Prediction of Gas Holdup during Gas Bubbling Process Based on Power Spectral Density Analysis on Acoustic Signals

Acoustic signals emitted during the gas bubbling process provide a unique perspective for nonintrusive monitoring of its status. The present work focuses on the flow dynamics and acoustic characteristics of the bubbling process. For a discrete bubble after detachment from the orifice, the acoustic frequency is mainly determined by the bubble radius, as the Minnaert equation states, which is influenced by gas velocities and orifice diameters. Mass transfer between the gas bubble and the ambient liquid has a negligible effect on the acoustic frequency. For bubble swarms with high gas holdup in practice, the resonant frequency, rather than the natural frequency of discrete bubbles, should be adopted as the acoustic characteristic. The coupled oscillator model with the time-delay effect, whose damping coefficient was corrected with the gas holdup, is capable of actually predicting the resonance frequency. These results provide a theoretical basis for fault monitoring of bubbling equipment.