Investigating the influence of dimensional scaling on

Renewable Energy 97 (2016) 162e168

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Renewable Energy journal homepage: www.elsevier.com/locate/renene

Investigating the influence of dimensional scaling on aerodynamic characteristics of wind turbine using CFD simulation Mohammad Hossein Giahi, Ali Jafarian Dehkordi* School of Mechanical Engineering, Tarbiat Modares University, Jalal Ale Ahmad Highway, Tehran, P.O. Box: 14115-143, Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 14 October 2015 Received in revised form 10 April 2016 Accepted 16 May 2016

Wind turbines are used in a variety of applications with different performance requirements. Investigating the influence of scaling on wind turbine characteristics can pave the way to utilize the experience gained from a smaller turbine for a larger one. In this paper, the effects of wind turbine size on aerodynamic characteristics of a rotor blade are examined using CFD simulation. NREL phase VI wind turbine rotor was simulated in order to validate the results and ensure the accuracy of the CFD model. A 2 MW wind turbine was then chosen as a large turbine and a scaled down model of its rotor was simulated numerically. The results of the simulation were introduced to Similarity Theory relations in order to predict the aerodynamic characteristics of the 2 MW wind turbine. The 2 MW turbine was also simulated and the results of the simulation were compared to predictions of Similarity Theory. It was observed that the results of the simulation completely follow the values predicted by Similarity Theory. Both Similarity Theory predictions and simulation results demonstrated that the torque increases with the cube of change in rotor diameter whereas the thrust value and aerodynamic forces grow with the square of change in diameter. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Wind turbine simulation Computational fluid dynamics Scaling Aerodynamics

1. Introduction Environmental concern in accordance with fossil fuel exhaustion has made wind energy one of the most widely accepted energy resources. Although analyzing the market shows continuous upscaling of wind turbines, there are still several challenges in technical and economic feasibility of these large scale machines. If the experience gained from the smaller turbine could be used for a larger one, cost can be reduced such that enhancement does not have to start from the first step. It is also useful to test a scaleddown model in a wind tunnel in order to analyze the power, torque, and other aerodynamic characteristics of a planned larger turbine and consequently reduce risks. For both situations, the study of scaling effects on wind turbine characteristics enables us to save calculation time and costs [1]. In this regard, Hand et al. [2] performed comprehensive experiments to attain information needed to quantify the full-scale aerodynamic behavior of horizontal-axis wind turbines. Blade surface pressures at five span locations on one blade as well as

* Corresponding author. E-mail addresses: [email protected] (M.H. Giahi), [email protected] (A. Jafarian Dehkordi). http://dx.doi.org/10.1016/j.renene.2016.05.059 0960-1481/© 2016 Elsevier Ltd. All rights reserved.

blade root bending moments, low-speed shaft bending moments and many other quantities were measured in their experiments. These data could be exploited to validate numerical simulations [3e5] for designing and analyzing wind turbines as is done in the present paper. Fingersh et al. [6] developed a reliable tool for estimating the cost of wind generated electricity based on different scales of turbines. Cost estimations are based on turbine rating, rotor diameter, hub height, and other key turbine components and subsystems. Annual energy production has been estimated based on the probability distributions of wind, standardized power curve, physical description of the turbine and estimations from aerodynamic and engineering principles. Griffith et al. [7] developed a 100-meter blade for a 13.2 MW horizontal axis wind turbine. The blade employed conventional architecture and fiberglass-only composite material reinforcement. The study began with a review of several large utility grade turbines (3e6 MW). Then geometric scaling of these models was performed to produce aeroelastic turbine models with 100-meter blades, which are analyzed to demonstrate the important effects of scale for large blades. Based on these preliminary analyses, the 100meter baseline blade model was developed. A detailed composite layup and geometry were also provided.

