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Numerical study on the horizontal axis turbines arrangement in a wind farm: Effect of separation distance on the turbine aerodynamic power output
J. Wind Eng. Ind. Aerodyn. 117 (2013) 11–17
Contents lists available at SciVerse ScienceDirect
Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Numerical study on the horizontal axis turbines arrangement in a wind farm: Effect of separation distance on the turbine aerodynamic power output Nak Joon Choi a, Sang Hyun Nam b, Jong Hyun Jeong b, Kyung Chun Kim c,n a
Graduate School of Mechanical Engineering, Pusan National University, Busan 609-735, Republic of Korea CFD Business Unit, DNDE Inc., Busan 612-021, Republic of Korea c School of Mechanical Engineering, Pusan National University, Busan 609-735, Republic of Korea b
art ic l e i nf o
a b s t r a c t
Article history: Received 2 October 2012 Received in revised form 14 February 2013 Accepted 7 April 2013 Available online 7 May 2013
This paper presents the results of a computational fluid dynamics (CFD) study of a wind farm with two sets of 2 MW class wind turbines. CFD analysis was calculated by using the commercial multi-purpose CFD solver ANSYS CFX. Blade design and modeling were based on blade element momentum theory. The rotational phase of two wind turbine rotors was synchronized, and the distance between the two wind turbines was changed from three to seven times of the rotor diameter. The tilting angle of the 2 MW class wind turbine was set to 51. A complete wind farm mesh is generated including the rotor, nacelle and tower. The results showed that there was a power output difference due to the wake effect between two wind turbines. The power output of the downstream wind turbine was changed with respect to the separation distance between wind turbines. The optimal compromise between wind farm construction cost, 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 output prediction. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Wind farm CFD Wake Power output Separation distance Interaction
1. Introduction Wind energy is a promising renewable energy resource to help overcome global warming and environmental pollution from the use of fossil fuel (Kiranoudis et al., 2001). Wind farms composed of large capacity wind turbines will become a main electrical energy source (Abderrazzaq and Hahn., 2006; Abderrazzaq., 2004). As wind turbines become larger, wind farm layout design becomes more important (Gonzalez et al., 2010). Among several wind farm layout design factors, wind turbine arrangement according to separation distance is one of the most critical factors for power output, annual energy production, availability, and lifetime of the wind turbine. Therefore, during wind farm layout design, separation distance and interaction between wind turbines must be carefully considered because they are directly connected to the initial investment cost, payback period and economic efficiency. To study aerodynamic power output of the 2 MW class wind turbine according to separation distance, an experimental method is unrealistic because of the high cost required and length of time involved. The computational fluid dynamics (CFD) approach can be
n
Corresponding author. Tel.: +82 51 510 2324; fax: +82 51 515 7866. E-mail address: [email protected] (K. Chun Kim).
0167-6105/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jweia.2013.04.005
successfully applied with minimum cost and time compared to the experimental method (Christiane Montavon and Jones, 2009). Before computer resources reached an adequate level, it was only possible to analyze a wind farm with an actuator disk, momentum source, and rather coarse elements, as used in previous wind farm CFD study results with various limitations (Sten et al., 2004). Due to the rapid development of computer resources, it is now possible to analyze an entire wind farm and evaluate sites with a full threedimensional (3-D) wind turbine model, as used in this wind farm CFD analysis. To the best of knowledge, no research has been reported in the literature that describes a CFD wind farm analysis using a full wind turbine model. The electrical power output of a horizontal axis wind turbine is proportional to the square of the rotor diameter and the cube of the wind speed. This behavior reflects a tendency toward larger scale wind turbines. The electrical power output of a wind turbine at the generator terminal can be written as P gen ¼
1 ρAV 3 ηC p ; 2
ð1Þ
where P gen 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), η is the overall efficiency and C p is the power coefficient.
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N.J. Choi et al. / J. Wind Eng. Ind. Aerodyn. 117 (2013) 11–17
The power coefficient can be written as Cp ¼
P ð1=2ÞρAV 3
;
ð2Þ
where P is the aerodynamic power output (hereafter called “power output”). The power coefficients of each wind turbine are not the same due to different power outputs resulting from different incident wind speeds. For a wind farm, the annual energy production is very important because it is directly connected to income from the sale of electricity. It is also affected by other factors such as separation distance and interaction. The annual energy production AEP can be written as AEP ¼ 24 365 Nf l ∑½P V pðV Þ;
ð3Þ
where N is the number of wind turbines, f l is the overall loss factor including separation distance and interaction effects, P V is the wind turbine power output according to wind speed (W) and pðV Þ is the Weibull distribution at the hub height. The tilted rotor, nacelle and tower must be considered to simulate an actual wind turbine. The power output of a downstream wind turbine may depend on the separation distance and the wake from the upstream wind turbine. In the wake region, a wind turbine is under a more severe environment, which could result in increased fatigue, which is a cause of decreased wind turbine lifetime and potential trouble sources. In theory, complete recovery of the power output of a downstream wind turbine requires an infinite separation distance between wind turbines. If enough separation distance is secured for the enhancement of the power output of a downstream wind turbine, more transmission cable is required and the cable laying cost rises. If insufficient separation distance is used to save cable and cable laying cost, annual energy production is reduced and there is a risk of fatigue problems due to the wake (Quarton., 1998). Therefore, an optimal compromise between cost, fatigue and annual energy production with respect to the separation distance between wind turbines is crucial. For this study, a 2 MW class wind turbine was designed and modeled with a tilted rotor, nacelle and tower. Based on a full 3-D wind turbine model, CFD analysis was performed to characterize power output according to the wind turbine separation distance.
