Transient Mixed‐Flow Models for Storm Sewers

A new dynamic mathematical model capable of simulating unsteady free surface‐pressurized flows is presented. The model allows two options. The first option simplifies the mixed‐flow problem to a free‐surface flow problem by adding a hypothetical slot at the crown of the pipe. The second option treats the two flow regimes separately but joined together by an interface which is regarded as a shock wave. The speed, location, and intensity of the shock wave are computed at every time step. Interactions between the shock wave and various structures such as junctions, inflow drop structures, overflow relief structures, surge relief structures, and upstream and downstream ends are simplified using appropriate boundary conditions. The method of characteristics is used. The model is applied to a new combined sewer network and some numerical results are presented. It is shown that the pressurization phenomenon is a very dynamic phenomenon even without rapid change of any boundary condition. The pressurization wave tends to become very steep shortly after its formation and generates waterhammer as well as surges upon collision with hydraulic structures. This example serves as a warning that less than a fully dynamic model should not be used for a system which undergoes a pressurization process.