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Aerodynamic shape optimisation of hovering rotors using compressible CFD

Published online by Cambridge University Press:  27 January 2016

C. B. Allen  and
T. C. S. Rendall
T. C. S. Rendall*
Affiliation:
Department of Aerospace Engineering, University of Bristol, Bristol, UK
*
[email protected]
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Abstract

Generic wrap-around shape optimisation technology is presented, and is applied to a helicopter rotor in hover, using compressible CFD as the aerodynamic model. An efficient domain element shape parameterisation method is used as the surface control and deformation method, and is linked to a radial basis function global interpolation, to provide direct transfer of domain element movements into deformations of the design surface and the CFD volume mesh. This method is independent of mesh type and size, and optimisation independence from the flow solver is achieved by obtaining sensitivity information for an advanced parallel gradient-based algorithm by finite-difference. The method is applied here to a two-bladed hovering rotor, with transonic tip speed, comparing the effects of global twist parameters and more local planform parameters. Significant torque reductions are achieved in both cases, and it is shown that using only three global twist parameters are extremely effective. Using 63 local and global parameters, large geometric changes are demonstrated, with both induced power and wave drag reduced.

Type
Research Article
Information
The Aeronautical Journal , Volume 115 , Issue 1170 , August 2011 , pp. 513 - 519
Copyright
Copyright © Royal Aeronautical Society 2011 