Fig. 1. 2 MW class wind turbine, front view (left) and side view (right).
2. MW class wind turbine and wind farm In the design of a 4 MW wind farm, two sets of 2 MW class wind turbines were used. Wind turbine blade design software called XD-BLADE, developed by Choi et al., is based on blade element momentum theory and was used for blade design (Choi et al., 2010). The main specifications of 2 MW class wind turbine are given in Table 1 (Bum-Suk Kim et al., 2009). The proposed wind turbine is shown in Fig. 1. The rotational direction of the rotor is clockwise. The arrangement and identification of the wind turbines are shown in Fig. 2. The rotational phase of each wind turbine is synchronized. The wind farm Table 1 Main specifications of 2 MW class wind turbine. Item
Value
Rotor diameter (m) Rated rotational speed (rpm) Tilting angle (1) Rated wind speed (m/s) Rated power output (kW) Tip speed ratio Hub height (m)
84.2 18.7 5 11 2000 7.5 85.2 Fig. 2. Arrangement and identification of wind turbines.
N.J. Choi et al. / J. Wind Eng. Ind. Aerodyn. 117 (2013) 11–17
13
Fig. 3. Wind farm configuration.
Fig. 4. Rotational mesh system (left) with blade surface mesh (right). Table 2 Range of L1 and L2. Case number
L1
L2
case case case case case
3D 4D 5D 6D 7D
28D 29D 30D 31D 32D
1 2 3 4 5
configuration is shown in Fig. 3. All distances were based on the rotor diameter D. The distance from the inlet to the upstream wind turbine is 7D. L1 and L2 were changed from 3D to 7D and 28D to 32D respectively for the CFD analysis according to separation distance change. The height of the wind farm flow field is 6D, and the distance from the downstream wind turbine to the outlet was kept at 18D. The range of L1 and L2 is given in Table 2.
3. CFD analysis for the wind farm The mesh system of the simulated wind farm was divided into two parts. One is a rotational mesh system for the rotor, including three blades and a hub. The other is a stationary mesh system for the nacelle, tower and flow field. The rotational mesh system with the blade surface mesh is shown in Fig. 4. A hexahedral mesh was used to enhance the convergence characteristics and calculation precision for the rotational mesh system. Y+ value of the blade is about 4 except root region of blade as shown in Fig. 5. The total mesh system, including the rotational and stationary regions, are shown in Fig. 6 for the representative example of case 3. A tetrahedral mesh was used for the stationary mesh system. The mesh density of the rotational region is much higher than that of the stationary region for a more precise power output calculation. The tilting angle of the 2 MW class wind turbine was set to 51. For tilted rotor, the application of a periodic boundary condition is impossible. Therefore, mesh generation for the whole wind farm including the rotor, nacelle and tower is needed. The mesh system details for the wind farm are given in Table 3. Steady state analysis was carried out. The boundary conditions of the wind farm are shown in Fig. 7. With focusing on the aerodynamic power output variation according to separation distance, uniform inlet wind speed was applied. A rated wind speed of 11 m/s and normal atmospheric pressure were applied to the inlet and outlet boundary conditions respectively. And inlet turbulence intensity is 18%. Symmetry boundary conditions were applied to the two sides. A free-slip condition was applied at the top, based on a no vertical wind speed gradient assumption, and a no-slip condition was applied to the bottom. The rotational region had a rated rotational speed of 18.7 rpm. So, the interface was
Fig. 5. Y+ contour around blade.
Fig. 6. Total mesh system including rotational and stationary region.