M.H. Giahi, A. Jafarian Dehkordi / Renewable Energy 97 (2016) 162e168

Small wind turbines regularly face poor performance due to laminar separation and formation of laminar separation bubbles on the blades. Singh et al. [8] have designed a new airfoil, permitting a small wind turbine to start up at lower wind speeds. The new airfoil also increased the startup torque and thus improved the overall performance of the turbine. A 400 W 2-blade wind turbine which its rotor was designed using the new airfoil was tested at wind speed range of 3e6 m/s. The results showed that the new 2-blade rotor produces more electrical power in comparison with the baseline 3-blade rotor at the same free stream velocity. Ashuri [9] investigated how up-scaling influences the offshore wind turbine performance employing integrated aero-servo-elastic design optimization. Using this method, 5, 10, and 20 MW wind turbines were designed and optimized, including the most relevant design. Based on those optimized turbines, scaling trends were constructed and formulated as a function of rotor diameter. Loading, mass, cost, and some other useful parameters are extracted to investigate the scaling phenomenon. The results demonstrated that constructing a 20 MW is technically possible, though economically not feasible. Sieros et al. [10] examined the theoretical implications of upscaling on weight and loads of wind turbines. Followed by theoretical method, empirical models of the increase in weight, cost, and loads as a function of scale were derived based on historical trends including the effects of both scale and technology advancements. Finally, based on a life cycle cost approach, a theoretical framework for optimal design of large wind turbines was developed. It was proved that for a given technology, up-scaling results in an unfavorable weight increase. Similarly it was shown that without technological improvements, the levelized component cost increases as the turbine size grows. Having had the aim of keeping the stresses in the up-scaled blade the same as the reference one, Capponi et al. [11] introduced a non-linear up-scaling approach. The blade in this research was modeled as a beam and the stresses due to the weight, aerodynamic, and centrifugal forces were considered. Using this method, the 5 MW NREL wind turbine blade was up-scaled to a 20 MW blade. Comparing the blade stress obtained through the nonlinear up-scaling approach to the linear one showed that the former decreases the aerodynamics and weight-induced stresses, while the centrifugal stresses were almost the same in linear and non-linear up-scaled blades. Lanzafame et al. [12] developed a 3-D CFD model of a Horizontal Axis Wind Turbine using the ANSYS Fluent solver. This model was used to predict wind turbine performance and evaluate the capabilities of a BEM-based 1-D model developed by the authors. A Moving Reference Frame model was used to simulate rotation and a steady state solver was employed. Using a calibrated transitional SST model, the errors between simulation results and experimental data were less than 6% for all simulations. The research concluded that the 3-D CFD model is therefore a useful tool for validating the design of wind turbine rotor. Garcia [13] collected a database of diverse wind turbine designs which includes more than 230 different wind turbines from 34 manufacturers with rotor diameter between 12.8 and 200 m. The database was analyzed in order to obtain up-scaling trend lines of different parameters and finally to introduce an up-scaling model. This model is used to calculate future up-scaled wind turbines from the trend lines. Ramos-Garcia et al. [14] validated a newly developed computational model against measurements and CFD simulations for five wind turbine rotors. The new model predicts the aerodynamic behavior of wind turbine blades subjected to unsteady motions. Viscous effects inside the boundary layer are taken into account and a free-wake model is employed to simulate the vorticity released by

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the blades in the wake. Although difficulties appeared in correct prediction of the tangential force at low and high tip speed ratios, the solver results showed an excellent agreement with the available data in standard operating conditions for all rotor cases. Make et al. [15] studied the flow over two floating wind turbines using RANS CFD calculations at model and full-scale Reynolds numbers conditions. Modern verification and validation procedures were used to assess uncertainties and to perform a validation of the numerical results against experimental data coming from constant uniform flow. Furthermore, the flow around the turbines and its performance has been examined both for model and full-scale turbines. A good agreement between the CFD results and the experimental data has been obtained. DOWEC, UPWIND, and WindPACT are also among the most relevant projects related to doing research on different aspect of up-scaling. The DOWEC project [16] focused on development needs for the design of large-scale offshore wind farms. The project ended up with preliminary design of a 6 MW wind turbine and addressed some issues related to larger scale turbines. UPWIND was the largest wind energy research project consisting of 15 scientific and industrial work packages. The project looked at the design of very large wind turbines (over 10 MW), both for onshore and offshore applications. UPWIND had several upscaling work packages to identify major technological and economic barriers, associated with the development of wind turbine technology. As part of this project, Lekou [17] investigated upscaling of composite material wind turbine blades considering various aspects of the structural design of blades including cost issues. The results of the research showed that major technological barriers for up-scaling of a blade structure using the currently applied technology are bonding technology, manufacturing issues and material strength. As part of the WindPACT program [18], Global Energy Concepts performed the Blade-Scaling Study to assess the scaling of materials and manufacturing technologies of blades of 40e60 m in length, and to develop scaling curves of estimated cost and mass for rotor blades in that size range. Direct design calculations were used to construct a computational blade-scaling model, which was then used to calculate structural properties for a wide range of aerodynamic designs and rotor sizes. The scaling model results were compared with mass data for commercial blades. For a given blade design, the scaling model indicates that blade mass and costs scale as a near-cubic of rotor diameter. In contrast, commercial blade designs have maintained a scaling exponent closer to 2.4 for lengths ranging between 20 and 40 m. A brief review of literature implies that CFD simulations were rarely employed to clarify the scaling effects on wind turbine characteristics. In spite of other studies, here the influence of scaling on aerodynamic characteristics of a wind turbine blade such as torque, thrust, and aerodynamic forces were investigated using CFD simulations. Also a comparison between the results of these simulations and predictions of the traditional similarity rules was made. In addition, the effect of blade size on number of mesh elements needed to obtain grid independency thus the computational time and cost was investigated in the present research. The results of the present paper pave the way to conduct further accurate investigations about scaling effects on blade structural characteristics such as blade weight and root stresses. 2. Scaling of wind turbines and rules of similarity Conventional scaling of turbine properties is accomplished by a dimensional analysis, whereby all length dependent variables are scaled according to a scale factor [7]. The theory of similarity is a

