Evolution and dynamics of vortex rings in a confined and asymmetric region

Vortex ring evolution in confined asymmetric geometries is critical to biological and engineering flows, yet the combined effects of confinement and asymmetry introduce dynamics not captured by studies of either factor alone. This study employs numerical simulations to investigate the three-dimensional evolution of vortex rings under such combined conditions, focusing on the roles of eccentricity (ε), Reynolds number (Re), and stroke ratio (L/D0). The evolution of the primary vortex ring (PVR) before transition into turbulence proceeds through three stages: symmetric growth, asymmetric inclination, and reorientation toward the confinement axis. The inclination arises from asymmetric interactions between the PVR and the boundaries. This interaction generates a boundary vortex ring (BVR) of unequal strength on the near-wall and far-wall sides, causing a differential circulation decay that drives the inclination. The reorientation stage is initiated as the PVR–BVR interaction strengthens with the growing inclination. This interaction promotes vorticity annihilation between opposite-signed segments of the PVR, and it is this annihilation-induced circulation loss that primarily redirects the vortex trajectory. Based on the slug model and the circulation-decay model for confined symmetric vortex rings, a scaling model is developed that quantitatively links the asymmetric circulation decay to the evolving inclination angle, showing good agreement with the simulations. The present study reveals the evolution and dynamics of vortex rings under confined asymmetric region, providing insight into vortex-mediated transport and dissipation in environments such as intracardiac filling.