Numerical and Experimental Analysis of the Pressurized Wave Front in a Circular Pipe

This paper focuses on pressurized wavefront behavior and an analysis of trapped air pockets. Flow behavior, trapped air-pocket pressure, and different pressurized wavefront shapes in addition to their propagation conditions were investigated to improve modeling of mixed flows with trapped air pockets in stormwater systems. Pipe slopes, inflow, and reservoir water-levels were considered in an experimental analysis of the initiation, propagation of the wavefront, and flow behavior. Results show that the formation, propagation, and stability of the wavefront shape are highly dependent on the reservoir water-level and pipe slope. Pressurized wavefronts take on different shapes depending on manhole water level, pipe slope, and air pressure. The shape of the pressurized wavefront is sharper when the initial pipe depth y* is set between 0.5 and 0.85. With low inflow, the pipe-filling phase is progressive and is accompanied by undulations with stronger curvature and short length on the free-surface flow zone. For mild slopes with low flow-rates, the pipe-filling process is achieved through progressive undulations with trapped air pockets. A two-phase numerical model is developed, combining the method of characteristics (MOCs) for solving the free-surface flow conditions, the rigid column for the pressurized flow conditions, and the ideal gas law. Numerical results are achieved by applying of the continuity equation taking into account any type of flow regime in the interface vicinities. The four equations that consider the direction of wavefront propagation and the type of pressurized or depressurized wavefront are then taken into account. In these equations, a minimum distance between the moving wavefront and the considered cross section on the fixed grid is imposed. Compliance with this minimum distance allows avoiding numerical instabilities that may affect the stability of the model. Good agreement is obtained between numerical and experimental results. This agreement demonstrates that pressure variations due to pressurized waves combined with trapped air-pockets can be reproduced by implementing the numerical model as a shock-fitting approach.