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 edgeof circular （2D） tube and opening. Computations based on this model are in goodagreement 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 thatthe main failure of the similarity theory （the false prediction of axial trajectory ofvortex ring） is due to its ignorance of the self-induced ring velocity （mutual inductionfor vortex pair）. We further reason why the similarity theory succeeds in its predictionof radial movement of vortex ring. The effects of various parameters such as turningangle α and piston speed U;（t） on the formation of vortex ring are investigated.Numerical result shows that turning angle α has no effect on circulation shed Γ.We also discuss Glezer （1988）’s summary on the influence of Up upon the sheddingcirculation, and finally give the variation of core distribution of vortex ring with αand U;（t）.