We have proposed a Dual-Bubble-Size (DBS) model featuring a stability condition describing the compromise of two dominant mechanisms, and then a stability-constrained multi-fluid model (SCMFA) integrating the DBS model into CFD simulation. This work further validates the model and extends to much higher flow rate, and then tentatively proposes a new model termed SCMF-B. It solves the conservative equations for a dense phase composed of small bubbles and liquid and a dilute phase involving large bubbles. The DBS model supplies the structure parameters of the two bubble classes such as the gas volume fraction of small bubbles, the ratio of drag coefficient to bubble diameter for large bubbles and the superficial gas velocity of large bubbles to close the SCMF-B model. A thorough comparison indicates that without any fitting parameters, the SCMF models are superior to the two-fluid model (TFM) with empirical drag correlations in the prediction of overall gas holdup, radial profile of gas holdup and liquid flow field over a wide range of operating gas velocities. By comparison, each SCMF model has its strength and weakness at different flow conditions. SCMF-B can better reproduce the plateau of overall gas holdup as a function of gas flow rate, and the relative error of radial profile of gas holdup is the smallest among all the models at relatively higher flow rate. SCMF-A is better for the lower and much higher gas flow rates. We also design a special and step-by-step strategy to ascertain the evolution from SCMF-A to SCMF-B. We find that the physical properties, flow rate and drag coefficient of different bubble classes have respective functions in the model evolution and only their synergistic effects could generate reasonable prediction. This suggests that the definition of two "fluids" in the SCMF-B in terms of the differences in dense and dilute phases, rather than the thermal physical properties, is reasonable only when all the above "external" and "internal" factors are taken into account. (C) 2013 Elsevier Ltd. All rights reserved.