Population balance equations with different bubble diameters are combined with classical Euler/Euler hydrodynamic simulation to investigate turbulent bubble flow in a vertical pipe in the present work. The universal basic averaged equations for bubble flow are developed by applying the volunm-averaging operator to the local instantaneous flow equations.Based on the analysis of the motion of the bubbles in the flow field and the influence of bubble coalescence and break-up

the constitutive relation is determined. Comparison of the available experimental data with the present model prediction shows that the model can be used to predict the local volume fraction

radial velocity profiles

turbulence kinetic energy

mean bubble diameter and the evolution of mean bubble diameter due to the reasonable consideration of the interaction between the two phases and the influence of bubble coalescence and break-up.