A pressure impulse theory for hemispherical liquid impact problems

TL;DR

This paper develops a pressure impulse theory for hemispherical liquid impacts, reducing the problem to solving Laplace's equation with boundary conditions, and validates it against numerical simulations.

Contribution

It introduces a novel pressure impulse approach for hemispherical impacts, linking flow structure to spherical harmonics and providing analytical insights.

Findings

Flow at impact is described by spherical harmonics.

Slip velocity exhibits a logarithmic singularity.

Theoretical results agree with Navier-Stokes simulations.

Abstract

Liquid impact problems for hemispherical fluid domain are considered. By using the concept of pressure impulse we show that the solution of the flow induced by the impact is reduced to the derivation of Laplace's equation in spherical coordinates with Dirichlet and Neumann boundary conditions. The structure of the flow at the impact moment is deduced from the spherical harmonics representation of the solution. In particular we show that the slip velocity has a logarithmic singularity at the contact line. The theoretical predictions are in very good agreement both qualitatively and quantitatively with the first time step of a numerical simulation with a Navier-Stokes solver named Gerris.