A FEM computational approach for gas-liquid flow in pipelines using a two-fluid model

Two-phase flow is typically observed in gas-liquid pipelines across diverse domains, including nuclear, petroleum, and chemical industries. As accurate prediction of flow characteristics is crucial for engineering applications, one-dimensional two-fluid models with various treatments have been extensively employed to mathematically describe the gas-liquid variations in the pipelines through a set of non-linear partial differential equations (PDEs). This paper presents a modularly designed algorithm that incorporates an implicit scheme coupled with the finite element method (FEM) to solve the one-dimensional two-fluid model with gas-liquid stratified calculation. To validate the accuracy of this algorithm, four cases utilizing varying mesh sizes, inlet flows, and outlet pressures are conducted to scrutinize numerical steady-state gas-liquid flow characteristics, and the consistency between the numerical variations computed through this algorithm and those from OLGA simulator is used to analyze transient gas-liquid behaviors. The steady-state flow fields reveal two distinct zones along the pipe: an intense momentum exchange zone influenced by the inlet nonequilibrium state and a gentle momentum exchange zone influenced by the gas compressibility. Notably, a finer mesh will yield more accurate descriptions of flow parameters in the intense zone, while a relatively sparser mesh suffices for the gentle zone. Additionally, the transient results reveal that the gas-liquid variations in the pipe under initial condition of single-phase gas can be divided into three stages: the gas expansion stage determined by gas compressibility, the gas spread stage influenced by the gas propulsion, and the liquid filling stage decided by the liquid kinetic motion. The consistent identification of the three stages in gas-liquid variations under initial conditions of different static fluids highlights the effectiveness and accuracy of the proposed numerical method in describing transient features.