Effect of Interfacial Pressure Term on Numerical Stability of a Two-Fluid Model

Mathematical ill-posedness of the governing equations is one the main causes of numerical instability encountered in numerical simulation of two-phase flow using a two-fluid model. It is known that the ill-posedness can be mitigated if the difference between the average pressures of gas and liquid phases is taken into consideration appropriately. In the present work, it was investigated how the numerical stability of the one-dimensional, two-fluid model is influenced by the interfacial pressure terms that express the pressure difference between bubbles and continuous liquid phase in bubbly two-phase flow. Analyses were carried out for adiabatic air-water two-phase flow and subcooled flow boiling. It was confirmed that the interfacial pressure terms are effective to mitigate the numerical instability induced by the mathematical ill-posedness of the two-fluid model. However, the standard interfacial pressure terms deteriorated the numerical stability in some cases. It was found that the simplified model in which the spatial gradients of relative velocity and fluid density are eliminated is effective for the mitigation of numerical instability in wider analytical conditions.