Abstract
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.
Highlights
The accurate simulation of turbulent multiphase flow is of crucial importance in a wide range of applications, from raindrop formation [11] to the pharmaceutical industry [15]
To characterize the strengths and weaknesses of the different phase field method (PFM) formulations, their performances have been benchmarked via 2D simulations and tested considering a 3D simulation of a droplet-laden turbulent flow
The formulations have first been benchmarked considering a rising bubble and the coalescence of two droplets in shear flow. These tests have been used to obtain important indications on the effect that the additional fluxes have in the description of coalescence phenomena, in the conservation of the interfacial profile and in the mass leakage among the phases
Summary
The accurate simulation of turbulent multiphase flow is of crucial importance in a wide range of applications, from raindrop formation [11] to the pharmaceutical industry [15]. The description of such flows poses several challenges, among them the description of topological changes, viscosity/density contrasts and surface tension forces [17]. In this context, the phase field method emerges as a powerful alternative to the more conventional methods such as front tracking (FT) [41], volume of fluid (VOF) [18,38] and level set (LS) [29,30]. The transport of the phase field variable is described by an advection–diffusion equation; the diffusive term (derived from a Ginzburg–Landau free energy functional) drives the system towards a minimum energy configuration and restores the phase field equilibrium profile across the interface
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