Interfacial Area Transport Equation for Bubble Coalescence and Breakup: Developments and Comparisons

Bubble coalescence and breakup play important roles in physical-chemical processes and bubbles are treated in two groups in the interfacial area transport equation (IATE). This paper presents a review of IATE for bubble coalescence and breakup to model five bubble interaction mechanisms: bubble coalescence due to random collision, bubble coalescence due to wake entrainment, bubble breakup due to turbulent impact, bubble breakup due to shearing-off, and bubble breakup due to surface instability. In bubble coalescence, bubble size, velocity and collision frequency are dominant. In bubble breakup, the influence of viscous shear, shearing-off, and surface instability are neglected, and their corresponding theory and modelling are rare in the literature. Furthermore, combining turbulent kinetic energy and inertial force together is the best choice for the bubble breakup criterion. The reviewed one-group constitutive models include the one developed by Wu et al., Ishii and Kim, Hibiki and Ishii, Yao and Morel, and Nguyen et al. To extend the IATE prediction capability beyond bubbly flow, two-group IATE is needed and its performance is strongly dependent on the channel size and geometry. Therefore, constitutive models for two-group IATE in a three-type channel (i.e., narrow confined channel, round pipe and relatively larger pipe) are summarized. Although great progress in extending the IATE beyond churn-turbulent flow to churn-annual flow was made, there are still some issues in their modelling and experiments due to the highly distorted interface measurement. Regarded as the challenges to be addressed in the further study, some limitations of IATE general applicability and the directions for future development are highlighted.

The Interfacial Area Weighted Area-Averaged Gas Velocity Model for the Interfacial Area Transport Equation in the System Analysis Code

The interfacial area transport equation is a more accurate and stable way to compute the interfacial area concentration than the traditional empirical correlation in the two-phase two-fluid model. And among the parameters in the two-group interfacial area transport equation, the interfacial area concentration weighted area-averaged gas velocity is an important parameter to close the two-group area-averaged interfacial area transport equation in the system analysis code. However, there has been no theory model to compute the interfacial area concentration weighted area-averaged gas velocity until now. So this study established the theory model for two-group interfacial area concentration weighted area-averaged gas velocity based on the drift-flux model for the two-phase dispersed bubble flow. The experimental data were selected from the published literature, which include the detailed two-phase interfacial structure experimental data for the slug bubble flow. The interfacial area concentration weighted area-averaged gas velocity model predicted the selected experimental data well, which validated the developed model. Moreover, the difference between the interfacial area concentration weighted area-averaged gas velocity and the void weighted area-averaged gas velocity is clarified quantitatively for the first time. The theory model developed in this study can be improved and then be used to compute the interfacial area weighted area-averaged gas velocity because it includes the empirical parameter of conventional drift-flux model.