Effect of different waveforms and harmonic frequency orders on bubble cavitation in dual-frequency ultrasonic intensification

Abstract

A numerical investigation of ultrasonic dual-frequency waveform assisted transesterification was performed. The dual-frequency waveforms of square waves (SQ + SQ), sine waves (SIN + SIN), and sawtooth waves (ST + ST) were explored. For non-sinusoidal signals, the Fourier coefficient and Fourier series were applied to convert the signal into the sum of sinusoidal waves in order to determine the bubble cavitation using Rayleigh-Plesset equation. The bubble radius ratios (R/Ro) of each waveform were evaluated to find the maximum value. At fundamental frequencies, the maximum R/Ro were 37.08, 31.65, and 12.06 for SQ + SQ, SIN + SIN and ST + ST, respectively. This revealed that the SQ + SQ had a stronger effect on the bubble size than the others. In summary, SQ + SQ had strongest influence on cavitation. Then, harmonic frequency orders (HFOs) were investigated for these two non-sinusoidal waveforms. For SQ + SQ, R/Ro increased with increasing HFO. The maximum R/Ro of 41.29 occurred at the 9th HFO and then started to decrease after this order. On the other hand, for ST + ST, increasing the HFO had no positive effect on the R/Ro. Additionally, increase in HFO would only promote R/Ro if combined waves amplitude were increased. Finally, the optimised HFO will be further used for the enhancement of biodiesel yield.