; ð3Þwhere N is the number of wind turbines, f l is the overall loss factorincluding separation distance and interaction effects, PV is thewind turbine power output according to wind speed (W) and pðV Þis the Weibull distribution at the hub height.

The tilted rotor, nacelle and tower must be considered tosimulate an actual wind turbine. The power output of a down-stream wind turbine may depend on the separation distance andthe wake from the upstream wind turbine. In the wake region, awind turbine is under a more severe environment, which couldresult in increased fatigue, which is a cause of decreased windturbine lifetime and potential trouble sources. In theory, completerecovery of the power output of a downstream wind turbinerequires an infinite separation distance between wind turbines.If enough separation distance is secured for the enhancement ofthe power output of a downstream wind turbine, more transmis-sion cable is required and the cable laying cost rises. If insufficientseparation distance is used to save cable and cable laying cost,annual energy production is reduced and there is a risk of fatigueproblems due to the wake (Quarton., 1998). Therefore, an optimalcompromise between cost, fatigue and annual energy productionwith respect to the separation distance between wind turbines iscrucial.

For this study, a 2 MW class wind turbine was designed andmodeled with a tilted rotor, nacelle and tower. Based on a full 3-Dwind turbine model, CFD analysis was performed to characterizepower output according to the wind turbine separation distance.

2. MW class wind turbine and wind farm

In the design of a 4 MW wind farm, two sets of 2 MW classwind turbines were used. Wind turbine blade design softwarecalled XD-BLADE, developed by Choi et al., is based on bladeelement momentum theory and was used for blade design (Choiet al., 2010). The main specifications of 2 MW class wind turbineare given in Table 1 (Bum-Suk Kim et al., 2009).

The proposed wind turbine is shown in Fig. 1. The rotationaldirection of the rotor is clockwise. The arrangement and identifi-cation of the wind turbines are shown in Fig. 2. The rotationalphase of each wind turbine is synchronized. The wind farm

Table 1Main specifications of 2 MW class wind turbine.

Item Value

Rotor diameter (m) 84.2Rated rotational speed (rpm) 18.7Tilting angle (1) 5Rated wind speed (m/s) 11Rated power output (kW) 2000Tip speed ratio 7.5Hub height (m) 85.2

Fig. 2. Arrangement and identification of wind turbines.

Fig. 3. Wind farm configuration.

Table 2Range of L1 and L2.

Case number L1 L2

case 1 3D 28Dcase 2 4D 29Dcase 3 5D 30Dcase 4 6D 31Dcase 5 7D 32D

Fig. 4. Rotational mesh system (left) with blade surface mesh (right).

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configuration is shown in Fig. 3. All distances were based on therotor diameter D. The distance from the inlet to the upstreamwindturbine is 7D. L1 and L2 were changed from 3D to 7D and 28D to32D respectively for the CFD analysis according to separationdistance change. The height of the wind farm flow field is 6D,and the distance from the downstream wind turbine to the outletwas kept at 18D. The range of L1 and L2 is given in Table 2.

Fig. 5. Y+ contour around blade.

Fig. 6. Total mesh system including rotational and stationary region.

Table 3Wind farm mesh system information.

Case number Number of nodes Number of elements

Case 1 8,464,891 9,692,058Case 2 8,467,147 9,703,509Case 3 8,466,905 9,700,265Case 4 8,470,774 9,719,918Case 5 8,469,927 9,714,268

3. CFD analysis for the wind farm

The mesh system of the simulated wind farm was divided intotwo parts. One is a rotational mesh system for the rotor, includingthree blades and a hub. The other is a stationary mesh system forthe nacelle, tower and flow field. The rotational mesh system withthe blade surface mesh is shown in Fig. 4. A hexahedral mesh wasused to enhance the convergence characteristics and calculationprecision for the rotational mesh system. Y+ value of the blade isabout 4 except root region of blade as shown in Fig. 5.

The total mesh system, including the rotational and stationaryregions, are shown in Fig. 6 for the representative example of case3. A tetrahedral mesh was used for the stationary mesh system.The mesh density of the rotational region is much higher than thatof the stationary region for a more precise power outputcalculation.

The tilting angle of the 2 MW class wind turbine was set to 51.For tilted rotor, the application of a periodic boundary condition isimpossible. Therefore, mesh generation for the whole wind farmincluding the rotor, nacelle and tower is needed. The mesh systemdetails for the wind farm are given in Table 3.

