Eigenvalue Analysis of Well-Posedness of Two-Fluid Single Pressure Model With Virtual Mass Force and Interfacial Pressure

Abstract

It is well know that the two-fluid single pressure model is currently widely used to analyze reactor transient accidents such as LOCA. Current mainstream reactor safety analysis codes such as RALAP5 and CATHARE are based on this single pressure model. However this model has been proved to be ill posed in the sense that the equation system is non-hyperbolic which will lead to numerical unphysical oscillation. Currently reactor safety analysis codes use the interfacial pressure and virtual mass force to solve the ill-posed non-hyperbolicity issue. The development of China’s self-owned reactor high fidelity system analysis code has attracted much attention in recent years, and studying on the ill-posedness of the two-fluid model and the improvement of the ill-posedness is an important basis to analyze these reactor accidents. In this paper, the ill-posedness regions of the two-fluid single pressure model is first investigated using the eigenvalue analysis method based on the Cauchy problem with initial conditions. Then the effect of the virtual mass force and the interfacial pressure is studied by this eigenvalue analysis method, and three types of virtual mass term in the momentum equation are discussed. The results show that the appropriate virtual mass force and interfacial pressure can well improve the ill-posedness of the single pressure model, and the appropriate combination of them can significantly improve the ill-posedness.