Two-fluid model for adiabatic laminar bubbly flow

The universal basic averaged equations for bubbly flow were developed by applying the time averaging operator to the local instantaneous flow equations. According to analysis of the motion of bubbles in the flow field, the constitutive relations for interfacial momentum exchanges caused by interface-averaged stress, and interfacial momentum exchanges caused by asymmetric stress distributions on interfaces which include drag, virtual mass force, lift and wall-force were determined. A new formulation was proposed for wall-force, which was derived from theoretic research and corrected by experimental data. Influence of bubble deformation on the flow was also considered as a correcting coefficient Cw in the formulation of wall-force. The analysis of the stress in the phases indicated that the stress in gas phase is negligible in comparison with interactions between the phases. The shear stress in liquid phase was derived as an averaged liquid viscous stress term and the relation for the fluctuating stress in laminar bubbly flow was given. A closed-two-fluid model was established to describe the flow. Comparison of the experimental data published in literature with the present model prediction showed that the present model can be applied to flows in a wider bubble size range due to the reasonable consideration of the near-wall effect.