A robust interface method for drop formation and breakup simulation at high density ratio using an extrapolated liquid velocity

A two-phase flow formulation for atomisation modelling is presented, with a Coupled Level Set/Volume Of Fluid (CLSVOF) technique adopted for interface-tracking. In order to achieve stable numerical solution at high density ratios, an extrapolated liquid velocity field is constructed and used in discretisation of the momentum equations. Solution accuracy is also improved when this field is also used in the scalar (VOF and Level Set) advection equations. A divergence-free algorithm is proposed to ensure satisfaction of the continuity condition for the extrapolated liquid velocity. The density and viscosity across the interface are treated sharply as a function of the Level Set to maintain the physical discontinuity. The developed method is shown to accurately predict drop formation in low Re liquid jets and the deformation and breakup morphology of a single droplet in uniform air flow at different Weber numbers (from 3.4 to 96). The mechanism for droplet breakup is determined based on an analysis of the simulation results. The computed Rayleigh-Taylor instability wavelength extracted from the acceleration of the simulated liquid droplet agrees well with experimental measurements and theoretical analysis, confirming that Rayleigh-Taylor instability dominates single drop breakup in the Weber number range studied. Finally, the influence of liquid viscosity on droplet breakup is numerically investigated; the critical Weber number separating deformation and breakup regimes is well predicted at different Ohnesorge numbers in comparison with the experimental data.