Enhancement of wind turbine aerodynamic performance by a numerical optimization technique

Transcription

1 Journal of Mechanical Science and Technology 26 (2) (202) 455~462 DOI 0.007/s Enhancement of wind turbine aerodynamic performance by a numerical optimization technique Hyung Il Kwon, Ju Yeol You and Oh Joon Kwon * Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon , Korea (Manuscript Received March 6, 20; Revised September 20, 20; Accepted October, 20) Abstract Sectional aerodynamic design optimization was performed to enhance the aerodynamic performance of horizontal axis wind turbine rotor blades based on a computational fluid dynamics technique. The proposed sectional optimization framework consists of airfoil section contour modeling by the PARSEC shape function and a modified feasible direction search algorithm. To enhance the aerodynamic performance of wind turbine rotor blades, the objective of the design framework was set to maximize the lift-over-drag ratio for each design section. A two-dimensional Navier-Stokes flow solver coupled with a transition turbulence model was used to evaluate the aerodynamic performance during the iterative design optimization procedure. The sectional flow conditions were extracted from the flow of a three-dimensional rotor blade configuration. The design framework was applied to the National Renewable Energy Laboratory Phase VI rotor blade. The design optimization was conducted at nine spanwise sections of the rotor blade. To validate the present methodology, the aerodynamic performances of the original baseline rotor and the rotor after the design optimization were compared by using a threedimensional Navier-Stokes flow solver. It was found that approximately % of torque enhancement was achieved after the aerodynamic shape design optimization. Keywords: Horizontal-axis wind turbine rotor blade; Numerical design optimization; Aerodynamic performance enhancement Introduction Wind turbine systems, which extract energy from the nature, have become increasingly important as one of the environmentally-friendly and sustainable energy-producing systems for reducing the dependency on fossil fuels. In this regard, research and development about the wind turbine systems have been actively performed. This research mainly focused on developing efficient large-scale wind turbine systems to obtain low-cost energy, particularly for horizontal-axis wind turbines. Although enlarging the size of the turbine rotors is a simple solution, this increases the aerodynamic and structural loads on the rotor blades at the same time. It also increases the initial manufacturing and installation cost. Thus, it is important to find a proper trade-off between the cost for development/installation and that of the extractable useful energy. It is known that approximately 60% of the total energy loss of typical wind turbine systems is the aerodynamic loss. Since large horizontal-axis wind turbines are very expensive, and are in operation for many years after the initial installation, it is important to design the wind turbine rotor blades in an aerodynamically This paper was recommended for publication in revised form by Associate Editor Byeong Rog Shin * Corresponding author. Tel.: , Fax.: address: ojkwon@kaist.ac.kr KSME & Springer 202 efficient manner such that the maximum possible energy conversion can be achieved for the initial investment cost. In the past, a few researches were conducted for the aerodynamic shape optimization of wind turbine rotor blades. Fuglsang and Madsen [] reported a study about the aeroelastic blade shape optimization based on the blade-element momentum theory (BEMT). In their study, the design variables from the planform of the rotor blade, such as the blade twist angle and the chord length, were used. The objective function was set to the cost of energy (COE). A COE reduction about 3% was obtained for the optimal shape of the blade. In the study by Xudong et al. [2] optimized 25 kw, 2 MW, and 5 MW class wind turbine blade planforms by using a BEMT-based framework. The results showed.% ~ 3.6% reduction of the COE. Chattot [3] introduced an optimization framework based on a helical vortex model, and performed a planform design optimization of the NREL phase VI rotor blades. A systematical parameter study was conducted. Blade planform shape design is important in improving the wind turbine aerodynamic performance, and has a merit of optimizing the overall turbine sizing. However, the sectional shape of the turbine blade is fixed during the design process, and thus a limited performance improvement is expected. In this regard, blade section optimization based on current computational fluid dynamics (CFD) techniques is a more direct

