A Semi-Implicit Numerical Method with a Symmetric Pressure Matrix for multi-dimensional two-phase flows

More sophisticated computer codes are needed for a detailed analysis of a two-phase flow in a nuclear reactor coolant system. Although extensive two-phase models were implemented into the system codes such as RELAP5 and TRAC, there computation scale is too large for the analysis of local behavior. Recently, computation fluid dynamics (CFD) codes are applied to this area. However, their two-phase flow applications are somewhat limited due to the lack of two-phase flow models. Hence, a component-scale thermal-hydraulic code CUPID had been developed at KAERI aiming at providing numerical solutions for issues such as downcomer boiling in the APR1400. In the CUPID-I code, a numerical method was proposed based on the semi-implicit method of the REPLAP5 for the application to multi-dimensional non-staggered unstructured grids. It had been verified against several conceptual problems. The pressure equation was obtained by solving mass, energy and momentum equations simultaneously, where the resulting pressure matrix became asymmetric. Unlike the one-dimensional case where the matrix is easily solved since it is basically tri-diagonal, it is expensive to solve the asymmetric matrix and sometimes it fails to get the solution. In the CUPID-M code,the pressure equation was modified so that the pressure matrix became symmetric by solving mass and momentum equations. The phase change and transient density terms of the mass conservation equations were linearized with respect to pressure. The steady state solutions were in good agreement with that of CUPID-I and the pressure solver was more fast and stable. However, the transient solution differed from CUPID-I since the energy variation was not considered in the mass conservation equations. In this study, the mass conservation equations are linearized with respect to energy as well as pressure to improve the transient solution. The calculations are compared to that of CUPID-I. The developed code is verified against FLUENT code for standard problems