Simulation of Water Level Fluctuations in a Hydraulic System Using a Coupled Liquid-Gas Model

A model for simulating vertical water level fluctuations with coupled liquid and gas phases is presented. The Preissmann implicit scheme is used to linearize the governing equations for one-dimensional transient flow for both liquid and gas phases, and the linear system is solved using the chasing method. Some classical cases for single liquid and gas phase transients in pipelines and networks are studied to verify that the proposed methods are accurate and reliable. The implicit scheme is extended using a dynamic mesh to simulate the water level fluctuations in a U-tube and an open surge tank without consideration of the gas phase. Methods of coupling liquid and gas phases are presented and used for studying the transient process and interaction between the phases, for gas phase limited in a chamber and gas phase transported in a pipeline. In particular, two other simplified models, one neglecting the effect of the gas phase on the liquid phase and the other one coupling the liquid and gas phases asynchronously, are proposed. The numerical results indicate that the asynchronous model performs better, and are finally applied to a hydropower station with surge tanks and air shafts to simulate the water level fluctuations and air speed.