Limitation in velocity of converging shock wave

TL;DR

This paper investigates the velocity limitations of converging shock waves in water, showing that variable compression leads to finite velocities and a bounded convergence radius, contrasting with traditional models predicting unlimited velocities.

Contribution

It introduces a model accounting for variable water compression behind the shock, revealing finite velocity limits and a specific convergence radius based on the adiabatic index.

Findings

Finite convergence radius depends on water's adiabatic index.

Shock and flow velocities are limited and do not increase indefinitely.

Traditional self-similar solutions predict unlimited velocities, which are contradicted by the new model.

Abstract

The commonly applied self-similar solution of the problem of the converging shock wave (shock) evolution with constant compression of the medium behind the shock front results in an unlimited increase of the medium velocity in the vicinity of the implosion. In this paper, the convergence of cylindrical shocks in water is analyzed using the mass conservation law, when the water compression behind the shock front is a variable. The model predicts a finite range of radii, which depends on the adiabatic index of water and where the increase in pressure exceeds the sum of the change of the kinetic and internal energy densities behind the shock front. In this range of radii only the finite increase of the shock and water flow velocities is realized.