Shape Optimization of an Asymmetric Airfoil for Low Wind Speed Region having Adjoint-Based Optimization Technique

Document Type : Regular Article


1 Mechanical Engineering Department, College of Engineering Pune, Pune, Maharashtra, 411005, India

2 Mechanical Engineering Department, National Institute of Technology, Agartala, Tripura, 799046, India



The land needed to install wind turbines is shrinking as power generation from renewable energy sources increases significantly. A large number of studies are being conducted to maximize the power extraction from wind turbines in areas with low wind speeds. Wind turbine blades play a significant role in utilizing the maximum amount of energy from the wind. The aerodynamic performance of a wind turbine blade depends on the airfoil shape. The shape optimization of an asymmetric S2027 airfoil for a low wind speed region was investigated using the adjoint-based optimization technique. The primary objectives of this study were to maximize the lift coefficient, minimize the drag coefficient, and maximize the lift-to-drag ratio. The optimization is based on the adjoint method for Reynolds number variation in the range of 2 × 105 to 5 × 105 and an angle of attack variation from 0° to 12°. A two-dimensional Reynolds–Averaged Navier–Strokes Computational Fluid Dynamics model was created with all the operating parameters and used for optimization. The aerodynamic performance was validated experimentally. For each optimization function, approximately 16 shapes were obtained. The aerodynamic performance for each optimized shape was determined under different operating conditions. Different airfoil shapes with a specific chord, leading and trailing edges, and span arrangement was obtained. The drag coefficient was reduced by 2%–30%; the lift coefficient was improved by 2%–35%, and the lift-to-drag ratio was improved up to 40%.


Bedon, G., S. De Betta and E. Benini (2016). Performance-optimized airfoil for Darrieus wind turbines. Renewable Energy 94, 328–340.##
Carpentieri, G., B. Koren and van M. J. L. Tooren (2007). Adjoint-based aerodynamic shape optimization on unstructured meshes. Journal of Computational Physics 224(1), 267–287.##
Chen, J. and Q. Wang (Eds.). (2018). Wind Turbine Airfoils and Blades. Science Press Ltd. and Walter de Gruyter GmbH, Beijing/Berlin/Boston.##
Della Vecchia, P., E. Daniele and E. D’Amato (2014). An airfoil shape optimization technique coupling PARSEC parameterization and evolutionary algorithm. Aerospace Science and Technology 32(1), 103–110.##
Diwakar, A., D. N. Srinath and S. Mittal (2010). Aerodynamic shape optimization of airfoils in unsteady flow. CMES - Computer Modeling in Engineering and Sciences 69(1), 61–89.##
Fuglsang, P. and C. Bak (2004). Development of the Risø wind turbine airfoils. Wind Energy 7(2), 145–162.##
Gomes, P. and R. Palacios (2020). Aerodynamic driven multidisciplinary topology optimization of compliant airfoils. AIAA Scitech 2020 Forum, 1 PartF, 2117–2130.##
Halila, G. L. O., J. R. R. A. Martins, K. J. Fidkowski (2020). Adjoint-based aerodynamic shape optimization including transition to turbulence effects. Aerospace Science and Technology 107, 106243.##
He, X., J. Wang, M. Yang, D. Ma, C. Yan and P. Liu (2016). Numerical simulation of Gurney flap on SFYT15thick airfoil. Theoretical and Applied Mechanics Letters 6(6), 286–292.##
Henriques, J. C. C., F. Marques da Silva, A. I. Estanqueiro and L. M. C. Gato (2009). Design of a new urban wind turbine airfoil using a pressure-load inverse method. Renewable Energy 34(12), 2728–2734.##
Kang, T. J. and W. G. Park (2013). Numerical investigation of active control for an S809 wind turbine airfoil. International Journal of Precision Engineering and Manufacturing 14(6), 1037–1041.##
Karpouzas, G. K. and E. De Villiers (2014). Level-set based topology optimization using the continuous adjoint method. OPT-i 2014 - 1st International Conference on Engineering and Applied Sciences Optimization, Proceedings June, 56–74.##
Liang, C. and H. Li (2018). Effects of optimized airfoil on vertical axis wind turbine aerodynamic performance. Journal of the Brazilian Society of Mechanical Sciences and Engineering 40(2).##
Nadarajah, S. K. and A. Jameson (2000). A comparison of the continuous and discrete adjoint approach to automatic aerodynamic optimization. Aerospace Science Meeting and Exhibit.##
Malone, J. B., J. C. Narramore and L. N. Sankar (1991). Airfoil design method using the Navier-Stokes equations. Journal of Aircraft 28(3), 216–224.##
Menter, F. R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal 32(8), 1598–1605.##
Mortazavi, S. M., M. R. Soltani and H. Motieyan (2015). A Pareto optimal multi-objective optimization for a horizontal axis wind turbine blade airfoil sections utilizing exergy analysis and neural networks. Journal of Wind Engineering and Industrial Aerodynamics 136, 62–72.##
Mukesh, R., K. Lingadurai and U. Selvakumar (2014). Airfoil shape optimization using non-traditional optimization technique and its validation. Journal of King Saud University - Engineering Sciences 26(2), 191–197.##
Othmer, C. (2014). Adjoint methods for car aerodynamics. Journal of Mathematics in Industry 4(1), 1–23.##
Petrone, G., D. C. Hill and M. E. Biancolini (2014). Track by track robust optimization of a F1 front wing using adjoint solutions and radial basis functions. 32nd AIAA Applied Aerodynamics Conference, June, 1–9.##
Ram, K. R., S. P. Lal and M. R. Ahmed (2019). Design and optimization of airfoils and a 20 kW wind turbine using multi-objective genetic algorithm and HARP_Opt code. Renewable Energy, 56–67.##
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), 1–23.##
Sharma, P., B. Gupta, M. Pandey, A. K. Sharma and R. Nareliya Mishra (2020). Recent advancements in optimization methods for wind turbine airfoil design: A review. Materials Today: Proceedings 47(16), 6556–6563.##
Srinath, D. N. and S. Mittal (2010). Optimal aerodynamic design of airfoils in unsteady viscous flows. Computer Methods in Applied Mechanics and Engineering 199(29–32), 1976–1991.##
Tezduyar, T. E., S. Mittal, S. E. Ray and R. Shih (1992). Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Computer Methods in Applied Mechanics and Engineering 95(2), 221–242.##
Wang, K., S. Yu, Z. Wang, R. Feng and T. Liu (2019). Adjoint-based airfoil optimization with adaptive isogeometric discontinuous Galerkin method. Computer Methods in Applied Mechanics and Engineering 344, 602–625.##
Wang, Q., J. Wang, J. Chen, S. Luo and J. Sun (2015). Aerodynamic shape optimized design for wind turbine blade using new airfoil series. Journal of Mechanical Science and Technology 29(7), 2871–2882.##
Volume 16, Issue 2 - Serial Number 70
February 2023
Pages 299-310
  • Received: 15 July 2022
  • Revised: 10 October 2022
  • Accepted: 10 October 2022
  • First Publish Date: 01 February 2023