Non-linear effects and shock formation in the focusing of a spherical acoustic wave : Numerical simulations and experiments in liquid helium

TL;DR

This paper investigates non-linear effects and shock formation in spherical acoustic wave focusing in liquid helium through numerical simulations and experiments, highlighting the importance of equation of state shape and shock dynamics.

Contribution

It provides a detailed numerical and experimental analysis of non-linear acoustic wave focusing, including shock formation, in spherical geometry in liquid helium, with improved modeling techniques.

Findings

Non-linearities are mainly due to the equation of state shape.

Shocks form beyond a certain oscillation amplitude.

Numerical simulations agree well with experimental data.

Abstract

The focusing of acoustic waves is used to study nucleation phenomena in liquids. At large amplitude, non-linear effects are important so that the magnitude of pressure or density oscillations is difficult to predict. We present a calculation of these oscillations in a spherical geometry. We show that the main source of non-linearities is the shape of the equation of state of the liquid, enhanced by the spherical geometry. We also show that the formation of shocks cannot be ignored beyond a certain oscillation amplitude. The shock length is estimated by an analytic calculation based on the characteristics method. In our numerical simulations, we have treated the shocks with a WENO scheme. We obtain a very good agreement with experimental measurements which were recently performed in liquid helium. The comparison between numerical and experimental results allows in particular to calibrate the vibration of the ceramics used to produce the wave, as a function of the applied voltage.