Numerical comparison of rapid-filling-pipe models with trapped air

Ling Zhou, Deyou Liu, Huan Wang, Chuanqi Ou, Xuebing Long

Thursday 2 july 2015

15:20 - 15:35h at South America (level 0)

Themes: (T) Water engineering, (ST) Hydraulic machinery and industrial flows

Parallel session: 12C. Engineering - Industrial

Air pockets often are entrapped in water pipe systems in power or pump stations, and urban supply and drainage sewer system etc. The phenomena of water filling pipe could arise if the entrapped air is not completely expelled from pipe systems. The existence of entrapped air pocket may abnormal pressure surge, especially during the rapid filling process. In this study, the authors introduce a full water elastic model (FWEM) to investigate flow transients in filling pipe containing entrapped air. The FWEM considers the elasticity of the whole water region, which is solved by using the methods of characteristics (MOC) of rectangular grid. The entrapped air is treated as ideal gas. The verification of the model is demonstrated by the authors’ measured data as well as the experimental results in the literatures. Moreover, the present study examines the range of validity associated with two simplifications on the mathematical model for the transient analyses of pipe systems with entrapped air pocket. First, the approximation is to neglect the movement of the air-water interface in the solution of the water hammer equations for water pressure and velocity. If MOC is used to solve the water hammer equations, the simplification of constant water length greatly reduces solution complexity because characteristics become linear paths in the x-t plane, and no interpolation is required to determine the variables of nodes on the previous time level. The calculation error associated with solving the governing equations decreases as the initial air fraction diminishes. The study investigates the valid range of initial air fraction for the fixed-water-length approximation, and discusses the error through using the approximation for systems with large entrapped air pockets. The second simplification is the application of the rigid water theory for the whole water phase. This simplification makes the governing equations simple and the solutions efficient, and avoids the complexity of MOC. The error of this model gradually diminishes as the initial air pocket volume increases because the compressibility of water phase can be neglected when the initial entrapped air pocket is large. The present study determines the valid range of this simplification.