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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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