Three-dimensional numerical flow modelling for estimation of spillway capacity

Water flow over a spillway was modelled numerically in two and three dimensions for various geometries. The model solved the Navier-Stokes equations with the k-epsilon turbulence model on a structured non;orthogonal grid. A method based on water continuity was used to calculate the movement of the water surface. Using an adaptive grid in the vertical direction, the location of the water surface was recalculated from an initially horizontal profile. After several iterations a steady solution emerged. The location of the water surface was used to calculate the capacity and the coefficient of discharge for the spillway. Physical model studies were carried out to determine the accuracy of the numerical model. The coefficient of discharge was also compared with empirical formulas. The deviation of the calculated coefficient of discharge was 1 % for the two-dimensional cases, and 0.5 % for the three-dimensional case. Reasonable agreement was also found for the pressure at the spillway bed, which was measured in one of the physical model studies. In another physical model study the water surface was measured, and this also compared well with the results from the numerical model.