# Study on Bubble Cavitation in Liquids for Bubbles Arranged in a Column Bubble Group
## 4 Fluent Analysis  
[PERSON] et al. [36] have used a CCD (charge-coupled device camera) to capture morphological changes of the growth and collapse of single bubbles, two-bubble groups, and five-bubble groups. Their experimental results show that morphological changes during a multi-bubble collapse vary with the spacing of bubbles. At the same time, they found that the outer bubble movement period is shorter and that the jet of outer bubbles is completed first. This method can control the cavitation bubbles' location, but cavitation bubbles can only form near the wall's surface; in this case, the influence of the wall's surface on cavitation bubble collapse cannot be ignored. Due to the influence of fluid properties, the micron scale of bubbles, instantaneous collapse, and other factors, it is impossible to accurately control bubbles in the bubble group, leading to the failure of bubble research under many conditions through experiments. With the development of computational fluid dynamics, numerical simulations have played an increasingly important role in the study of bubble dynamics. Simulation of the cavitation process by Fluent software can show the micro-bubble growth process and the rapid collapse process, as well as reflect the mutual coupling process of bubbles in the bubble group and the non-spherical change of the bubbles. It has been pointed out that under a weak coupling effect between bubbles, bubbles maintain the shape of the hemisphere most of the time without contact and fusion, but, when the bubbles collapse, they form an interfacing jet [12]. We simulated the growth and collapse process of bubbles for five and seven bubbles set in a line using Fluent software with an initial radius of 30 \(\upmu\)m and a distance of 200 \(\upmu\)m between bubbles. It can be found from Equation (9) that when the number of bubbles is five the resonance frequency of the bubbles is 89.8 kHz and that when the number of bubbles is seven the resonance frequency of the bubbles is 88.4 kHz. Using a volume of fluid (VOF) 2D axisymmetric analysis has the advantage of easy realization, small computational complexity, and high precision, and traces the volume of fluid in the grid, not the motion of the fluid particles [37]. For the simulation domain, shown in Figure 5, the calculation field is 3 mm \(\times\) 6 mm, the number of cells is 253,000, the number of nodes is 254,331, and the calculation step is 0.01\(\upmu\)s. The liquid medium is water and the gas inside the bubble is nitrogen. In the process of simulation and calculation, the ultrasonic field is driven from the left side, for which \(P_{a}=p_{a}\sin(2\pi ft)\)--\(p_{a}\) is the amplitude of the ultrasonic pressure and \(f\) is the ultrasonic frequency. The right side is the free interface and the outlet pressure is the hydrostatic pressure, which is an atmospheric pressure. The ultrasonic frequency \(f\) is 26 kHz, which is smaller than the resonance frequency of the bubble, and the ultrasonic pressure amplitude \(p_{a}\) is 1.2 bar. Then we obtained Figures 6-9. Figures 6 and 8 show that the bubble has grown well and remained spherical under the ultrasonic field. Due to the mutual restriction of the bubbles during the growth process, the two bubbles at the outer field can reach maximum volume first in the expansion process, and the maximum volume is larger than the inner bubble volume. In time, all bubbles begin to shrink simultaneously. In the process of shrinkage, the outer bubbles shrink slightly faster, becoming an ellipsoid first, and can maintain their ellipsoid shape while continuously shrinking. When contracted to a certain extent, the outer two bubbles begin to collapse first, forming a micro-jet and directing it towards the bubbles back and along the axial center of the wire-packing group to break the bubbles one by one until the group is completely torn open.