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very simple but powerful theory to investigate the wind turbine scaling effects on its different characteristics. Using this theory, the flow condition is the same in both large and small cases if the following criteria are met [1]: a. The tip speed ratio is maintained in both cases. b. The blade profile and the number of blades are kept the same. c. Proportional adjustments are made to all dimensions containing radius, profile chord, and spar size. In this situation, the triangles of velocity and the relative velocity angles at every related blade cross-section is the same for large and small wind turbines; therefore, flow condition would be the same for the two cases. Based on these considerations, the effects of the scaling on the performance characteristics of the rotor, forces at the blade, stress at the blade root, and dynamic characteristics can be determined. In the present paper the impact of scaling on aerodynamics parameters are examined. These parameters are presented in Table 1. In these equations, parameter “D” indicates wind turbine rotor diameter (twice the distance of rotor center to blade tip). The results obtained by CFD simulation will be compared to predictions of the theory of similarity. In addition to parameters introduced in Table 1, the number of grid elements in simulation and as a result the computational time dependency on scale of the turbine is of interest. Scaling of the turbine not only affects the values of torque, thrust, and aerodynamic forces but also other parameters like blade stresses and weight. Linear scaling law predicts that mass scales with D3 as the size increases. Due to the influence of the ongoing efforts in airfoil developments as well as having better manufacturing techniques, the mass scaling of the blade has a relation with size which is below D3 but still higher than D2 [9]. The stress from the weight increases proportionally to the blade length; hence, a major limitation for further up-scaling is the blade weight. Although there are several important aspects on structural relevant parameters, the goal of this paper is to investigate scaling effects on aerodynamic parameters using CFD tool, so these items which include structural analysis were not discussed further in the paper.

3. Wind turbine modeling, simulation domains To validate the results of the CFD model, NREL PHASE VI wind turbine rotor [2] was modeled and the simulation results were compared to experimental data available in scientific literature. This turbine is equipped by a 2-blade rotor with the diameter of 10.06 m which uses S809 airfoil at all span sections. The blades of the turbine have a fixed pitch angle of 5 and the rotor is rotating at rotational speed of 72 rpm. In order to investigate the effects of scaling on wind turbine characteristics, a 3-blade 2 MW wind turbine was employed as the large wind turbine [19]. This turbine had been erected at Tejaereborg, Denmark in 1987. The main characteristics of the turbine are presented in Table 2. This turbine was

Table 1 The relativity of aerodynamic parameters to wind turbine rotor diameter. Parameter Torque Thrust Aerodynamic forces

