Airfoil Shape Optimization of a Horizontal Axis Wind Turbine Blade using a Discrete Adjoint Solver

Document Type : Regular Article


1 Centre de Développement des Energies Renouvelables, CDER, B.P 62 Route de l’Observatoire, 16340, Bouzaréah, Alger, Algerie

2 Univ. Lille, CNRS, ONERA, Arts et Metiers Institute of Technology, Centrale Lille, UMR 9014 – LMFL - Laboratoire de Mécanique des Fluides de Lille - Kampé de Fériet, F-59000 Lille, France



In this study, airfoil shape optimization of a wind turbine blade is performed using the ANSYS Fluent Adjoint Solver. The aim of this optimization process is to increase the wind turbine output power, and the objective function is to maximize the airfoil lift to drag ratio (Cl/CD ). This study is applied to the NREL phase VI wind turbine, therefore, the S809 airfoil is used as a reference profile. First, for the validation of the applied numerical model, steady-state simulations are carried out for the S809 airfoil at various angles of attack. Then, the optimization is performed with the airfoil set at a fixed angle of attack, , considering three Reynolds numbers, Re =3 105,4.8 10 and 106. Next, computations are performed for the fluid flow around the optimized airfoils at angles of attack AOA= 6.1° ranging from 0° to 20°. The results show that (i) the lift to drag ratios of the optimized airfoils are significantly improved compared to the baseline S809 airfoil, (ii) this improvement is sensitive to the Reynolds number, and (iii) the Cl/CD ratios are also improved for another angle of attack values. Thereafter, the optimized airfoils are used for the design of the NREL Phase VI blade and the aerodynamic performances of this new wind turbine are assessed using the open-source code QBlade. These latter results indicate that when the blades are designed with the optimized airfoils, the wind turbine aerodynamic performances increase significantly. Indeed, at a wind speed of 10 m/s, the power output of the wind turbine is improved by about 38% compared to that of the original turbine.


