Coupling of the Interface Tracking and the Two-Fluid Models for the Simulation of Incompressible Two-Phase Flow

Abstract

The volume of fluid (VOF) method, which uses an interface tracking algorithm for the simulation of the two-phase flow, is coupled with the “two-fluid” model, which is based on time and space averaged equations and cannot track the interface explicitly. The idea of the present work is to use the VOF method in the parts of the computational domain where the grid density allows surface tracking. In the parts of the domain where the flow is too dispersed to be described by the interface tracking algorithms, the two-fluid model is used. The equations of the two-fluid model are less accurate than the VOF model due to the empirical closures required in the averaged equations. However, in the case of the sufficiently dispersed flow, the two-fluid model results are still much closer to the real world than the results of the VOF method, which do not have any physical meaning when the grid becomes too coarse. Each model in the present work uses a separate set of equations suitable for description of two-dimensional, incompressible, viscous two-phase flow. Similar discretization techniques are used for both sets of equations and solved with the same numerical method. Coupling of both models is achieved via the volume fraction of one of the fluids, which is used in both models. A special criterion for the transition between the models is derived from the interface reconstruction function in the VOF method. An idealized vortical flow and the Rayleigh–Taylor instability are used as tests of the coupling. In both cases the time development causes mixing of the fluids and dispersion of the interface that is beyond the capabilities of the model based on the VOF method. Therefore the two-fluid model gradually replaces the interface tracking model. In the final stages of the Rayleigh–Taylor instability, when both fluids are approaching their final positions and the tractable interface appears again, the two-fluid model is gradually replaced by the VOF method.