A Dual Scale Approach to Predicting Sub-Filter Shear Driven Velocities on a Phase Interface with Vortex Sheet Method

A method to predict sub-filter velocities in the presence of shear on a liquid-gas phase interface for use in a dual scale LES-DNS model is presented. The method reconstructs the sub-filter velocity field on a Refined Local Surface Grid (RLSG) coaligned with the flow solver grid in a narrow band near the interface. A vortex sheet is employed at the interface location and evolves in time along with the interface by an unsplit geometric Volume-of-Fluid scheme using PLIC reconstruction and ELVIRA estimated normals. The shear-induced velocities due to the vortex sheet are evaluated in a vortex-in-cell type approach where a vorticity field is extrapolated to the underlying grid with a numerically smooth delta function. A stream function equation can then be constructed with the continuous vorticity distribution and solved to evaluate the self-induced vortex sheet velocities. The method is tested against results from prior literature and a comparison between the inviscid vortex sheet method and a viscous Navier-Stokes solution is presented.