Numerical study of a laminar vortex ring of a polymer solution

In this study, we investigate the laminar vortex ring of the polymer solution in numerical simulations. We examine the flow structure of the vortex core and the evolution of the vortex ring, with comparison with those of the Newtonian vortex ring. The advection speed of the solitary vortex ring of the polymer solution is found to decrease with time, following an approximate power scaling, similar to that of the Newtonian vortex ring. The dependence of this power scaling on the polymer viscosity ratio and the Weissenberg number of the flow is examined. The power scaling decreases as the polymer viscosity ratio is increased or the Weissenberg number is decreased. The similar scenario is also observed for the circulation of the solitary vortex ring.