Modelling of Two-Phase Flow with Second-Order Accurate Scheme

Abstract

A second-order accurate scheme based on high-resolution shock-capturing methods was used with a typical two-phase flow model which is used in the computer codes for simulation of nuclear power plant accidents. The two-fluid model, which has been taken from the computer code RELAP5, consists of six first-order partial differential equations that represent 1D mass, momentum, and energy balances for vapour and liquid. The partial differential equations are ill-posed—nonhyperbolic. The hyperbolicity required by the presented numerical scheme was obtained in the practical range of the physical parameters by minor modification of the virtual mass term. No conservative form of the applied equations exists, therefore, instead of the Riemann solver, more basic averaging was used for the evaluation of the Jacobian matrix. The equations were solved using nonconservative and conservative basic variables. Since the source terms are stiff, they were integrated with time steps which were shorter than or equal to the convection time step. The sources were treated with Strang splitting to retain the second-order accuracy of the scheme. The numerical scheme has been used for the simulations of the two-phase shock tube problem and the Edwards pipe experiment. Results show the importance of the closure laws which have a crucial impact on the accuracy of two-fluid models. Advantages of the second-order accurate schemes are evident especially in the area of fast transients dominated by acoustic phenomena.