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Constrained, multipoint shape optimisation for complex 3D configurations

Published online by Cambridge University Press:  04 July 2016

J. Elliott
Affiliation:
Fluid Dynamics Research LaboratoryMIT Department of Aeronautics and AstronauticsMassachusetts, USA
J. Peraire
Affiliation:
Fluid Dynamics Research LaboratoryMIT Department of Aeronautics and AstronauticsMassachusetts, USA

Abstract

A method for performing three-dimensional, multipoint, lift-constrained drag minimisation for complex aircraft configurations is presented. Parameters representing the aircraft geometry are the design variables used in the solution of an optimisation problem. The compressible Euler equations for the flow are discretised on automatically generated unstructured meshes, and the sensitivities of the objective function and the constraints with respect to the design parameters are efficiently calculated using the discrete adjoint method. In addition, the solution algorithm has been parallelised making the approach feasible for practical applications. Several constrained minimisation strategies are discussed and some numerical tests are carried out for a lift-constrained, two-dimensional problem. The strategy found to work best is demonstrated for the three-dimensional optimisation of a wing-body configuration operating in transonic and supersonic conditions. It is concluded that Euler-based optimisation can be useful as a first step in the design process but that most applications involving transonic flows do require viscous flow modelling to avoid unrealistic pressure distributions.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 1998 

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References

1. Arminjon, P. and Dervieux, A. Construction of TVD-like artificial viscosities on 2-dimensional arbitrary FEM grids. INRIA Report 1111, 1989.Google Scholar
2. Beux, F. and Dervieux, A. Exact-gradient shape optimization of a 2-D Euler flow, Finite Elements in Analysis and Design, 1992, 12, pp 281302.Google Scholar
3. Dennis, J. and Schnabel, R. Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ, USA, 1983.Google Scholar
4. Drela, M. Design and optimization method for multi-element airfoils. AIAA, 93-0969, 1993.Google Scholar
5. Elliott, J. Aerodynamic Optimization Based on the Euler and Navier-Stokes Equations Using Unstructured Grids, PhD thesis, Dept of Aeronautics and Astronautics, MIT, 1998.Google Scholar
6. Elliott, J. and Peraire, J. Aerodynamic design using unstructured meshes, AIAA-96-1941, 1996.Google Scholar
7. Elliott, J. and Peraire, J. Practical 3D aerodynamic design and optimization using unstructured meshes, AIAA J, 1997, 35, (9) pp 14791485.Google Scholar
8. Gill, P.E., Murray, W. and Wright, M.H. (Eds) Practical Optimization, Academic Press, 1981.Google Scholar
9. Hirsch, C. Numerical Computation of Internal and External Flows, Vol 2, John Wiley and Sons, Chichester, UK, 1990.Google Scholar
10. Iollo, A., Kuruvila, G. and Taasan, S. Pseudo-time method for optimal shape design using the Euler equations, Technical Report 95-59, ICASE, 1995.Google Scholar
11. Iollo, A. and Salas, M.D. Contribution to the optimal shape design of two-dimensional internal flows with embedded shocks, Technical Report 95-28, ICASE, 1995.Google Scholar
12. Jameson, A. Aerodynamic design via control theory, J Scientific Computing, 1988, 3, pp 233260.Google Scholar
13. Jameson, A. Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence in transonic and hypersonic flows, AIAA-93-3359, 1993.Google Scholar
14. Jameson, A., Pierce, N.A. and Martinelli, L. Optimum aerodynamic design using the Navier-Stokes equations, AIAA-97-0110, January 1997.Google Scholar
15. Lovell, D. and Doherty, J. Aerodynamic design of aerofoils and wings using a constrained optimisation method, In: 19th Congress of the International Council of Aeronautical Sciences, Anaheim, California, USA, September 1994.Google Scholar
16. Newman, J., Newman, P.A., Taylor, A.C. and Hou, G.-W. Efficient nonlinear static aeroelastic wing analysis. Submitted to Computers and Fluids, December 1996.Google Scholar
17. Newman, J. and Taylor, A. Three-dimensional aerodynamic shape sensitivity analysis and design optimization using the Euler equations on unstructured grids, AIAA-96-2464, 1996.Google Scholar
18. Newman, J., Taylor, A. and Burgreen, G. An unstructured grid approach to sensitivity analysis and shape optimization using the Euler equations, AIAA-95-1646, 1995.Google Scholar
19. Peraire, J., Peiro, J. and Morgan, K. Finite element multigrid solution of Euler flows past installed aeroengines, Computational Mechanics, 1993, 11, pp 433451.Google Scholar
20. Reuther, J., Jameson, A., Alonso, J.J., Rimunger, M.J. and Saun-Ders, D. Constrained multipoint aerodynamic shape optimization using an adjoint formulation and parallel computers, AIAA-97-0103, January 1997.Google Scholar
21. Shubin, G. and Frank, P. A comparison of two closely-related approaches to aerodynamic design optimization, In: 3rd International Conference on Inverse Design Concepts and Optimization in Engineering Sciences, October 1991.Google Scholar
22. Sobieski, J. Sensitivity of complex, internally coupled systems, AIAA J, 1990, 28, (1).Google Scholar
23. Sweby, P. High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM J Numer Anal, October 1984, 21, (5), pp 995–101.Google Scholar
24. Message Passing Interface Forum. MPI: A message-passing interface standard, Int J Supercomputer Applications, 1994, 8, (3/4).Google Scholar