Relativity to rotor diameter M2 M1

3 ¼

D2 D1

Table 2 Tejaereborg wind turbine main characteristics. Characteristic

Value

Rotor diameter Rotational speed Airfoil profile Twist angle Chord length

61.1 m 22.36 rpm NACA 4443-4412 8 @ root to 0 @ tip 315 cm @ root to 90 cm @ tip

then scaled down 6 times to form the small wind turbine. The effect of tower, nacelle, and ground boundary layer was ignored and the wind profile was assumed to be uniform; thus the simulation domain can be assumed to be periodic and only a slice of the domain was simulated. The NREL rotor has two blades so, only half of the domain is simulated while the Tejaereborg is a 3-blade turbine; thus one-third of the domain is modeled. These domains are demonstrated in Fig. 1. The complexity, computational time resources, and physics of the problem have to be considered in choosing how to model rotational effects. Based on these issues, the Multiple Reference Frame (MRF) model was chosen in the present work as it is an optimal compromise between accuracy and computational time. The MRF method is a steady-state approximation in which different cell zones can be assigned different rotational speeds. The flow in the moving cell zones is solved using the rotating reference frame equations while in stationary cell zones the equations reduce to their stationary forms. Fig. 2 shows the rotating and stationary zones that constitute the simulation domain for both NREL and Tejaereborg wind turbines. 4. Governing equations, boundary conditions, and grid generation Governing equations of fluid flow are time-averaged continuity in accordance with the time-averaged momentum equations (RANS equations [20]). These relations are shown as follows:

vui ¼0 vxi

(1)

vui vu 1 v eff þ Gi þ uj i ¼ t vt vxj r vxj ij

(2)

teff ¼ pdij þ m ij

vui vuj þ vxj vxi

!

¼

F2 F1

¼

D2 D1

2 D2 D1

(3)

The last term in eq. (3) is Reynolds stress term that is modeled by a turbulence model. The turbulence model used in this paper is standard k u model in which the turbulence viscosity is related to turbulence kinetic energy and turbulence frequency as follows:

mt ¼

rk u

(4)

The transport equations for turbulence kinetic energy and turbulence frequency are introduced below [21]:

DðrkÞ v ¼ P b* ruk þ Dt vxj

"

2

T2 T1

ru’i u’j

DðruÞ au v ¼ P bru2 þ Dt vxj k

rk vk m þ sk u vxj

"

#

rk vu m þ su u vxj

(5) # (6)


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Fig. 1. Domain zones and boundary conditions for NREL (Left) and Tejaereborg (Right) wind turbines.

Fig. 2. Grid appearance on blade surface as well as boundary layer mesh on blade cross section.

In these equations, P is the turbulence production rate while

a ¼ 5=9, b ¼ 0:075, b* ¼ 0:09, sk ¼ 2, and su ¼ 2 are constant values [22]. RANS equations, discussed above, are used to solve the 3-D turbulent steady state incompressible flow using the k-u turbulence model equations for closure. The grid type used is a prism type in vicinity of the blade as shown in Fig. 2. An inflation layer (boundary layer) was employed to capture the boundary layer on surface of the blade. The number of layers is then increased gradually to obtain a proper yþ [23]. The mesh generated for the other parts of the solution domain is an unstructured tetrahedral grid. The Boundary conditions of the inlet and outlet are set to be velocity inlet and pressure outlet, respectively. These boundaries are positioned at 4 R (R is the radius of the turbine rotor) in front of and 16 R behind the rotor, respectively. The velocity direction at inlet is normal to the boundary. The boundary condition at far-field is set to be tangential velocity with the same value as the inlet velocity. This surface is placed 6 R away from the rotor center to ensure that it has a little effect on interested region which is the blade surface. Rotational periodicity is the last boundary condition which is used at slice sections of both rotating and stationary zones. The interface between these zones is set to be frozen rotor condition. The fluid is considered to be incompressible air at 25 C and its reference pressure is set to be 1 atm. The advection term is

discretized using high resolution upwind method and the residual convergence criterion is set to be 105 . 5. Results and discussion In the first part of this section the validation process as well as the verification results is presented. The study on the effects of scaling on aerodynamic characteristics is then performed and at last the effect of scaling on number of grid elements is discussed. 5.1. Validation As mentioned before, NREL wind turbine was chosen to insure that the results of the simulation are accurate enough for investigating scaling effects. Fig. 3 shows the results of the shaft torque obtained from simulation compared with experimental data for different grid element numbers. Since there is a little difference between the results of the 7 and 9 million elements grids, the grid with the 7 million elements was chosen. The average relative error between the results and the data is below 10%. The difference between simulation results and experimental data in the mid-range wind velocities is due to the separation phenomena which the CFD model used in the present paper is unable to capture its effects properly. This is the velocity range in which the turbines produce the best, so in practice this error might be more prominent. The

166


1800

30% aspect ratio. This is due to the separation effect at root section of the blade as the rotor is stall controlled. As was mentioned before, The Tejaereborg wind turbine is a pitch control machine so there is a little flow separation within the blade span.

