Modeling of interfacial flows based on an explicit volume diffusion concept

Abstract

A novel volume of fluid model (VoF) called explicit volume diffusion (EVD) is developed for the simulation of interfacial flows, including those with turbulence and primary spray atomisation. The EVD model is derived by volume averaging the VoF equations over a physically-defined length scale. This introduces unclosed sub-volume flux, sub-volume stress and volume averaged surface tension force. Sub-volume fluctuations arise due to both turbulent motions and other interface dynamics which can, in general, occur in both laminar and turbulent flows. Both of these types of fluctuations are attenuated by the volume averaging process. The sub-volume flux is closed by a gradient diffusion model and involves an explicit volume diffusion coefficient that is linked to the physical length scale. The sub-volume stress closure introduces an explicit volume viscosity augmented by turbulent viscosity in turbulent flows. The volume averaged surface tension force closure is based on fractal properties of wrinkled sub-volume interfaces. These closures are evaluated through a priori analysis of resolved flow simulations for a series of two-dimensional laminar and three-dimensional turbulent interfacial shear flows. Subsequently, full EVD simulations are validated for these shear flows and for a laboratory airblast spray jet. Numerical convergence is demonstrated by keeping the physical length scale constant while reducing the numerical grid size so that numerical diffusion diminishes and becomes overwhelmed by the explicit volume diffusion. A sensitivity analysis is also conducted for variations in the physical length scale, which is compared to the boundary layer thickness on the light fluid side of the interface.