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Application of generic algorithms in aerodynamic optimisation design procedures

Published online by Cambridge University Press:  03 February 2016

R. P. Clayton  and
R. F. Martinez-Botas
R. P. Clayton
Affiliation:
Department of Mechanical Engineering, Imperial College London, London, UK
R. F. Martinez-Botas
Affiliation:
Department of Mechanical Engineering, Imperial College London, London, UK
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Abstract

Direct optimisation techniques using different methods are presented and compared for the solution of two common flows: a two dimensional diffuser and a drag minimisation problem of a fixed area body. The methods studied are a truncated Newton algorithm (gradient method), a simplex approach (direct search method) and a genetic algorithm (stochastic method). The diffuser problem has a known solution supported by experimental data, it has one design performance measure (the pressure coefficient) and two design variables. The fixed area body also has one performance measure (the drag coefficient), but this time there are four design variables; no experimental data is available, this computation is performed to assess the speed/progression of solution.

In all cases the direct search approach (simplex method) required significantly smaller number of evaluations than the generic algorithm method. The simplest approach, the gradient method (Newton) performed equally to the simplex approach for the diffuser problem but it was unable to provide a solution to the four-variable problem of a fixed area body drag minimisation. The level of robustness obtained by the use of generic algorithm is in principle superior to the other methods, but a large price in terms of evaluations has to be paid.

Type
Research Article
Information
The Aeronautical Journal , Volume 108 , Issue 1090 , December 2004 , pp. 611 - 620
Copyright
Copyright © Royal Aeronautical Society 2004 

