A model for turbulent polydisperse two-phase flow in vertical channels

A polydisperse two-phase flow model is developed and used to analyze the effect of the bubble size on the radial phase distribution in vertical upward channels. The two-fluid model is evaluated considering that the bubble size distribution can be represented with groups of constant mass. The model accounts for interfacial momentum transfer terms arising from drag, lift, turbulent dispersion and wall forces for the different bubble sizes. The turbulence is modeled with the k–ε model for bubbly flow. A two-phase wall logarithmic law is developed to evaluate the boundary conditions for the k–ε and the two-fluid models. The turbulence in the buffer and laminar near-wall regions is evaluated considering the asymptotic consistency of the k–ε model approaching the solid surface. The model is able to predict the transition from the near-wall gas volume fraction peaking to the core peaking beyond a critical bubble size. The double gas volume fraction peak experimentally observed when both, small and big bubbles, are present can be also simulated. The model was numerically solved for fully developed flow by means of a finite difference method and the results were compared against the experimental data measured by others in air/water vertical ducts.