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References

1. Li, W. Huyse, L. and Padula, S. Profile Optimisation Method for Robust Aerofoil Shape Optimisation in Viscous Flows NASA/TM-2003-212408. NASA/CR-2001-211042. icase report no 2001-22.Google Scholar
2. Hicks, R.M., Murman, E.M. and Vanderplaats, G.N. An Assessment of Aerofoil Design by Numerical Optimisation NASA TMX-3092, Ames Research Center, Moffett Field, California, USA, July 1974.Google Scholar
3. Hicks, R.M. and Henne, P.A. Wing design by numerical optimization, J Aircr, 1978, 15, pp 407–412.Google Scholar
4. Reuther, J., Jameson, A., Farmer, J., Martinelli, L. and Saunders, D. Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation RIACS Technical Report 96.02 January 1996. Presented at the AIAA 34th Aerospace Sciences Meeting and Exhibit, January 1996, AIAA paper 96-0094.Google Scholar
5. Chung, H.S. and Alonso, J. Multiobjective optimization using approximation model-based genetic algorithms AIAA 2004-4325 10th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization 30 August – 1 September, 2004/Albany, New York, USA.Google Scholar
6. Gumbert, C.R., Hou, G. and Newman, P.A. Simultaneous Aerodynamic Analysis and Design Optimization (SAADO. for a 3D Rigid Wing AIAA 99-3296).Google Scholar
7. Wong, W.S., Le Moigne, A. and Qin, N. Parallel adjoint-based optimisation of a blended wing body aircraft with shock control bumps, Aeronaut J, March 2007, 111, (1117), pp 165–174.Google Scholar
8. Gumbert, C.R., Hou, G. and Newman, P.A. Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) for a 3D Flexible Wing AIAA 2001-1107.Google Scholar
9. Jameson, A., Leoviriyakit, K. and Shankaran, S. Multi-point aero-structural optimization of wings including variations, 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, USA, January 2007.Google Scholar
10. Allen, C.B. Parallel simulation of unsteady hovering rotor wakes, Int J Numerical Methods in Engineering, 2006, 68, (6), pp 632–649.Google Scholar
11. Allen, C.B. Convergence of steady and unsteady formulations for inviscid hovering rotor solutions, Int J Numerical Methods in Fluids, 2003, 41, (9), pp 931–949.Google Scholar
12. Allen, C.B. An unsteady multiblock multigrid scheme for lifting forward flight rotor simulation, Int J Numerical Methods in Fluids, 2004, 45, (9), pp 973–984 (DOI 10.2/fld.711).Google Scholar
13. Celi, R. Recent applications of design optimisation to rotorcraft – A survey, J Aircr, 1999, 36, (1).Google Scholar
14. Le PAPE, A. and Beaumier, P. Numerical optimisation of helicopter rotor aerodynamic performance in hover, Aerospace Science and Technology, 2005, 9, pp 191–201.Google Scholar
15. Dumont, A., Le PAPE, A., Peter, J. and Huberson, S. Aerodynamic shape optimisation of hovering rotors using a discrete adjoint of the RANS equations, Presented at AHS 65th Annual Forum, Grapevine, TX, May 2009.Google Scholar
16. Nadarajah, S. and Tatossian, C. Adjoint-based aerodynamic shape optimsation of rotorcraft blades, AIAA-2008-0322, 26th AIAA Applied Aerodynamics Conference, Hawaii, USA, August 2008.Google Scholar
17. Choi, S., Pottsdam, M., Lee, K.H., Iaccarino, G. and Alonso, J.J. Helicopter rotor design using a time-spectral and adjoint-based method, AIAA 2008-5810, 12th AIAA/ISSMO Multidisciplinary Analysis and Optimisation Conference, 2008, Victoria, BC, Canada.Google Scholar
18. Nielsen, E.J., Lee-Rausch, E.M. and Jones, W.T. Adjoint-based design of rotors using the navier-stokes equations in a noninertial frame, Presented at AHS 65th Annual Forum, Grapevine, TX, May 2009.Google Scholar
19. Imiela, M. High-fidelity optimization framework for helicopter rotors, proceedings 25th European Rotorcraft Forum, Hamburg, Germany, 2009.Google Scholar
20. Imiela, M. Investigation of aeroelastic effects for a helicopter main rotor in hover, proceedings 26th European Rotorcraft Forum, Paris, France, 2010.Google Scholar
21. Johnson, C.S. and Barakos, G.N. Optimising aspects of rotor blades in forward flight, AIAA paper 2011-1194, Proceedings 49th AIAA Aerospace Sciences Meeting including the New Horizons Forumand Aerospace Exposition, Orlando, Florida, USA, 4-7 January 2011.Google Scholar
22. Johnson, C.S. and Barakos, G.N. A framework for optimising aspects of rotor blades, Aeronaut J, March 2011, 115, (1163), pp 147–161.Google Scholar
23. Morris, A.M., Allen, C.B. and Rendall, T.C.S. CFD-based optimization of aerofoils using radial basis functions for domain element parameterization and mesh deformation, Int J Numerical Methods in Fluids, 2008, 58, (8), pp 827–860.Google Scholar
24. Morris, A.M., Allen, C.B. and Rendall, T.C.S. Domain-element method for aerodynamic shape optimization applied to modern transport wing, AIAA J, 2009, 47, (7), pp 1647–1659.Google Scholar
25. Allen, C.B., Rendall, T.C.S. and Morris, A.M. Computational-fluid-dynamics-based twist optimization of hovering rotors, J Aircr, 47, (6), 2010, pp 2075–2085.Google Scholar
