Mass conservation improved Phase Field Methods for turbulent multiphase flows simulations

Phase Field Method (PFM) has emerged as a powerful tool for the simulation of multiphase flows. The method has great potentials 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. Two improved PFM formulations (profile-corrected and flux-corrected) have been specifically developed to overcome the previously mentioned drawbacks. The improved formulations are tested and compared against the classic one, particularly focusing on the drawbacks of the classic formulation. Different benchmarks have been tested, starting from laminar cases up to the more challenging simulation of a droplet-laden turbulent flow. Our aim is to benchmark the different phase field method formulations, with the final goal of laying down useful guidelines for the accurate simu- lation of multiphase turbulent flows with the phase field method.