A Phase-Conditioned Filtering of Incompressible Interfacial Multiphase Flow Equations: APriori Study for the Modeling of LES Subgrid Scale Terms

A priori analysis consists in deriving subgrid scale terms from the explicit filtering of a 3D Direct Numerical Simulation (DNS) database. It is a step in the development of subgrid scale models for Large Eddy Simulation (LES). The main issue for LES multiphase flows is the development of subgrid scale models well suited for two-phase interfacial flows. More particularly, coupling between turbulence and the interface separating both liquid and gas phases is not yet taken into account accurately by two-phase flow LES models. To improve the understanding of this coupling, DNS about a freely decaying homogeneous isotropic turbulence case in a periodic cubic box has been performed in a previous work. Two planar interfaces are added in the middle of the computational box separated by 5% of the length box. Two-phase interfacial flow simulations are carried out with an incompressible flow solver coupled to a ghost-fluid level-set front capturing method. A parametric study based on the surface tension coefficient has been performed. The aim of the work presented in this manuscript is to evaluate subgrid scale terms deriving from the explicit filtering of this DNS database. Classical central filter is not used, but rather a phase-conditioned filter to derive phase-filtered LES equations for separated two-phase flows. Three subgrid scale terms are obtained. The first one derives from the convective (classical) term. The two last ones derive from the phase-coupling terms and are related to the stress tensor jump across the interface. The magnitudes of the different subgrid scale terms are compared for different Weber numbers and for different filter sizes.