A Momentum-Consistent One-Fluid Formulation of Evaporating Two-Phase Flows in a Sharp Volume-of-Fluid Framework

The one-fluid formulation of two-phase flows regularizes the discontinuity at the phase interface as a single fluid with varying properties and adds additional source terms to satisfy jump conditions (e.g., surface tension). While well-suited for non-evaporative flows, analytical and numerical inconsistencies appear if phase change occurs due to the local volume dilatation at the interface, which may cause a momentum imbalance and affect the flow dynamics. Corrections to the momentum jump are implemented in the presence of phase change in the non-conservative one-fluid formulation of the momentum equation for incompressible flows coupled to a sharp Volume-of-Fluid approach: (a) two body forces are added in the context of the Continuum Surface Force model to address the ill-defined convective term; and (b) the flow solver is modified to include a preliminary predictor-projection step to shift the Stefan flow before integrating the momentum equation with a second predictor-projection step. A physically meaningful pressure field is recovered in the limit of low viscosity while using standard discretization schemes in the one-fluid framework. Further, the corrections improve the spatial and temporal smoothness of the pressure field. However, issues remain with the regularization of the viscous term due to the discrete evaluation of the one-fluid velocity gradients.