考虑气泡形状及气泡诱导湍流的聚并模型

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.