The water entry surface seal behavior of spheres at intermediate speed regimes

Abstract

This research focuses on the water entry of spheres in the surface seal regime. Herein, surface seal occurs in the wake of a sphere impact with the water surface and is characterized by splash dome over and cavity pull-away between the \emph{low-speed} ($U<30$~m/s) and \emph{high-speed} ($U>165$~m/s) regimes for various sphere diameters $D$. The established empirical scaling laws for pinch-off time $t_p$ hold well for both low and high speeds (i.e., respectively $ t_pUD^{-1}~C_d^{-1/2}=const$ and $ t_pUD^{-1}~C_d^{-1/2}\propto Ca^{-1}$) but the transition deserves refinement. The intermediate regime in particular scales as $t_pUD^{-1}~C_d^{-1/2}\propto Ca^{-1/2}$, which means that the pressure reduction inside the cavity determines the surface seal dynamics as speeds increase. We also report on the transition from deep to surface seal, where the seal time is scaled more like a deep seal. The partial pull-away, ripples on the cavity surface, and the secondary pinch-off are also reported.