Population balance modeling for air–water bubbly flow in a vertical U

Bubbly flow in U-bend is widely encountered in two-phase flow systems because of its compactness and high heat transfer coefficient. The modeling of phase distributions, velocity fields, and interfacial area concentration in the U-bend is crucial for the analysis of mass, momentum, and energy transportation processes in the equipment. However, this subject has not received enough attention yet. In this paper, the combination of population balance model and two-fluid model was used in the simulation of air–water bubbly flow in a U-bend with 24 mm inner diameter and 96？mm curvature. The homogeneous multiple size group model was used to solve the population balance equation and reconstruct the bubble size distribution function. The phase distribution at 0°, 90°, and 180° was predicted and the results showed that the superficial velocities of gas and liquid phase were the control parameters. Under higher gas superficial velocity, the buoyant force is dominant and makes the bubbles concentrate on the outer side of the tube wall; while under lower gas superficial velocity, the centrifugal force is dominant and makes the bubbles concentrate on the inner side of the tube wall. These results met well with the experimental results of Usui