Mass-conservation-improved phase field methods for turbulent multiphase flow simulation

The phase field method has emerged as a powerful tool for the simulation of multiphase flow. The method has great potential for further developments and applications: it has a sound physical basis, and when associated with a highly refined grid, physics is accurately rendered. However, in many cases, especially when dealing with turbulent flows, the available computational resources do not allow for a complete resolution of the interfacial phenomena and some undesired effects such as shrinkage, coarsening and misrepresentation of surface tension forces and thermo-physical properties can affect the accuracy of the simulations. In this paper, we present two improved phase field method formulations (profile-corrected and flux-corrected), specifically developed to overcome the previously mentioned drawbacks, and we benchmark their performance versus the classic one. The formulations are first tested considering the rise of a bubble in a quiescent fluid and the interaction of two droplets in laminar shear flow; then, their performances are compared in the simulation of a droplet-laden turbulent flow. The aim of this work is to review and benchmark the different phase field method formulations, with the final goal of laying down useful guidelines for the accurate simulation of turbulent multiphase flow with the phase field method.