2 456 H. I. Kwon et al. / Journal of Mechanical Science and Technology 26 (2) (202) 455~462 approach to maximize the aerodynamic performance improvement, in addition to the blade planform shape design. Wind turbine rotor blades usually operate at relatively low speed. To maximize the aerodynamic performance in this flow speed, rotor blade sections typically have high thickness ratios, compared to aircraft wing sections. Because the flow around thick airfoils easily separates, the effect of viscosity, including laminar-to-turbulent transition, should be considered. In that sense, simple aerodynamic performance prediction models based on empirical aerodynamic coefficients, such as the BEMT and the lifting-line theory, are not adequate to accurately analyze the flow around wind turbine rotor blades. Thus, first-principles based flow solvers should be adopted for further improvement of the wind turbine rotor blade performance prediction and design optimization. In the present study, aerodynamic shape optimization of rotor blade sections was performed based on a state-of-the-art CFD technique to enhance the aerodynamic performance of horizontal-axis wind turbines. The blade sections were extracted from a three-dimensional baseline rotor blade configuration, and these sections were optimized by using a twodimensional design optimization framework. The objective function was set to maximize the section lift-over-drag ratio. During the design process, a two-dimensional Navier-Stokes flow solver based on unstructured meshes coupled with a turbulence model including the laminar-to-turbulent transition effect was used. For validation, the National Renewable Energy Laboratory (NREL) Phase VI rotor blade was selected as the baseline configuration, because experimental data are available for comparison. The resultant aerodynamic performances between the optimized blade and the baseline blade were compared by using a three-dimensional Navier-Stokes flow solver based on the same numerical schemes with those of the two-dimensional flow solver used in the design. 2. Shape function and curve fitting 2. PARSEC shape function Fig.. Definition of PARSEC shape function. Design optimization by directly considering all coordinates of the target geometry as the design variables is extremely difficult because of the cost involved in handling a large number of design variables. To reduce the number of design variables and the cost, the airfoil contour can be modeled by introducing proper shape functions which express the design geometry by a few representative parameters. Currently, various shape functions are available, such as the B-spline [4], the Bezier Curve [5] and the PARSEC shape function [6]. Among them, the control variables of the PARSEC shape function are known to be more related to the flow physics, and thus are suitable for representing the aerodynamic configurations operating in low subsonic flow regimes. Fig. shows the geometrical meaning of the control variables used in the PARSEC shape function. r LE represents the leading-edge radius, and Z TE is the Z coordinate at the trailing edge. ΔZ TE is the design offset. Also, α TE and β TE are the geometrical angles for describing the trailing-edge shape. At the mid-chord surface, (X, Z) up,lo are the coordinates of the maximum and minimum Z locations, and Z XX up,lo are the secondorder derivatives at those locations. The total number of design variables can be reduced to 9 out of by freezing the two variables, Z TE,, ΔZ TE. The arbitrary geometric configuration of an airfoil can be described by the linear combination of these variables as 6 i= i 0.5 Z = a ( p) X () i where ai ( p) is the constant containing the information about the geometrical shape as defined by the PARSEC shape function. 2.2 Definition of design configuration To construct the initial geometry for the optimization frame work, the control variables of the PARSEC shape function have to be determined. In the present study, these control variables represent the S809 airfoil [7] utilized as the blade section for the NREL Phase VI rotor. To obtain these values requires solving a sub-optimization problem, known as curve fitting. For this purpose, a hybrid genetic algorithm (HGA) [8] was applied to minimize the following equation: 2 ( exact PARSEC ). (2) OBJ = y y Here, y exact is the exact coordinates set of the S809 airfoil, and y PARSEC is the coordinate set generated by the PARSEC shape function. By minimizing Eq. (2), the approximated control variables of the PARSEC shape function for the airfoil can be obtained. For this hybrid genetic algorithm of the suboptimization problem, the number of population is 200, and the maximum generation is 4,000. Also, the probabilities of the cross-over, mutation, re-insertion and regeneration are 0.6, 0.0, 0.2 and 0.7, respectively. In addition, the elitism strategy, which serves to maintain the elite individual in the present generation, is implemented for the efficient searching of the design space. In Table, the ranges of variation of the chromosomes,

