Interactions of periodically generated vortex rings

Periodically generated vortex rings are observed in nature such as cardiovascular flows. We set up a series of simulations to study the dynamics of vortex rings in both transient and quasi-steady state. Our set-up consists of a circular cylinder through which a periodic pulsed jet is pushed into a tank. Our visualizations showed that for test cases with high non-dimensional period (T^*, i.e., equivalent to formation time) or low Re, the stopping vortices surrounding the leading ones remain circular and intact; however, by decreasing T^* and increasing Re the stopping vortices become unstable and form hairpin vortices. Our observations in quasi-steady state showed that two distinct interaction patterns exist. For cases with short T^*, vortex pairing occurs after about one period downstream, which makes reaching the quasi-steady take longer. The stability of pairing process is affected by the Re. For cases with higher T^*, a train of vortex rings is generated in the quasi-steady state.