Table 3 Wind farm mesh system information. Case number
Number of nodes
Number of elements
Case Case Case Case Case
8,464,891 8,467,147 8,466,905 8,470,774 8,469,927
9,692,058 9,703,509 9,700,265 9,719,918 9,714,268
1 2 3 4 5
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N.J. Choi et al. / J. Wind Eng. Ind. Aerodyn. 117 (2013) 11–17
Table 4 Power output and power output ratio. Case number
Wind turbine ID
Power output (kW)
Power output ratio
Case 1
WT1 WT2 WT1 WT2 WT1 WT2 WT1 WT2 WT1 WT2
2034 715 2055 987 2071 1257 2073 1306 2074 1380
35%
Case 2 Case 3 Case 4 Case 5
48% 60% 63% 66%
Fig. 7. Boundary conditions of wind farm.
considered to change the coordinate system between the rotational region and the stationary region. This simulations were used the commercial multi-purpose CFD solver ANSYS CFX (ver. 12.1) for the wind farm simulation. RANSbased shear stress transport with a transition model (SST model) was selected. The SST model is based on the κ–ω model near the wall. So, the SST model turns out powerful to predict turbulent frequency in the boundary layer. CFD analysis was carried out for each of the five cases according to the changes in L1 and L2.
4. Results and discussions Based on simulation results, the power outputs of the wind turbines are given in Table 4. Aerodynamic power output of the each wind turbine was calculated by multiplying torque and angular velocity of the rotor. The power output of the downstream wind turbine was changed with respect to the separation distance between wind turbines. This result implies a strong interaction between the wind turbines in the wind farm. In theory, a complete recovery of the downstream wind turbine's power output requires infinite separation distance between wind turbines. The power output of the upstream wind turbine increased slightly as the separation distance L1 increased. This is why there was no incident wind speed change to the upstream wind turbine, and the interaction effect of the downstream turbine on the upstream turbine weakened as separation distance L1 increased. The power output of the downstream wind turbine was changed significantly as separation distance L1 was changed from 3D to 5D. The main reason is that the downstream turbine was placed in the strong wake effect region behind the upstream wind turbine. The surprising result is that the power output of the downstream wind turbine was 35% compared to the upstream wind turbine when the downstream turbine was placed at a distance 3D from the upstream wind turbine. As separation distance L1 increased, the wake effect decreased; then, the axial direction wind speed recovered and power output finally increased. The recovery rate was higher in the range of L1 from 3D to 5D. For the range L1 from 5D to 7D, the power output change of the downstream wind turbine was not significant. Compared to the region L1 from 3D to 5D, L1 from 5D to 7D seemed to be a rather weak wake interaction region. This behavior suggests that a relatively small increase in the power output of the downstream wind turbine can be expected even though the separation distance L1 increased beyond 7D.
Fig. 8. Power output of downstream wind turbine and power output ratio.
The power output ratio shown in Table 4 is defined as the power output of the downstream wind turbine divided by the power output of the upstream turbine. The ratio shows a nonlinear relationship with respect to the separation distance between wind turbines. This is because the wake length from the upstream wind turbine was almost constant, but the location of the downstream wind turbine could be inside or outside the strong wake region according to the separation distance. When the downstream wind turbine was placed in the strong wake region of the upstream wind turbine, the power output of the downstream wind turbine decreased due to the reduced incident wind speed compared to the upstream wind speed (Ole Rathmann et al., 2012). The power output of the downstream wind turbine and the power output ratio are illustrated in Fig. 8. Both quantities show a similar nature since the power output change of the upstream wind turbine was small. As previously discussed, the slope changes significantly at a separation distance of 5D. This point can be chosen as a criterion to divide the strong wake region from the weak wake region. A polynomial curve fit for the power output of the downstream wind turbine based on the MW unit can be written as P DWT ¼ 0:019x4 −0:385x3 þ 2:743x2 −8:063x þ 9:052;
ð4Þ
where P DWT is the power output of the downstream wind turbine (MW) and x is the non-dimensional separation distance between wind turbines based on rotor diameter D. It is possible to expand the power output prediction for a similar case with a different wind turbine capacity using the nondimensional power output ratio according to separation distance. The power output ratio can be written as P ratio ¼ 0:007x4 −0:141x3 þ 0:998x2 −2:884x þ 3:250; where P ratio is the power output ratio.
ð5Þ
N.J. Choi et al. / J. Wind Eng. Ind. Aerodyn. 117 (2013) 11–17
If the rated wind speed is applied, the power output of the downstream wind turbine can be calculated by multiplying a given rated power output of the wind turbine and the power output ratio according to the non-dimensional separation distance. The axial direction wind speed field for each analysis case at the hub height is shown in Figs. 9–13, where the wake effect and the interaction between two turbines are clearly identified (Hansen et al., 2006). For case 4 and 5, the wake effect on the downstream wind turbine was weaker compared to case 1, 2, and 3 since the downstream wind turbine was placed outside the strong wake region of the upstream wind turbine. The axial direction wind speed to the downstream wind turbine at the hub height increased as the separation distance increased due to the recovery of the wind speed. As a result, the power output of the downstream wind turbine increased in turn. An isometric view of the axial direction wind speed at the hub height is shown in Fig. 14 for the representative example of case 3. The wake from the upstream wind turbine reached the downstream wind turbine (Emilio Migoyq and Javier, 2007), which means that the incident wind speed to the downstream turbine decreased and the power output of the downstream turbine decreased as well. The pressure distribution and streamlines of the blade pressure side and suction side are shown in Figs. 15 and 16, respectively, for
15
Fig. 11. Axial direction wind speed at the hub height for case 3.
