Toward a fully resolved volume of fluid simulation of the phase inversion problem

Abstract

This paper presents an enstrophy-resolved simulation of the phase inversion problem using the volume of fluid (VOF) method. This well-known benchmark for modeling multiphase flows features a buoyancy-driven unsteady motion of a light fluid into a heavy one followed by several large- and small-scale interfacial processes such as deformation, ligament formation, interface breakup, and coalescence. A fully resolved description of such flow is advantageous for a priori and a posteriori evaluations when developing new subgrid-scale closure models for large eddy simulation of two-phase flows. However, most of the previous attempts in performing the direct numerical simulation of this problem have been unsuccessful to reach grid-independent high-order flow statistics such as enstrophy. The key contribution of this paper lies in proposing a new converging configuration for this problem by reducing the Reynolds and Weber numbers. The new setup reaches grid convergence for all the flow characteristics on a 512^3 grid. Particularly, the enstrophy which has always revealed a grid-dependent behavior in all the previous studies converges for the proposed setup. Also, we analyze the temporal evolution of interfacial structures including the statistics of the total interfacial area during the process on different grid resolutions. First, no convergence on the interfacial area is observed and the possible reasons for lack of convergence are discussed. The potential remedies are investigated through a comprehensive parameter study. The findings highlight that (i) the enstrophy always converges for these moderate Re and We numbers, and (ii) the convergence of the total interfacial area is sensitive to the choice of initial and wall boundary conditions. Then, a new setup based on this sensitivity analysis is proposed that succeeded in full convergence for enstrophy and a partial convergence for the total interfacial area. The numerical simulations were carried out using the VOF solvers of OpenFOAM with a comparison between the algebraic and geometric schemes. Besides, the convergence of size distribution of dispersed structures is investigated. The present study provides insight into the possible directions toward a DNS of phase inversion problem with all the flow and interfacial structures resolved, which is essential for the future development of multiphase flow models.