Numerical analysis of effect of Reynolds number on interaction of density-stratified fluid with a vortex ring

Abstract

In this study, the effect of Reynolds number ( Re) on the mixing process of a two-layer density-stratified fluid, caused by the interaction between a vortex ring and the density interface, was numerically investigated using an improved vortex-in-cell method. The density-stratified fluid consisted of water (upper layer) and an aqueous sodium chloride (NaCl) solution (lower layer). Re of the simulated vortex ring was varied from 644 to 1932. We numerically investigated the behavior of the vortex ring and density-stratified fluid, and compared the same with that from a previously conducted experimental study from the literature. The vortex structure generated during the interaction was visualized in three dimensions. Furthermore, the mixing process was evaluated in terms of the stirring index, gradient of concentration, and stirring efficiency. The mixing behavior of the vortex ring was a function of the interaction pattern. For example, for a large Re, with the penetrative pattern, the stirring efficiency reached a constant value that was smaller than that from the partially penetrative pattern. The results showed that a strong stirring caused by an increase in Re of the vortex ring would not always lead to effective mixing.