Fig. 12. Axial direction wind speed at the hub height for the case 4.
Fig. 9. Axial direction wind speed at the hub height for case 1.
Fig. 13. Axial direction wind speed at the hub height for the case 5.
Fig. 10. Axial direction wind speed at the hub height for case 2.
case 3. It is shown that there is a rather uniform pressure distribution on the blade pressure side compared to that of the blade suction side. The pressure difference for each blade section can contribute to the source of driving torque. The streamlines of
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N.J. Choi et al. / J. Wind Eng. Ind. Aerodyn. 117 (2013) 11–17
Fig. 14. Isometric view of axial direction wind speed at the hub height for case 3.
Fig. 17. Turbulence intermittency of wind turbines.
The wake can affect turbulence intermittency on the downstream wind turbine blade. The turbulence intermittency is shown in Fig. 17 for the representative example of case 3. The blue color represents the laminar region and the red color represents the turbulent region. The laminar region decreased at the downstream wind turbine blade compared to the laminar region of the upstream wind turbine blade due to the wake effect.
5. Conclusions
Fig. 15. Pressure distribution and streamlines of blade pressure side.
Fig. 16. Pressure distribution and streamlines of blade suction side.
the blade root region moved to the radial direction due to centrifugal force and by the pressure difference between the root region and outboard region. These streamlines are separated from the blade surface by the stall phenomenon.
A CFD study of the power output of a tandem arrangement of two sets of 2 MW class wind turbines was successfully performed using a full 3-D wind turbine model. The effect of separation distance between two turbines was found to be crucial for the conceptual design of a wind farm layout. Surprisingly, the power output of a downstream wind turbine was changed from 35% to 66% compared to that of an upstream wind turbine as the separation distance was changed from 3D to 7D. There was a nonlinear relationship between the power ratio and the nondimensional separation distance. As the separation distance increased, the power output of the downstream wind turbine increased because the wake effect became weaker. Beyond a separation distance of 5D, the rate of increase in power output of the downstream wind turbine decreased since the downstream wind turbine was placed outside the strong wake region of the upstream turbine. Hence, 5D can be a design criterion for the separation distance of a two-turbine arrangement. The results of this study can be effectively applied to a wind farm 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 be carried out in the future. These results will show quantitative characteristics of wind farms.
Acknowledgment This study was financially supported by the National Research Foundation (NRF) of Korea through a Grant funded by the Korean Government no. 2011-0030663), and by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) funded by
N.J. Choi et al. / J. Wind Eng. Ind. Aerodyn. 117 (2013) 11–17
Ministry of Knowledge Economy nos. 2011201010030-11-2-300, 20114010203080. References Abderrazzaq, M.A., Hahn., B., 2006. Analysis of the turbine standstill for a grid connected wind farm (case study). Renewable Energy 31, 89–104. Abderrazzaq., M.H., 2004. Energy production assessment of small wind farms. Renewable Energy 29, 2261–2272. Bum-Suk Kim, Hark-Jin Eum, Mann-Eung Kim, et al. 2009. Unidirectional fluid structure interaction simulation of a 2 mw wind turbine blade. World Wind Energy Conference. S46_1. Choi, N.J., Kim, J.S., Lee, S.M., 2010. Development and application of XD-BLADE software for the horizontal axis wind turbine blade design. KWEA Spring Conference. pp.261–266. Christiane Montavon, Ian Jones, Chris Staples, et al., 2009 Practical Issues In The Use Of Cfd For Modelling Wind Farms. European Wind Energy Conference.
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Emilio Migoyq, Antonio Crespo, Javier, Garcia, 2007. Comparative study of the behavior of wind-turbines in a wind farm. Energy, 1871–1885. Sten Frandsen, Rebecca Barthelmie, Sara Pryor, et al., 2004, Analytical modeling of wind speed deficit in large offshore wind farms. European Wind Energy Conference. Gonzalez, Javier Serrano, Gonzalez, Angel G., Mora, Jose Castro, et al., 2010. Optimization of wind farm turbines layout using an evolutive algorithm. Renewable Energy 35, 1671–1681. Hansen, M.O.L., Sorensen, J.N., Voutsinas, S., et al., 2006. State of the art in wind turbine aerodynamics and aeroelasticity. Progress in Aerospace Sciences 42, 285–330. Kiranoudis, C.T., Voros, N.G., Maroulis., Z.B., 2001. Short-cut design of wind farms. Energy Policy 29, 567–578. Ole Rathmann, Sten Frandsen, Rebecca Barthelmie, 2007. Wake modelling for intermediate and large wind farms. European Wind Energy Conference. Paper BL3.199. Quarton., D.C., 1998. The evolution of wind turbine design analysis—a twenty year progress review. Wind Energy 1, 5–24.
