Chapter 3.2 - Theory of Shock Waves: 3.2 Shock Waves in Liquids

Abstract

This chapter explains the theory of shock waves in liquids as it is less well known. In order to simplify the presentation of the theory of shock waves in liquids, 1D water flow is considered. The propagation of a one-dimensional (1D) disturbance in the x-direction is given by Euler's equation of motion. Further, shock waves in water due to underwater explosion of high explosives is discussed. Shock waves generated by underwater explosions are usually observed via high-speed photography t ogether with standard shadowgraph systems. A didactic description of the experimental procedure of underwater shock wave research conducted at the Shock Wave and Condensed Matter Research Center in Kumamoto University in Japan is presented. The experiments are carried out in an explosion chamber. The simplified arbitrary Lagrangian-Eulerian (SALE) method is used to simulate the experiments. The calculation using the SALE method is divided into three phases: phase 1: an explicit Lagrangian calculation, in which the velocity field is updated by the effects of all the forces acting on the flow field. Phase 2: a Newton-Raphson iteration that provides the time-advanced pressures and velocities. Lastly, phase 3:performance of all the advective flux of the mass calculations and the mesh rezoning.