Vortex ring-tube reconnection in a viscous fluid

Abstract

The vortex ring-tube reconnection in a viscous fluid was investigated using a proposed vortex-in-cell method combined with a large eddy simulation model (LVIC). This method was verified using simulations of the Taylor–Green vortex flow at the Reynolds numbers (Re) 200 and 2000. The results show that the present method can capture the small-scale vortex structures in turbulent flows well. Besides, a Lagrangian method for passive scalar transport was successfully developed to track the vortex dynamics. The LVIC was then applied to three simulations of the interaction of a vortex ring at ReΓr(Γ/ν)=10000 and a vortex tube at ReΓt=1000, 5000, and 10 000. At ReΓr=10000 and ReΓt=1000, the effects of the tube on the ring are trivial while the ring breaks it into two parts and entrains them. The flow’s energy spectrum remains unchanged with time, the small-scale vortices are not generated, and the ring’s motion plays a key role in the flow. Moreover, the helicity distribution on the vortices is negligible. At ReΓr=10000 and ReΓt=5000, the tube breaks into two parts, and the leaving part of the tube interacts forcefully with the ring to form the small-scale vortices at the high wavenumbers. The population of small-scale vortex structures increases with time, and the large-scale vortices are twisted after the impingement. At ReΓr=10000 and ReΓt=10000, the impingement of the ring on the tube leads to their breakdown and reconnection. A part of the ring interacts with the leaving part of the tube to form a secondary ring, while the rest replaces the leaving part to reconnect the tube. The population of small-scale vortex structures and helicity distribution increase in this flow stage because of the interaction of the secondary ring wake and connection vortices. However, after the reconnection, the population and helicity distribution on the vortex structures significantly decrease. The smallest-scale vortex structure and the most effective mixing occur with ReΓr=10000 and ReΓt=5000.