Multiphase flows with two or more immiscible liquids, separated by a sharp interface with surface tension, occur in a large variety of environmental and industrial flow problems. The ability to accurately predict such flows has implications for safety, economy, and ecology. As a scale resolving technique, large eddy simulation (LES) is a turbulence model that has the potential to describe such flows with good accuracy. However, during the filtering process of the two-phase flow equations, several unclosed terms appear that are unknown from single-phase flow and their modelling is not yet standardized in the open literature. In this paper, the unknown terms are systematically analyzed based on a-posteriori LES and comparison with a direct numerical simulation (DNS) database. It is shown that the closures for each unknown term strongly interact with the other terms and as well with the numerical scheme. Therefore, only a modelling strategy consisting of a complete set of sub-models and numerical discretization can be identified, rather than individual optimal models. Several promising alternatives are identified and discussed, based on existing and newly developed turbulence and interfacial subgrid scale (SGS) closures.

Compared to Large Eddy Simulation (LES) of single-phase flows, which has become a mature and viable turbulence modelling technique, the LES of two-phase flows with moving immiscible interfaces is at a rather early development stage. There is no standard set of governing equations for two-phase flow LES, but rather a variety of different formulations, all with advantages and disadvantages. This paper discusses and analyses in detail the governing equations for two-phase flow LES in the context of the Volume of Fluid method, as well as suitable Subgrid Scale closures for the different unknown terms. A particular focus is on the Favre filtered one fluid formulation of the momentum equations, but a comparison with the filtered and the volume averaged version of the balance equations is made as well. Differences and commonalities between the different approaches are discussed and, based on a priori analysis of explicitly filtered Direct Numerical Simulation data, suitable closure models for a posteriori analysis are identified.