Steady state analysis was carried out. The boundary conditionsof the wind farm are shown in Fig. 7. With focusing on theaerodynamic power output variation according to separationdistance, uniform inlet wind speed was applied. A rated windspeed of 11 m/s and normal atmospheric pressure were applied tothe inlet and outlet boundary conditions respectively. And inletturbulence intensity is 18%. Symmetry boundary conditions wereapplied to the two sides. A free-slip condition was applied at thetop, based on a no vertical wind speed gradient assumption, and ano-slip condition was applied to the bottom. The rotational regionhad a rated rotational speed of 18.7 rpm. So, the interface was

Fig. 7. Boundary conditions of wind farm.

Table 4Power output and power output ratio.

Case number Wind turbine ID Power output (kW) Power output ratio

Case 1 WT1 2034 35%WT2 715

Case 2 WT1 2055 48%WT2 987

Case 3 WT1 2071 60%WT2 1257

Case 4 WT1 2073 63%WT2 1306

Case 5 WT1 2074 66%WT2 1380

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considered to change the coordinate system between the rota-tional region and the stationary region.

This simulations were used the commercial multi-purpose CFDsolver ANSYS CFX (ver. 12.1) for the wind farm simulation. RANS-based shear stress transport with a transition model (SST model)was selected. The SST model is based on the κ–ω model near thewall. So, the SST model turns out powerful to predict turbulentfrequency in the boundary layer. CFD analysis was carried out foreach of the five cases according to the changes in L1 and L2.

Fig. 8. Power output of downstream wind turbine and power output ratio.

4. Results and discussions

Based on simulation results, the power outputs of the windturbines are given in Table 4. Aerodynamic power output of theeach wind turbine was calculated by multiplying torque andangular velocity of the rotor.

The power output of the downstream wind turbine waschanged with respect to the separation distance between windturbines. This result implies a strong interaction between the windturbines in the wind farm. In theory, a complete recovery of thedownstream wind turbine's power output requires infinite separa-tion distance between wind turbines.

The power output of the upstream wind turbine increasedslightly as the separation distance L1 increased. This is why therewas no incident wind speed change to the upstream wind turbine,and the interaction effect of the downstream turbine on theupstream turbine weakened as separation distance L1 increased.The power output of the downstream wind turbine was changedsignificantly as separation distance L1 was changed from 3D to 5D.The main reason is that the downstream turbine was placed in thestrong wake effect region behind the upstream wind turbine. Thesurprising result is that the power output of the downstream windturbine was 35% compared to the upstream wind turbine whenthe downstream turbine was placed at a distance 3D from theupstream wind turbine. As separation distance L1 increased, thewake effect decreased; then, the axial direction wind speedrecovered and power output finally increased. The recovery ratewas higher in the range of L1 from 3D to 5D. For the range L1 from5D to 7D, the power output change of the downstream windturbine was not significant. Compared to the region L1 from 3D to5D, L1 from 5D to 7D seemed to be a rather weak wake interactionregion. This behavior suggests that a relatively small increase inthe power output of the downstream wind turbine can beexpected even though the separation distance L1 increasedbeyond 7D.

The power output ratio shown in Table 4 is defined as thepower output of the downstream wind turbine divided by thepower output of the upstream turbine. The ratio shows a nonlinearrelationship with respect to the separation distance between windturbines. This is because the wake length from the upstream windturbine was almost constant, but the location of the downstreamwind turbine could be inside or outside the strong wake regionaccording to the separation distance. When the downstream windturbine was placed in the strong wake region of the upstreamwind turbine, the power output of the downstream wind turbinedecreased due to the reduced incident wind speed compared tothe upstream wind speed (Ole Rathmann et al., 2012).

The power output of the downstream wind turbine and thepower output ratio are illustrated in Fig. 8. Both quantities show asimilar nature since the power output change of the upstreamwind turbine was small. As previously discussed, the slopechanges significantly at a separation distance of 5D. This pointcan be chosen as a criterion to divide the strong wake region fromthe weak wake region.

A polynomial curve fit for the power output of the downstreamwind turbine based on the MW unit can be written as

PDWT ¼ 0:019x4−0:385x3 þ 2:743x2−8:063xþ 9:052; ð4Þwhere PDWT is the power output of the downstream wind turbine(MW) and x is the non-dimensional separation distance betweenwind turbines based on rotor diameter D.

