Improvement of the two-fluid momentum equation for turbulent bubbly flows

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A two-fluid model is widely employed to predict gas–liquid two-phase flows. Conventional two-fluid equations, derived by assuming that all phases are interpenetrating continua, occasionally yield impractical results. For example, the bubble velocity is predicted to be higher than the water velocity for a horizontal fully developed bubbly flow. One solution for this irrational result is two-fluid momentum equations based on the motion of fluid particles. This study revisits the particle-motion-based two-fluid equations. Previously, it was validated only with respect to the difference between the bubble and liquid velocities. Recently, we observed an erroneous prediction of the void fraction distribution by the existing particle-motion-based momentum equations. This study, through rigorous analysis, discovered that this error could be resolved by neglecting the turbulent kinetic energy term in the particle-motion-based equation for the gas phase. Subsequently, the revised momentum equations were applied to the vertical and horizontal air–water bubbly flows. The conventional and revised momentum equations produced similar results for upward bubbly flows because the relative velocity between the bubble and water phases was mainly governed by buoyancy. For horizontal bubbly flows, the revised momentum equations led to a downward shift in the liquid velocity distributions, which was attributed to the modified momentum diffusion term. At a higher modification factor of turbulent dispersion, the velocity distributions exhibited an upward shift. We conclude that the optimization of physical models should be based on the revised two-fluid momentum equations.