A Hybrid Numerical Method for Homogeneous Equilibrium Two-Phase Flows in One Space Dimension

Abstract

This paper discusses a hybrid numerical method to calculate homogeneous equilibrium two-phase flows in one space dimension. A finite difference method is used for field solution while the method of characteristics is employed for treating boundary conditions. The boundary method is a new method that uses an integral procedure for precise specification of boundary values leading to an accurate overall solution. No extraneous information, or nonphysical approximation, is required as often is the case in most other attempts where the boundary error was the cause of difficulties and was detrimental to the inaccuracy of the overall solution and the eventual numerical instability due to the large gradient in phase distribution commonly existing near the boundaries. Procedures for many types of boundary conditions commonly encountered in reactor system analyses have been formulated and discussed. Sample problems have been calculated for two-phase water/steam mixture and single-phase nitrogen gas. The results are presented to demonstrate the degree of accuracy attainable from the hybrid method. The basic method discussed may be generalized to apply to more general nonequilibrium two-phase flow models with unequal phase velocities provided real characteristics exist.