Contents lists available at SciVerse ScienceDirect
Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Numerical study on the horizontal axis turbines arrangement in a wind farm: Effect of separation distance on the turbine aerodynamic power output Nak Joon Choi a, Sang Hyun Nam b, Jong Hyun Jeong b, Kyung Chun Kim c,n a
Graduate School of Mechanical Engineering, Pusan National University, Busan 609-735, Republic of Korea CFD Business Unit, DNDE Inc., Busan 612-021, Republic of Korea c School of Mechanical Engineering, Pusan National University, Busan 609-735, Republic of Korea b
art ic l e i nf o
a b s t r a c t
Article history: Received 2 October 2012 Received in revised form 14 February 2013 Accepted 7 April 2013 Available online 7 May 2013
This paper presents the results of a computational fluid dynamics (CFD) study of a wind farm with two sets of 2 MW class wind turbines. CFD analysis was calculated by using the commercial multi-purpose CFD solver ANSYS CFX. Blade design and modeling were based on blade element momentum theory. The rotational phase of two wind turbine rotors was synchronized, and the distance between the two wind turbines was changed from three to seven times of the rotor diameter. The tilting angle of the 2 MW class wind turbine was set to 51. A complete wind farm mesh is generated including the rotor, nacelle and tower. The results showed that there was a power output difference due to the wake effect between two wind turbines. The power output of the downstream wind turbine was changed with respect to the separation distance between wind turbines. The optimal compromise between wind farm construction cost, 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 output prediction. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Wind farm CFD Wake Power output Separation distance Interaction
1. Introduction Wind energy is a promising renewable energy resource to help overcome global warming and environmental pollution from the use of fossil fuel (Kiranoudis et al., 2001). Wind farms composed of large capacity wind turbines will become a main electrical energy source (Abderrazzaq and Hahn., 2006; Abderrazzaq., 2004). As wind turbines become larger, wind farm layout design becomes more important (Gonzalez et al., 2010). Among several wind farm layout design factors, wind turbine arrangement according to separation distance is one of the most critical factors for power output, annual energy production, availability, and lifetime of the wind turbine. Therefore, during wind farm layout design, separation distance and interaction between wind turbines must be carefully considered because they are directly connected to the initial investment cost, payback period and economic efficiency. To study aerodynamic power output of the 2 MW class wind turbine according to separation distance, an experimental method is unrealistic because of the high cost required and length of time involved. The computational fluid dynamics (CFD) approach can be
n
Corresponding author. Tel.: +82 51 510 2324; fax: +82 51 515 7866. E-mail address: [email protected] (K. Chun Kim).
0167-6105/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jweia.2013.04.005
successfully applied with minimum cost and time compared to the experimental method (Christiane Montavon and Jones, 2009). Before computer resources reached an adequate level, it was only possible to analyze a wind farm with an actuator disk, momentum source, and rather coarse elements, as used in previous wind farm CFD study results with various limitations (Sten et al., 2004). Due to the rapid development of computer resources, it is now possible to analyze an entire wind farm and evaluate sites with a full threedimensional (3-D) wind turbine model, as used in this wind farm CFD analysis. To the best of knowledge, no research has been reported in the literature that describes a CFD wind farm analysis using a full wind turbine model. The electrical power output of a horizontal axis wind turbine is proportional to the square of the rotor diameter and the cube of the wind speed. This behavior reflects a tendency toward larger scale wind turbines. The electrical power output of a wind turbine at the generator terminal can be written as P gen ¼
1 ρAV 3 ηC p ; 2
ð1Þ
where P gen 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), η is the overall efficiency and C p is the power coefficient.
12
N.J. Choi et al. / J. Wind Eng. Ind. Aerodyn. 117 (2013) 11–17
The power coefficient can be written as Cp ¼
P ð1=2ÞρAV 3
;
ð2Þ
where P is the aerodynamic power output (hereafter called “power output”). The power coefficients of each wind turbine are not the same due to different power outputs resulting from different incident wind speeds. For a wind farm, the annual energy production is very important because it is directly connected to income from the sale of electricity. It is also affected by other factors such as separation distance and interaction. The annual energy production AEP can be written as AEP ¼ 24 365 Nf l ∑½P V pðV Þ;
ð3Þ
where N is the number of wind turbines, f l is the overall loss factor including separation distance and interaction effects, P V is the wind turbine power output according to wind speed (W) and pðV Þ is the Weibull distribution at the hub height. The tilted rotor, nacelle and tower must be considered to simulate an actual wind turbine. The power output of a downstream wind turbine may depend on the separation distance and the wake from the upstream wind turbine. In the wake region, a wind turbine is under a more severe environment, which could result in increased fatigue, which is a cause of decreased wind turbine lifetime and potential trouble sources. In theory, complete recovery of the power output of a downstream wind turbine requires an infinite separation distance between wind turbines. If enough separation distance is secured for the enhancement of the power output of a downstream wind turbine, more transmission cable is required and the cable laying cost rises. If insufficient separation distance is used to save cable and cable laying cost, annual energy production is reduced and there is a risk of fatigue problems due to the wake (Quarton., 1998). Therefore, an optimal compromise between cost, fatigue and annual energy production with respect to the separation distance between wind turbines is crucial. For this study, a 2 MW class wind turbine was designed and modeled with a tilted rotor, nacelle and tower. Based on a full 3-D wind turbine model, CFD analysis was performed to characterize power output according to the wind turbine separation distance.
