Characterization of the velocity fields generated by flow initialization in the CFD simulation of multiphase flows

Recent improvements in numerical algorithms for Eulerian-based CFD simulations of multiphase flows can now recover the exact balance between the pressure and surface tension terms within the momentum equation. This has led to the minimization of the so called “spurious velocities”: unphysical flows appearing at interfaces when using implementations of the Continuum Surface Force technique to model surface tension forces. Nevertheless, non-null velocity fields are still observed in the proximity of interfaces despite the absence of external forces, and it will be shown here that they can still considerably influence the accuracy of two-phase flow simulations. This study demonstrates that the evolution of these velocity fields is due to the generation of a capillary wave at the beginning of the simulation. This arises from the inability of the surface tension algorithm to evaluate a constant interface curvature from the initial color function field, although this is obtained by mapping an exact circumference on the computational grid, which then generates an initial perturbation that evolves as a capillary wave. A linear stability analysis of a two-dimensional circular static droplet subjected to initial small amplitude perturbations is here developed and compared with the results of CFD simulations to corroborate this thesis. This methodology provides a novel insight on the nature and behavior of spurious currents and their influential parameters, and it yields results which are not only in line with previous observations but also unify some contrasting trends reported in the literature. It is observed that the velocity magnitude induced by the capillary wave scales with the surface tension coefficient and the inverse of the fluid density and droplet radius. Furthermore, it decreases when refining the computational mesh only if the interface curvature estimations converge to the exact value, while otherwise showing the opposite trend.