Chemical Engineering and Processing: Process Intensification ( IF 4.3 ) Pub Date : 2020-09-06 , DOI: 10.1016/j.cep.2020.108134 Varinrumpai Seithtanabutara , Kittichai Jookjantra , Tanakorn Wongwuttanasatian
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.
中文翻译:
双频超声强化中不同波形和谐波频率阶次对气泡空化的影响
进行了超声双频波形辅助酯交换反应的数值研究。探索了方波(SQ + SQ),正弦波(SIN + SIN)和锯齿波(ST + ST)的双频波形。对于非正弦信号,应用傅里叶系数和傅里叶级数将信号转换为正弦波之和,以便使用Rayleigh-Plesset方程确定气泡空化。评价每个波形的气泡半径比(R / R o)以找到最大值。在基本频率下,最大R / R oSQ + SQ,SIN + SIN和ST + ST分别为37.08、31.65和12.06。这表明,SQ + SQ对气泡大小的影响要强于其他大小。总之,SQ + SQ对空化的影响最大。然后,研究了这两个非正弦波形的谐波频率阶数(HFO)。对于SQ + SQ,R / R o随着HFO的增加而增加。最大的R / R o为41.29,发生在第9个HFO,然后在此顺序之后开始降低。另一方面,对于ST + ST,增加HFO对R / R o无积极影响。此外,HFO的增加只会促进R / R o如果组合波振幅增加。最后,优化的HFO将进一步用于提高生物柴油的产量。