On the formation of vortex rings and pairs

The axisymmetric vortex sheet model developed by Nitsche & Krasny (1994) has been extended to study the formation of vortex rings (pairs) at the edge of circular (2D) tube and opening. Computations based on this model are in good agreement with the experiments (Didden (1979) for circular tube and Auerbach (1987) for 2D tube and opening). Using this new model, evidences are provided to show that the main failure of the similarity theory (the false prediction of axial trajectory of vortex ring) is due to its ignorance of the self-induced ring velocity (mutual induction for vortex pair). We further reason why the similarity theory succeeds in its prediction of radial movement of vortex ring. The effects of various parameters such as turning angle α and piston speedU _p (t) on the formation of vortex ring are investigated. Numerical result shows that turning angle α has no effect on circulation shed τ. We also discuss Glezer (1988)'s summary on the influence ofU _p upon the shedding circulation, and finally give the variation of core distribution of vortex ring with α andU _p (t). The project is supported by National Natural Science Foundation of China and Doctoral Program of Institution of Higher Education