Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-04T19:46:11.623Z Has data issue: false hasContentIssue false
  • English
  • Français

Development and validation of an efficient direct numerical optimisation approach for aerofoil shape design

Published online by Cambridge University Press:  03 February 2016

M. Khurana  and
H. Winarto
M. Khurana
Affiliation:
[email protected], The Sir Lawrence Wackett Aerospace Centre, RMIT University, Melbourne, Australia
H. Winarto
Affiliation:
[email protected], The Sir Lawrence Wackett Aerospace Centre, RMIT University, Melbourne, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

Intelligent shape optimisation architecture is developed, validated and applied in the design of high-altitude long endurance aerofoil (HALE). The direct numeric optimisation (DNO) approach integrating a geometrical shape parameterisation model coupled to a validated flow solver and a population based search algorithm are applied in the design process. The merit of the DNO methodology is measured by computational time efficiency and feasibility of the optimal solution. Gradient based optimisers are not suitable for multi-modal solution topologies. Thus, a novel particle swarm optimiser with adaptive mutation (AM-PSO) is developed. The effect of applying the PARSEC and a modified variant of the original function, as a shape parameterisation model on the global optimal is verified. Optimisation efficiency is addressed by mapping the solution topology for HALE aerofoil designs and by computing the sensitivity of aerofoil shape variables on the objective function. Variables with minimal influence are identified and eliminated from shape optimisation simulations. Variable elimination has a negligible effect on the aerodynamics of the global optima, with a significant reduction in design iterations to convergence. A novel data-mining technique is further applied to verify the accuracy of the AM-PSO solutions. The post-processing analysis, to swarm optimisation solutions, indicates a hybrid optimisation methodology with the integration of global and local gradient based search methods, yields a true optima. The findings are consistent for single and multi-point designs.

