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Two-dimensional vortex motion in the cross-flow of a wing-body configuration

Published online by Cambridge University Press:  26 April 2006

T. W. G. De Laat  and
R. Coene
T. W. G. De Laat
Affiliation:
Flight Test Department, Royal Netherlands Air Force, Binckhorstlaan 135, PO Box 20703, 2500 ES The Hague, The Netherlands
R. Coene
Affiliation:
Department of Aerospace Engineering, Delft University of Techonology, Kluyverweg, 1, PO Box 5058, 2600 GB Delft, The Netherlands
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Abstract

For a two-dimensional potential flow, Föppl obtained the equilibrium positions for a symmetric vortex pair behind a circular cylinder in a uniform oncoming flow. In this article it is shown that such an equilibrium is in general possible for a vortex in a stagnation flow (e. g. in a corner). Furthermore it is found that a vortex near such an equilibrium position will rotate with a definite frequency around this equilibrium. Expressions are derived for the frequencies associated with the closed orbits of the vortices in the case of equilibrium of a vortex in a stagnation flow and for the equilibrium of the symmetric vortex pair behind a circular cylinder in oncoming flow. For the large-amplitude case the vortex trajectories are claculated using a fifth-order Runge-Kutta integration method. The analysis is then extended to the case of a simple wing-body combination in a cross-flow such as arises for a slender aircraft at an angle of attack with vortices generated by strakes or at the front part of the body. At the wint-body junctions the motions of the vortices may be periodic, quasi-periodic or the vortices may be swept away, depending on the initial conditions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 305 , 25 December 1995 , pp. 93 - 109
Copyright
© 1995 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics Cambridge University Press.
Ericsson, L. E. 1987 Vortex-induced bending oscillation of a swept wing. J. Aircraft 24, 195–202.Google Scholar
Hall, R. M. Erickson, G. E., Straka, W. A. et al. 1990 Impact of nose-probe-chines on the vortex flows about the F-16C. AIAA-90-0386.
Lamb, H. 1932 Hydrodynamics. Dover.
Lighthill, M. J. 1985 An Informal Introduction to Theoretical Fluid Mechanics. Clarendon Press.
Lin, C. C. 1941 On the motion of vortices in two dimensions-II. Some further investigations on the Krichhoff-Routh function. Nat. Acad. Sci. 27, 575–577.Google Scholar
Milne-Thomson, L. M. 1967 Theoretical Hydrodynamics, 5th edn. MacMillan.
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.