Evolutionary Airfoil Shape Optimization Coupling Parameterization Methods with Lagrangian Vortex Method
Main Article Content
Abstract
In the present paper, the evolutionary algorithm for single-objective optimization is developed using a genetic algorithm and employing polynomial-based (PARSEC) and radial basis function (RBF) functions for NACA 2412 airfoil parameterization. The determination of the objective functions (aerodynamic coefficients) are performed using the Lagrangian vortex particle method. The results of the lift coefficient at the wide range of angle of attack using the vortex particle method shows a good agreement with experimental data listed in the literature. For the optimization results, the lift coefficient obtained from the PARSEC method is optimized to be larger for the whole range of AoAs; while it still keeps the stall region at the upper surface of the airfoil to be the same as that of the original airfoil. In addition, the RBF method illustrates the lift coefficients larger at the range of AoA from -5 to 14 but stall occurs earlier than the original airfoil.
Keywords
optimization, vortex particle method, viscous flow
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
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Sections, Dover Publications, Inc., New York, 1959.
numerical optimization to the design of low-speed
airfoils, NASA TM X-3213, Ames Research Center,
Moffet Field, CA, 1975.
[2] Q. Ruizhan, Z. Ziqiang, A variable fidelity optimization
framework using second-order multi-point additive
scaling functions applied to airfoil design, in: 25th
International Congress of the Aeronautical Sciences,
Hamburg, Germany, 3–8 September, 2006.
[3] M. Khurana, Airfoil geometry parameterization through
shape optimizer and computational fluid dynamics, in:
46th AIAA Aerospace Sciences Meeting and Exhibit,
USA, 7th–10th January, 2008.
https://doi.org/10.2514/6.2008-295
[4] J. A. Samareh, A survey of shape parameterization
techniques, CEAS/AIAA/ ICASE/NASA Langley
International Forum on Aeroelasticity and Structural
Dynamics, Williamsburg, VA, June 22–25, 1999.
[5] R. W. Derksen, T. Rogalsky, Bezier-PARSEC: An
optimized aerofoil parameterization for design,
Adv.Eng. Softw., vol. 41, pp. 923–930, 2010.
https://doi.org/10.1016/j.advengsoft.2010.05.002
[6] F. Grasso, Multi-objective numerical optimization
applied to aircraft design, PhD thesis, Aerospace
Engineering, Department of Aerospace Engineering,
University of Naples Federico II, 2008.
[7] R. M. Hicks, P. A. Henne, Wing design by numerical
optimization, J. Aircr., vol. 15(7), pp. 407–412, 1978.
https://doi.org/10.2514/3.58379
[8] G. M. Robinson, A. J. Keane, Concise orthogonal
representation, J. Aircr., vol. 38(3), pp. 580–583, 2001.
https://doi.org/10.2514/2.2803
[9] H. Sobieczky, Parametric airfoils and wings, Recent
Development of Aerodynamic Design Methodologies,
Springer, 1999, pp. 71–87.
https://doi.org/10.1007/978-3-322-89952-1_4
[10] A. Forrester, A. Sobester, A. Keane, Engineering
Design Via Surrogate Modelling: A Practical Guide,
John Wiley & Sons, 2008.
https://doi.org/10.1002/9780470770801
[11] H. Sobieczky, Geometry generator for CFD and applied
aerodynamics, in: Courses and Lecture International,
1997.
https://doi.org/10.1007/978-3-7091-2658-5_9
[12] H. Sobieczky, Parametric airfoils and wings, in: K.
Fujii, G.S. Dulikravich (Eds.), Notes on Numerical
Fluid Mechanics, vol. 68, pp. 71–88, 1998.
https://doi.org/10.1007/978-3-322-89952-1_4
[13] E. Makoto, Wind turbine airfoil optimization by particle
swarm method, Ms.D. thesis, Department of
Mechanical and Aerospace Engineering, Case Western
Reserve University, 2011.
[14] M. Y. V. Pehlivanoglu, Representation method effects
on vibrational genetic algorithm in 2-D airfoil design, J.
Aeronaut. Space Technol., vol. 4 (2), pp. 7–13, 2009.
https://doi.org/10.1016/j.jksues.2013.04.003
[15] D. Vecchia, Pierluigi, E. Daniele, and E. DʼAmato., An
airfoil shape optimization technique coupling PARSEC
parameterization and evolutionary algorithm,
Aerospace Science and Technology, vol. 32(1), pp.
103-110, 2014.
https://doi.org/10.1016/j.ast.2013.11.006
[16] C. B. Allen, D. J. Poole, and T. C. Rendall,
Wing aerodynamic optimization using efficient
mathematically-extracted modal design
variables, Optimization and Engineering, vol. 19, pp.
453-477, 2018.
https://doi.org/10.1007/s11081-018-9376-7
[17] R. Mukesh, K. Lingadurai, and U. Selvakumar, Airfoil
shape optimization using non-traditional optimization
technique and its validation, Journal of King Saud
University-Engineering Sciences, vol. 26(2), pp. 191-
197, 2014.
https://doi.org/10.1016/j.jksues.2013.04.003
[18] D. V. Dung, L. R. Zuhal, H. Muhammad, Twodimensional fast Lagrangian vortex method for
simulating flows around a moving boundary, Journal of
Mechanical Engineering, vol. 12(1), pp. 31-46, 2015.
[19] S. Koziel, X. S. Yang, Computational Optimization,
Methods and Algorithms, 2011, pp. 19-20.
https://doi.org/10.1007/978-3-642-20859-1
[20] K. F. Man, K. S. Tang, S. Kwong, Genetic Algorithms
: Concepts and Designs, 1999.
https://doi.org/10.1007/978-1-4471-0577-0
[21] P. D. Vecchia, E. Daniele, E. D’Amato, An airfoil shape
optimization technique coupling PARSEC
parameterization and evolutionary algorithm,
Aerospace Science and Technology, vol. 32, pp. 103-
110, 2014.
https://doi.org/10.1016/j.ast.2013.11.006
[22] K. Slawomir, X. S. Yang, Computational optimization:
An overview. Computational Optimization, Methods
and Algorithms (2011): 1-11.
[23] S. Jung, W. Choi, L. S. Martins-Filho, F. Madeira, An
implementation of self-organizing maps for airfoil
design exploration via multi-objective optimization
technique, Journal of Aerospace Technology and
Management, pp. 193-202, 2016.
https://doi.org/10.5028/jatm.v8i2.585
[24] Y. Saad, M. H. Schultz GMRES: A generalised minimal
residual algorithm for solving nonsymmetric linear
systems, SIAM Journal of Scientific Computing, vol.
7(3), 1986.
https://doi.org/10.1137/0907058
[25] Abbott, I. H., and A. E. von Doenhoff: Theory of Wing
Sections, Dover Publications, Inc., New York, 1959.