Airfoil shape optimization using Bézier curve and genetic algorithm
Abstract
There are different types of airfoil used in many applications such as energy production, aerospace, mixing of fluid products. Design optimization studies are still being carried out on the airfoil type structures. The airfoil section is the most important factor affecting the quality and efficiency of the performed work. The aim of this study is the optimization of the airfoil shape to generate more lift than the original airfoil shape creates. For this purpose, Bézier curves are used to generate the airfoil polar points, XFOIL is used as a flow solver and MATLAB is used to create optimization codes using the genetic algorithm. The results show that the created optimal airfoil shape produces more lift than the original airfoil shape. In this study, design optimization studies are supported by flow analysis using ANSYS Fluent.
Keyword : parametric design, Bézier curve, computational fluid dynamics, airfoil shape optimization, genetic algorithm
How to Cite
Ayaz Ümütlü, H. C., & Kiral, Z. (2022). Airfoil shape optimization using Bézier curve and genetic algorithm. Aviation, 26(1), 32–40. https://doi.org/10.3846/aviation.2022.16471
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Anitha, D., Shamili, G. K., Ravi Kumar, P., & Sabari Vihar, R. (2018). Air foil shape optimization using Cfd and parametrization methods. Materials Today: Proceedings, 5(2), Part I, 5364–5373. https://doi.org/10.1016/j.matpr.2017.12.122
Della Vecchia, P., Daniele, E., & D’Amato, E. (2014). An airfoil shape optimization technique coupling PARSEC parameterization and evolutionary algorithm. Aerospace Science and Technology, 32(1), 103–110. https://doi.org/10.1016/j.ast.2013.11.006
Derksen, R. W., & Rogalsky, T. (2010). Bezier-PARSEC: An optimized aerofoil parameterization for design. Advances in Engineering Software, 41(7–8), 923–930. https://doi.org/10.1016/j.advengsoft.2010.05.002
Drela, M. (1989). XFOIL: An analysis and design system for low Reynolds number airfoils. In T. J. Mueller (Eds.), Low Reynolds Number Aerodynamics. Lecture Notes in Engineering, Vol. 54 (pp. 1–12). Springer. https://doi.org/10.1007/978-3-642-84010-4_1
Ebrahimi, M., & Jahangirian, A. (2014). Aerodynamic optimization of airfoils using adaptive parameterization and genetic algorithm. Journal of Optimization Theory and Applications, 162(1), 257–271. https://doi.org/10.1007/s10957-013-0442-1
Fazil, J., & Jayakumar, V. (2011). Investigation of airfoil profile design using reverse engineering Bezier curve. Journal of Engineering and Applied Sciences, 6(7), 43–52.
Fincham, J. H. S., & Friswell, M. I. (2015). Aerodynamic optimisation of a camber morphing aerofoil. Aerospace Science and Technology, 43, 245–255. https://doi.org/10.1016/j.ast.2015.02.023
Hansen, T. H. (2018). Airfoil optimization for wind turbine application. Wind Energy, 21(7), 502–514. https://doi.org/10.1002/we.2174
Jeong, J. H., & Kim, S. H. (2018). Optimization of thick wind turbine airfoils using a genetic algorithm. Journal of Mechanical Science and Technology, 32(7), 3191–3199. https://doi.org/10.1007/s12206-018-0622-x
Kharal, A., & Saleem, A. (2012). Neural networks based airfoil generation for a given Cp using Bezier-PARSEC parameterization. Aerospace Science and Technology, 23(1), 330–344. https://doi.org/10.1016/j.ast.2011.08.010
Khurana, M. S., Winarto, H., & Sinha, A. K. (2008). Application of swarm approach and artificial neural networks for airfoil shape optimization. In 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, MAO, 5954, 1–15. https://doi.org/10.2514/6.2008-5954
Koreanschi, A., Sugar Gabor, O., Acotto, J., Brianchon, G., Portier, G., Botez, R. M., Mamou, M., & Mebarki, Y. (2017). Optimization and design of an aircraft’s morphing wing-tip demonstrator for drag reduction at low speed, Part I – Aerodynamic optimization using genetic, bee colony and gradient descent algorithms. Chinese Journal of Aeronautics, 30(1), 149–163. https://doi.org/10.1016/j.cja.2016.12.013
Kulfan, B. M. (2008). Universal parametric geometry representation method. Journal of Aircraft, 45(1), 142–158. https://doi.org/10.2514/1.29958
Lim, H. W., & Kim, H. (2019). Multi-objective airfoil shape optimization using an adaptive hybrid evolutionary algorithm. Aerospace Science and Technology, 87, 141–153. https://doi.org/10.1016/j.ast.2019.02.016
Lu, X., Huang, J., Song, L., & Li, J. (2018). An improved geometric parameter airfoil parameterization method. Aerospace Science and Technology, 78, 241–247. https://doi.org/10.1016/j.ast.2018.04.025
Mauclère, X. (2009). Automatic 2D airfoil generation, evaluation and optimisation using MATLAB and XFOIL [Master’s thesis, Technical University of Denmark].
