On the modelling of population balance in isothermal vertical bubbly flows—Average bubble number density approach

To model the spatial evolution of the geometrical structure of the gas bubbles in isothermal vertical bubbly flow conditions, the population balance approach has been employed and merged with the three-dimensional two-fluid model. The population balance is realized by incorporating an average bubble number density transport equation into a commercial computational fluid dynamics (CFD) code ANSYS CFX 10. The coalescence and breakage effects of the gas bubbles are formulated according to the bubble coalescence by random collision driven by turbulence and wake entrainment while for bubble breakage by the impact of turbulent eddies. Three models representing these coalescence and breakage mechanisms proposed by Wu et al. [1], Hibiki and Ishii [2] and Yao and Morel [3] are assessed. Local radial distributions of the five primitive variables in bubbly flows: void fraction, Sauter mean diameter, interfacial area concentration, and gas and liquid velocities, are compared with two experimental data of Liu and Bankoff [4] and [5] and Hibiki et al. [6]. Close agreements between the predictions and measurements demonstrated the capability of the average bubble number density transport equation in modelling bubbly flow conditions.