Evaluation of a Subgrid Surface Dynamics Model for Dual-Scale Modeling of Surface Tension Effects

Direct Numerical Simulation remains a prohibitively expensive task in Computational Fluid Dynamics, even more so for cases involving atomization. Instead of DNS, a dual-scale modeling approach (Gorokhovski and Herrmann, 2008) that describes turbulent phase interface dynamics in a Large Eddy Simulation spatial filtering context is proposed. Spatial filtering of the equations of fluid motion introduce several sub-filter terms that require modeling. Instead of developing individual closure models for the interface associated terms, the dual-scale approach uses an exact closure by explicitly filtering a fully resolved realization of the phase interface. This resolved realization is maintained using a Refined Local Surface Grid approach (Herrmann, 2008) employing an unsplit geometric Volume-of Fluid method (Owkes and Desjardins, 2014). Advection of the phase interface on this DNS scale requires a reconstruction of the fully resolved interface velocity. In this work, adaptations for a Sub-Grid Surface Dynamics (SGSD) model (Herrmann 2013) are applied to the VOF context. The SGSD model creates velocities that are not divergence-free and therefore must be corrected with a projection/correction step as in the Fractional Step Method. Since divergence-free velocities are needed only in the direct proximity of the phase interface, one can restrict the projection/correction to a narrow band surrounding the interface. Several implementations involving the size and boundary conditions of the Poisson equation are explored. Various test cases such as the oscillation period and damping of a weakly deformed mode 2 drop, the behavior of a stable and unstable Rayleigh-Plateau column, and viscous capillary break up of a ligament are used to evaluate the SGSD model.