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A structure-coupled CFD method for time-marching flutter analysis

Published online by Cambridge University Press:  03 February 2016

N. V. Taylor
Affiliation:
University of Bristol, UK
C. B. Allen
Affiliation:
University of Bristol, UK
A. Gaitonde
Affiliation:
University of Bristol, UK
D. P. Jones
Affiliation:
University of Bristol, UK

Abstract

Aeroelastic analysis is a critical area of the aircraft design process, as a good understanding of the dynamic behaviour of the wing structure is essential to safe operation of the vehicle. The inevitable inaccuracies present in the modelling of such phenomena impose mass penalties, as large safety margins are necessitated, which in turn lead to overly stiff designs. In an effort to reduce the uncertainty in analysis methods, fully coupled CFD and structural models are under widespread development. This paper describes the results produced by such a system for a series of test cases based on the AGARD445.6 and MDO wings. Results relating to the latter are of particular interest, as significant variations were found to be produced by the different methodologies used in previous studies, the precise cause of which could not be isolated. In an effort to provide this isolation, a detailed description of the method used is given, including the interpolation scheme between the structural model and the aerodynamic surface, and particular attention is given to the issue of aerofoil shape preservation.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 2004 

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References

1. Koused, K.A. and Bendiksen, O.O. Non-linear aspects of the transonic aeroelastic stability problem, 1988, AIAA Paper 88-2306. Also in AIAA/ASME/ASCE/AHS 29th Structures, structural dynamics and materials conference.Google Scholar
2. Kousen, K.A. and Bendiksen, O.O. Limit cycle phenomena in computational transonic aeroelasticity, J Aircr, November-December 1994, 31, (6), pp 12571263.Google Scholar
3. Alonso, J.J. and Jameson, A. Fully-implicit time-marching aeroelastic solutions, January 1994, AIAA Paper 94-0056.Google Scholar
4. Guruswamamy, G.P. Unsteady aerodynamic and aeroelastic calculations for wings using Euler equations, AIAA J, March 1990, 28, (3), pp 461469.Google Scholar
5. Robinson, B.A., Batina, J.T. and Yang, H.T. Aeroelastic analysis of wings using the Euler equations with a deforming mesh, J Aircr, November 1991, 28, (11), pp 781788.Google Scholar
6. Meijer, J.J., Hounjet, M.H.L., Eussen, B.J.G. and Prananta, B.B. Nlr-Tu delf experience in unsteady aerodynamics and aeroelastic simulaiton applications, March 1998, Technical Report 822, AGARD, Numerical Unsteady Aerodynamics and Aeroelastic Simulation, pp 11–1-11–21.Google Scholar
7. Schultze, S. Transonic aeroelasric simulation of a flexible wing section, March 1998, Technical Report 822, AGARD, Numerical Unsteady Aerodynamics and Aeroelastic Simulation, pp 10–1-10–20.Google Scholar
8. Goura, G.S.L., Badcock, K.J., Woodgate, M.A. and Richards, B.E. Implicit method for the time marching analysis of flutter, Aeronaut J, April 2001, 105, (4), pp 199214.Google Scholar
9. Bendisksen, O.O. and Kousen, K.A. Transonic flutter analysis using the Euler equations, 1987, AIAA Paper 87-0911-CP.Google Scholar
10. Batina, J.Y. and Young, T.Y. Application of transonic codes to aero-elastic modelling of airfoils including active controls, J Aircr, August 1984, 21, (8), pp 623630.Google Scholar
11. Lee-Rausch, E.M. and Batina, J.T. Wing flutter boundary prediction using unsteady Euler aerodynamic method, J Aircr, March-April 1995, 32, (2), pp 416422.Google Scholar
12. Stephens, C.H., Arena, A.S. and Gupta, K.K. CFD-based aeroservoelastic predictions with comparisons to benchmark experimental data, AIAA Paper 99-0766.Google Scholar
13. Sedaghat, A., Cooper, J.E., Wright, J.R. and Leung, A.Y.T. Curve fitting approach for transonic flutter prediction, Aeronaut J, September 2003, 107, (1007), p 565572.Google Scholar
14. Kandil, O.A., Massey, S.J. and Sheta, E.F. Structural dynamics–CFD interaction for computation of vertical tail buffet, Aeronaut J, August/September 1996, 100, (997), pp 297303.Google Scholar
15. Haase, W., Selmin, V. and Winzell, B. (Eds). Progress in Computational flow-structure interaction, 2003, Vol 81, Notes on Numerical Fluid Mechanics and Multidisciplinary Design. Springer-Verlag.Google Scholar
16. Girodoux-Lavgne, P., Grisval, J.P., Guillemot, S., Henshaw, M., Karlsson, A., Selmin, V., Smith, J., Teupootahiti, E. and Winzell, B. Comparison of static and dynamic fluid-structure interaction solutions in the case of a highly flexible modern transport aircraft wing, J Aerospace Sci and Tech, 2003, 7, pp 121133.Google Scholar
17. Schmidt, W., Jameson, A. and Turkel, E. Numerical solutions of the Euler equations by finite volume methods using runge-kutta time stepping schemes, 1981, AIAA Paper 81-1259.Google Scholar