Type
Research Article
Information
The Aeronautical Journal , Volume 114 , Issue 1160 , October 2010 , pp. 611 - 628
Copyright
Copyright © Royal Aeronautical Society 2010 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Somers, D.M.. Subsonic aerofoil design. Website: Access Date 7th October 2009. http://www.aerofoils.com/design.pdf.Google Scholar
2. Hicks, R.M. and Henne, P.A.. Wing design by numerical optimisation. J Aircr, 1977, 15, pp 407–413.Google Scholar
3. Keane, A.J. and Nair, P.B., Computational Approaches for Aerospace Design: The Pursuit of Excellence, John Wiley & Sons, West Sussex, England, UK, 2005.Google Scholar
4. Gallart, M.S.. Development of a Design Tool for Aerodynamic Shape Optimisation of Aerofoils. Master’s thesis, Department of Mechanical Engineering, University of Victoria, Australia, 2002.Google Scholar
5. Vicini, A. and Quagliarella, D.. Inverse and direct aerofoil design using a multiobjective genetic algorithm. AIAA J, 1997, 35, pp 1499–1505.Google Scholar
6. Topliss, M.E., Toomer, C.A. and Hills, D.P.. Aerodynamic optimisation using analytic descriptions of the design space, J Aircr, 35, pp 882–890, 1998.Google Scholar
7. Peigin, S. and Epstein, B.. Efficient approach for multipoint aerodynamic wing design of business jet aircraft. AIAA J, 2007, 45, pp 2612–2621.Google Scholar
8. D’Angelo, S. and Minisci, E.A.. Multi-objective evolutionary optimisation of subsonic aerofoils by kriging approximation and evolutionary control. The 2005 IEEE Congress on Evolutionary Computation, 2, pp 1262–1267, 2005.Google Scholar
9. Sobieczky, H.. Parametric aerofoils and wings, Numerical Fluid Dynamics, 1998, 68, pp 71–88.Google Scholar
10. Chaouat, B.. Reynolds stress transport modelling for high-lift aerofoil flows, AIAA J, 2006, 44, pp 2390–2402.Google Scholar
11. Hellsten, A.. New advanced k-w turbulence model for high lift aerodynamics. AIAA J, 2005, 43, pp 1857–1869.Google Scholar
12. Scholz, U., Windte, J. and Radespiel, R.. Validation of the RANS-simulation of laminar separation bubbles on aerofoils, Aerospace Science and Technology, 10, 2005, pp 484–494.Google Scholar
13. Choi, S. and Kwon, O.. Aerodynamic characteristics of elliptic aerofoils at high Reynolds numbers, J Aircr, 2008, 45, pp 641–650.Google Scholar
14. Kern, S.. Evaluation of turbulence models for high-lift military aerofoil flowfields. In 34th Aerospace Sciences Meeting & Exhibit, Reno, NV, USA, 1996.Google Scholar
15. Namgoong, H.. Aerofoil Optimisation of Morphing Aircraft. PhD thesis, Aerospace Engineering, Purdue, Indiana, USA, 2005.Google Scholar
16. Nakahashi, K., Takahashi, S. and Obayashi, S.. Inverse design optimization of transonic wings based on multi-objective genetic algorithms. AIAA J, 37, pp 1656–1662, 1999.Google Scholar
17. Khurana, M., Winarto, H and Sinha, A.. Aerofoil optimisation by swarm algorithm with mutation and artificial neural networks. In 47th AIAA Aerospace Sciences Meeting, Orlando, Florida, USA, 2009.Google Scholar
18. Giannakoglou, K.C. and Papadimitriou, D.I., Adjoint Methods for Shape Optimisation, 4, pp 79–108, 2008, Springer-Verlag Berlin/Heidelberg.Google Scholar
19. Holland, J.. Adaption in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, Michigan, USA, 1974.Google Scholar
20. Gelatt, S., Kirkpatrick, C.D. and Vecchi, M.P., Optimisation by simulated annealing, Science. New Series, 1983, 220, pp 671–680.Google Scholar
21. Colorni, A. and Maniezzo, V.. Distributed optimisation by ant colonies. In European Conference on Artificial Life, Paris, France, pp 134–142, 1991.Google Scholar
22. Kennedy, J. and Eberhart, R.. Particle swarm optimisation. In IEEE International Conference on Neural Networks, Perth, Australia, pp 1942–1948, 1995.Google Scholar
23. Drela, M and Harold, Y.. XFOIL 6.9. http://www.web.mit.edu/drela/Public/web/xfoil/, last access on 18 February 2010.Google Scholar
24. Shi, Y. and Eberhart, R.. A modified particle swarm optimiser. In IEEE World Congress on Computation Intelligence, pp 69–73, 1998.Google Scholar
25. Eberhart, R.C. and Shi, Y.. Particle swarm optimisation: Developments, application, and resources. in IEEE Congress on Evolutionary Computation CEC2001, pp 81–86, 2001.Google Scholar
26. Halgamuge, S.K., Ratnaweera, A. and Watson, H.C.. Self-organising hierarchical particle swarm optimiser with time-varying acceleration coefficients. IEEE Transactions on Evolutionary Computation, 2004, 8, pp 240–255.Google Scholar
27. Luo, Q., Chen, M.R. and Lu, Y.Z.. A novel hybrid algorithm with marriage of particle swarm optimisation and external optimisation. Technical report, Shanghai Jiaotong University, China.Google Scholar