Melin, T. (2013). Parametric airfoil catalog, Part II: Göttingen 673 to YS930: An aerodynamic and geometric comparison between parametrized and point cloud airfoils. Linköping University Electronic Press.
Mengistu, T., & Ghaly, W. (2008). Aerodynamic optimization of turbomachinery blades using evolutionary methods and ANN-based surrogate models. Optimization and Engineering, 9(3), 239–255. https://doi.org/10.1007/s11081-007-9031-1
Messac, A. (2015). Optimization in practice with MATLAB®: For engineering students and professionals. Cambridge University Press. https://doi.org/10.1017/CBO9781316271391
Morgado, J., Vizinho, R., Silvestre, M. A. R., & Páscoa, J. C. (2016). XFOIL vs CFD performance predictions for high lift low Reynolds number airfoils. Aerospace Science and Technology, 52, 207–214. https://doi.org/10.1016/j.ast.2016.02.031
Mukesh, R., Lingadurai, K., & Selvakumar, U. (2014). Airfoil shape optimization using non-traditional optimization technique and its validation. Journal of King Saud University – Engineering Sciences, 26(2), 191–197. https://doi.org/10.1016/j.jksues.2013.04.003
Reddy, S. R., Sobieczky, H., Dulikravic, G. S., & Abdoli, A. (2016). Multi-element winglets: Multi-objective optimization of aerodynamic shapes. Journal of Aircraft, 53(4), 992–1000. https://doi.org/10.2514/1.C033334
Ribeiro, A. F. P., Awruch, A. M., & Gomes, H. M. (2012). An airfoil optimization technique for wind turbines. Applied Mathematical Modelling, 36(10), 4898–4907. https://doi.org/10.1016/j.apm.2011.12.026
Rogers, D. F., & Adams, J. A. (1990). Mathematical elements for computer graphics. McGraw-Hill.
Salunke, N. P., Junad Ahamad, R. A., & Channiwala, S. A. (2014). Airfoil parameterization techniques: A review. American Journal of Mechanical Engineering, 2(4), 99–102. https://doi.org/10.12691/ajme-2-4-1
Sripawadkul, V., Padulo, M., & Guenov, M. (2010). A comparison of airfoil shape parameterization techniques for early design optimization. In 13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2010, 9050. https://doi.org/10.2514/6.2010-9050
Sun, G., Sun, Y., & Wang, S. (2015). Artificial neural network based inverse design: Airfoils and wings. Aerospace Science and Technology, 42, 415–428. https://doi.org/10.1016/j.ast.2015.01.030
Tandis, E., & Assareh, E. (2017). Inverse design of airfoils via an intelligent hybrid optimization technique. Engineering with Computers, 33(3), 361–374. https://doi.org/10.1007/s00366-016-0478-6
Timnak, N., & Jahangirian, A. (2018). Multi-point optimization of transonic airfoils using an enhanced genetic algorithm. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 232(7), 1347–1360. https://doi.org/10.1177/0954410017690549
White, F. M. (2011). Fluid mechanics (7th ed.). McGraw-Hill.