3 H. I. Kwon et al. / Journal of Mechanical Science and Technology 26 (2) (202) 455~ Table. Limits of control variables and curve fitting results. Lower limit Upper limit Optimal value r LE X up Z up X lo Z lo Z XX up Z XX lo α TE -3 deg 3 deg deg β TE -3 deg - deg deg Table 2. Constraints of design optimization. # Constraint details I Maximum thickness should be larger than or equal to original airfoil II Section area should be equal to original airfoil III Drag should be less than or equal to original airfoil q q g j ( X ) q q j * F( X ) α = MIN ( 0., ). (5) df( X ) dg ( X ) [ ] [ ] dα * dα * Here, g j represents the j-th constraint. The direction determined by Eq. (4) is defined as the Fletcher-Reeves conjugate direction. This direction remains valid if there are no active or violated constraints. If the position of the design vector does not satisfy the constraints, the process of obtaining the directional vector is not a deterministic process anymore. In this case, it is necessary to solve a sub-optimization problem to determine the direction of the design vector [9]. 3.2 Constraints and objective function Fig. 2. Representation of airfoil contour by curve fitting. namely the control variables, are presented in the second and third columns. The fourth column shows the optimal results, known as the fittest chromosomes. Using these fittest chromosomes, the S809 airfoil shape is expressed by the PARSEC shape function as in Fig. 2. It is shown that the contour obtained from the curve fitting represents the initial shape very well, demonstrating the validity of the sub-optimization process. 3. Optimization methodology 3. Optimization algorithm We used a gradient-based optimization algorithm based on a finite-difference technique. This algorithm searches the optimal point by calculating the gradient of the objective in the constrained design space. This algorithm is known to be simple and intuitive. In addition, compared to other numerical optimization algorithms, such as the genetic algorithm, it requires relatively low computational cost. To search the optimal region from q- to q stage, the design vector X movement is determined by the feasible directional vector S and the scalar parameter α * as q q * q X = X + α S. (3) The directional vector S is described as q 2 q q F( X ) q ( ) q 2 2 S = F X + S (4) F( X ) and the scalar parameter α * is determined as The objective function adopted in the present study is the ratio of airfoil lift to drag, which represents the fundamental aerodynamic performance of airfoils. For the two-dimensional lift and drag coefficients, the objective function can be written as OBJ C l = w (6) C d where w is the weight factor. In the present design framework, the weight factor was fixed to.0 at first. During the iterative design process, if the calculation by the Navier-Stokes flow solver diverges by pursuing a non-physical shape, then this factor was changed to 0.3 as a penalty of the false evaluation. Since the direction of the design vector in the design space is also determined by the constraints, these constraints in the optimization framework should also be determined carefully. In the present study, the constraints in Table 2 were applied so that most of the geometrical properties of the original S809 airfoil section are to be retained. 4. Aerodynamic performance prediction 4. Numerical methods We adopted a vertex-centered finite-volume scheme based on an unstructured mesh technique to discretize the governing Navier-Stokes flow equations. The inviscid fluxes were calculated by using 2nd-order Roe s flux difference splitting method, and the viscous fluxes were computed based on a central differencing. A dual time stepping method and the Gauss- Seidel iteration were used for the time integration. Since wind turbine rotor blades have relatively thick airfoil sections, and operate in low subsonic speed, the effect of la-

4 458 H. I. Kwon et al. / Journal of Mechanical Science and Technology 26 (2) (202) 455~462 Table 3. Operating condition of NREL Phase VI wind turbine rotor. Configuration Upwind Free stream velocity 7 m/s Rotor radius m Blade taper 2: Rotation speed 72 rpm Rotational direction CCW(viewed from upwind) Blade tip pitch angle 3 degrees Rated power 9.8 kw Fig. 3. Framework of design optimization. minar-turbulent transition including local laminar separation bubble is important for accurately predicting the aerodynamic performance. For this purpose, the SST turbulence model which handles laminar-turbulent transition [0] was adopted in the present study. 4.2 Wind turbine configuration and operating condition The operating condition and the overall configuration parameters of the target NREL Phase IV wind turbine rotor blade are summarized in Table 3. Out of the several experimental test conditions [], the one at the nominal operating condition with a freestream wind speed of 7 m/sec was chosen in the present study. The direction of flow is along the rotor axis of rotation such that steady flow exists regardless of the azimuthal position of the blade. 5. Framework of design optimization In Fig. 3, the framework of the design optimization adopted in the present study is presented. The framework can be divided into two parts. The first part is to achieve the sectional aerodynamic optimization in which the optimization algorithm, the shape function, and the two-dimensional Navier-Stokes flow solver are all combined. The optimization algorithm provides the design vector, and the airfoil contour is determined by the definition of the shape function. Then the coordinates of the airfoil are delivered to the CFD analysis. With the information of the airfoil geometry, the computational mesh is constructed, and the Navier-Stokes flow analysis is conducted to determine the aerodynamic force coefficients. Then the results from the analysis are conveyed back to the optimization algorithm. This iterative procedure is repeated until a satisfactory converged result is obtained. The optimization algorithm finds the