Numerical Modeling of the Transition between Free Surface and Pressurized Flow in Storm Sewers
Stormwater drainage systems are typically composed of a network of closed conduits designed to operate under normal conditions in an open-channel, free-surface flow regime. Nevertheless, during intense rain events, the conduits may fill completely, undergoing a transition to a closed-pipe, pressurized flow. For sufficiently rapid filling, this transition will occur through a moving interface that advances into the free-surface portions of the system. In particular, if the system geometry restricts the escape of air ahead of the advancing front, the air pressurization will induce a motion in the underlying water.
The complexity of the system geometries and the flow dynamics requires the use of numerical models to simulate the phenomenon. Previous numerical models have not incorporated all aspects of the air pressurization in their formulation. In this chapter, we present a study comparing two different model approaches. The first model is based on the assumption that the pressurized portion of the flow may be described by a rigid column approach, and makes use of the method of the characteristics (MOC) to describe the free surface portion of the flow. The second model is based on the Preissmann Slot method, which allows the sewer surcharging, but also permits the application of open-channel equations throughout the pipe. Within this method two different numerical schemes were compared: the Lax-diffusive scheme, and the Lax-Wendroff predictor-corrector scheme. The numerical results were compared with results from a laboratory model, comprising a 14.8 m-long, 9.4 cm-diameter pipeline. In the model, inflow was suddenly initiated into a fill box at one end of the model, while at the other end there was a surge chamber in which the water level was recorded with a digital camera during the pipeline filling process. Measurements of water depth variation with time were obtained at selected pipe sections during the filling process. In particular, the motion induced by the pressurization of the air was recorded to document the effect.
The rigid column model, despite its conceptual simplicity, is able to predict the fill box behavior fairly well, although it is not able to give a detailed pressure distribution along the pipeline, which might be of importance in some applications. On the other hand, the Preissmann Slot based models were able to predict that detailed description, both during the pipe filling process and subsequently, when closed pipe transients are observed. While numerical diffusion is present in the results presented by the Lax-diffusive scheme, the Lax-Wendroff solution was characterized by pressure oscillations at the moving flow regime interface that are considered to be due to numerical rather than physical processes. Future model improvements will be guided by additional experiments as well as implementation of a more sophisticated numerical scheme.
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