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The results of recent developments of analytical vortex ring models and the applications of these models to interpretation of the experimentally observed dynamics of vortex ring-like structures in gasoline sprays, under non-evaporating conditions, are summarized. Analytical formulae in the limit of small Reynolds numbers (Re), are compared with numerical solutions. Particular attention is focused on the generalized vortex ring model in which the time evolution of the thickness of the vortex ring core L is approximated as atb, where a and b are constants (1 ≤ b ≤ 1/2). This model incorporates both the laminar model for b=1/2 and fully turbulent model for b=1/4. The values of velocities in the region of maximal vorticity, predicted by the generalized vortex ring model, are compared with the results of experimental studies of fuel droplets distributed in vortex ring-like structures in two gasoline injectors, under cold-start, engine-like conditions.

Recently developed liquid and gas phase models for fuel droplet heating and evaporation, suitable for implementation into computational fluid dynamics (CFD) codes, are reviewed. The analysis is focused on the liquid phase model based on the assumption that the liquid thermal conductivity is infinitely large (infinite thermal conductivity (ITC) model), and the so called effective thermal conductivity (ETC) model. Seven gas phase models are compared. It is pointed out that the gas phase model, taking into account the finite thickness of the thermal boundary layer around the droplet predicts the evaporation time closest to the one based on the approximation of experimental data. In most cases, the droplet evaporation time depends strongly on the choice of the gas phase model. The dependence of this time on the choice of the liquid phase model, however, is weak if the droplet break-up processes are not taken into account.