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

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.