基于FTM方法的双气泡融合特性模拟

采用界面追踪法(FTM)对气泡融合现象进行数值模拟，将模拟结果与文献结果进行对比，验证了计算模型的准确性。结果表明，同轴双气泡上升速度均高于单独气泡的上升速度，且融合后气泡与等直径单气泡上升速度相同。气泡间距较小时，跟随气泡的上升速度更高。引导气泡的厄特沃什数Eo=0.36~9，Eo较大时两气泡上升阶段时间较短，但接触阶段时间较长，接触阶段气泡间的液膜在压力作用下逐渐变薄，最终破裂，气泡融合。Eo?4.16时，气泡融合所需时间随Eo增加而增加；Eo?4.16时，气泡融合所需时间不再变化。莫顿数Mo=0.57，Eo=5.04~18.72时，存在特定的双气泡初始角度?c，当0?≤?≤?c时，双气泡相互排斥；当?c≤?≤90?时，双气泡融合，且?c随Eo增加而降低.

Numerical simulation of coalescence of double bubbles using FTM

The front tracking method (FTM), which can track the maker points and capture the changes of the interface accurately was used to simulate the phenomenon of bubble coalescence. All governing equations were solved by using a second-order accurate project method, using centered-differences on a fixed, staggered grid and considering the effect of surface tension at the interface. The numerical simulations were compared with experimental and computational results from other literatures which modified the accuracy of calculation model. In this work, the rising process of coaxial bubbles and the process after fusion were analyzed in detail, and the existence of specific initial angle ?c and the relationship between ?c and Eotvos number (Eo) were analyzed. It was found that the rising velocity of both bubbles were higher than single bubble, and the coalesced bubble had the equal velocity with equivalent diameter single bubble in the rising process of coaxial double bubbles. The trailing bubble had higher velocity with the shorter distance of bubbles. In the range of Eo of leading bubble was 0.36~9, the time of rising stage was shorter and the time of contact stage was longer when the Eo of leading bubble increased. During contact stage, the thickness of liquid film between bubbles decreased because of the effect of pressure. Liquid film broke and coalescence of bubbles happened in the coalescence moment. The required time of coalescence increased as the distance of bubbles or Eo increased. However, the required time was stable as Eo was larger than 4.16. When the Morton number (Mo) was 0.57 and the range of Eo of leading bubble was 5.04~18.72, it was found that there was a specific initial angle ?c. The two bubbles repelled each other for 0?≤?≤?c but merge for ?c≤?≤90?, and ?c decreased with the increase of Eo.