Population balance modelling of isothermal bubbly-cap flows using two-group averaged bubble number density apporach

Considerable attention has been concentrated on describing the temporal and spatial evolution of two-phase geometrical structure caused by the effects of bubble interactions in gas-liquid flows. In the published literature, the transport phenomena of dispersed bubbles in bubbly flow conditions can be regarded in a similar view of the drag and interaction of spherical bubbles, which have brought about the development of most coalescence and break-up mechanisms based primarily on the assumption of interaction between such bubbles. Nevertheless, cap bubbles which are precursors to the formation of slug units in the slug flow regime with increasing volume fraction become ever more prevalent at high gas velocity conditions. It has been shown through many experiments that interaction behaviors between non-spherical bubbles in a liquid flow are remarkably different when compared to those of spherical bubbles. It is therefore imperative additional mechanisms of bubble interactions need to be considered, particularly for cap bubbles, in addition to typical mechanisms that have been established for spherical bubbles. In this work, a two-group modeling of bubbly-cap flows via the transport equations of the average bubble number density has been considered to predict the bubble size distribution of the different bubbles co-flowing with the liquid. Based on the computational fluid dynamics (CFD) framework, a three-fluid model was solved, one set of conservation equations for the liquid phase while two sets of conservation equations for the gas phase with one being Group 1 spherical bubbles and the other depicting Group 2 cap bubbles. The drag and non-drag characteristics of the different sizes and shapes of bubbles were thus accounted via the different momentum equations representing Groups 1 and 2 bubbles. In this initial assessment, the bubble mechanistic models proposed by Hibiki and Ishii (2000) have been adopted to describe the intra-group and inter-group interactions. The numerical predictions were evaluated against the experiment data of the TOPFLOW facility for vertical, upwards, air-water flows in a large pipe diameter (Lucas et al., 2010).