Abstract: For mathematical modelling of bubble coalescence, the cross-sectional area of the collision tube and the turbulent kinetic energy carried by the colliding bubbles are two key factors to determine the bubble coalescence rate due to turbulent collision. In most coalescence models, the shape of colliding bubbles is assumed to be spheric and the mean turbulent velocity correlation under shear turbulence (ST) condition is used to calculate the turbulent kinetic energy of the colliding bubbles. However, for the gas-liquid bubbly flow, the shape of bubbles transforms gradually from sphere to ellipsoid and spherical-cap with the increase of the bubble's volume. Furthermore, the influence of bubble-induced turbulence (BIT) has shown to be significant in the gas-liquid bubbly flow, especially along with the increase of the volume fraction of gas bubbles. When the bubble coalescence rate is calculated, the shape of bubbles affects the frequency of collision while the dominated turbulence mechanism affects the probability of a successful coalescence event. Based on the Prince and Blanch coalescence model, the present study proposed a coalescence model that considered the bubble shape variations as well as the joint effect of ST and BIT. Also, the turbulent kinetic energy transfer and the eddy-bubble response in the wake of spherical-capped bubble has been considered for the bubble coalescence due to BIT wake entrainment. Population balance model (PBM) has been used in the computational fluid dynamics (CFD) simulations for bubble columns to validate the proposed model. Comparisons have been made via simulation results of bubble size distributions (BSD) predicted by coalescence models with/without considering bubble shape variations and BIT. It is found that considering the shape of bubbles and the joint effect of shear turbulence and BIT, the proposed coalescence model significantly improves the prediction results of BSD and further affects the predictions of other important fluid dynamic parameters.

Key words: bubble, turbulence, coalescence model, population balance model, bubble column, gas-liquid two-phase flow

摘要： 在描述气泡聚并的碰撞筒(Collision Tube)理论中，气泡沿碰撞方向的横截面积及其所携带的湍动能是决定碰撞速率的两个关键点。在气液鼓泡流动中，随着气泡体积增大，气泡形状由球形向椭球形、球帽形转变，其相应的投影面积也发生变化。由于气泡对液相的强烈作用，液相湍流中剪切湍流和由气泡尾涡诱导的湍流涡漩二者共存，并且在不同的时空范围内对即将发生碰撞的气泡所携带的湍动能产生影响。针对Prince and Blanch聚并模型中的球形气泡假定和剪切湍流作用，本研究建立了考虑气泡形状和气泡诱导湍流的气泡聚并过程动力学模型，并基于群体平衡模型进行了模拟。研究结果表明，在气泡聚并模型中考虑气泡形状变化、气泡诱导湍流和剪切湍流的共同作用，能够准确捕捉气液鼓泡流动中气泡的尺寸分布特征，并且能够进一步影响气液两相的动力学特性预测结果。

关键词: 气泡, 湍流, 聚并模型, 群平衡模型, 鼓泡塔, 气液两相流