Collisions of vortex rings with hemispheres

Abstract

A numerical investigation was conducted on $Re_{\varGamma _{0}}=3000$ vortex rings colliding with wall-mounted hemispheres to study how their relative sizes affect the resulting vortex dynamics and structures. The hemisphere to vortex ring diameter ratio ranges from $D/d=0.5$ to $D/d=2$ . Secondary/tertiary vortex rings are observed to result from hemispheric surface boundary layer separations rather than wall boundary layer separations as the diameter ratio increases. While those for $D/d\leq 1$ hemispheres can be attributed to sequential hemispheric and wall boundary layer separations, the primary vortex ring produces a series of secondary/tertiary vortex rings only along the $D/d=2$ hemispheric surface. This indicates that the presence of the wall makes little difference when the hemisphere is sufficiently large. On top of comparing vortex ring circulations and translational velocities between hemisphere and flat-wall based collisions, present collision outcomes have also been compared with those predicted by specific discharge velocity models. Additionally, comparisons of vortex core trajectories and vortex ring formation locations with earlier cylindrical convex surface based collisions provide more clarity on differences between two- and three-dimensional convex surfaces. Finally, vortex flow models are presented to account for the significantly different flow behaviour as the hemisphere size varies. Specifically, the vortex flow model for the $D/d=2$ hemisphere hypothesizes that the recurring tertiary vortex ring formations cease only when the primary vortex ring slows down sufficiently for the last tertiary vortex ring to entangle with it and render it incoherent. Until that happens, the primary vortex ring will continue to induce more tertiary vortex rings to form, with potential implications for heat/mass transfer optimizations.