Finite difference method

Abstract: High-pressure water jets are used to cut and drill into rocks by generating cavitating water bubbles in the jet which collapse on the surface of the rock target material. The dynamics of submerged bubbles depends strongly on the surrounding pressure, temperature and liquid surface tension. The Rayleigh-Plesset (RF) equation governs the dynamic growth and collapse of a bubble under various pressure and temperature conditions. A numerical finite difference model is established for simulating the process of growth, collapse and rebound of a cavitation bubble travelling along the flow through a nozzle producing a cavitating water jet. A variable time-step technique is applied to solve the highly non-linear second-order differential equation. This technique, which emerged after testing four finite difference schemes (Euler, central, modified Euler and Runge-Kutta-Fehiberg (RKF)), successfully solves the Rayleigh-Plesset (RP) equation for wide ranges of pressure variation and bubble initial sizes and saves considerable computing time. Inputs for this model are the pressure and velocity data obtained from a CFD (computational fluid dynamics) analysis of the jet. Copyright (c) 2007 John Wiley & Sons, Ltd.