Numerical test and eigenvalue analysis for a two-phase channel flows for energy conversion systems like fuel cells or water electrolysers with flow regime transitions are performed by using the well-posed system of equation that takes into account the pressure jump at the phasic interface. The interfacial pressure jump terms derived from the definition of surface tension which is based on the surface physics make the conventional two-fluid model hyperbolic without any additive terms, i.e., virtual mass or artificial viscosity terms. The four-equation system has three sets of eigenvalues; each of them has an analytical form of real eigenvalues relevant to the sonic speeds with phasic velocities of three typical flow regimes such as dispersed, slug, and separated flows. Further, the eigenvalues for the flow transition regions can also be obtained numerically for smooth calculation of flow regime transitions. The sonic speeds agree well not only with the earlier experimental data but also with those of an analytical model. Owing to the hyperbolicity of this model, we can adopt an upwind method, which is one of the well-known Godunov type upwind methods. A typical example of two-phase flows shows that the present model can simulate the phase separation caused by density difference of two-phase fluids.

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