Free-surface flows under impacting droplets

Abstract

A numerical method which fulfils the free-surface boundary conditions and extrapolates the fluid velocity in to empty grid cells outside the fluid region on a fixed Cartesian grid system is presented. The complex, three-dimensional, vortex structures formed via surface/vortex interaction and induction between vortices have been computed using the proposed technique implemented within a level-set method for both vertical and oblique droplet impacts in incompressible fluids. The present results have been validated through numerical tests which confirm zero tangential shear at the free-surface and comparisons with experimental observations of cavity and vortex ring formation underneath the impact location. In some cases, transitions from a concentric vortex ring to a fully three-dimensional vortex structure has been confirmed. Whilst the primary vortex ring is initiated at the highly curved contact surface between the droplet and receiving surface, azimuthal instabilities are manifested in the shear layer around the cavity crater developing after the vertical impact, resulting in axial counter-rotating vorticity between the cavity and descending vortex ring. Underlying mechanisms which induce local deformation of the free-surface, creating a so-called scar, due to the sub-surface vortices at the oblique impacts are also discussed.

A study of droplet impact on static films using the BB-LIF technique

“…In fact, if the curve is extrapolated, the minimum droplet thickness reaches zero at Re H ∼ 20,000. In (Watanabe et al 2008;Hsiao et al 1988), it is shown that at thicker films, the droplet and cavity react to produce vortex rings. There is no liquid at the centre of the ring, which means that the minimum thickness is zero as predicted by this extrapolation.…”

Evolution of the 2011 Tohoku Earthquake Tsunami on the Pacific Coast of Hokkaido

“…Watanabe, Saruwatari and Ingram (2008) presented a numerical extrapolation technique for computing three-dmesnional free-surface flows. In this method, a so-called ghost velocity is extrapolated to fulfill the dynamic boundary condition at the free-surface.…”

Splash, Vortices and Turbulent Shears in Partial Dam-Break Flows -- Splash Model of Wave-Breaking and Overtopping --

“…In the computation of free-surface flows on the fixed grids, where the fluid flow in the air is disregarded, the velocity outside of the fluid region needs to be extrapolated from the inner velocity in order to be able to compute the convective equation and update the surface location. In this study, an extrapolation technique which ensures the zero tangential shear dynamic condition (5) has been used (Watanabe et al 2008). This approach ensures that in regions of surface deformation with high curvature the correct surface-vortex interactions have been obtained.…”