Yang, F., Yue, Z., Li, L., & Yang, W. (2018). Aerodynamic optimization method based on Bezier curve and radial basis function. In Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 232(3), 459–471. https://doi.org/10.1177/0954410016679433
Ziemkiewicz, D. (2017). Simple parametric model for airfoil shape description. AIAA Journal, 55(12), 4390–4393. https://doi.org/10.2514/1.J055986
Della Vecchia, P., Daniele, E., & D’Amato, E. (2014). An airfoil shape optimization technique coupling PARSEC parameterization and evolutionary algorithm. Aerospace Science and Technology, 32(1), 103–110. https://doi.org/10.1016/j.ast.2013.11.006
Derksen, R. W., & Rogalsky, T. (2010). Bezier-PARSEC: An optimized aerofoil parameterization for design. Advances in Engineering Software, 41(7–8), 923–930. https://doi.org/10.1016/j.advengsoft.2010.05.002
Drela, M. (1989). XFOIL: An analysis and design system for low Reynolds number airfoils. In T. J. Mueller (Eds.), Low Reynolds Number Aerodynamics. Lecture Notes in Engineering, Vol. 54 (pp. 1–12). Springer. https://doi.org/10.1007/978-3-642-84010-4_1
Ebrahimi, M., & Jahangirian, A. (2014). Aerodynamic optimization of airfoils using adaptive parameterization and genetic algorithm. Journal of Optimization Theory and Applications, 162(1), 257–271. https://doi.org/10.1007/s10957-013-0442-1
Fazil, J., & Jayakumar, V. (2011). Investigation of airfoil profile design using reverse engineering Bezier curve. Journal of Engineering and Applied Sciences, 6(7), 43–52.
Fincham, J. H. S., & Friswell, M. I. (2015). Aerodynamic optimisation of a camber morphing aerofoil. Aerospace Science and Technology, 43, 245–255. https://doi.org/10.1016/j.ast.2015.02.023
Hansen, T. H. (2018). Airfoil optimization for wind turbine application. Wind Energy, 21(7), 502–514. https://doi.org/10.1002/we.2174
Jeong, J. H., & Kim, S. H. (2018). Optimization of thick wind turbine airfoils using a genetic algorithm. Journal of Mechanical Science and Technology, 32(7), 3191–3199. https://doi.org/10.1007/s12206-018-0622-x
Kharal, A., & Saleem, A. (2012). Neural networks based airfoil generation for a given Cp using Bezier-PARSEC parameterization. Aerospace Science and Technology, 23(1), 330–344. https://doi.org/10.1016/j.ast.2011.08.010
Khurana, M. S., Winarto, H., & Sinha, A. K. (2008). Application of swarm approach and artificial neural networks for airfoil shape optimization. In 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, MAO, 5954, 1–15. https://doi.org/10.2514/6.2008-5954
Koreanschi, A., Sugar Gabor, O., Acotto, J., Brianchon, G., Portier, G., Botez, R. M., Mamou, M., & Mebarki, Y. (2017). Optimization and design of an aircraft’s morphing wing-tip demonstrator for drag reduction at low speed, Part I – Aerodynamic optimization using genetic, bee colony and gradient descent algorithms. Chinese Journal of Aeronautics, 30(1), 149–163. https://doi.org/10.1016/j.cja.2016.12.013
Kulfan, B. M. (2008). Universal parametric geometry representation method. Journal of Aircraft, 45(1), 142–158. https://doi.org/10.2514/1.29958
Lim, H. W., & Kim, H. (2019). Multi-objective airfoil shape optimization using an adaptive hybrid evolutionary algorithm. Aerospace Science and Technology, 87, 141–153. https://doi.org/10.1016/j.ast.2019.02.016
Lu, X., Huang, J., Song, L., & Li, J. (2018). An improved geometric parameter airfoil parameterization method. Aerospace Science and Technology, 78, 241–247. https://doi.org/10.1016/j.ast.2018.04.025
Mauclère, X. (2009). Automatic 2D airfoil generation, evaluation and optimisation using MATLAB and XFOIL [Master’s thesis, Technical University of Denmark].