Fig. 1. 2 MW class wind turbine, front view (left) and side view (right).
2. MW class wind turbine and wind farm In the design of a 4 MW wind farm, two sets of 2 MW class wind turbines were used. Wind turbine blade design software called XD-BLADE, developed by Choi et al., is based on blade element momentum theory and was used for blade design (Choi et al., 2010). The main specifications of 2 MW class wind turbine are given in Table 1 (Bum-Suk Kim et al., 2009). The proposed wind turbine is shown in Fig. 1. The rotational direction of the rotor is clockwise. The arrangement and identification of the wind turbines are shown in Fig. 2. The rotational phase of each wind turbine is synchronized. The wind farm Table 1 Main specifications of 2 MW class wind turbine. Item
Value
Rotor diameter (m) Rated rotational speed (rpm) Tilting angle (1) Rated wind speed (m/s) Rated power output (kW) Tip speed ratio Hub height (m)
84.2 18.7 5 11 2000 7.5 85.2 Fig. 2. Arrangement and identification of wind turbines.
N.J. Choi et al. / J. Wind Eng. Ind. Aerodyn. 117 (2013) 11–17
13
Fig. 3. Wind farm configuration.
Fig. 4. Rotational mesh system (left) with blade surface mesh (right). Table 2 Range of L1 and L2. Case number
L1
L2
case case case case case
3D 4D 5D 6D 7D
28D 29D 30D 31D 32D
1 2 3 4 5
configuration is shown in Fig. 3. All distances were based on the rotor diameter D. The distance from the inlet to the upstream wind turbine is 7D. L1 and L2 were changed from 3D to 7D and 28D to 32D respectively for the CFD analysis according to separation distance change. The height of the wind farm flow field is 6D, and the distance from the downstream wind turbine to the outlet was kept at 18D. The range of L1 and L2 is given in Table 2.
3. CFD analysis for the wind farm The mesh system of the simulated wind farm was divided into two parts. One is a rotational mesh system for the rotor, including three blades and a hub. The other is a stationary mesh system for the nacelle, tower and flow field. The rotational mesh system with the blade surface mesh is shown in Fig. 4. A hexahedral mesh was used to enhance the convergence characteristics and calculation precision for the rotational mesh system. Y+ value of the blade is about 4 except root region of blade as shown in Fig. 5. The total mesh system, including the rotational and stationary regions, are shown in Fig. 6 for the representative example of case 3. A tetrahedral mesh was used for the stationary mesh system. The mesh density of the rotational region is much higher than that of the stationary region for a more precise power output calculation. The tilting angle of the 2 MW class wind turbine was set to 51. For tilted rotor, the application of a periodic boundary condition is impossible. Therefore, mesh generation for the whole wind farm including the rotor, nacelle and tower is needed. The mesh system details for the wind farm are given in Table 3. Steady state analysis was carried out. The boundary conditions of the wind farm are shown in Fig. 7. With focusing on the aerodynamic power output variation according to separation distance, uniform inlet wind speed was applied. A rated wind speed of 11 m/s and normal atmospheric pressure were applied to the inlet and outlet boundary conditions respectively. And inlet turbulence intensity is 18%. Symmetry boundary conditions were applied to the two sides. A free-slip condition was applied at the top, based on a no vertical wind speed gradient assumption, and a no-slip condition was applied to the bottom. The rotational region had a rated rotational speed of 18.7 rpm. So, the interface was
Fig. 5. Y+ contour around blade.
Fig. 6. Total mesh system including rotational and stationary region.