28. Fu, J., Wang, L., Wang, X. and Zhen, L.. A novel probability binary particle swarm optimisation algorithm and its application, J Software, 2008, 3, pp 28–35.Google Scholar
29. Qin, A.K. and Liang, J.J.. Comprehensive learning particle swarm optimiser for global optimisation of multimodal functions, IEEE Transactions on Evolutionary Computation, 2006, 10, pp 281–295.Google Scholar
30. Lambert-Torres, P.B., Alvarenga, G.B. and Esmin, A.A.A. Hybrid evolutionary algorithm based on PSO and GA mutation. In Proceedings of the Sixth International Conference on Hybrid Intelligent Systems HIS ‘06), Auckland, New Zealand, 2006.Google Scholar
31. Jancic, M., Stacey, A. and Grundy, I.. Particle swarm optimisation with mutation. In Evolutionary Computation, Canberra, Australia, pp 1425–1430, 2003.Google Scholar
32. Higashi, N. and Iba, H.. Particle swarm optimization with Gaussian mutation. In Swarm Intelligence Symposium, Indianapolis, Indiana, USA, pp 72–79, 2003.Google Scholar
33. Shi, Z., Qin, , Yu, F. and Wang, Y., Adaptive Inertia Weight Particle Swarm Optimization, pp 450–459, Springer-Verlag Berlin/Heidelberg, 2006.Google Scholar
34. Srinivasan, D. and Seow, T.H.. Particle swarm inspired evolutionary algorithm PS-EA) for multicriteria optimisation problems. In Proceedings of Evolutionary Computation, Canberra, Australia, pp 147–165, 2003.Google Scholar
35. Eberhart, R.C. and. Shi, Y.. Fuzzy adaptive particle swarm optimization. In Proceedings of Evolutionary Computation, Seoul, Korea, pp 101–106, 2001.Google Scholar
36. Ma, L.H., Zheng, Y.l. and Qian, J.X.. Empirical study of particle swarm optimizer with an increasing inertia weight. Technical report, Shanghai Jiaotong University, China, 2003.Google Scholar
37. Zheng, J., Cui, Z. and Sun, H., Adaptive Velocity Threshold Particle Swarm Optimisation, pp 327–332. Springer-Berlin/Heidelberg, 2006.Google Scholar
38. Fang, S.K.S. and Chang, J.M., A Modified Particle Swarm Optimiser Using an Adaptive Dynamic Weight Scheme, pp 56–65. Springer-Berlin/Heidelberg, 2007.Google Scholar
39. Robinson, J.J. and Rahmat-Samii, Y.. Particle swarm optimisation in electromagnetics. IEEE Transactions on Antennas and Propagation, 2004, 52, pp 397–407.Google Scholar
40. Wei, J and Wang, Y.. A dynamical particle swarm algorithm with dimension mutation, IJCSNS International J Computer Science and Network Security, 2006,6, pp 221–224.Google Scholar
41. Rasmussen, T.K., Lovbjerg, M and Krink, T.. Hybrid particle swarm optimizer with breeding and subpopulations. In Proceedings of Genetic and Evolutionary Computing Conference, San Francisco, California, USA, pp 469–476, 2001.Google Scholar
42. Zhang, W.J., Xie, X.F. and Yang, Z.L.. A dissipative particle swarm optimization. In Congress on Evolutionary Computation, Hawaii, USA, pp 1456–1461, 2002.Google Scholar
43. Khurana, M., Winarto, H. and Sinha, A.. Application of swarm approach and artificial neural networks for aerofoil shape optimization. In 12th AIAA/ISSMO Multidisciplinary Analysis and Optimisation, Victoria, British Columbia, Canada, 2008.Google Scholar
44. Morris, M.D.. Factorial sampling plans for preliminary computational experiments, Technometrics, 1991, 33, pp 161–174.Google Scholar
45. Campolongo, F., Saltelli, A., Tarantola, S. and Ratto, M., Sensitivity Analysis in Practice. John Wiley and Sons, Ispra, Italy, 2004.Google Scholar
46. Carboni, J., Campolongo, F. and Saltelli, A.. An effective screening design for sensitivity analysis of large models, Environmental Modelling & Software, 2007, 22, pp 1509–1518.Google Scholar
47. Kohonen, T., Self-Organising Maps. Springer, Berlin, Germany, 1995.Google Scholar
48. Viscovery. Viscovery SOMine 5.1. http://www.viscovery.net, last access on 18 February 2010.Google Scholar
49. Kulfan, B.M. and Bussoletti, J.E.. Fundamental parametric geometry representations for aircraft component shapes. In 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, Virginia, USA, 2006.Google Scholar
50. Huyse, L. and Lewis, R.M.. Aerodynamic shape optimization of two-dimensional aerofoils under uncertain conditions. Technical report, NASA Langley Research Center, 2001.Google Scholar
51. Lewis, R.M., Huyse, L., Padula, S.L. and Li, W.. Probabilistic approach to free-form aerofoil shape optimization under uncertainty.Google Scholar
52. Murayama, M., Jeong, S. and Yamamoto, K.. Efficient optimization design method using kriging model. In AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA.Google Scholar