MODELING OF 3-DIMENSIONAL LINEAR PRESSURE FIELDS IN SONOCHEMICAL REACTORS WITH HOMOGENEOUS AND INHOMOGENEOUS DENSITY DISTRIBUTIONS OF CAVITATION BUBBLES

A new model is presented for the numerical calculation of pressure fie lds in liquids with an inhomogeneous distribution of cavitation bubble s. To calculate the pressure field in a homogeneous single-phase fluid , the Helmholtz integral and the Kirchhoff integral are solved numeric ally. The Helmholtz integral equation and the Kirchhoff integral are u sed for the calculation of the acoustic field in a homogeneous fluid f or all kinds of transducers of various shapes. The first term of the i ntegral equation embodies a simple superposition of the pressure field s of several point sources, which serves to simulate a harmonic vibrat ing surface, while the Kirchhoff integral calculates the pressure fiel d which emerges from the boundaries. With a new technique the three-di mensional time-independent pressure field is calculated gradually in t he beam direction. With this procedure one is able to combine the Helm holtz integral with a wave propagation in liquids with inhomogeneous d istributions of cavitation bubbles. Compared to a single-phase fluid, gas bubbles in a liquid lead to a heavy change of phase velocity and s ound attenuation. These changes are determined and considered for ever y step in the beam direction. With this technique, one should be able to calculate the pressure field in a sonochemical reactor with a suffi cient approximation which serves to predict the spatial distribution o f cavitation events. These events are related to the yield of chemical reactions.