Modeling of interfacial flows based on an explicit volume diffusion concept

Abstract

A novel volume of fluid (VoF) model called explicit volume diffusion (EVD) is developed for the simulation of interfacial flows, including those with turbulence and primary spray atomization. It is derived by volume averaging the VoF equations over an explicit, physically-defined length scale. Fluctuations at the sub-volume scales, which can arise due to interface dynamics or turbulence, are attenuated by the volume averaging process and their effects appear in unclosed terms representing sub-volume flux, sub-volume stress, and volume averaged surface tension force. Models are proposed for each of these. The sub-volume flux is closed by a gradient diffusion model and involves an explicit volume diffusion coefficient, that is, linked to the explicit length scale. The sub-volume stress closure introduces an explicit volume viscosity that can be augmented by a turbulent viscosity in turbulent flows. The volume averaged surface tension force closure is based on a fractal representation of the wrinkled sub-volume interface. To test the closures individually and the EVD model overall, a series of two-dimensional laminar and three-dimensional turbulent interfacial shear flows and a laboratory-scale airblast spray jet are considered. Numerical convergence is demonstrated by keeping the explicit volume length scale constant while refining the numerical grid such that the numerical diffusion diminishes and becomes overwhelmed by the explicit volume diffusion. Sensitivity analyses are also conducted for variations in the explicit length scale which may be linked to the boundary layer thickness on the light fluid side of the interface.