A VoF-Based Consistent Mass-Momentum Transport for Two-Phase Flow Simulations

The most part of two-phase flows relevant to industrial applications is characterized by high density ratios that make numerical simulations of such kind of flows still challenging in particular when the interface assumes complex shape and is distorded by high shear. In this paper a new strategy, to overcome the numerical instabilities induced by the large densities/shears at the interface, is described for staggered cartesian grids. It consists in a consistent mass-momentum advection algorithm where mass and momentum transport equations are solved in the same control volumes. The mass fluxes are evaluated through the Volume-of-Fluid color function and directly used to calculate momentum convective term. Two and three-dimensional high-density test cases (the density ratio goes from 10³ to 10⁹) are presented. The new algorithm shows signifcantly improvements compared to standard advection methods therefore suggesting the applicability to the complete atomization process simulations.