Trajectories of Vortex Rings Formed from Tube and Orifice Openings at Small Stroke Ratios

The sudden ejection of a jet of slug length $L$ and diameter $D$ from a tube or orifice opening engenders the formation of a vortex ring for $L$/$D\sim $ 1. For a vortex ring close to the tube/orifice exit at jet termination ($L$/$D<<$ 1), the results of Sheffield (\textit{Phys. Fluids}, \textbf{20}, 1977) suggest the vortex ring will travel back into the generator. Sheffield, however, only considered 2D (planar) flows and did not consider the vortex formation process. In the present investigation, $L$/$D<<$ 1 behavior is studied computationally for tube and orifice openings at a jet Reynolds number of 2000 and 0.02 $