On the numerical study of isothermal vertical bubbly flow using two population balance approaches

摘要

Two population balance approaches based on the MUltiple-SIze-Group (MUSIG) model and one-group average bubble number density (ABND) model for handling the bubble size distribution of gas-liquid bubbly flows under isothermal conditions are assessed. Three forms of coalescence and breakage mechanisms by Wu et al. [1998. One-group interfacial area transport in vertical bubbly flow. International Journal of Heat Mass Transfer 41, 1103-1112], Hibiki and Ishii [2002. Development of one-group interfacial area transport equation in bubbly flow systems. International Journal of Heat Mass Transfer 45, 2351-2372] and Yao and Morel [2004. Volumetric interfacial area prediction in upwards bubbly two-phase flow. International Journal of Heat Mass Transfer 47, 307-328] are incorporated in the ABND model. To examine the relative merits of both approaches, local radial distributions of five primitive variables in bubbly flows: void fraction, Sauter mean bubble diameter, interfacial area concentration, and gas and liquid velocities, are compared against the experimental data of Liu and Bankoff [1993a. Structure of air-water bubbly flow in a vertical pipe-I. Liquid mean velocity and turbulence measurements. International Journal of Heat Mass Transfer 36, 1049-1060; 1993b. Structure of air-water bubbly flow in a vertical pipe-II. Void fraction, bubble velocity and bubble size distribution. International Journal of Heat Mass Transfer 36, 1061-1072] and Hibiki et al. [2001. Axial interfacial area transport of vertical bubble flows. International Journal of Heat Mass Transfer 44, 1869-1888]. In general, both of the ABND model and MUSIG model predictions yield close agreement with experimental results. To account for the range of different bubble sizes in the gas-liquid bubbly flows; the resolution required is achieved through the application of the MUSIG model. Nevertheless, computational times increase by a factor of two when compared to applying the simpler ABND model. To further exploit the models' capabilities, investigations are carried out by extending the two population approaches beyond the bubbly flow regime of higher void fraction, particularly in the transition regime. The numerical results are found to be grossly over-predicted, which expose the inherent limitations of the models. It is known that bubbles in this regime are generally highly distorted and closely packed instead of spherical shape and allowed to move freely in bubbly flow regime. (C) 2007 Elsevier Ltd. All rights reserved.