Abstract
A new airfoil shape parameterization method is developed, which extended the Bezier curve to the generalized form with adjustable shape parameters. The local control parameters at airfoil leading and trailing edge regions are enhanced, where have significant effect on the aerodynamic performance of wind turbine. The results show this improved parameterization method has advantages in the fitting characteristics of geometry shape and aerodynamic performance comparing with other three common airfoil parameterization methods. The new parameterization method is then applied to airfoil shape optimization for wind turbine using Genetic Algorithm (GA), and the wind turbine special airfoil, DU93-W-210, is optimized to achieve the favorable Cl/Cd at specified flow conditions. The aerodynamic characteristic of the optimum airfoil is obtained by solving the RANS equations in computational fluid dynamics (CFD) method, and the optimization convergence curves show that the new parameterization method has good convergence rate in less number of generations comparing with other methods. It is concluded that the new method not only has well controllability and completeness in airfoil shape representation and provides more flexibility in expressing the airfoil geometry shape, but also is capable to find efficient and optimal wind turbine airfoil. Additionally, it is shown that a suitable parameterization method is helpful for improving the convergence rate of the optimization algorithm.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Chen X, Agarwal R K. Optimization of wind turbine blade airfoils using a multi-objective genetic algorithm. Journal of Aircraft, 2013, 50(2): 519–527.
Kulfan B M. Universal parametric geometry representation method. Journal of Aircraft, 2008, 45(1): 142–158.
Samareh J A. A survey of shape parameterization techniques. NASA Conference Publication, Williamsburg, U.S.A, 1999; pp.333–343.
Song W, Keane A J. A study of shape parameterization methods for airfoil optimization. 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, U.S.A, 2004; pp.2031–2038.
Liao Y P, Liu L, Long T. Investigation of various parametric geometry representation methods for airfoils. Applied Mechanics and Materials, 2012, 110: 3040–3046.
El Majd B A, Désidéri J A, Duvigneau R. Multilevel strategies for parametric shape optimization in aerodynamics. European Journal of Computational Mechanics/ Revue Européenne de Mécanique Numérique, 2008, 17(1–2): 149–168.
Straathof M H, L. Van Tooren M J. Extension to the class-shape-transformation method based on B-splines. AIAA Journal, 2011, 49(4): 780–790.
Samareh J A. Novel multidisciplinary shape parameterization approach. Journal of Aircraft, 2001, 38(6): 1015–1024.
Lassila T, Rozza G. Parametric free-form shape design with PDE models and reduced basis method. Computer Methods in Applied Mechanics and Engineering, 2010, 199(23): 1583–1592.
Kulfan B M, Bussoletti J E. Fundamental parametric geometry representations for aircraft component shapes. AIAA paper, 2006, No.2006-6948, Portsmouth, Virginia, USA.
Jones W T, Samareh-Abolhassani J. A grid generation system for multi-disciplinary design optimization. 12th Computational Fluid Dynamics Conference, San Diego, U.S.A, 1995; pp. 657–665.
Marco N, Lanteri S. A two-level parallelization strategy for Genetic Algorithms applied to optimum shape design. Parallel Computing, 2000, 26(4): 377–397.
Shahrokhi A, Jahangirian A. Airfoil shape parameterization for optimum Navier-Stokes design with genetic algorithm. Aerospace science and technology, 2007, 11(6): 443–450.
Zhang F, Chen S, Khalid M. Multi-point optimization of transonic wing by real-coded genetic algorithm. The Eleventh Annual Conference of the CFD Society of Canada, Vancouver, Canada, 2003.
Sobieczky H. Parametric Airfoils and Wings. Notes on Numerical Fluid Mechanics, 1998, 71–88.
Sobieczky H. Computational methods for the design of adaptive airfoils and wings. 3rd Conference on Numerical Methods in Fluid Mechanics, Cologne, Germany, 1979; pp. 269–278.
Hicks R M, Henne P A. Wing design by numerical optimization. Journal of Aircraft, 1978, 15(7): 407–412.
Fuglsang P, Bak C. Development of the RisØ wind turbine airfoils. Wind Energy, 2004, 7(2): 145–162.
Far in G. Curves and Surfaces for Computer Aided Geometric Design. New York: Academic press, 1988, 44–48.
Chen Q Y, Wang G Z. A class of Bézier-like curves. Computer Aided Geometric Design, 2003, 20: 29–39.
Balu R, Selvakumar U. Optimum hierarchical Bezier parameterization of arbitrary curves and surfaces. Proceedings of the 11th Annual CFD Symposium, Bangalore, India, 2009; pp.46–48.
Castonguay P, Nadarajah S. Effect of shape parameterization on aerodynamic shape optimization. 45th AIAA Aerospace Sciences Meeting and Exhibit, Nevada, U.S.A, 2007; pp. 1–20.
Wold S. Spline functions in data analysis. Technometrics, 1974, 16(1): 1–11.
Yang L, Zeng X M. Bézier curves and surfaces with shape parameters. International Journal of Computer Mathematics, 2009, 86(7): 1253–1263.
Potsdam M A, Guruswamy G P. A parallel multiblock mesh movement scheme for complex aeroelastic applications. AIAA Paper, 2001, No.2001-0716 Reno, Nevada, USA.
W.A. Timmer, R.P.J.O.M. van Rooij. Summary of the Delft University wind turbine dedicated airfoils. AIAA-2003-0352, Reno, Nevada, USA.
Author information
Authors and Affiliations
Additional information
This work was funded by the National Natural Science Foundation of China (No.51376024), and the Specialized Research Fund for the Doctoral Program of Higher Education (No.20131101110015), China.
Rights and permissions
About this article
Cite this article
Liu, Y., Yang, C. & Song, X. An airfoil parameterization method for the representation and optimization of wind turbine special airfoil. J. Therm. Sci. 24, 99–108 (2015). https://doi.org/10.1007/s11630-015-0761-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11630-015-0761-7