Finite-Element Analysis of Double-Free-Surface Flow through Slit in Dam

The fluid loads on some hydraulic structures and the free-surface profiles of the flow need to be determined for design purposes. This is a difficult task because the governing equations have nonlinear boundary conditions. The goal of the present work is to develop a suitable and accurate numerical procedure for the computation of free-surface profiles, velocity and pressure distributions, and flow rate for a 2D gravity fluid flow through a conduit in the pattern of a free jet. The problem involves two highly curved unknown free surfaces and arbitrary curve-shaped boundaries. These features make the problem more complicated than the flow under a sluice gate or over a weir. A combination of a variable domain and a fixed domain finite-element method is used to solve the problem. The results of the calculations show good agreement with previous flow solutions for the water surface profiles and pressure distributions throughout the flow domain and on the gate. Results are also confirmed by conducting a hydraulic model test.