Akram, M. T. and M. H. Kim (2021). Aerodynamic Shape Optimization of NREL S809 Airfoil for Wind Turbine Blades Using Reynolds-Averaged Navier Stokes Model—Part II. Applied Sciences 11(5), 2211.##
Ali, B., G. Ouahiba, O. Hamid and B. Ahmed (2019). Aerodynamic optimization of active flow control over S809 airfoil using synthetic jet. In 2018 International Conference on Wind Energy and Applications in Algeria, IEEE.##
ANSYS Fluent User’s Guide, Release 2020 R2.##
Bekhti, A., O. Guerri and T. Rezoug (2016). Flap/lead-lag computational investigations on NREL S809 airfoil. Mechanics and Industry 17(6), 606.##
Chen, J., Q. Wang, S. Zhang, P. Eecen and F. Grasso (2016). A new direct design method of wind turbine airfoils and wind tunnel experiment. Applied Mathematical Modelling 40(3), 2002-2014.##
Day, H., D. Ingham, L. Ma and M. Pourkashanian (2021). Adjoint based optimisation for efficient VAWT blade aerodynamics using CFD. Journal of Wind Engineering and Industrial Aerodynamics 208, 104431.##
Derakhshan, S., A. Tavaziani and N. Kasaeian (2015). Numerical shape optimization of a wind turbine blades using artificial bee colony algorithm. Journal of Energy Resources Technology, Transactions of the ASME 137(5).##
Dhert, T., T. Ashuri and J. R. R. A. Martins (2017). Aerodynamic shape optimization of wind turbine blades using a Reynolds-averaged Navier–Stokes model and an adjoint method. Wind Energy 20(5), 909-926.##
Ge, M., H. Zhang, Y. Wu and Y. Li (2019). Effects of leading edge defects on aerodynamic performance of the S809 airfoil. Energy Conversion and Management 195, 466-479.##
Grasso, F. (2012). Hybrid optimization for wind turbine thick airfoils. In Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.##
Guma, G., G. Bangga, T. Lutz and E. Krämer (2021). Aeroelastic analysis of wind turbines under turbulent inflow conditions. Wind Energy Science 6(1), 93-110.##
He, Y. and R. K. Agarwal (2014). Shape Optimization of NREL S809 Airfoil for Wind Turbine Blades Using a Multiobjective Genetic Algorithm. International Journal of Aerospace Engineering.##
Johansen, J. (1999). Unsteady Airfoil Flows with Application to Aeroelastic Stability. Technical University of Denmark.##
Kamali Moghadam, R., H. Jalali and A. Haghiri (2020). Wave drag reduction of SC(2)0410 airfoil using new developed inviscid compressible adjoint method. Journal of Applied Fluid Mechanics 13(4), 1277-1287.##
Karbasian, H. R., J. A. Esfahani and E. Barati (2016). Effect of acceleration on dynamic stall of airfoil in unsteady operating conditions. Wind Energy 19(1), 17-33.##
Khalil, Y., L. Tenghiri, F. Abdi and A. Bentamy (2020). Improvement of aerodynamic performance of a small wind turbine. Wind Engineering 44(1), 21-32.##
Li, H. C., Z. M. Yang, L. Zhang and R. Li (2021). Adjoint optimization method for head shape of high- speed maglev train. Journal of Applied Fluid Mechanics 14(6), 1839-1850.##
Li, J. Y., R. Li, Y. Gao and J. Huang, (2010). Aerodynamic optimization of wind turbine airfoils using response surface techniques. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 224(6), 827-838.##
Li, S., Y. Li, C. Yang, X. Zhang, Q. Wang, D. Li, W. Zhong and T. Wang (2018). Design and testing of a lut airfoil for straight-bladed vertical axis wind turbines. Applied Sciences 8(11), 2266.##
Menter, F. R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal 32(8), 1598-1605.##
Moshfeghi, M. and N. Hur (2017). Numerical study on the effects of a synthetic jet actuator on S809 airfoil aerodynamics at different flow regimes and jet flow angles. Journal of Mechanical Science and Technology 31(3), 1233-1240.##
Munoz-Paniagua, J., J. García, A. Crespo and F. Laspougeas (2015). Aerodynamic optimization of the nose shape of a train using the adjoint method. Journal of Applied Fluid Mechanics 8(3), 601-612.##
Nadarajah, S. K. and A. Jameson (2000). A comparison of the continuous and discrete adjoint approach to automatic aerodynamic optimization. In 38th Aerospace Sciences Meeting and Exhibit, Reno, NV,U. S. A.##
Perez-Blanco, H. and M. McCaffrey (2013). Aerodynamic performance of preferred wind turbine airfoils. Proceedings of the ASME Turbo Expo 6, 743-752.##
Ramsay, R., Hoffman, M., and Gregorek, G. (1995). Effects of Grit Roughness and Pitch Oscillations on the S809 Aerofoil. NREL/TP-442-7817, National Renewable Energy Laboratory, Golden, CO.##
Ribeiro, A. F. P., A. M. Awruch and H. M. Gomes (2012). An airfoil optimization technique for wind turbines. Applied Mathematical Modelling 36(10), 4898-4907.##
Rodriguez, C. V. and C. Celis (2022). Design optimization methodology of small horizontal axis wind turbine blades using a hybrid CFD/BEM/GA approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44(6), 254.##
Sale, D., A. Alberto, M. Michael and Y. Li (2013). Structural optimization of composite blades for wind and hydrokinetic turbines. In Proceedings 1 St Marine Energy Technology Conference, Washington.##
Schramm, M., B. Stoevesandt and J. Peinke (2018). Optimization of airfoils using the adjoint approach and the influence of adjoint turbulent viscosity. Computation 6(1), 5.##
Shi, X., S. Xu, L. Ding and D. Huang (2019). Passive flow control of a stalled airfoil using an oscillating micro-cylinder. Computers and Fluids 178, 152-165.##
Simms, D. A., M. M. Hand, L. J. Fingersh and D. W. Jager (1999). Unsteady Aerodynamics Experiment Phases II-IV Test Configurations and Available Data Campaigns. National Renewable Energy Lab. Golden, CO (United States).##
Somers, D. M. (1997). Design and Experimental Results for the S809 Airfoil. Nat Renew Energy Lab.##
Tahani, M., G. Kavari, M. Masdari and M. Mirhosseini (2017). Aerodynamic design of horizontal axis wind turbine with innovative local linearization of chord and twist distributions. Energy 131, 78-91.##
Timmer, W. A. and R. P. J. O. M. Van Rooij (2003). Summary of the delft university wind turbine dedicated airfoils. Journal of Solar Energy Engineering 125(4), 488-496.##
Viterna, L. A. and D. C. Janetzke (1982). Theoretical and Experimental Power from Large Horizontal-Axis Wind Turbines. National Aeronautics and Space Administration, Cleveland, OH (USA). Lewis Research Center.##
Vučina, D., I. Marinić-Kragić and Z. Milas (2016). Numerical models for robust shape optimization of wind turbine blades. Renewable Energy 87, 849-862.##
Wang, H., B. Zhang, Q. Qiu and X. Xu (2017). Flow control on the NREL S809 wind turbine airfoil using vortex generators. Energy 118, 1210-1221.##
Wang, L., X. Liu and A. Kolios (2016). State of the art in the aeroelasticity of wind turbine blades: Aeroelastic modelling. Renewable and Sustainable Energy Reviews 64, 195-210.##
Xudong, W., W. Z. Shen, W. J. Zhu, J. N. Sørensen and C. Jin (2009). Shape optimization of wind turbine blades. Wind Energy 12(8), 781-803.##
Zhong, J., J. Li and P. Guo (2017). Effects of leading-edge rod on dynamic stall performance of a wind turbine airfoil. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 231(8), 753-769 .##