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Three-dimensional indicial response of finite aspect ratio yawed wings

Published online by Cambridge University Press:  03 February 2016

C. E. Manglano-Villamarin
Affiliation:
School of Engineering, Cranfield University, Cranfield, UK
S. T. Shaw
Affiliation:
School of Engineering, Cranfield University, Cranfield, UK

Abstract

The influence of finite aspect ratio and yaw on the computed indicial response of a pitching wing has been studied using numerical solutions of the unsteady Euler equations. The indicial response was obtained directly from computations of the unsteady flow around two- and three-dimensional wings subjected to a step change in incidence at Mach numbers between 0·2 and 0·7. The data reveal several important characteristics in the behaviour of the unsteady response of three-dimensional wings. The initial response is shown to be independent of both aspect ratio and yaw confirming the results of linearized theory. During the subsequent development of the unsteady response significant differences are observed between the two- and three-dimensional behaviours as a consequence of changes to both wing aspect ratio and yaw angle. The formation and spanwise propagation of acoustic waves due to finite aspect ratio is shown to have a significant influence on the development of the unsteady forces, while for yawed wings the results indicate that the manner in which the windward and leeward tip vortices form is important. Based upon these observations it is suggested that the current practice within the rotorcraft community in which two-dimensional indicial response functions are employed may be unreliable for the advancing blade.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 2007 

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References

1. Beddoes, T.S., Representation of airfoil behaviour, Vertica, 1983, 7, (2), pp 183197.Google Scholar
2. Beddoes, T.S., Practical calculation of unsteady lift, Vertica, 1984, 8, (1), pp 5571.Google Scholar
3. Leishman, J.G., Indicial lift approximations for two-dimensional subsonic flow as obtained from oscillatory measurements, J Aircr, 1993, 30, (3), pp 340351.Google Scholar
4. Sitaraman, J., Baeder, J.D. and Iyengar, V., On the field velocity approach and geometric conservation law for unsteady flow simulations, 2003, AIAA Paper 2003-3835, 16th AIAA Computational Fluid Dynamics Conference.Google Scholar
5. Shaw, S.T. and Qin, N., Calculation of compressible indicial response, Aeronaut J, 2000, 104, (1042), pp 665673.Google Scholar
6. Shaw, S.T. and Qin, N., Study of the aerodynamics of in-plane motion, 2001, Proceedings of the IMECHE, Part G, 215, pp 89104.Google Scholar
7. Gaitonde, A.L. and Jones, D.P., The use of pulse responses and system reduction for 2D unsteady flows using the Euler equations, Aeronaut J, 2002, 106, (1063), pp 483492.Google Scholar
8. Beedy, J., Barakos, G., Badcock, K. and Richards, B., Non-linear analysis of stall flutter based on the ONERA aerodynamic model, Aeronaut J, 2003, 107, (1074), pp 495509.Google Scholar
9. Beddoes, T.S., A wake model for high-resolution air-loads, 1985, US Army/American Helicopter Society Conference on Rotorcraft Basic Research, Raleigh.Google Scholar
10. Beddoes, T.S., Two- and three-dimensional indicial methods for rotor dynamic air-loads, 1989, AHS Specialists meeting on rotorcraft dynamics, Arlington.Google Scholar
11. Beddoes, T.S., A 3-D separation model for arbitrary planforms, 1991, 47th Annual Forum of the American Helicopter Society.Google Scholar
12. Beddoes, T.S., 3D dynamic stall — correlation study, 1991, Westland Helicopter Internal Report, Aero-Tech Note Gen/166.Google Scholar
13. Singh, R. and Baeder, J.D., The direct calculation of indicial lift response of a wing using computational fluid dynamics, J Aircr, 1997, 34, (4), pp 465471.Google Scholar
14. Sitaraman, J. and Baeder, J.D., Computational-fluid-dynamics-based enhanced indicial aerodynamic models, J Aircr, 2004, 41, (4), pp 798810.Google Scholar
15. Sperijse, S.P., Multi-grid Solution of the Steady Euler Equations, 1987, PhD dissertation, Centrum voor Wiskunde en Informatica, Amsterdam.Google Scholar
16. Osher, S. and Solomon, F., Upwind difference schemes for hyperbolic systems of conservation laws, Mathematics of Computation, 38, (158), pp 339374.Google Scholar
17. Shaw, S.T., Numerical Study of the Unsteady Aerodynamics of Helicopter Rotor Aerofoils, 1999, PhD thesis, Cranfield University.Google Scholar
18. Van Leer, B., Towards the ultimate conservative difference scheme V: A second order sequel to Godunov’s method, 1979, J Computational Physics, 32, pp 101136.Google Scholar
19. Karypis, G. and Kumar, V., Multi-level k-way partitioning scheme for irregular graphs, J of Parallel and Distributed Computing, 1998, 48, (1), pp 96129.Google Scholar
20. Roache, P.R., Verification and Validation in Computational Science and Engineering, 1998, Hermosa publishing.Google Scholar
21. Lomax, H., Indicial aerodynamics, AGARD Manual of Aeroelasticity, 1960, Part 2, Chapter 6.Google Scholar
22. Tobak, M., On the use of indicial function concept in the analysis of unsteady motions of wings and wing-tail combinations, 1954, NACA Report R-1188.Google Scholar
23. Lau, B.H., Louie, A.W., Sotiriou, C.P. and Griffiths, N., Correlation of the Lynx-XZ170 flight test results up to and beyond the stall boundary, 1993, Proceedings of the 49th Forum of the American Helicopter Society.Google Scholar
24. Hansford, R.E. and Vorwald, J., Dynamics workshop on rotor vibratory loads prediction, 1998, J American Helicopter Society, 43, (1), pp 7687.Google Scholar
25. Sitaraman, J., Datta, A., Baeder, J.D. and Chopra, I., Fundamental understanding and prediction of rotor vibratory loads in high-speed forward flight, 2003, Proceedings of 29th European Rotorcraft Forum.Google Scholar