feasible and usable direction by using the gradients of the objective and constraint functions. Once the direction is determined, the design vector is moved. This procedure is regarded as one design iteration. When the optimization algorithm shows no further improvement of the objective function, the iterative process ends automatically. Then the information about the optimal shape of the airfoil section formatted by the variables of the PARSEC shape function is reported to the user. The second part of the design framework is to confirm the improvement of the aerodynamic performance of the optimized rotor blade by comparing the result with the original one through a three-dimensional CFD analysis. In this analysis, the airfoil sections along the span obtained from the twodimensional design optimization are collected and are reconfigured into a three-dimensional rotor blade through a CAE modeling process. Then three-dimensional mesh generation around the rotor blade is made, and the Navier-Stokes flow calculation is made for the complete wind turbine configuration. The results are compared in terms of the wind turbine torque and thrust. 6. Results and discussion 6. Validation of two-dimensional flow solver Before performing the design optimization, we validated the capability of the present two-dimensional Navier-Stokes flow solver for predicting the aerodynamic performance. The calculations were made for the S809 airfoil section adopted for the NREL Phase VI rotor blade. The results are compared with those of the NREL experimental data []. A hybrid mesh was used to capture the viscous boundary layer near the airfoil surface accurately and efficiently. On the airfoil surface, quadrilateral elements were constructed, while isotropic triangular elements were filled in the outer region as in Fig. 4. The airfoil wake region was also packed with highaspect ratio quadrilateral elements up to five chord lengths downstream from the trailing edge to capture the shear flow better. The total number of nodes was 47,600, and the corresponding number of cells was 88,790. The calculations were made at a Reynolds number of for four angles of attack of 0,.02, 9.22 and 4.24 degrees. In Fig. 5, the predicted chordwise wall pressure distributions are compared with the experimental data [7]. It shows that the results are in good agreement over the entire airfoil surface for all angle-of-attack cases tested. At the angle of attack of 9.22 degrees, the flow starts to separate from the trailing edge, and as the angle of attack further increases, the separation point moves upstream up to near the half chord at the angle of attack of 4.24 degrees. It was observed that laminar separation bubble exists at low angles of attack before the flow fully separates. At zero degree angle of attack, separation bubbles form on both upper and lower surfaces near the mid chord as shown in Fig. 6. When the

5 H. I. Kwon et al. / Journal of Mechanical Science and Technology 26 (2) (202) 455~ Fig. 4. Two-dimensional computational mesh around S809 airfoil. Fig. 6. Laminar separation bubbles at zero degree angle of attack. Fig. 7. Predicted aerodynamic force coefficients compared with experimental data. Fig. 5. Predicted chordwise pressure distributions compared with experimental data. flow passes over the bubbles, the flow characteristics change from laminar to turbulent, accompanying a sudden change of pressure, as shown in the chordwise pressure distributions in Fig. 5. It is known that capturing this locally separated flow is critical for accurately predicting the airfoil aerodynamic performance, particularly for wind turbine rotor blades. The predicted lift and drag coefficients in terms of angle of attack are compared with the experiment [7] in Fig. 7. It is shown that good agreement is obtained, particularly at low angles of attack where the design optimization of the present study is mostly performed. 6.2 Blade section optimization Instead of directly performing expensive three-dimensional shape optimization of wind turbine rotor blades, we did twodimensional airfoil section design optimizations at the selected spanwise locations of the rotor blade. Among 20 sections introduced in the NREL technical report [], nine sections were chosen for this purpose as shown in Table 4. The calculations were made on a mesh similar to the one in Fig. 4 with the total number of nodes of 66,320 and the total number of cells of 0,745. The flow condition at each section is different depending on the rotor blade geometric configuration and the operating condition. This flow condition is evaluated and summarized in Table 4. The Reynolds number at each section is defined based on the local chord length and the resultant relative velocity which is the sum of the wind turbine rotational speed and the incoming free stream velocity. The local angle of attack (α local ) is acquired by assessing the geometric angle of attack (α g ) due to the relative wind direction, the blade twist angle (ø), and the local blade pitch angle (β). The results of the two-dimensional design optimization at each section are summarized in Table 5. It is shown that significant improvement is obtained in the objective function and the ratio of lift to drag after the design optimization for all sections of the blade, particularly at outboard sections. This contributes to the overall aerodynamic performance enhancement of the wind turbine rotor blade. α = φ + β α. (7) local g In Fig. 8, the tendency of variation of the design variables of the PARSEC shape function during the sectional optimization

