Optimisation of 20 kHz sonoreactor geometry on the basis of numerical simulation of local ultrasonic intensity and qualitative comparison with experimental results

Abstract

The intensity distribution of the ultrasonic energy is, after the frequency, the most significant parameter to characterize ultrasonic fields in any sonochemical experiment.Whereas in the case of low intensity ultrasound the measurement of intensity and its distribution is well solved, in the case of high intensity (when cavitation takes place) the measurement is much more complicated. That is why the predicting the acoustic pressure distribution within the cell is desirable.A numerical solution of the wave equation gave the distribution of intensity within the cell. The calculations together with experimental verification have shown that the whole reactor behaves like a resonator and the energy distribution depends strongly on its shape.The agreement between computational simulations and experiments allowed optimisation of the shape of the sonochemical reactor. The optimal geometry resulted in a 2 strong increase in intensity along a large part of the cell. The advantages of such optimised geometry are (i) the ultrasonic power necessary for obtaining cavitation is low, (ii) low power delivered to the system results in only weak heating; consequently no cooling is necessary and (iii) the "active volume" is large, i.e. the fraction of the reactor volume with high intensity is large and is not limited to a vicinity close to the horn tip.

FEM simulation of a sono-reactor accounting for vibrations of the boundaries

“…The present simulation suggests that, exciting the sono-reactor near a resonant frequency could help to avoid this problem. This has been mentioned in precedent studies, and confirmed experimentally [9].…”

“…Simulation predicts that a noticeable energy fraction can be transmitted to the liquid in the cooling jacket, which may therefore undergo cavitation. This opens the possibility to design sono-reactors in which the working liquid is insulated from the sonotrode by a solid wall, which constitutes an interesting feature for electrochemical reactions, where electrical currents leaking through the metallic sonotrode should be avoided [9].…”

“…In past studies, the walls of the vessel enclosing the liquid have been either also considered as infinitely soft (P = 0) [9], or infinitely rigid [8]. The latter condition imposes a zero normal velocity, which, for mono-harmonic waves, using (6), translates to ∇P.n = 0.…”

“…This continuity equation is used as a boundary conditions for equation (9) governing the vibration of the solid.…”

“…Precedent studies generally treat the vessel boundaries either as infinitely rigid walls [8], or infinitely soft [9]. Solid boundaries may in fact be thin enough to vibrate and deform, and these effects must be considered, if one seeks precisely the resonant modes of the system.…”