Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-18T21:02:43.007Z Has data issue: false hasContentIssue false
  • English
  • Français

The three-dimensional interaction of a streamwise vortex with a large-chord lifting surface: theory and experiment

Published online by Cambridge University Press:  26 April 2006

Gustavo C. R. Bodstein ,
Albert R. George  and
C.-Y. Hui
Gustavo C. R. Bodstein
Affiliation:
Department of Mechanical Engineering, EE/COPPE/UFRJ, CP 68503, CEP 21945-970, Rio de Janeiro, RJ, Brazil
Albert R. George
Affiliation:
Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853-7501, USA
C.-Y. Hui
Affiliation:
Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853-7501, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The three-dimensional vortex flow that develops around a close-coupled canard-wing configuration is characterized by a strong interaction between the vortex generated at the canard and the aircraft wing. In this paper, a theoretical potential flow model is devised to uncover the basic structure of the pressure and velocity distributions on the wing surface. The wing is modelled as a semi-infinite lifting-surface set at zero angle of attack. It is assumed that the vortex is a straight vortex filament, with constant strength, and lying in the freestream direction. The vortex filament is considered to be orthogonal to the leading-edge, passing a certain height over the surface. An incompressible and steady potential flow formulation is created based on the three-dimensional Laplace's equation for the velocity potential. The boundary-value problem is solved analytically using Fourier transforms and the Wiener-Hopf technique. A closed-form solution for the velocity potential is determined, from which the velocity and pressure distributions on the surface and a vortex path correction are obtained. The model predicts an anti-symmetric pressure distribution along the span in region near the leading-edge, and a symmetric pressure distribution downstream from it. The theory also predicts no vertical displacement of the vortex, but a significant lateral displacement. A set of experiments is carried out to study the main features of the flow and to test the theoretical model above. The experimental results include helium-soap bubble and oil-surface flow pattern visualization, as well as pressure measurements. The comparison shows good agreement only for a weak interaction case, whereas for the case where the interaction is strong, secondary boundary-layer separation and vortex breakdown are observed to occur, mainly owing to the strong vortex-boundary layer interaction. In such a case the model does not agree well with the experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 322 , 10 September 1996 , pp. 51 - 79
Copyright
© 1996 Cambridge University Press

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

Barrows, T. M. 1977 Simplified methods of predicting aircraft rolling moments due to vortex encounters. J. Aircraft 14, 434–439.Google Scholar
Batchelor, G. K. 1964 Axial flow in trailing vortices. J. Fluid Mech. 20, 645–658.Google Scholar
Bodstein, G. C. R. 1993 A theoretical and experimental study of the interaction of a streamwise vortex with a surface. PhD thesis, Cornell University, USA.
Bodstein, G. C. R., George, A. R. & Hui, C.-Y. 1993 Vortex/surface interaction. AIAA Paper 93-0863.
Carrier, G. F., Krook, M. & Pearson, C. E. 1983 Functions of a Complex Variable - Theory and Technique. Hod Books.
Chow, J. S., Zilliac, G. G. & Bradshaw, P. 1993 Measurements in the near field of a turbulent wingtip vortex. AIAA Paper 93-0551.
Chuang, F.-S. & Conlisk, A. T. 1989 The effect of interaction on the boundary layer induced by a convected rectilinear vortex. J. Fluid Mech. 200, 337–365.Google Scholar
Doligalski, T. L. & Walker, J. D. A. 1984 The boundary layer induced by a convected two-dimensional vortex. J. Fluid Mech. 139, 1–28.Google Scholar
Filotas, L. T. 1971 Solution of the lifting line equation for twisted elliptic wings. J. Aircraft 8, 835–836.Google Scholar
Garg, A. K. & Leibovich, S. 1979 Spectral characteristics of vortex breakdown flowfields. Phys. Fluids 22, 2053–2064.Google Scholar
Goldstein, R. J. 1983 Fluid Mechanics Measurements Hemisphere.
Hall, M. G. 1964 The structure of concentrated vortex cores. Prog. Aeronaut. Sci. 7, 53–110.Google Scholar
Hall, M. G. 1972 Vortex breakdown. Ann. Rev. Fluid Mech. 4, 195–218.Google Scholar
Ham, H. D. 1975 Some conclusions from an investigation of blade-vortex interaction. J. Am. Helicopter Soc. October, pp. 26–31.Google Scholar
Hancock, G. J. 1971 Aerodynamic loading induced on a two-dimensional wing by a free vortex in incompressible flow. Aeronaut. J. R. Aeronaut. Soc. 75, 413–416.Google Scholar
Harvey, J. K. & Perry, F. J. 1971 Flowfield produced by trailing vortices in the vicinity of the ground. AIAA J. 9, 1659–1660.Google Scholar
Hoeijmakers, H. W. M. 1990 Modeling and numerical simulation of vortex flows in aerodynamics. AGARD-CP-494.
Jones, W. P. 1972 Vortex-elliptic wing interaction. AIAA J. 10, 225–227.Google Scholar
Jung, Y. & Seath, D. D. 1988 Spanwise displacement of a line vortex above a wing - a simple calculation scheme. J. Aircraft 25, 476–478.Google Scholar
Leibovich, S. 1978 The structure of vortex breakdown. Ann. Rev. Fluid Mech. 10, 221–246.Google Scholar
McAllister, K. W. & Tung, C. 1984 Airfoil interaction with an impinging vortex. NASA Tech. Paper 2273.Google Scholar
McMillan, O. J., Schwind, R. G., Nielsen, J. N. & Dillenius, F. E. 1978 Rolling moments in a trailing vortex flowfield. J. Aircraft 15, 280–286.Google Scholar
Maltby, R. L. & Keating, R. F. A. 1962 The surface oil flow technique for use in low speed wind tunnels. AGARDograph, AGARD-AG-70, pp. 29–38.
Maskew, B. 1983 Predicting aerodynamic characteristics of vortical flows on three-dimensional configurations using a surface-singularity panel method. AGARD-CP-342.
Mehta, R. D. & Lim, T. T. 1984 Flow visulization study of a vortex/wing interaction. NASA Tech. Memo. 86656.Google Scholar
Milne-Thompson, L. M. 1975 Theoretical Hydrodynamics, 3rd edn. Macmillan.
Nobel, B. 1958 Methods Based on the Wiener-Hopf Technique for Partial Differential Equations. Pergamon.
Patel, M. H. & Hancock, G. J. 1974 Some experimental results of the effect of a streamwise vortex on a two-dimensional wing. Aeronaut. J. R. Aeronaut. Soc. 78(760). 151–155.Google Scholar
Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T. 1989 Numerical Recipes The Art of Scientific Computing (FORTRAN Version). Cambridge University Press.
Seath, D. D. & Wilson, D. R. 1986 Vortex-airfoil interaction tests. AIAA Paper 86-0354.
Silver, L. W. 1966 An investigation of the interaction of a trailing vortex with a lifting-surface. MS thesis, MIT, Cambridge, MA, USA.
Smith, W. G. & Lazzeroni, F. A. 1960 Experimental and theoretical study of a rectangular wing in a vortical wake at low speed. NASA Tech. Note D-339.Google Scholar
Srinivasan, G. R., Chyu, W. J. & Steger, J. L. 1981 Computation of simple three-dimensional wing-vortex interaction in transonic flow. AIAA Paper 81-1206.
Van Dyke, M. 1956 Second-order subsonic airfoil theory including edge effects. NASA Rep. 1274.Google Scholar
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Parabolic, Stanford, CA.