Melin, T. (2013). Parametric airfoil catalog, Part II: Göttingen 673 to YS930: An aerodynamic and geometric comparison between parametrized and point cloud airfoils. Linköping University Electronic Press.
Mengistu, T., & Ghaly, W. (2008). Aerodynamic optimization of turbomachinery blades using evolutionary methods and ANN-based surrogate models. Optimization and Engineering, 9(3), 239–255. https://doi.org/10.1007/s11081-007-9031-1
Messac, A. (2015). Optimization in practice with MATLAB®: For engineering students and professionals. Cambridge University Press. https://doi.org/10.1017/CBO9781316271391
Morgado, J., Vizinho, R., Silvestre, M. A. R., & Páscoa, J. C. (2016). XFOIL vs CFD performance predictions for high lift low Reynolds number airfoils. Aerospace Science and Technology, 52, 207–214. https://doi.org/10.1016/j.ast.2016.02.031
Mukesh, R., Lingadurai, K., & Selvakumar, U. (2014). Airfoil shape optimization using non-traditional optimization technique and its validation. Journal of King Saud University – Engineering Sciences, 26(2), 191–197. https://doi.org/10.1016/j.jksues.2013.04.003
Reddy, S. R., Sobieczky, H., Dulikravic, G. S., & Abdoli, A. (2016). Multi-element winglets: Multi-objective optimization of aerodynamic shapes. Journal of Aircraft, 53(4), 992–1000. https://doi.org/10.2514/1.C033334
Ribeiro, A. F. P., Awruch, A. M., & Gomes, H. M. (2012). An airfoil optimization technique for wind turbines. Applied Mathematical Modelling, 36(10), 4898–4907. https://doi.org/10.1016/j.apm.2011.12.026
Rogers, D. F., & Adams, J. A. (1990). Mathematical elements for computer graphics. McGraw-Hill.
Salunke, N. P., Junad Ahamad, R. A., & Channiwala, S. A. (2014). Airfoil parameterization techniques: A review. American Journal of Mechanical Engineering, 2(4), 99–102. https://doi.org/10.12691/ajme-2-4-1
Sripawadkul, V., Padulo, M., & Guenov, M. (2010). A comparison of airfoil shape parameterization techniques for early design optimization. In 13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2010, 9050. https://doi.org/10.2514/6.2010-9050
Sun, G., Sun, Y., & Wang, S. (2015). Artificial neural network based inverse design: Airfoils and wings. Aerospace Science and Technology, 42, 415–428. https://doi.org/10.1016/j.ast.2015.01.030
Tandis, E., & Assareh, E. (2017). Inverse design of airfoils via an intelligent hybrid optimization technique. Engineering with Computers, 33(3), 361–374. https://doi.org/10.1007/s00366-016-0478-6
Timnak, N., & Jahangirian, A. (2018). Multi-point optimization of transonic airfoils using an enhanced genetic algorithm. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 232(7), 1347–1360. https://doi.org/10.1177/0954410017690549
White, F. M. (2011). Fluid mechanics (7th ed.). McGraw-Hill.
Yang, F., Yue, Z., Li, L., & Yang, W. (2018). Aerodynamic optimization method based on Bezier curve and radial basis function. In Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 232(3), 459–471. https://doi.org/10.1177/0954410016679433
Ziemkiewicz, D. (2017). Simple parametric model for airfoil shape description. AIAA Journal, 55(12), 4390–4393. https://doi.org/10.2514/1.J055986