An unstructured finite-volume level set / front tracking method for two-phase flows with large density-ratios

Abstract

We extend the unstructured LEvel set / froNT tracking (LENT) method for handling two-phase flows with strongly different densities (high-density ratios) by providing the theoretical basis for the numerical consistency between the mass and momentum conservation in the collocated Finite Volume discretization of the single-field two-phase Navier-Stokes equations. Our analysis provides the theoretical basis for the mass conservation equation introduced by Ghods and Herrmann [3] and used in [4, 5, 6, 7, 8]. We use a mass flux that is consistent with mass conservation in the implicit Finite Volume discretization of the two-phase momentum convection term, and solve the single-field Navier-Stokes equations with our SAAMPLE segregated solution algorithm [2]. The proposed $\rho$LENT method recovers exact numerical stability for the two-phase momentum advection of a spherical droplet with density ratios ranging in $[1, 10^4]$. Numerical stability is demonstrated for in terms of the relative $L_\infty$ velocity error norm, for density-ratios in the range of $[1, 10^4]$, dynamic viscosity-ratios in the range of $[1, 10^4]$ and very strong surface tension forces, for challenging mercury/air and water/air fluid pairings. In addition, the solver performs well in cases characterized by strong interaction between two phases, i.e., oscillating droplets and rising bubbles. The proposed $\rho$LENT method is applicable to any other two-phase flow simulation method that discretizes the single-field two-phase Navier-Stokes Equations using the collocated unstructured Finite Volume Method but does not solve an advection equation for the phase indicator using a flux-based approach, by adding the proposed geometrical approximation of the mass flux and the auxiliary mass conservation equation to the solution algorithm.