This paper presents three volume of fluid (VoF)-based methods for large eddy simulations of atomizing sprays with different treatments of the unresolved interface. The turbulent filtered VoF model uses conventional turbulent viscosity models to close the combined interfacial and turbulent sub-grid fluctuations. The hybrid turbulence filtering and artificial compression model includes an additional artificial compression term that is applied along regions where the liquid–air interface is continuous, while conventional turbulence filtering is activated in regions with discrete liquid objects. The new explicit volume diffusion model (EVD) is based on the concept of averaging the VoF equations over explicitly defined physical volumes that are independent of the numerical grid. Closure models of the sub-volume flux and stress terms introduce explicit volume diffusion and explicit volume viscosity that are physically defined and linked to the volume size. Numerical convergence is achieved by reducing the grid size while keeping the explicit volume size constant. The models are tested for two experimental atomizing spray cases with different Weber numbers. The superior numerical convergence of the EVD model is demonstrated by analysis of the mean and rms of the volume fraction and velocity fields. Two models for the surface tension force are investigated for the EVD simulations. Compared with the simple surface tension model which neglects sub-grid fluctuations, an improved volume-averaged model based on fractal properties of wrinkled sub-volume interfaces gives better predictions of the mean volume fraction relative to the experimental data but requires selection of a model constant.

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.