A focused liquid jet formed by a water hammer in a test tube

TL;DR

This study models the formation of a focused liquid jet in a test tube caused by water hammer effects, incorporating pressure wave dynamics and cavitation to explain experimental observations.

Contribution

It introduces a one-dimensional pressure wave model with acoustic impedance mismatching to explain jet formation and cavitation phenomena in water hammer events.

Findings

The model captures unsteady jet features and interface vibrations.

Cavitation onset correlates with increased jet velocity.

Pressure wave interactions explain experimental results.

Abstract

We investigate motion of a gas-liquid interface in a test tube induced by a large acceleration via impulsive force. We conduct simple experiments in which the tube partially filled with a liquid falls under gravity and impacts a rigid floor. A curved gas-liquid interface inside the tube reverses and eventually forms an elongated jet (i.e. the so-called a focused jet). In our experiments, there arises either vibration of the interface or increment in the velocity of a liquid jet accompanied by the onset of cavitation in the liquid column. These phenomena cannot be explained by considering pressure impulse in a classical potential flow analysis, which does not account for finite speeds of sound as well as phase change. Here we model such water-hammer events as a result of one-dimensional pressure wave propagation and its interaction with boundaries through acoustic impedance mismatching. The method of characteristics is applied to describe pressure wave interactions and the subsequent cavitation. The proposed model is found to allow us to capture the unsteady features of the liquid jet.