Mathematical Modelling Of Air-water Two-phase Flows

Air-water two-phase flows exist in a wide range in the hydraulic engineering. Because of its complexity, most of the studies were carried out by experiments and only a little has been achieved in theory and numerical modelling.This paper tried to give a systematic study on the mathematical modelling of air-water two-phase flow, using the theory and methodology of fluid dynamics of two-phase system and computational fluid dynamics.First, the paper introduced the instantaneous and local equations of two-phase system, together with the jump conditions at the interfaces,and established the space(time)-averaged equatious. Secend, the closure problems were discussed, which are caused by introducing the volume fractions, interphase transfer terms and fluctuation correlatives to the averaged equations, and it was indicated that different model should be established for different flow by making model hypothesis according to their each characteristics. And then, the flows in hydraulic engineering can be diveded into three patterns—diluent bubble dispersed flow, foaming flow near the interface and water dispersed flow. For the first flow pattern, which is most common in the engineering, two kinds of mathematical models, known as homogeneous model and two-fluid model are established. After these, discretization and solution algorithms are given to the models. Finally, some examples have been calculated to test the models. Comparision between the computation results and experiment dates shows, that the air conentration distributions agree with experiment, the velocities, turbuleut variables and other variables are reasonable, and the rising velocities of babble are close to that of experiment.