Table 3 Wind farm mesh system information. Case number
Number of nodes
Number of elements
Case Case Case Case Case
8,464,891 8,467,147 8,466,905 8,470,774 8,469,927
9,692,058 9,703,509 9,700,265 9,719,918 9,714,268
1 2 3 4 5
14
N.J. Choi et al. / J. Wind Eng. Ind. Aerodyn. 117 (2013) 11–17
Table 4 Power output and power output ratio. Case number
Wind turbine ID
Power output (kW)
Power output ratio
Case 1
WT1 WT2 WT1 WT2 WT1 WT2 WT1 WT2 WT1 WT2
2034 715 2055 987 2071 1257 2073 1306 2074 1380
35%
Case 2 Case 3 Case 4 Case 5
48% 60% 63% 66%
Fig. 7. Boundary conditions of wind farm.
considered to change the coordinate system between the rotational region and the stationary region. This simulations were used the commercial multi-purpose CFD solver ANSYS CFX (ver. 12.1) for the wind farm simulation. RANSbased shear stress transport with a transition model (SST model) was selected. The SST model is based on the κ–ω model near the wall. So, the SST model turns out powerful to predict turbulent frequency in the boundary layer. CFD analysis was carried out for each of the five cases according to the changes in L1 and L2.
4. Results and discussions Based on simulation results, the power outputs of the wind turbines are given in Table 4. Aerodynamic power output of the each wind turbine was calculated by multiplying torque and angular velocity of the rotor. The power output of the downstream wind turbine was changed with respect to the separation distance between wind turbines. This result implies a strong interaction between the wind turbines in the wind farm. In theory, a complete recovery of the downstream wind turbine's power output requires infinite separation distance between wind turbines. The power output of the upstream wind turbine increased slightly as the separation distance L1 increased. This is why there was no incident wind speed change to the upstream wind turbine, and the interaction effect of the downstream turbine on the upstream turbine weakened as separation distance L1 increased. The power output of the downstream wind turbine was changed significantly as separation distance L1 was changed from 3D to 5D. The main reason is that the downstream turbine was placed in the strong wake effect region behind the upstream wind turbine. The surprising result is that the power output of the downstream wind turbine was 35% compared to the upstream wind turbine when the downstream turbine was placed at a distance 3D from the upstream wind turbine. As separation distance L1 increased, the wake effect decreased; then, the axial direction wind speed recovered and power output finally increased. The recovery rate was higher in the range of L1 from 3D to 5D. For the range L1 from 5D to 7D, the power output change of the downstream wind turbine was not significant. Compared to the region L1 from 3D to 5D, L1 from 5D to 7D seemed to be a rather weak wake interaction region. This behavior suggests that a relatively small increase in the power output of the downstream wind turbine can be expected even though the separation distance L1 increased beyond 7D.
Fig. 8. Power output of downstream wind turbine and power output ratio.
The power output ratio shown in Table 4 is defined as the power output of the downstream wind turbine divided by the power output of the upstream turbine. The ratio shows a nonlinear relationship with respect to the separation distance between wind turbines. This is because the wake length from the upstream wind turbine was almost constant, but the location of the downstream wind turbine could be inside or outside the strong wake region according to the separation distance. When the downstream wind turbine was placed in the strong wake region of the upstream wind turbine, the power output of the downstream wind turbine decreased due to the reduced incident wind speed compared to the upstream wind speed (Ole Rathmann et al., 2012). The power output of the downstream wind turbine and the power output ratio are illustrated in Fig. 8. Both quantities show a similar nature since the power output change of the upstream wind turbine was small. As previously discussed, the slope changes significantly at a separation distance of 5D. This point can be chosen as a criterion to divide the strong wake region from the weak wake region. A polynomial curve fit for the power output of the downstream wind turbine based on the MW unit can be written as P DWT ¼ 0:019x4 −0:385x3 þ 2:743x2 −8:063x þ 9:052;
ð4Þ
where P DWT is the power output of the downstream wind turbine (MW) and x is the non-dimensional separation distance between wind turbines based on rotor diameter D. It is possible to expand the power output prediction for a similar case with a different wind turbine capacity using the nondimensional power output ratio according to separation distance. The power output ratio can be written as P ratio ¼ 0:007x4 −0:141x3 þ 0:998x2 −2:884x þ 3:250; where P ratio is the power output ratio.
ð5Þ
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If the rated wind speed is applied, the power output of the downstream wind turbine can be calculated by multiplying a given rated power output of the wind turbine and the power output ratio according to the non-dimensional separation distance. The axial direction wind speed field for each analysis case at the hub height is shown in Figs. 9–13, where the wake effect and the interaction between two turbines are clearly identified (Hansen et al., 2006). For case 4 and 5, the wake effect on the downstream wind turbine was weaker compared to case 1, 2, and 3 since the downstream wind turbine was placed outside the strong wake region of the upstream wind turbine. The axial direction wind speed to the downstream wind turbine at the hub height increased as the separation distance increased due to the recovery of the wind speed. As a result, the power output of the downstream wind turbine increased in turn. An isometric view of the axial direction wind speed at the hub height is shown in Fig. 14 for the representative example of case 3. The wake from the upstream wind turbine reached the downstream wind turbine (Emilio Migoyq and Javier, 2007), which means that the incident wind speed to the downstream turbine decreased and the power output of the downstream turbine decreased as well. The pressure distribution and streamlines of the blade pressure side and suction side are shown in Figs. 15 and 16, respectively, for
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Fig. 11. Axial direction wind speed at the hub height for case 3.
