Modelling of a two-phase vortex-ring flow using an analytical solution for the carrier phase

A transient axially symmetric two-phase vortex-ring flow is investigated using the one-way coupled, two-fluid approach. The carrier phase parameters are calculated using the approximate analytical solution suggested by Kaplanski and Rudi (Phys. Fluids vol. 17 (2005) 087101-087107). Due to the vortical nature of the flow, the mixing of inertial admixture can be accompanied by crossing particle trajectories. The admixture parameters are calculated using the Fully Lagrangian Approach (FLA). According to FLA, all of the dispersed phase parameters, including the particle/droplet concentration, are calculated from the solution to the system of ordinary differential equations along chosen particle trajectories; FLA provides high-accuracy particle number calculations even in the case of crossing particle trajectories (multi-valued fields of the dispersed media). Two flow regimes corresponding to two different initial conditions are investigated: (i) injection of a two-phase jet; and (ii) propagation of a vortex ring through a cloud of particles. It was shown that the dispersed media may form folds and caustics in these flows. In both cases, the ranges of governing parameters leading to the formation of mushroom-like clouds of particles are identified. The caps of the mushrooms contain caustics or edges of folds of the dispersed media, which correspond to particle accumulation zones.