Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-17T14:39:41.608Z Has data issue: false hasContentIssue false

Unsteady flow around helicopter rotor blade sections in forward flight

Published online by Cambridge University Press:  04 July 2016

S. T. Shaw
Affiliation:
College of AeronauticsCranfield UniversityBedford, UK
N. Qin
Affiliation:
College of AeronauticsCranfield UniversityBedford, UK

Abstract

The aerodynamic performance of aerofoils performing unsteady motions is important for the design of helicopter rotors. In this respect the study of aerofoils undergoing in-plane oscillations (translation along the horizontal axis) provides useful insight into the flow physics associated with the advancing blade in forward flight. In this paper a numerical method is developed in which the unsteady thin layer Navier-Stokes equations are solved for aerofoils performing rigid body motions. The method has been applied to the calculation of the flowfield around a NACA 0012 aerofoil performing in-plane motions representative of high-speed forward flight. Comparison of computed pressure data with experimental measurements is generally found to be good. The quantitative differences observed between computations and experiment are thought to have arisen mainly as a consequence of the low aspect ratio of the model rotor employed in the windtunnel tests.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 1999 

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. Maresca, C, Favier, D. and Rebont, J. Experiments on an aerofoil at high angle of incidence longitudinal oscillations, J Fluid Mech, 1979, 92, pp 671690.Google Scholar
2. Gursul, I. and Ho, C. High aerodynamic loads on an airfoil submerged in an unsteady free stream, A1AA J, April 1992, 30, (4), pp 11171118.Google Scholar
3. Shih, C. and Ho, C. Vorticily balance and time scales of a two-dimensional airfoil in an unsteady freestrcam, Phys Fluids, February 1994, 6, (2), pp 710723.Google Scholar
4. Gursul, I., Lin, H. and Ho, C. Effects of times scales on lift of airfoils in an unsteady free stream, AIAA J, April 1994, 32, (4), pp 797801.Google Scholar
5. Gursul, I., Lin, H. and Ho, C. Parametric effects on lift force of an air foil in unsteady free stream, AIAA J, May 1996, 34, (5), pp 10851087.Google Scholar
6. Krause, E. and Scweitzer, W.B. The effect of an oscillatory free stream-How on a NACA-4412 profile at large relative amplitudes and low Reynolds numbers, Exp in Fluids, 1990, 9, pp 159166.Google Scholar
7. Morinishi, K. and Muratu, S. Numerical solutions of unsteady oscillating flows past an airfoil, AIAA Paper 92-3212, July 1992.Google Scholar
8. Lerat, A. and Sides, J. Numerical simulation of unsteady transonic flows using the Euler equations in integral form, ONERA TP-79-10, February 1979.Google Scholar
9. Habibie, I., Laschka, B. and Weishaupl, C. Analysis of unsteady flows around wing profiles at longitudinal accelerations, Proceedings of the 19th 1CAS conference. Paper 2.8.1, 1994.Google Scholar
10. Lin, C.Q. and Pahlke, K. Numerical solution of Euler equations for aerofoils in arbitrary unsteady motion, Aeronaut J, June 1994, 98, (6), pp 207214.Google Scholar
11. Pahlke, K., Blazez, J. and Kirchner, A. Time-accurate computations for rotor flows, Proceedings of the Royal Aeronautical Society CFD conference, Paper 15, 1994.Google Scholar
12. Shaw, S.T. and Qin, N. Solution of the Navier-Stokes equations for the flow around an aerofoil in an oscillating free stream. Proceedings of the 22nd ICAS conference, Paper 1.1.3, 1996.Google Scholar
13. Shaw, ST. and Qin, N. Solution of the Navier-Stokes equations for combinedtranslation-pitchoscillations,22ndEuropeanRotorcraft forum, Paper 55, 1996.Google Scholar
14. Ferziger, J.H. and Peric, M. Computational Methods for Fluid Dynamics, Springer-Verlag, 1996.Google Scholar
15. Baldwin, B. and Lomax, H. Thin layer approximation and algebraic model for turbulent flows, AIAA Paper 78-257, January 1978.Google Scholar
16. Osher, S. and Solomon, F. Upwind difference schemes for hyperbolic systems of conservationlaws. Mathematics of Computation, April 1982, 38, (158), pp 339374.Google Scholar
17. Van Leer, B. Towards the ultimate conservative difference scheme V: A second order sequel to Godunov's method, J Comp Physics, 1979, 32, pp 101136.Google Scholar
18. Qin, N. and Richards, B.E. Sparse quasi-Newton method for Navier-Stokes solution. Notes in Numerical Fluid Dynamics, 1990, 29, pp 474483.Google Scholar
19. Qin, N., Xu, X and Richards, B.E. Newton-like methods for fast high resolution simulation of hypersonic viscous flows. Computer Systems in Engineering, 1992, 3, pp 429435.Google Scholar
20. Qin, N., Scriba, K.W., and Richards, B.E., Shock-shock, shock-vortex interection and aerodynamic heating in hypersonic corner flow, Aeronaut .I, 1991, 95, (5). pp 152160.Google Scholar
21. Badcock, K and Gaitonde, A.L. An unfactored implicit moving mesh method for the two-dimensional unsteady N-S equations, Int J Num Meth Fluids, 1996, 23, pp 607631.Google Scholar
22. Chakravarthy, S.R. and Rai, M.M. An implicit form for the Osher upwind scheme, AIAA J, May 1996, 24, (5), pp 735743.Google Scholar
23. Orkwis, P.D. and Vanden, K.J. On the accuracy of numerical versus analytical Jacobians, AIAA Paper 94-0176, 1994.Google Scholar
24. Sperijse, S.P. Multigrid Solution of the Steady Euler Equations, PhD dissertation, Centrum voor wiskunde en informatica, Amsterdam, 1987.Google Scholar
25. Sonneveld, P. CGS: A fast Lanczos type solver for non-symmetric linear systems, S1AM J Sci Stat Comp, 1989, 10.Google Scholar
26. Saad, Y. GMRES: A generalised minimal residual algorithm for solving non-symmetric linear systems, SIAM J Sci Stat Comp, 1986, (117), pp 856869.Google Scholar
27. Van Der Vorst, H. and Vuik, C. GMRESR: A family of nested GMRES methods, Numerical Linear Algebra with Applications, 1993, 1,(1).Google Scholar
28. Shaw, ST. Comparison of the convergence behaviour of three linear solvers for large, sparse unsymmetric matrices, Cranfield University, COA Report No 9504, July 1995.Google Scholar
29. Badcock, K.J. and Richards, B.R. Implicit time-stepping methods for the Navier-Stokes equations, AIAA J, March 1996, 34, pp 555559.Google Scholar
30. Tauber, M.E., Chang, I.C., Caughey, D.A. and Phillipe, J.J. Comparison of calculated and measured pressures on straight and swept tip model rotor blades, NASA TM 85872, December 1983.Google Scholar
31. Caradonna, F.X. and Philippe, J.J. The flow over a helicopter blade tip in the transonic regime, Vertica, 1978, 2, (1), pp 4360.Google Scholar
32. Rimon, A., Tauber, M.E., Saunders, D.A. and Caughey, D.A. Computation of transonic flow about helicopter rotor blades, AIAA J, May 1986, 24, (5), pp 722727.Google Scholar
33. Tijdeman, H. Investigations of the transonic flow around oscillating aerofoils, NLR TR-77090 U, 1977.Google Scholar