Representation method effects on vibrational genetic algorithm in 2-D airfoil design

Bu makalede iki boyutlu kanat tasarımı dahilinde kanat profil geometrisi temsil yönteminin optimizasyon sürecine etkileri test edilmiştir. Temsil yöntemleri olarak Parsec formülasyonu ve Bezier parametrik eğri yaklaşımı, optimizasyon yöntemi olarak ise reel kodlu titreşimli genetic algoritma dikkate alınmıştır. Yapılan çalışma sonucu Parsec yönteminin ses altı akış şartlarında tersten tasarım probleminde daha kısa sürede optimizasyona imkan sağladığı,buna karşılık Bezier parametrik eğri yönteminin ise ses civarı akış şartlarında daha çabuk yakınsamaya olanak verdiği gözlemlenmiştir.

İki boyutlu kanat profili tasarımında geometri temsil yönteminin titreşimli genetik algoritma üzerine etkileri

In this article, two different curve representation methods; Parsec and Bezier representation methods are tested via vibrational genetic algorithm [VGA] to show the effect of representation method on search type optimization process in 2-D airfoil design. From the results obtained, it is concluded that Parsec method has a better performance in subsonic flow conditions within the inverse design problem. On the other hand, it is also concluded that Bezier representation method is more efficient than Parsec in transonic flow regime.

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  • [1] Sobieczky H., Parametric Airfoils and Wings, in: Notes on Numerical Fluid Mechanics, pp.71-88, Vieweg, 1998.
  • [2] Wu H-Y., Yang S., Liu F., and Tsai H-M, Comparison of Three Geometric Representations of Airfoils for Aerodynamic Optimization, AIAA 2003– 4095,16th AIAA Computational Fluid Dynamics Conference June 23–26, 2003.
  • [3] Farin G., Curves and Surfaces for Computer Aided Geometric Design; A practical Guide, Academic Press, Inc., p. XVI, 1993.
  • [4] Rogers F. D., “An Introduction to NURBS with Historical Perspective”, USA, p. 10, 2001.
  • [5] Klein M., Sobieczky H., Sensitivity of Aerodynamic Optimization to Parameterized Target Functions, Proc. Int. Symp. On Inverse Problems an Engineering Mechanics, Japan, 2001.
  • [6] von Doenhoff E. A., Abbott H. I., “Theory of Wing Sections”, Dover Publications, Inc., p. 111-115, 1959.
  • [7] Nemec M., Optimal Shape Design Of Aerodynamic Configurations: A Newton-Krylov Approach, A thesis for the degree of Doctor of Philosophy, Toronto, 2003.
  • [8] Chang I-C., Torres F. C., and Tung C., Geometric Analysis of Wing Sections, NASA Technical Memorandum 110346, 1995.
  • [9] Hajek J., Parameterization of Airfoils and Its Application in Aerodynamic Optimization, WDS'07 Proceedings of Contributed Papers, Part I, p. 233–240, 2007.
  • [10] Wu H-Y., Yang S., Liu F., and Tsai H-M, Comparison of Three Geometric Representations of Airfoils for Aerodynamic Optimization, AIAA 2003– 4095,16th AIAA Computational Fluid Dynamics Conference June 23–26, 2003.
  • [11] Mousavi A., Castonguay P., Nadarajah S. K, Survey Of Shape Parameterization Techniques and its Effect on 3-Dimensional Aerodynamic Shape Optimization, AIAA document.
  • [12] Baysal O., Eleshaky M., Aerodynamic Design Optimization Using Sensitivity Analysis and Computational Fluid Dynamics, AIAA Journal, Vol. 30, No 3, p. 718-725, 1992.
  • [13] Vanderplaats, G. N., Numerical Optimization Techniques for Engineering Design. McGraw-Hill Book Company, New York, 1984.
  • [14] Holland J. H., Adaptation in Natural and Artificial Systems, the University of Michigan Press, p. 21-22, 1975.
  • [15] Shahrokhi A., Jahangirian A., Airfoil shape parameterization for optimum Navier–Stokes design with genetic algorithm, Aerospace Science and Technology 11 [2007] 443–450.
  • [16] Song W., and Keane A. J., A Study of Shape Parameterization Methods for Airfoil Optimization, 10th AIAA Multidisciplinary Analysis and Optimization Conference, Albany, New York, AIAA 2004-4482, 2004.
  • [17] Hacioglu A., Using Genetic Algorithm in Aerodynamic Design and Optimization, Ph. D. Thesis, Technical University of Istanbul, 2003.
  • [18] Vatandas E., Hacioglu A., Ozkol I., Vibrational Genetic Algorithm (VGA) and Dynamic Mesh in the Optimization of 3D Wing Geometries, Inverse Problems in Science and Engineering, Vol.15, No. 6, p. 643-657, 2007.
  • [19] Pehlivanoglu Y. V., Baysal O., and Hacioglu A., Path planning for autonomous UAV via VGA, Aircraft Engineering and Aerospace Technology: An International Journal, Volume 79 · Number 4 · 2007 · 352–359.