Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-28T04:37:06.125Z Has data issue: false hasContentIssue false
  • English
  • Français

Time-linearised transonic computations including entropy, vorticity and shock wave motion effects

Published online by Cambridge University Press:  04 July 2016

E. Ly  and
J. Nakamichi
E. Ly
Affiliation:
Department of Mathematics and Statistics, RMIT University, Melbourne, Australia
J. Nakamichi
Affiliation:
Structures and Materials Research Center, National Aerospace Laboratory of Japan (NAL), Tokyo, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

The effect of small perturbations on steady nonlinear transonic small disturbance flowfields, in the context of two-dimensional flows governed by the general-frequency transonic small disturbance equation with nonreflecting far-field boundary conditions, is investigated. This paper presents a time-linearised time-domain solution method that includes effects due to the shock-generated entropy and vorticity and shock wave motions. The solution procedure correctly accounts for the small-amplitude shock wave motion due to small unsteady changes in the aerofoil boundary conditions, and correctly models a flowfield with embedded strong shock waves. Steady and first harmonic pressure distributions for the NACA 0003 aerofoil with a harmonically oscillating flap, and NACA 0012 aerofoil undergoing a sinusoidal pitching oscillation, are predicted and compared with the Euler results.

Type
Research Article
Information
The Aeronautical Journal , Volume 107 , Issue 1077 , November 2003 , pp. 687 - 695
Copyright
Copyright © Royal Aeronautical Society 2003 

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. Gear, J.A., Ly, E. and Phillips, N.J.T., Time marching finite difference solution of the modified transonic small disturbance equation, 1997, Proceedings of the Eighth Biennial Computational Techniques and Applications Conference (CTAC97), Australian and New Zealand Industrial and Applied Mathematics (ANZIAM), Adelaide, Australia, 29 September – 1 October 1997, pp 209–216.Google Scholar
2. LY, E. and Gear, J.A., Time-linearized transonic computations including shock wave motion effects, J Aircr, November/December 2002, 39, (6), pp 964–972.Google Scholar
3. Hafez, M. and Lovell, D., Entropy and vorticity corrections for transonic flows, July 1983, AIAA Paper 83-1926.Google Scholar
4. Whitlow, W., Hafez, M.M. and Osher, S.J., An entropy correction method for unsteady full potential flows with strong shocks, J Fluids and Structures, 1987, 1, pp 401–414.Google Scholar
5. Batina, J.T., Unsteady transonic small-disturbance theory including entropy and vorticity effects, J Aircr, 1989, 26, (6), pp 531–538.Google Scholar
6. Dang, T.Q. and Chen, L.T., An Euler correction method for two-and three-dimensional transonic flows, 1987, AIAA Paper 87-0522.Google Scholar
7. Traci, R.M., Albano, E.D. and Farr, J.L., Small disturbance transonic flows about oscillating airfoils and planar wings, August 1975, AFFDL TR-75-100, Air Force Flight Dynamics Lab, Wright-Patterson AFB, OH, USA.Google Scholar
8. Traci, R.M., Albano, E.D. and Farr, J.L., Perturbation method for transonic flows about oscillating airfoils, AIAA J, 1976, 14, (9), pp 1258–1265.Google Scholar
9. Schippers, H. and Hounjet, M.H.L., Two complementary approaches to transonic potential flow about oscillating airfoils, J Aircr, 1988, 25, (5), pp 395–398.Google Scholar
10. Hounjet, M.H.L., NLR inviscid transonic unsteady loads prediction methods in aeroelasticity, March 1992, Transonic unsteady aerodynamics and aeroelasticity, Paper CP-507, AGARD, pp 12.1–12.16.Google Scholar
11. Greco, P.C., Lan, C.E. and Lim, T.W., Frequency domain unsteady transonic aerodynamics for flutter and limit cycle oscillation prediction, January 1997, AIAA Paper 97-0835.Google Scholar
12. Fung, K.Y., Yu, N.J. and Seebass, R., Small unsteady perturbations in transonic flows, AIAA J, 1978, 16, (8), pp 815–822.Google Scholar
13. Ly, E., Gear, J.A. and Phillips, N.J.T., Simulated shock motion using a time-linearised transonic code, 1998, Proceedings of the Third Biennial Engineering Mathematics and Applications Conference (EMAC98), The Institution of Engineers of Australia and Australian and New Zealand Industrial and Applied Mathematics (ANZIAM), Adelaide, Australia, 13-16 July 1998, pp 331–334.Google Scholar
14. Ly, E., Improved approximate factorisation algorithm for the steady subsonic and transonic flow over an aircraft wing, 1998, Proceedings of the 21st Congress of the International Council of the Aeronautical Sciences (ICAS 1998), AIAA and ICAS, Melbourne, Australia, 13-18 September 1998, Paper A98-31699.Google Scholar
15. Batina, J.T., Unsteady transonic algorithm improvements for realistic aircraft applications, J Aircr, 1989, 26, (2), pp 131–139.Google Scholar
16. Tijdeman, H., Investigations of the transonic flow around oscillating airfoils, October 1977, NLR TR 77090 U, National Aerospace Laboratory, NLR, Amsterdam, The Netherlands.Google Scholar
17. Kwak, D., Nonreflecting far-field boundary conditions for unsteady transonic flow computation, AIAA J, 1981, 19, (11), pp 1401–1407.Google Scholar
18. Ly, E., Gear, J.A. and Phillips, N.J.T., Improved approximate factorisation algorithm, 1997, Proceedings of the Eighth Biennial Computational Techniques and Applications Conference (CTAC97), Australian and New Zealand Industrial and Applied Mathematics (ANZIAM), Adelaide, Australia, 29 September – 1 October 1997, pp 393–400.Google Scholar
19. Catherall, D., Optimum approximate-factorization schemes for two-dimensional steady potential flows, AIAA J, 1982, 20, (8), pp 1057–1063.Google Scholar
20. Engquist, B. and Osher, S., Stable and entropy satisfying approximations for transonic flow calculations, Mathematics of Computation, 1980, 34, (149), pp 45–75.Google Scholar
21. Murman, E.M., Analysis of embedded shock waves calculated by relaxation methods, AIAA J, 1974, 12, (5), pp 626–633.Google Scholar
22. Kheirandish, H.R., Goro, B. and Nakamichi, J., Numerical investigation of flutter, Int J Computational Fluid Dynamics, 1999, 12, pp 279–290.Google Scholar
23. Nakamichi, J. and Kheirandish, H.R., Nonlinear flutter simulation of NAL non-powered SST experimental airplane and related wind tunnel tests, 2001, CEAS/AIAA/AIAE International Forum on Aeroelasticity and Structural Dynamics, Madrid, Spain, April 2001.Google Scholar
24. Fuglsang, D.F. and Williams, M.H., Non-isentropic unsteady transonic small disturbance theory, April 1985, AIAA Paper 85-0600.Google Scholar