The numerical solution of the transient two-phase flow in rigid pipelines

Consideration is given in this paper to the numerical solution of the transient two-phase flow in rigid pipelines. The governing equations for such flows are two coupled, non-linear, hyperbolic, partial differential equations with pressure dependent coefficients. The fluid pressure and velocity are considered as two principle dependent variables. The fluid is a homogeneous gas-liquid mixture for which the density is defined by an expression averaging the two-component densities where a polytropic process of the gaseous phase is admitted. Instead of the void fraction, which varies with the pressure, the gas-fluid mass ratio (or the quality) is assumed to be constant, and is used in the mathematical formulation. The problem has been solved by the method of non-linear characteristics and the finite difference conservative scheme. To verify their validity, the computed results of the two numerical techniques are compared for different values of the quality, in the case where the liquid compressibility and the pipe wall elasticity are neglected. Copyright (C) 1999 John Wiley & Sons, Ltd.