1600 Shaft Torque Nm

1400 1200 1000

5.2. Investigating the scaling effects on aerodynamic parameters

800

Experimental 2,053,870 Elements 3,701,607 Elements 5,172,881 Elements 7,067,160 Elements 9,072,672 Elements

600 400 200 0 3

8

13 18 Wind Speed m/s

23

The Tejaereborg wind turbine as the large wind turbine as well as its scaled model was simulated and the aerodynamic parameters resulted from the simulation was then compared to predicted results of the Similarity Theory. A similar procedure as was done for NREL was carried out to find the most appropriate grid considering both accuracy and computational time. Afterward, several simulations were performed in different wind speeds with different blade pitch angles in order to find the pitch angle in which the wind turbine produces its highest power at each wind speed. The wind speed was set to be 7, 10, 12.5, 15, 17.5, and 20 m/s. Fig. 5 shows the shaft torque resulted from the simulations for small scale, large scale, and the predictions of the Similarity Theory which were obtained through relations presented in Table 1. It is worth mentioning that for wind speeds of more than 15 m/s the maximum obtainable torque is more than the torque that can produce the output power of 2 MW. Therefore, the real machine might, due to the generator limits, not be able to convert all of the torque to power. In this situation, the pitch control system changes the pitch angle of the blade so that the output power of the turbine remains by 2 MW. This controlled change in pitch angle is not considered here because the aim of the paper is to investigate the maximum obtainable theoretical torque from an aerodynamic view

28

Fig. 3. NREL turbine shaft torque versus wind speed for different mesh element numbers.

turbine which is chosen to study scaling effects (Tejaereborg wind turbine) is a pitch control machine; there is a little flow separation within the blade span. Hence, the overall conclusion can be promising to get accurate results in simulating wind turbine to investigate the scaling effects. Fig. 4 shows the pressure coefficient value at two different radial cross sections for two inlet velocity values of 7 m/s and 20 m/s. The figure shows that in 7 m/s the simulation results are completely compatible with experimental data [24]. In 20 m/s the results and the data are slightly different especially on suction side of airfoil at

Wind Speed 7 m/s , r/R=30%

-3.2 -2.8 -2.4 -2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6

Cp

Cp

Simulation Experimental

0

-5

0.2

0.4

0.6

1

-3


0

1.2

-3


-4

0.2

0.4

0.6

-2 -1 0

0.8

1

X/Chord Wind Speed 20 m/s , r/R=80%

1.2


-2

Cp

Cp

0.8

X/Chord Wind Speed 20 m/s , r/R=30%

Wind Speed 7 m/s , r/R=80%

-2.8 -2.4 -2 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6

-1 0 1

1

2

2 0

0.2

0.4

0.6

X/Chord

0.8

1

1.2

0

0.2

0.4

0.6

X/Chord

0.8

Fig. 4. Pressure coefficient on blade surface at two redial cross sections for wind speeds of 7 m/s (top) and 20 m/s (bottom).

1

1.2

5000

Large Scale Turbine (CFD) Predicted By Simularity Small Scale Turbine (CFD)

4500 4000 3500

4000

3000 3000

2500 2000

2000

1500

Shaft Torque (nm)

1000

1000

500 0

0 5

10

15

1600

Large Scale Turbine (CFD) Predicted By Similarity Small Scale Turbine (CFD)

30050 25050

1400 1200 1000

20050

800 15050

600

10050

400

5050

200 0

50 5

20

7

9

11

13

15

17

19

21

Wind Speed (m/s)

Wind Speed (m/s) Fig. 5. Comparison of shaft torque value obtained from simulation and the values 3 2 predicted by Similarity Theory M2 ¼ M1 D . D1

without considering any electrical or mechanical limitations. The results of the simulation are in complete agreement with predictions of the Similarity Theory. The relative error between the results is below 2% for all wind speeds except for 7 m/s which is 8%. This relatively large difference between the results of the simulation and Similarity Theory at this point is because of the incompatibility between the real flow regime and fully turbulent model in small scale wind turbine. Because of the size of the turbine, the Reynolds number in root regions of the small scale wind turbine blade is not as high as the Reynolds number for fully turbulent flow. As the fully turbulent approximation was used in simulation and no transitional model was used, the simulation assumes that the flow is fully turbulent and laminar flow as well as transition effects are not captured in the simulation. Fig. 6 shows the thrust value for large scale, small scale, and the values predicted by similarity rules. The results of the simulation are completely in accordance with the values predicted by Similarity Theory. Fig. 7 shows the edge-wise aerodynamic force results obtained from simulation in accordance with the values predicted by Similarity Theory. As demonstrated in the figure, the values are in complete agreement for all wind speeds except for wind velocity value of 7 m/s in which a relative error of 15% is present between the result of the simulation and the value predicted by Similarity Theory. The explanation for this error is the same as the one presented for the torque value. The flap-wise aerodynamic force also

