Dynamics of vortex rings in the spray from a swirl injector

The dynamics of vortex rings in the spray injected from a swirl injector is investigated both experimentally and numerically. An original three-dimensional (3D) simulation code is developed to analyze the two-phase flow consisting of liquid droplets and ambient air, in which the equations of motion of droplets and the dynamical equation for the ambient air flow are solved simultaneously accounting for secondary atomization of droplets. It is confirmed that the tip penetration obtained by the present numerical simulation agrees very well with the experimental results conducted by us. The formation of vortex rings and their role in the process of entrainment of ambient air are investigated numerically. It is found that many vortex rings are created successively in an earlier period, but only one vortex ring survives in the later period. The tip penetration increases in a power law with time in the earlier period and logarithmically in time in the later period. The difference in the time dependence of the tip penetration between the two periods is accounted for by the change in the structure of vortex rings being created or surviving. The translational velocity of the vortex ring, which solely survived in the later period, was estimated to decrease logarithmically in time before it collapses and disappears, and the maximum entrainment of ambient air into the spray core was identified as being located in the region near the sole vortex. Spectral analysis is performed to investigate the deformation of the sole vortex ring in the later period, which shows that the vortex-ring structure changes its form, having coarse or fine wavy deformation in turn repeatedly.