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.

CFD Analysis of S-Gamma Model Coupled With Two-Group Interfacial Area Transport Equations and AMUSIG Model for a Large Diameter Pipe

This paper describes the modeling of flow regimes beyond bubbly flows in a large diameter channel considering polydispersity and bubble induced turbulence using the Eulerian two-fluid approach. A two-bubble-group approach with two-group interfacial area transport equations (IATEs) is used to demonstrate flow phenomena in a large diameter pipe. Source and sink terms for mass and momentum exchanges between the two groups of bubbles and for bubble coalescence and breakup mechanisms are implemented. For predicting particle size and its distribution, S-Gamma (Sγ) model is used. The Sγ model with two-group IATEs are evaluated by comparing local distributions of void fractions and Sauter mean diameters with results of adaptive-multiple-size-group (AMUSIG) models and experimental dataset developed by Schlegel et al., (2012) for model validations. It shows that two-group IATEs with Sγ model predict reasonably accurate flow characteristics of beyond bubbly flow regimes, but also show shortcomings in their accuracies predicting local distributions, which imply that further studies for modeling of interfacial force are needed.

Interfacial Area Transport Model for Bubbly Flow System in Vertical Rod Bundle With Spacer Grids

In relation to the modeling of the one-dimensional interfacial area transport equation for an adiabatic bubbly flow in a vertical rod bundle, some existing models of sink and source terms were reviewed and evaluated. Based on the reviewed interaction mechanisms of bubbles and turbulent eddies, a new interfacial area transport model has been proposed. Two important impacts on bubble interaction have been taken into account in the new model: the effects of spacer grids with mixing vanes and the impacts of geometry structure. The spacer grids breakup large bubbles into small bubbles resulting in enhanced bubble random collision at the downstream of the spacer grids. Void transport is the main contribution between spacer grids. The new interfacial area transport model has been evaluated against the obtained experimental data in 17 bubbly flow conditions. The results indicate that the new model can predict the interfacial area concentration with the relative error of 19.9%. It is recognized that the proposed model is promising for predicting the interfacial area concentration for a bubbly flow in a rod bundle.