300

Fig. 7. Comparison of edgewise aerodynamic force value obtained from simulation and 2 2 the values predicted by Similarity Theory F2 ¼ F1 D . D1

has the same trend as the edge-wise one. The results discussed in this section confirmed that the torque increases with the cube of change in rotor diameter. The thrust value and aerodynamic forces also grow with the square of change in diameter. This implies that developing of lighter and stronger materials is inevitable to obtain the ability of constructing larger wind turbines. In industry there is a clear focus on decreasing the weight in order to decrease critical edgewise fatigue loads [25]. As described in previous parts of this paper, the similarity rules are valid only if the flow condition is the same for large and small wind turbines. It is always assumed that the lift and drag coefficients are independent of the relative velocity. This is true for common airfoils if the Reynolds number is larger than 200,000 [1]. Thus the acceptable agreement seen in the results of this paper may not be valid if the small wind turbine is scaled down so that the Re number falls far below 200,000.

5.3. Investigating the effect of wind turbine blade size on number of mesh elements One of the most important issues in numerical simulation is to obtain the minimum number of mesh elements in which the results are independent of grid. Fig. 8 shows the output power of the turbines obtained by simulation at wind speed of 15 m/s for 6 different grid numbers. As it is obvious in the figure, the changes in 2500

15 13

250

70 60

2000

150

7 5

100

Large Scale Turbine (CFD) Predicted By Similarity Small Scale Turbine (CFD)

50 0 5

7

9

11

13

15

17

19

50

Power (KW)

9

Thrust (n)

Thrust (Kn)

11 200

1500

40 30

1000

20

3 1 -1

21

Wind Speed (m/s) Fig. 6. Comparison of thrust value obtained from simulation and the values predicted 2 2 by Similarity Theory T2 ¼ T1 D . D1

Power (Kw)

Shaft torque (knm)

5000

35050

167

Edgwwise Aerodynamic Force (KN)

6000

Edgwwise Aerodynamic Force (KN)


500

Large Scale Turbine (CFD)

10

Small Scale Turbine (CFD)

0 0

2000000

4000000

6000000

8000000

0 10000000

Mesh number Fig. 8. Output power of the turbines at wind speed of 15 m/s for 6 different grid numbers.

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power value are small for both curves as the mash number increases more than 4 million elements so, for both large- and smallsized wind turbines the grid with approximately 5 million elements was chosen. The result is surprising because increasing the turbine size has no significant influence on number of mesh elements needed to obtain grid independency. But this might be true within the scaling size conducted on in this paper and might not be correct for scaling-up or scaling-down of the turbine beyond what is done in this paper. 6. Conclusion In the present paper, the effects of scaling on wind turbine aerodynamic parameters including shaft torque, thrust, and aerodynamic forces on the blade were investigated. The results of the CFD simulation were in complete agreement with the values predicted by traditional similarity in all wind speed ranges except for low wind speed where there was a little difference between the simulation results and the predictions. This difference is because of the incompatibility between the real flow regime which is not fully turbulent in some regions of the blade span and the fully turbulent model which was employed to simulate the flow. Exponential increase of aerodynamic forces as the turbine size grows necessitates developing of lighter and stronger materials to obtain the ability of constructing larger wind turbines. The number of mesh elements needed to obtain grid independency was almost the same for largeand small-sized wind turbines. The results of this paper are encouraging to provoke researchers for further accurate examinations of scaling effects on blade structural characteristics utilizing numerical techniques. References [1] R. Gasch, J. Twele, Scaling wind turbines and rules of similarity, in: R. Gasch, J. Twele (Eds.), Wind Power Plants, Springer Berlin Heidelberg, 2012, pp. 257e271 (English). [2] M.M. Hand, D. Simms, L. Fingersh, D. Jager, J. Cotrell, S. Schreck, S. Larwood, Unsteady Aerodynamics Experiment Phase VI: Wind Tunnel Test Configurations and Available Data Campaigns, Technical Report, National Renewable Energy Laboratory, Colorado, 2001. [3] Y.P. Chen, A Study of the Aerodynamic Behavior of a NREL Phase VI Wind Turbine Using the CFD Methodology, M.Sc. thesis, Wright State University, Ohio, United States, 2011.

