Multi-frequency sonoreactor characterisation in the frequency domain using a semi-empirical bubbly liquid model

Recently, multi-frequency systems were reported to improve performance in power ultrasound applications. In line with this, digital prototyping of multi-frequency sonoreactors also started gaining interest. However, the conventional method of simulating multi-frequency acoustic pressure fields in the time-domain led to many challenges and limitations. In this study, a multi-frequency sonoreactor was characterised using frequency domain simulations in 2-D. The studied system consists of a hexagonal sonoreactor capable of operating at 28, 40 and 70 kHz. Four frequency combinations were studied: 28-40, 28-70, 40-70 and 28-40-70 kHz. A semi-empirical, modified Commander and Prosperetti model was used to describe the bubbly-liquid effects in the sonoreactor. The root-mean-squared acoustic pressure was compared against experimental validation results using sonochemiluminescence (SCL) images and was noted to show good qualitative agreement with SCL results in terms of antinode predictions. The empirical phase speed calculated from SCL measurements was found to be important to circumvent uncertainties in bubble parameter specifications which reduces error in the simulations. Additionally, simulation results also highlighted the importance of geometry in the context of optimising the standing wave magnitudes for each working frequency due to the effects of constructive and destructive interference.