It is possible to expand the power output prediction for asimilar case with a different wind turbine capacity using the non-dimensional power output ratio according to separation distance.The power output ratio can be written as

Pratio ¼ 0:007x4−0:141x3 þ 0:998x2−2:884xþ 3:250; ð5Þwhere Pratio is the power output ratio.

Fig. 11. Axial direction wind speed at the hub height for case 3.

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If the rated wind speed is applied, the power output of thedownstreamwind turbine can be calculated by multiplying a givenrated power output of the wind turbine and the power outputratio according to the non-dimensional separation distance.

The axial direction wind speed field for each analysis case atthe hub height is shown in Figs. 9–13, where the wake effect andthe interaction between two turbines are clearly identified(Hansen et al., 2006). For case 4 and 5, the wake effect on thedownstream wind turbine was weaker compared to case 1, 2, and3 since the downstream wind turbine was placed outside thestrong wake region of the upstream wind turbine. The axialdirection wind speed to the downstream wind turbine at thehub height increased as the separation distance increased due tothe recovery of the wind speed. As a result, the power output ofthe downstream wind turbine increased in turn.

An isometric view of the axial direction wind speed at the hubheight is shown in Fig. 14 for the representative example of case 3.The wake from the upstream wind turbine reached the down-stream wind turbine (Emilio Migoyq and Javier, 2007), whichmeans that the incident wind speed to the downstream turbinedecreased and the power output of the downstream turbinedecreased as well.

The pressure distribution and streamlines of the blade pressureside and suction side are shown in Figs. 15 and 16, respectively, for

Fig. 9. Axial direction wind speed at the hub height for case 1.

Fig. 10. Axial direction wind speed at the hub height for case 2.

Fig. 12. Axial direction wind speed at the hub height for the case 4.

Fig. 13. Axial direction wind speed at the hub height for the case 5.

case 3. It is shown that there is a rather uniform pressuredistribution on the blade pressure side compared to that of theblade suction side. The pressure difference for each blade sectioncan contribute to the source of driving torque. The streamlines of

Fig. 14. Isometric view of axial direction wind speed at the hub height for case 3.

Fig. 15. Pressure distribution and streamlines of blade pressure side.

Fig. 16. Pressure distribution and streamlines of blade suction side.

Fig. 17. Turbulence intermittency of wind turbines.

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the blade root region moved to the radial direction due tocentrifugal force and by the pressure difference between the rootregion and outboard region. These streamlines are separated fromthe blade surface by the stall phenomenon.

The wake can affect turbulence intermittency on the down-streamwind turbine blade. The turbulence intermittency is shownin Fig. 17 for the representative example of case 3. The blue colorrepresents the laminar region and the red color represents theturbulent region. The laminar region decreased at the downstreamwind turbine blade compared to the laminar region of theupstream wind turbine blade due to the wake effect.

5. Conclusions

A CFD study of the power output of a tandem arrangement oftwo sets of 2 MW class wind turbines was successfully performedusing a full 3-D wind turbine model. The effect of separationdistance between two turbines was found to be crucial for theconceptual design of a wind farm layout. Surprisingly, the poweroutput of a downstream wind turbine was changed from 35% to66% compared to that of an upstream wind turbine as theseparation distance was changed from 3D to 7D. There was anonlinear relationship between the power ratio and the non-dimensional separation distance. As the separation distanceincreased, the power output of the downstream wind turbineincreased because the wake effect became weaker. Beyond aseparation distance of 5D, the rate of increase in power outputof the downstream wind turbine decreased since the downstreamwind turbine was placed outside the strong wake region of theupstream turbine. Hence, 5D can be a design criterion for theseparation distance of a two-turbine arrangement.

The results of this study can be effectively applied to a windfarm layout design, site evaluation, and power output prediction.CFD analysis of the wind farm with staggered wind turbines,different rotor rotational phases, and elevation differences will becarried out in the future. These results will show quantitativecharacteristics of wind farms.

Acknowledgment

This study was financially supported by the National ResearchFoundation (NRF) of Korea through a Grant funded by the KoreanGovernment no. 2011-0030663), and by the Korea Institute ofEnergy Technology Evaluation and Planning (KETEP) funded by

N.J. Choi et al. / J. Wind Eng. Ind. Aerodyn. 117 (2013) 11–17 17

Ministry of Knowledge Economy nos. 2011201010030-11-2-300,20114010203080.

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