Numerical Investigation of Rectangular Pipe Free Overfall for Various Upstream Conditions

This paper examines the relationship between the flow rate and outflow depth for flow in a rectangular pipe with the outflow running partially full of a free nappe through a series of computational fluid dynamics (CFD) simulations. The results are presented for two different upstream inlet conditions, namely, flooded, in which the pipe inlet is fully submerged, and partially full, wherein there is a free surface at the pipe inlet. The results are presented for the outflow normalized brink depth as a function of the nondimensional flow rate $q^{*}=(q/\sqrt{g{D}^3})$. For $q^{*}$ less than 0.575, the outflow conditions are the same regardless of the inflow boundary conditions. However, for larger $q^{*}$, there is a bifurcation in the outflow behavior. When the pipe inlet is fully submerged and $q^{*}>0.575$, the flow transitions to the so-called bubble-washout regime, and the brink depth is larger than for the case in which the pipe inlet is only partially full. These results indicate that if the brink depth from a pipe is to be used to quantify the pipe discharge, it is important to know the upstream flow conditions in order to know which flow regime is controlling the outflow.