Modeling of linear pressure fields in sonochemical reactors considering an inhomogeneous density distribution of cavitation bubbles

Abstract

Although a lot of experimental work was done on the investigation of chemical effects of power ultrasound, only very few efforts were directed towards engineering aspects, like optimum design and scale-up of sonochemical reactors. This paper deals with the calculation of acoustic fields and energy density distributions in sonochemical reactors with an inhomogeneous distribution of cavitation bubbles, which are a basis for the design of sonochemical reactors of various geometrical shapes. The time-dependent wave equation applied to a damped wave propagation represents the basis of our theory. A new model is presented for the numerical calculation of three-dimensional pressure fields in liquids taking into account an inhomogeneous distribution of wave parameters due to the presence of the cavitation bubbles. Compared to a single-phase fluid, gas bubbles in a liquid lead to a heavy change of phase velocity and sound attenuation. These changes are calculated for every time step and volume element of the reactor. Employing this technique, one should be able to calculate the pressure field in a sonochemical reactor with a sufficient accuracy which serves to predict the spatial distribution of cavitation events.