6 460 H. I. Kwon et al. / Journal of Mechanical Science and Technology 26 (2) (202) 455~462 Table 4. Selected design sections and local flow conditions. Section Radial distance(m) Span station (r/r) Reynolds number ( 0 5 ) Angle of attack (deg) A B C D E F G H I Fig. 9. Spanwise distribution of chord length and twist angle for NREL Phase VI rotor blade. Table 5. Comparison of aerodynamic performance before and after design optimization. Section C l C d (0-2 ) OBJ C l C d (0-2 ) Baseline airfoil Optimized airfoil OBJ A B C D E F G H I Fig. 8. Tendency of design parameters after sectional design optimization. framework is presented. Considering the low subsonic twodimensional aerodynamic theory, it is natural to observe that the leading-edge radius is driven to be increased at all sections of the blade for the improvement of lift. Meanwhile, variation of the design parameters associated with the trailing edge configuration is noticeable only at selected spanwise stations. 6.3 Performance of optimized wind turbine rotor To demonstrate the performance enhancement of the wind turbine rotor blade after the section design optimization, the aerodynamic performances of the original NREL Phase VI rotor blade and the designed rotor blade are compared by using a three-dimensional Navier-Stokes flow solver. The numerical schemes are the same as those of the two-dimensional flow solver adopted for the design optimization. The results are also compared with the experimental data of the original rotor blade []. In Fig. 9, the twist angle and the chord length distribution at each section of the rotor blade are presented for the complete span composed of a circular cylinder at the root and a S809 airfoil section outboard with a transition region in between. For the efficient three-dimensional simulations, a periodic boundary condition was imposed between the rotor blades, and the flow around one blade was solved. The far-field boundary from the rotor blade was set three times larger than the rotor radius. Along the axial flow direction, the far-field domain was set at five times of the rotor radius away from the rotor. In Fig. 0, the overall computational domain and the corresponding boundary conditions are presented along with the rotor blade. The top and bottom surfaces were set as the inflow and extrapolation conditions, respectively. The no-slip viscous wall boundary condition was imposed at the blade surface. To predict the flow inside the boundary layer accurately, 30 prism layers were accumulated with a stretching ratio of.2. The total number of nodes and cells used was approximately and , respectively, for both the baseline and optimized blades. The Reynolds number of the flow is based on the chord length at 75% span. In Fig., the resultant chordwise wall pressure distributions of the baseline blade and the optimized blade are compared with the experimental data [] of the baseline rotor blade. It is shown that the predicted pressure distribution of the baseline rotor blade compares very well with the experiment, demonstrating the capability of the present flow solver for accurately predicting the rotor blade performance. Not only the suction peak but also the pressure at the mid chord are well predicted both on the upper and lower surfaces of the blade. After the design optimization of the blade, the blade loading is increased for all spanwise stations due to the section configuration change, particularly on the blade upper surface caused by the enlargement of the leading-edge radius of curvature.

7 H. I. Kwon et al. / Journal of Mechanical Science and Technology 26 (2) (202) 455~ Table 6. Comparison of sectional load coefficients between the optimized blade and the baseline blade. Baseline blade Optimized blade Improvement (%) r/r C n C t C n C t C n C t % 7.39% % 3.38% % 6.40% % 7.46% % 6.32% Fig. 0. Details of computational mesh and boundary condition. (a) r/r = 0.3 (b) r/r = 0.47 Fig. 2. Comparison of load coefficients between optimized blade, baseline blade and experimental data. no. of taps Cp + C i pi+ t = ( )( i+ i) 2 i= C y y. (9) (c) r/r = 0.63 (d) r/r = 0.80 (e) r/r = 0.95 Fig.. Comparison of chordwise pressure distributions between optimized blade, baseline blade and experimental data. The predicted chordwise pressure distributions are integrated to obtain the sectional normal and tangential force coefficients at each blade section. These load coefficients are the important performance indicators of wind turbine rotor blades. no. of taps Cp + C i pi+ n = ( )( i+ i) 2 i= C x x, (8) Here, x and y are the coordinates of the airfoil normalized by the chord length. The predicted load coefficients from the present calculations are compared with the experimental data [] in Fig. 2. It is shown that good comparison of the blade loading is obtained between the prediction and the experiment for the baseline rotor blade, again confirming the capability of the present flow solver for predicting the rotor blade