Classification of bubbles in vertical gas–liquid flow: Part 2 – A model evaluation S.C.P. Cheung a , G.H. Yeoh b,c , F.S. Qi a,d , J.Y. Tu a,⇑ a School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Victoria 3083, Australia b Australian Nuclear Science and Technology Organisation (ANSTO), Locked Bag 2001, Kirrawee DC, NSW 2232, Australia c School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney, NSW 2052, Australia d School of Materials and Metallurgy, Northeastern University, Shenyang 110004, PR China article info Article history: Available online 31 October 2011 Keywords: Gas–liquid two-phase flow Three-fluid model Two-group average bubble number density Intra-group mechanisms Inter-group mechanisms abstract Three-fluid model along with two-group average bubble number density equations have been applied for the classification of bubbles in vertical gas–liquid flow. The current study focused on (i) consideration of three-fluid model transport equations governing the conservation of mass and momentum, (ii) formula- tion of two-group averaged bubble number density equations, (iii) classification of bubble interaction between spherical bubbles (Group-1) and cap bubbles (Group-2), (iv) consideration of source and sink terms via the proposal of Hibiki and Ishii (Nuclear Engineering and Design 202, 39–76) in the averaged bubble number density equations and (v) assessment by means of the experimental data sets at the bubbly-to-cap flow transition. Reasonable agreement has been achieved between the measured and predicted local and axial distributions of void fraction, interfacial area concentration (IAC) and volume equivalent bubble diameter. This preliminary assessment demonstrated the capability of the current approach in capturing the interfacial transport of bubbly to cap flow transition. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Based on the interpenetrating media approach, the inter-phase exchanges of mass, momentum and energy can be modeled as interfacial transfer terms acting on each phase. Two sets of conser- vations (one conservation equation for mass, momentum and en- ergy of the gas phase as well as liquid phase) can be written in terms of phase-averaged properties. In this sense, the interaction between the two phases is fully described by the constitutive rela- tionships governing the inter-phase mass, momentum and energy exchange. Generally, these interfacial transfer terms comprise the interfacial area concentration (IAC) or bubble Sauter mean diame- ter. In order to properly solve the two sets of conservation equa- tions, the local IAC or bubble size needs to be determined through suitable mechanistic models accounting for the physical interaction between the two phases and the gradual transition be- tween the different flow regimes. Considerable attention has been concentrated towards describ- ing the temporal and spatial evolution of the two-phase geometri- cal structure, which is caused by the effects of coalescence and break-up processes through interactions among bubbles and be- tween bubbles and turbulent eddies in turbulent flows. The major phenomenological mechanisms in bubbly flow conditions have been identified: (a) coalescence through random collision driven by turbulent eddies, (b) coalescence due to the acceleration of the following bubble in the wake of the preceding bubble, and (c) break-up due to the impact of turbulent eddies. Appropriate mechanistic models by Wu et al. (1998), Hibiki and Ishii (2002) and Yao and Morel (2004) for interfacial area transport (IAT) and Prince and Blanch (1990), Chesters (1991), Luo and Svendsen (1996), Martinez-Bazan et al. (1999a,b), Lehr et al. (2002) and Lo and Zhang (2009) for multi-size bubble consideration have been established. The transport phenomena of dispersed bubbles in bubbly flow conditions can be regarded in a similar view of the drag and inter- action mechanisms of spherical bubbles. As aforementioned, most coalescence and break-up mechanisms have been principally based on the assumption of interaction between spherical bubbles. Nevertheless, cap bubbles which are precursors to the formation of slug units in the slug flow regime, become prevalent at high gas velocity conditions. With increasing volume fraction, accumulation of large unsteady gas volumes within these mixing regions subse- quently produces the churn-turbulent flow regime. Experiments performed by Hibiki and Ishii (2000a) have shown that the interac- tion behaviors between non-spherical bubbles in the liquid flow, which may be classified as cap-slug-churn-turbulent bubbles, are generally different when compared to those of spherical bubbles. Additional mechanisms of bubble interactions need therefore to be considered. Focusing on the intra-group mechanisms of spheri- cal bubbles, the usual coalescence and break-up processes due to random collisions and turbulent impact have been realized. The in- tra-group mechanisms for non-spherical bubbles take however a 0301-9322/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmultiphaseflow.2011.10.009 ⇑ Corresponding author. Address: SAMME, RMIT University, Bundoora, Melbourne, Victoria 3083, Australia. Tel.: +61 3 9925 6191; fax: +61 3 9925 6108. E-mail address: jiyuan.tu@rmit.edu.au (J.Y. Tu). International Journal of Multiphase Flow 39 (2012) 135–147 Contents lists available at SciVerse ScienceDirect International Journal of Multiphase Flow journal homepage: www.elsevier.com/locate/ijmulflow