Abstract:This paper presents the volume of fluid (VOF) model and its governing equations. A three-dimensional transient model of water-filling pipelines is solved numerically by using k~εturbulent model. The paper gives a water-filling mathematical model of liquid volume fraction against time. The characteristics and energy losses in the gas-liquid two-phase flow are also analyzed. The modeling results show that there are four flow regimes, which are stratified, slug, plug and bubbly, exist in water-filling pipelines. The gas will move to downstream water networks with flow as plug and bubbly flow patterns. The reasons for the increased energy losses of two-phase flow, which are more than single-phase flow, are due to the interaction between the interfaces of gas and liquid and the increasing of average friction factor between the fluid and pipe walls. In inclined downward pipes, the axial velocity profiles in horizontal centerline are symmetrical. In vertical centerline the axial velocity profiles of gas and liquid near the top and the bottom of the pipe appear peaks, respectively. While on the interface of gas and liquid the one appears the slowest.