26. Jameson, A. Aerodynamic design via control theory, J Sci Comput, 1988, 3, pp 233–260.Google Scholar
27. Reuther, J Aerodynamic Shape Optimisation Using Control Theory, NASA Technical report NASA-CR-201064, 1996.Google Scholar
28. Jameson, A. Automatic Design of Transonic Aerofoils to Reduce the Shock Induced Pressure Drag In Proceedings of the 31st Israel Annual Conference on Aviation and Aeronautics, Tel Aviv, Israel, pp 5–17, February 1990.Google Scholar
29. Pickett, R.M., Rubinstein, M.F. and Nelson, R.B. Automated structural synthesis using a reduced number of design coordinates, AIAA J, 1973, 11, (4), pp 494–498.Google Scholar
30. Watt, A. and Watt, M. Advanced Animation and Rendering Techniques, Addison-Wesley, New York, USA, 1992, Chapter 17.Google Scholar
31. http://www.optimalsolutions.us/ Google Scholar
32. Anderson, W.K., Karman, S.L. and Burdyshaw, C. Geometry parame-terisation method for multidisciplinary applications, AIAA J, 2009, 17, (6), pp 1568–1578.Google Scholar
33. Bloor, M.I.G. and Wilson, M.J. Efficient parameterisation of generic aircraft geometry, J Aircr, 1995, 32, (6), pp 1269–1275.Google Scholar
34. Braibant, V. and Fleury, C. Shape optimal design using B-splines, Computer Methods in Applied Mechanics and Engineering, August 1984, 44, (3), pp 247–267.Google Scholar
35. Kulfan, B.M. A universal parametric geometry representation method – CST 45th AIAA Aerospace Sciences Meeting and Exibit 8-11 January 2007, Reno, Nevada, USA.Google Scholar
36. Samareh, J.A. Survey of shape parameterisation techniques for high-fidelity multidisciplinary shape optimisation, AIAA J, May 2001, 39, (5), pp 877–884.Google Scholar
37. Nadarajah, S., Castonguay, P. and Mousavi, A. Survey of shape parameterization techniques and its effect on three-dimensional aerodynamic shape optimisation, AIAA-2007-3837,18th AIAA Computational Fluid Dynamics Conference, Miami, FL, USA, 25-28 June 2007.Google Scholar
38. Rendall, T.C.S. and Allen, C.B. Unified fluid-structure interpolation and mesh motion using radial basis functions, Int J Numerical Methods in Engineering, 2008, 74, (10), pp 1519–1559.Google Scholar
39. Rendall, T.C.S. and Allen, C.B. Efficient mesh motion using radial basis functions with data reduction algorithms, J Computational Physics, 228, (17), 2009, pp 6231–6249.Google Scholar
40. Rendall, T.C.S. and Allen, C.B. Parallel efficient mesh motion using radial basis functions with application to multi-bladed rotors, Int J Numerical Methods in Engineering, 2010, 81, (1), pp 89–105.Google Scholar
41. Buhmann, H. Radial Basis Functions, Cambridge University Press, 1st ed, 2005.Google Scholar
42. Wendland, H. Scattered Data Approximation, Cambridge University Press, 1st ed, 2005.Google Scholar
43. Mackman, T.J. and Allen, C.B. Investigation of an adaptive sampling method for data interpolation using radial basis functions, Int J for Num Methods in Engineering, 2010, 83, (7), pp 915–938.Google Scholar
44. Caradonna, F.X. and Tung, C. Experimental and analytical studies of a model helicopter rotor in hover, NASA TM-81232, September 1981.Google Scholar
45. Zhou, J.L., Tits, A.L. and Lawrence, C.T. User’s Guide for FFSQP Version 3.7: A Fortran Code for Solving Optimisation Programs, Possibly Minimax, with General Inequality Constraints and Linear Equality Constraints, Generating Feasible Iterates, Institute for Systems Research, University of Maryland, Technical Report SRC-TR-92-107r5, College Park, 1997.Google Scholar
46. Zhou, J.L. and Tits, A.L. Nonmonotone line search for minimax problems, J Optimisation Theory and Applications, 1993, 76, (3), pp 455–476.Google Scholar
47. Panier, E. and Tits, A.L. On combining feasibility, descent and superlinear convergence in inequality constrained optimisation, Mathematical Programming, 1993, 59, pp 261–276.Google Scholar
48. Allen, C.B. Towards automatic structured multiblock mesh generation using improved transfinite interpolation, Int J Numerical Methods in Engineering, 2008, 74, (5), pp 697–733.Google Scholar
49. Allen, C.B. Parallel universal approach to mesh motion and application to rotors in forward flight, Int J Numerical Methods in Engineering, 2007, 69, (10), pp 2126–2149.Google Scholar
50. Parpia, I.H. Van-Leer flux vector splitting in moving co-ordinates, AIAA J, 1988, 26, pp 113–115.Google Scholar
51. Allen, C.B. Multigrid acceleration of an upwind euler code for hovering rotor flows, Aeronaut J, September 2001, 105, (1051), pp 517–524.Google Scholar
52. Perry, F.J. Aerodynamics of the helicopter worldspeed record, Presented at the 43rd Annual National Forum of the American Helicopter Society, May 1987.Google Scholar
53. Isaacs, N.C.G. and Harrison, R.J. Investigation of retreating blade stall mechanisms using flight test pressure measurements, Presented at the 45th Annual National Forum of the American Helicopter Society, May 1989.Google Scholar