18. Krol, N. and Jain, R.K. Solution of two dimensional Euler equations — experience with a finite volume code, October 1987, Technical Report DFVLR-FB 87-41, DLR.Google Scholar
19. Jameson, A. Time dependent calculations using multigrid with applications to unsteady flows past airfoils and wings, AIAA Paper 91-1596.Google Scholar
20. Gaitonde, A.L. A dual-time method for the solution of the unsteady Euler equations, Aeronaut J, October 1994, 98, (978), pp 283291.Google Scholar
21. Allen, C.B. The reduction of numerical entropy generated by unsteady shockwaves, Aeronaut J, January 1997, 101, (1001), pp 916.Google Scholar
22. Badcock, K.J., Sim, G. and Richards, B.E. Aeroelastic studies using transonic flow CFD modelling, 1995, International Forum on Aeroelasticity and Structural Dynamics, June 1995, pp 81.118.12.Google Scholar
23. Prananta, B.B., Hounjet, M.H.L. and Zwaan, R.J. Thin layer Navier-Stokes solver and its application for aeroelastic analysis of an airfoil in transonic flow, 1995, International Forum on Aeroelasticity and Structural Dynamics, pp 1.11.9, June 1995.Google Scholar
24. Prananta, B.B. and Hounjet, M.H.L. Aeroelastic simulation with advanced CFD methods in 2-D and 3-D transonic flow, 1996, RAeS Symposium on Unsteady Aerodynamics, 1718 July 1996, London, UK.Google Scholar
25. Schulster, D.M., Beran, P.S. and Huttsell, L.J. Applications of the en3dae euler/navier-stokes aeroelastic method, 1998, Technical Report 822, AGARD. Numerical Unsteady Aerodynamic and Aeroelastic Simulations, March 1998, pp 3–1-3–11.Google Scholar
26. Vlachos, N. Aero-structural coupling in transonic flow: comparison of strong and weak coupling schemes, May 1999, Report DERA/ASF/3662U - AERO.RK5615.Google Scholar
27. Djayapertapa, L. A Computational Method for Coupled Aerodynamic-Structural Calculations in Unsteady Transonic Flow with Active Control Study, 2001, PhD thesis, Aerospace Engineering Department, Bristol University.Google Scholar
28. Geradin, M. and Rixen, D. Mechanical Vibrations, 1997, Second edition, John Wiley and Sons, Chichester, UK.Google Scholar
29. Bathe, K.J. Finite Element Procedures in Engineering Analysis, 1982, Prentice Hall, Englewood Cliffs. New Jersey, USA.Google Scholar
30. Appa, K., Yankulich, M. and Cowan, D.L. The determination of load and slope transformation matrices for aeroelastic analysis, J Aircr, 1985, 22, pp 734736.Google Scholar
31. Appa, K. Finite surface splines, J Aircr, 1989, 26, pp 495496.Google Scholar
32. Guruswamy, G.P. A review of numerical fluids/structures interface methods for computations using high-fidelity equations, Computers and Structures, 2002, 80, pp 3141.Google Scholar
33. Goura, G.S.L. Time Marching Analysis of Flutter using Computational Fluid Dynamics, 2001, PhD thesis, Department of Aerospace Engineering, Glasgow University.Google Scholar
34. Goura, G.S.L., Badcock, K.J., Woodgate, M.A. and Richards, B.E. A data exchange method for fluid-structure intraction problems, Aeronaut J, April 2001, 105, (4), pp 215221.Google Scholar
35. Duchon, J. Splines minimising rotation-invariant semi-norms in Sobolev spaces, Constructive Theory of Functions of Several Variables, 1976, Springer (Germany).Google Scholar
36. Madych, W.R. and Nelson, S.A. Multivariate interpolation: a variational theory, J Approx Theory Applic, 1990.Google Scholar
37. Smith, M.J. Hodges, D.H. and Cesnik, C.E.S. Evaluation of computational algorithms to interface for fluid structure interaction, J Aircr, 2000, 37, (2), pp 282295.Google Scholar
38. Frank, R. Scattered data interpolation: test of some methods, Mathematics of Computations, 1982, 38, pp 181199,.Google Scholar
39. Jones, D.P. Force transfer in aeroelastic calculations, December 2002, Technical Report AE047, University of Bristol.Google Scholar
40. Jones, D.P. Interpolation method in CFD-CSD calculations, 2004, in preparation.Google Scholar
41. Yates, E.C. Standard aeroelastic configurations for dynamic response i-wing 445.6, September 1985, Technical Report 765 AGARD, includes Tech Report Tn-D-1616 as an Appendix.Google Scholar
42. Yates, E.C., Land, N.S. and Foughner, J.T. Measured and calculated subsonic and transonic flutter characteristics of a 45 deg sweptback wing platform in air and in Freon-12 in the Langley transonic dynamics tunnel, March 1963, Technical Report Tn-D-1616, NASA.Google Scholar
43. Taylor, N.V. Unsteady aerodynamic simulation by flight control system integration with structure-coupled CFD, November 2003, Technical Report AE046, University of Bristol.Google Scholar
44. Allen, C.B., Fenwick, C.L., Taylor, N.V. and Djayapertapa, L. Investigation of flutter suppresion by active control, 2003, AIAA Paper 2003-3510, 21st AIAA Applied Aerodynamics Conference, Florida, June 2003.Google Scholar
45. Goura, G.S.L., Badcock, K.J., Woodgate, M.A. and Richards, B.E. Notes on MDO test case, unpublished report supplied by Glasgow University.Google Scholar