Transient flow of homogeneous gas‐liquid mixtures in pipelines

Abstract

To accurately predict transient flow in homogeneous gas‐liquid mixtures in rigid and quasi‐rigid pipes, two mathematical models based on the gas‐fluid mass ratio are presented. The fluid pressure and velocity are considered as two principal dependent variables and the gas‐fluid mass ratio is assumed to be constant. By application of the conservation of mass and momentum laws, non‐linear hyperbolic systems of two differential equations are obtained and integrated numerically by a finite difference conservative scheme. The fluid density is defined by an expression averaging the two‐component densities where a polytropic process of the gaseous phase is admitted. The rigid model is deduced by neglecting the liquid compressibility and the pipe wall elasticity against the gas deformability. The quasi‐rigid model takes into account these two parameters. The effect of fluid compressibility on transient pressure behaviour is then analysed and confronted to the pipe wall elasticity. Numerical solutions are compared with numerical results available in literature and experiment developed in the laboratory. The results show that the pressure wave propagation is significantly influenced by the gas‐fluid mass ratio and the elasticity of the pipe wall. They indicate that the pipe elasticity and liquid compressibility may be neglected for great values of gas‐fluid mass ratio but not for the smaller ones.