A new interfacial pressure jump term using a closure mechanistic model and a higher-order upwind numerical method are developed to solve the two-phase critical flow problems only with the two-fluid model and the numerical scheme. Since the critical flow phenomenon depends much on the speed of signal propagation and the mixture velocity of two-phase media, it is important for the system of equations to produce real eigenvalues representing the speed of pressure wave.
Interfacial surface tension force based on the physics of phasic interface and the bubble-dynamics is applied to the two-fluid six-equation model of two-phase flow in order to eliminate numerical instability. The pressure discontinuity across a thin interface due to the surface tension force is compactly represented by a function of the fluid bulk moduli. Inclusion of the differential form of the surface tension terms have made the governing equations hyperbolic, even without any conventional additive terms like virtual mass or artificial dissipative terms in the momentum equations.
Real eigenvalues are obtained for the system of equations due to the surface tension term, for the bubbly, slug, and annular two-phase flow regimes. The speed of sound for two-phase mixture derived as a function of the system eigenvalues has shown excellent agreement with the existing experimental data. The equations system can also provide the eigenvalues representing the void wave speed as well as the pressure wave speed and eliminate the closure problem for the bubbly flow regime by using of a mechanistic model for bubble radius based on the kinematic wave speed.
Interfacial surface tension force term has been introduced in the momentum equations of the two-fluid, two-phase flow while we keep at the same time the conventional virtual mass force as a source term. The governing equations with surface tension terms produced a hyperbolic system having real eigenvalues for the bubbly flow, regardless whether the virtual ma...