[4] R. Lanzafame, M. Messina, Advanced brake state model and aerodynamic post-stall model for horizontal axis wind turbines, Renew. Energy 50 (0) (2013) 415e420, 2//. [5] C. Tongchitpakdee, S. Benjanirat, L.N. Sankar, Numerical simulation of the aerodynamics of horizontal axis wind turbines under yawed flow conditions, Trans.-Am. Soc. Mech. Eng. J. Sol. Energy Eng. 127 (4) (2005) 464e474. [6] L.J. Fingersh, M.M. Hand, A.S. Laxson, Wind Turbine Design Cost and Scaling Model, Technical report, National Renewable Energy Laboratory (NREL), Colorado, United States, 2006. [7] D.T. Griffith, T.D. Ashwill, The Sandia 100-meter All-glass Baseline Wind Turbine Blade: SNL100-00, Technical report, Sandia National Laboratories, California, United States, 2011. [8] R.K. Singh, M.R. Ahmed, Blade design and performance testing of a small wind turbine rotor for low wind speed applications, Renew. Energy 50 (2013) 812e819, 2//. [9] T. Ashuri, Beyond Classical Upscaling: Integrated Aeroservoelastic Design and Optimization of Large Offshore Wind Turbines, PhD thesis, Delft University of Technology, Delft, Netherlands, 2012. [10] G. Sieros, P. Chaviaropoulos, J.D. Sørensen, B. Bulder, P. Jamieson, Upscaling wind turbines: theoretical and practical aspects and their impact on the cost of energy, Wind Energy 15 (No. 1) (2012) 3e17. [11] P.C. Capponi, T. Ashuri, G.J. van Bussel, B. Kallesøe, A non-linear upscaling approach for wind turbine blades based on stresses, in: European Wind Energy Conference and Exhibition, Belgium, Brussels, 2010, pp. 115e118. [12] R. Lanzafame, S. Mauro, M. Messina, Wind turbine CFD modeling using a correlation-based transitional model, Renew. Energy 52 (2013) 31e39, 4//. [13] J.P.S.D.L. García, Wind Turbine Database, M.sc. Thesis, Department of Applied Mechanics, Chalmers University of Technology, Goteborg, Sweden, 2013. [14] N. Ramos-García, J.N. Sørensen, W.Z. Shen, Validation of a three-dimensional viscouseinviscid interactive solver for wind turbine rotors, Renew. Energy 70 (2014) 78e92, 10//. [15] M. Make, G. Vaz, Analyzing scaling effects on offshore wind turbines using CFD, Renew. Energy 83 (2015) 1326e1340, 11//. [16] H. Hendriks, M. Zaaijer, DOWEC: Executive Summary of the Public Research Activities, Technical report, 2004. [17] D.J. Lekou, Scaling Limits & Costs Regarding WT Blades, Technical report, Centre for Renewable Energy Sources, Pikermi, Greece, 2010. [18] D.A. Griffin, WindPACT Turbine Design Scaling Studies Technical Area 1œComposite Blades for 80-to 120-meter Rotor, Technical report, National Renewable Energy Laboratory, 2001. [19] E. Hau, J. Langenbrinck, W. Palz, WEGA: Large Wind Turbines, Not Avail, 1993. [20] P.A. Durbin, B.A.P. Reif, Reynolds averaged NaviereStokes equations, in: Statistical Theory and Modeling for Turbulent Flows, John Wiley & Sons, Ltd, 2010, pp. 45e56. [21] D.C. Wilcox, Turbulence Modeling for CFD, DCW Industries La Canada, CA, 1998. [22] Ansys, ANSYS CFX-solver Theory Guide, ANSYS Inc, 2010. [23] A. Fluent, Fluent 14.0 User’s Guide, 2011. [24] M.M. Yelmule, E.A. VSJ, CFD predictions of NREL Phase VI rotor experiments in NASA/AMES wind tunnel, Int. J. Renew. Energy Res. (IJRER) 3 (2) (2013) 261e269. [25] F. Jensen, A. Kling, J. Sørensen, Scale-up of wind turbine blades-changes in failure type, in: Proceedings of EWEA Annual Event, 2012.