performance. After the design optimization, both normal and tangential force coefficients are increased for all spanwise sections of the blade. These results are summarized in Table 6 at five spanwise sections of the blade. Approximately 4 to 8% of enhancement was obtained for the sectional normal force coefficient, while the sectional tangential force coefficient increased by approximately 6 to 7%. In the NREL technical report [], two parameters which represent the total performance of wind turbine rotor blades were introduced. One is EAEROTH (estimated AEROdynamic THrust) as the indicator of the total force acting in the direction of freestream, and the other is EAEROTQ (estimated Aerodynamic TorQue) as the indicator of the total torque acting in the direction of blade rotation. These parameters can be estimated as n= 5 EAEROTH = 2 CTH QNORM n n arean, (0) n=

8 462 H. I. Kwon et al. / Journal of Mechanical Science and Technology 26 (2) (202) 455~462 Table 7. Performance enhancement after design optimization. Baseline blade Optimized blade Improvement EAEROTH(N) % EAEROTQ(Nm) % n= 5 EAEROTQ = 2 CTQ QNORM n n arean rn () n= where QNORM n is the sectional dynamic pressure at the stagnation point, and area n is the area of each trapezoidal panel. The sectional thrust and torque coefficients are defined as CTH = Cn sin( φ + β) + Ct cos( φ + β), (2) C = C cos( φ + β) C sin( φ + β). (3) TQ n t In Table 7, the total thrust and torque coefficients of the rotor blade before and after the design optimization are presented. It shows that a significant improvement of torque by approximately % was obtained from the present rotor blade optimization, while an additional penalty of approximately 8% thrust increment was accompanied. 7. Concluding remarks Aerodynamic performance enhancement of wind turbine rotor blades was investigated by using an aerodynamic design optimization framework. Considering very long and slender horizontal-axis wind turbine rotor blades, the effect of threedimensional aerodynamic features is neglected, and the blade airfoil section configuration was optimized at selected spanwise stations of the blade. For this purpose, a two-dimensional sectional design optimization technique was developed based on a state-of-the-art computational fluid dynamics technique. This section design framework was utilized to maximize the ratio of airfoil lift to drag. The present design framework was applied to optimize the blade airfoil section of the National Renewable Energy Laboratory (NREL) Phase VI rotor blade. The optimized airfoil sections are re-configured to reconstruct a three-dimensional rotor blade, and the performance of the optimized rotor blade was predicted by using a three-dimensional flow solver. The results are compared with those of the original baseline rotor blade to demonstrate the capability of the present methodology. It was found that approximately % of torque enhancement was obtained from the present aerodynamic shape design optimization. Acknowledgment This work supported by the Human Resources Development of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy (No N-BL-HM-E ). The authors would like to acknowledge the support from KISTI supercomputing center through the strategic support program for the supercomputing application research. Nomenclature C TH C TQ C n C t C l C d C p OBJ g j Re c References : Thrust coefficient : Torque coefficient : Sectional normal force coefficient : Sectional tangential force coefficient : Two-dimensional lift coefficient : Two-dimensional drag coefficient : Wall pressure coefficient : Objective function : Constraints : Reynolds number : Characteristic length [] P. Fuglsang and H. A. Madsen, Optimization method for wind turbine rotors, Journal of Wind Engineering and Industrial Aerodynamics, 80 (999) [2] W. Xudong, W. Z. Shen, W. J. Zhu, J. N. Sørensen and C. Jin, Shape optimization of wind turbine blades, Journal of Wind Energy, 2 (2009) [3] J. J. Chattot, Optimization of wind turbines using helicoidal vortex model, American Society of Mechanical Engineering, 2 (2009) [4] L. Piegl and W. Tiller, The NURBS Book, Springer, New York (995). [5] P. Venkataraman, A new procedure for airfoil definition, AIAA CP (995). [6] H. Sobieczky, Parametric airfoils and wings, Notes on Numerical Fluid Mechanics, 68 (988) [7] D. M. Somers, Design and experimental results for the S809 airfoil, NREL/SR (997). [8] D. T. Pham and G. Jin, A hybrid genetic algorithm, Proc. 3 rd World Congress on Expert Systems, Seoul, Korea, 2 (996) [9] G. N. Vanderplaats and S. R. Hansen, DOT user's manual, VMA Engineering (989). [0] R. B. Langtry and F. R. Menter, Correlation based transition modeling for unstructured parallelized computational fluid dynamics codes, AIAA Journal, 47 (2009) [] M. M Hand, D. A. Simms, L. J. Fingersh, D. W. Jager, J. R. Cotrell, S. Schreck and S. M. Larwood, Unsteady aerodynamics experiment phase vi:wind tunnel test configurations and available data campaigns, NREL/TP , NREL (200). Kwon, Hyung-Il received his B.S. in Aerospace Engineering from Inha University, Korea. He received his M.S in Aerospace System Engineering at Computational Aerodynamics and Design Optimization Laboratory, KAIST. His research interest is numerical aerodynamic design optimization.