Numerical simulation and experimental study of the behaviour of vortex rings (1994)

The research was directed at an understanding of the behaviour of vortex rings under more realistic and complex conditions than those considered previously. A numerical method using a control volume finite difference technique was employed to simulate vortex ring behaviour in various vessel geometries. Unlike in other studies, buoyancy effects were included. The flow behaviour of the fluids in a tank due to the formation and motion of the vortex rings was studied. Several computer models have been developed for numerical simulation of various conditions. The conditions that were simulated are: (1) the effects of injecting Reynolds number and Richardson number on the penetration of a laminar vortex ring through a stratified layer of sharp or linear temperature change along the interface; (2) the formation and motion of a single vortex ring ejected from a tube centrally located near fluid free surface of a cylindrical tank, for stratified non-Newtonian power law model fluids with Richardson numbers of 0.0, 0.01 and 0.1 and power law indices of 0.17, 0.571 and 1.5; (3) the formation and motion of primary and secondary vortex rings ejected from an orifice plate, centrally located in the bottom or middle level of a tank having thermally stratified water depth to tank diameter ratios of 1.695 and 2.77, with and without a peripheral gap around the generating plate. The numerical results showed that: (1) the penetration and trajectory of a laminar vortex ring is virtually independent of the injection Reynolds number, but primarily dependent on Richardson number; (2) laminar vortex rings in a power law fluids behave inviscidly, virtually the same as in Newtonian fluids for a certain range of injecting Reynolds numbers; (3) secondary vortex rings generated at a plate type orifice have similar trajectories and vorticity intensities to those of primary vortex rings for a trapezoidal injecting velocity-time profile. This results in a the doubling of the mass transportation and most probably more efficient mixing; the vorticity created at the plate periphery and also along the vessel wall can have a notable effect on the behaviour of the primary and secondary vortex rings, and so does the vorticity at region remote from the generating device. The intensity of the vorticity created in this manner is dependent of parameters such as, peripheral gaps between the impeller and the vessel wall, the orifice size, and the velocity-time profile for the generating plate. This phenomenon has not been described before and appears to be of considerable interest for both fundamental and mixing studies. Some empirical experiments have been preformed and there appears to be good agreement with the numerical simulation studies. The flow visualization clearly displays the formation and motion of the primary and secondary vortex rings, and rolling up, transportation, transition and turbulent decay of a laminar vortex ring within its travelling distance. Experimental results demonstrate that the behaviour of vortex rings and the interaction of primary and secondary vortex rings are very dependent on displacement-time motion profile of the generating device