Additional Friction Factor Optimized for Modeling Transient Flows Following Air-Pocket Entrapment in Stormwater Systems

The gravity flow in sewer systems may change to partially pressurized flow for reasons including rapid filling, and maintenance and repair. During this alteration, air can be entrapped and becomes highly pressurized, and this air pressure can negatively impact the sewer system and hydraulic infrastructure. The available mathematical models in this field mostly overestimate the peak pressures and underestimate the attenuation. In partially pressurized transient flows following air-pocket entrapment, the frictional force, similar to other forces, can be affected by the unsteady behavior of the flow and by the air-pocket size. Therefore, using a constant steady-state friction factor for the numerical simulation is a simplistic approximation. In this study, an additional friction factor, which has the same form as the steady-state Darcy-Weisbach friction factor, is proposed using dimensional analysis and calibrated by experimental data. Two well-known mathematical models, the rigid column and the method of characteristics models, were used for the numerical simulation. It was found that, compared with a constant steady-state friction factor, the additional friction factor can improve the numerical results significantly, including the overestimation of the pressure peak values, and can predict the attenuation behavior.