Numerical convergence of volume of fluid based large eddy simulations of atomizing sprays

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. Published under license by AIP Publishing.