A Numerical Modelling of Two-Phase Flow System

A two-dimensional two-fluid model for two-phase flow system is proposed. This two-dimensional model is based on the hyperbolic one-dimensional model which is improved in its mathematical property by adopting the interfacial pressure jump terms in the momentum equations. Owing to this surface-tension effect incorporated in the momentum equations, eigenvalues of the equation system can be obtained analytically and they are proved to be all real. The eigenvectors can also be obtained analytically with linearly independent form. Further, they consist of phasic convective velocities, the sound speed of gas phase, and the sound speed of liquid phase. Consequently, the governing equation system is mathematically hyperbolic with reasonable characteristic speeds by which the upwind numerical method avails. Advantages and possibility of the present model are discussed in some detail.