Discrete air model for large scale rapid filling process contained entrapped air

In this paper, a discrete air model (DAM) is developed to capture the discontinuous characteristics of air at different locations during the rapid filling process in long-range, large-scale water pipeline. By introducing the continuity and momentum equations of air and combining them with the water control equation and the interface continuity equation, an improved model based on the uniform air is derived. The accuracy of the model is verified by comparing it with experimental data and the results of the original uniform air model (UAM). Subsequently, a long-range, large-scale pipeline was considered to investigate the dynamic properties of air in large systems, which had not been covered in previous studies. Additionally, the influence of air dynamic characteristics on initial air volume affected by different air lengths and various pipe diameters in large systems - is further studied. Results show that an increased pipe diameter expands the contact area of the air-water interface, often resulting in the UAM underestimating the maximum peak pressure. The propagation process of transient waves in air is divided into three stages: propagation stage with multiple variation, maximum value stage with interface propulsive, and stability stage with several fluctuations, which corresponds to the pressure fluctuation curve. This explains the occurrence of small fluctuations and peaks in the curve. Therefore, the peak pressure simulated by the proposed DAM offers a better understanding of wave behaviours.