Fig. 12. Axial direction wind speed at the hub height for the case 4.
Fig. 9. Axial direction wind speed at the hub height for case 1.
Fig. 13. Axial direction wind speed at the hub height for the case 5.
Fig. 10. Axial direction wind speed at the hub height for case 2.
case 3. It is shown that there is a rather uniform pressure distribution on the blade pressure side compared to that of the blade suction side. The pressure difference for each blade section can contribute to the source of driving torque. The streamlines of
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Fig. 14. Isometric view of axial direction wind speed at the hub height for case 3.
Fig. 17. Turbulence intermittency of wind turbines.
The wake can affect turbulence intermittency on the downstream wind turbine blade. The turbulence intermittency is shown in Fig. 17 for the representative example of case 3. The blue color represents the laminar region and the red color represents the turbulent region. The laminar region decreased at the downstream wind turbine blade compared to the laminar region of the upstream wind turbine blade due to the wake effect.
5. Conclusions
Fig. 15. Pressure distribution and streamlines of blade pressure side.
Fig. 16. Pressure distribution and streamlines of blade suction side.
the blade root region moved to the radial direction due to centrifugal force and by the pressure difference between the root region and outboard region. These streamlines are separated from the blade surface by the stall phenomenon.
A CFD study of the power output of a tandem arrangement of two sets of 2 MW class wind turbines was successfully performed using a full 3-D wind turbine model. The effect of separation distance between two turbines was found to be crucial for the conceptual design of a wind farm layout. Surprisingly, the power output of a downstream wind turbine was changed from 35% to 66% compared to that of an upstream wind turbine as the separation distance was changed from 3D to 7D. There was a nonlinear relationship between the power ratio and the nondimensional separation distance. As the separation distance increased, the power output of the downstream wind turbine increased because the wake effect became weaker. Beyond a separation distance of 5D, the rate of increase in power output of the downstream wind turbine decreased since the downstream wind turbine was placed outside the strong wake region of the upstream turbine. Hence, 5D can be a design criterion for the separation distance of a two-turbine arrangement. The results of this study can be effectively applied to a wind farm 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 be carried out in the future. These results will show quantitative characteristics of wind farms.
Acknowledgment This study was financially supported by the National Research Foundation (NRF) of Korea through a Grant funded by the Korean Government no. 2011-0030663), and by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) funded by
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Ministry of Knowledge Economy nos. 2011201010030-11-2-300, 20114010203080. References Abderrazzaq, M.A., Hahn., B., 2006. Analysis of the turbine standstill for a grid connected wind farm (case study). Renewable Energy 31, 89–104. Abderrazzaq., M.H., 2004. Energy production assessment of small wind farms. Renewable Energy 29, 2261–2272. Bum-Suk Kim, Hark-Jin Eum, Mann-Eung Kim, et al. 2009. Unidirectional fluid structure interaction simulation of a 2 mw wind turbine blade. World Wind Energy Conference. S46_1. Choi, N.J., Kim, J.S., Lee, S.M., 2010. Development and application of XD-BLADE software for the horizontal axis wind turbine blade design. KWEA Spring Conference. pp.261–266. Christiane Montavon, Ian Jones, Chris Staples, et al., 2009 Practical Issues In The Use Of Cfd For Modelling Wind Farms. European Wind Energy Conference.
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Emilio Migoyq, Antonio Crespo, Javier, Garcia, 2007. Comparative study of the behavior of wind-turbines in a wind farm. Energy, 1871–1885. Sten Frandsen, Rebecca Barthelmie, Sara Pryor, et al., 2004, Analytical modeling of wind speed deficit in large offshore wind farms. European Wind Energy Conference. Gonzalez, Javier Serrano, Gonzalez, Angel G., Mora, Jose Castro, et al., 2010. Optimization of wind farm turbines layout using an evolutive algorithm. Renewable Energy 35, 1671–1681. Hansen, M.O.L., Sorensen, J.N., Voutsinas, S., et al., 2006. State of the art in wind turbine aerodynamics and aeroelasticity. Progress in Aerospace Sciences 42, 285–330. Kiranoudis, C.T., Voros, N.G., Maroulis., Z.B., 2001. Short-cut design of wind farms. Energy Policy 29, 567–578. Ole Rathmann, Sten Frandsen, Rebecca Barthelmie, 2007. Wake modelling for intermediate and large wind farms. European Wind Energy Conference. Paper BL3.199. Quarton., D.C., 1998. The evolution of wind turbine design analysis—a twenty year progress review. Wind Energy 1, 5–24.