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References

1. Lighthill, J.M. A new method of two-dimensional aerodynamic design, 1945, ARC R&M 2112.Google Scholar
2. Demeulenaere, A. and Van Den Braembussche, R. Three-dimensional inverse design method for turbomachinery blading design, 1996, ASME Paper No. 96-GT-39.Google Scholar
3. Jameson, A. Optimum aerodynamic design via boundary control, Optimum design methods for aerodynamics, 1994, AGARD Rep 803.Google Scholar
4. Culberson, J.C. On the futility of blind search, 1996, Technical Report TR-96-18, Dept of Computer Science, University of Alberta.Google Scholar
5. Wolpert, D.H. and Macready, W.G. No free lunch theorems for search, 1996, Technical Report SFI-TR-95-02-010, Santa Fe Institute.Google Scholar
6. Arora, J.S. Introduction to Optimum Design, 1989, McGraw-Hill, New York.Google Scholar
7. Vanderplaats, G.N. Numerical optimization techniques for engineering design: with applications, 1984, McGraw-Hill, New York.Google Scholar
8. Chen, H.Q., Glowinski, R., He, J.W., Kearsley, A.J., Périaux, J. and Pironneau, O. Remarks on optimal shape design problems, 1994, Frontiers of Computational Fluid Dynamics, Caughey, D.A. and Hafez, M.M. (Eds), Ch 5, pp 67–80, Wiley, Chichester.Google Scholar
9. Nelder, J.A. and Mead, R. Downhill simplex method in multidimensions, Comp J, 1965, 7, pp 308–313.Google Scholar
10. Hooke, R. and Jeeves, T.A. Direct search solution of numerical and statistical problems, J ACM, 1961, 8, pp 212–229.Google Scholar
11. Van Der Velden, A. Tools for applied engineering optimization, 1994, Optimum Design Methods for Aerodynamics, Ch 8, AGARD Rep 803.Google Scholar
12. Holland, J.H. Adaption in Natural and Artificial Systems, 1975, Univ Michigan Press, Ann Arbor.Google Scholar
13. Goldberg, D.E. Genetic Algorithms in Search, Optimization, and Machine Learning, 1988, Addison-Wesley, Reading, MA.Google Scholar
14. Beasley, D., Bull, D.R. and Martin, R.R. An overview of genetic algorithms: Part 1, Fundamentals Uni Comp, 1993, 15, (2), pp 58–69.Google Scholar
15. Kirkpatrick, S., Gelatt, C.D. and Vecchi, M.P. Optimization by simulated annealing, Science, 1983, 220, (4598), pp 671–680.Google Scholar
16. Périaux, J., Sefrioui, M., Stoufflet, B. and Mantel, B. Robust Genetic Algorithms for Optimization Problems in Aerodynamic Design, 1995, Ch 19, pp 371–396. In WINTER et al (39).Google Scholar
17. Poloni, C. Hybrid GA for Multi Objective Aerodynamic Shape Optimization, 1995, chapter 20, pages 397-415. In WINTER et al (39).Google Scholar
18. Doorly, D. Parallel Genetic Algorithms for Optimization in CFD, 1995, Ch 13, pp 251–270. In WINTER et al (39).Google Scholar
19. Quagliarella, D. and Cioppa, A.D. Genetic algorithms applied to the aerodynamic design of transonic airfoils. J Aircr, 1995, 32, pp 889–891.Google Scholar
20. Obayashi, S. and Takanashi, S. Genetic optimization of target pressure distributions for inverse design methods, 1995, Paper AIAA-95-1649-CP.Google Scholar
21. Quagliarella, D. Genetic Algorithms Applications in Computational Fluid Dynamics, 1995, Ch 21, pp 417-442, In WINTER et al (39).Google Scholar
22. Yamamoto, K. and Inoue, O. Applications of genetic algorithm to aerodynamic shape optimization, 1995, Paper AIAA-95-1650-CP.Google Scholar
23. Baysal, O. and Eleshaky, M.E. Aerodynamic design optimization using sensitivity analysis and computational fluid dynamics. AIAA J, 1992, 30, pp 718–725.Google Scholar
24. Borggaard, J. and Burns, J. A sensitivity equation approach to shape optimization in fluid flows, Flow Control, 1995, Gunzburger, M. (Ed), pp 49–78, Springer-Verlag.Google Scholar
25. Svenningsen, K.H., Madsen, J.I. Hassing, N.H. and Päuker, W.H.G. Optimization of flow geometries applying quasianalytical sensitivity analysis, Appl Math Modelling, 1996, 20, pp 214–224.Google Scholar
26. Bardina, J., Lyrio, A., Kline, S.J., Ferziger, J.H. and Johnston, J.P. A prediction method for planar diffuser flows, Trans ASME, J Fluids Eng, 1981, 103, pp 315–321.Google Scholar
27. Reneau, L.R., Johnston, J.P. and Kline, S.J. Performance and design of straight, two-dimensional diffusers. Trans ASME, J Basic Eng, 1967, pp 141–150.Google Scholar
28. Ward-Smith, A.J. Internal Fluid Flow: The Fluid Dynamics of Flow in Pipes and Ducts, 1980, Clarendon, Oxford.Google Scholar
29. Esdu, , London. Performance in incompressible flow of plane-walled diffusers with single-plane expansion, 1974, data sheet 74015 edition.Google Scholar
30. Yakhot, V. and Orszag, S.A. Renormalization group analysis of turbulence, I. Basic theory, J Sci Comp, 1986, 1, (1), pp 3–51.Google Scholar
31. Yakhot, V. Orszag, S.A. Thangam, S. Gatski, T.B. and Speziale, C.G. Development of turbulence models for shear flows by a double expansion technique, Phys Fluids A, 1992, 4, (7), pp 1510–1520.Google Scholar
32. Lai, Y.G., So, R.M.C. and Hwang, B.C. Calculation of planar and conical diffuser flows, AIAA J, 1989, 27, (5), pp 542–548.Google Scholar
33. Ganesan, V., Suzuki, K., Narayana, P.A.A. and Swamy, N.V.C. Numerical prediction of boundary-layer development in a two-dimensional diffuser. J Inst Energy, 1988, LXI, pp 192–200.Google Scholar
34. Ganesan, V., Suzuki, K., Narayana, and Chithambaran, V.K. Investigations of mean and turbulent flow characteristics of a two dimensional plane diffuser, Expts in Fluids, 1991, 10, (4), pp 205–212.Google Scholar
35. Ziman, H.J. Computer Prediction of Chemically Reacting Flows in Stirred Tanks, 1990, PhD thesis, University of London.Google Scholar
36. Nash, S.G. Newton-type minimisation via the Lanczos method, 1984, SIAM J Numer Anal, 21, pp 770–778.Google Scholar
37. Press, W.H. Flannery, B.P. Teukolsky, S.A. and Vetterling, W.T. Numerical Recipes in C: The Art of Scientific Computing, 1993, 2nd edition, CUP, Cambridge.Google Scholar
38. Krishnakumar, K. Micro-genetic algorithms for stationary and non-stationary function optimization, SPIE, 1989, 1196, Intelligent Control and Adaptive Systems, pp 289–296.Google Scholar
39. Winter, G., Périaux, J., Galàn, M. and Cuestra, P. (Eds), Genetic Algorithms in Engineering and Computer Science, 1995, Wiley, Chichester.Google Scholar