Analysis of the explicit volume diffusion subgrid closure for the Σ−Y model to interfacial flows over a wide range of Weber numbers

Abstract

The explicit volume diffusion (EVD) method was recently proposed for simulating interfacial flows based on the volume of fluid method. In this work, the EVD equations are derived rigorously from the $\Sigma -Y$ (surface density and mass fraction) perspective under the large eddy simulation (LES) framework. Volume averaging is applied over an explicit length scale ${\ell }_V$ that is grid-independent. The sub-volume flux and stress are closed through gradient diffusion and viscosity models that account for the presence of an interface and turbulence, and have the correct limits in the absence of interface vorticity and in the pure phases. An EVD equation for $\Sigma$ is introduced for the first time to model the volume averaged surface tension. The EVD model and closures are tested for three different liquid jet breakup cases: a series of laminar round jets in the Rayleigh-Plateau regime ($12<W{e}_l<34$), a turbulent coaxial air-blast jet ($W{e}_g=75$) and a high Weber number turbulent crossflow ($W{e}_g=330$). Numerical convergence and sensitivity to ${\ell }_V$ are investigated, along with comparisons to linear theory, experimental data, empirical correlations and previous simulations. The effects of the closures on flow dynamics and key dimensionless numbers are also analysed.