Smooth and Stepped Converging Spillway Modeling Using the SPH Method

Abstract

Three-dimensional (3D) simulations using the smoothed particle hydrodynamics (SPH) method were performed for smooth and stepped spillways with converging walls, in order to evaluate the influence of the wall deflection and the step macro-roughness on the main non-aerated flow properties. The simulations encompassed a 1V:2H sloping spillway, wall convergence angles of 9.9° and 19.3°, and discharges corresponding to skimming flow regime, in the stepped chute. The overall development of the experimental data on flow depths, velocity profiles, and standing wave widths was generally well predicted by the numerical simulations. However, larger deviations in flow depths and velocities were observed close to the upstream end of the chute and close to the pseudo-bottom of the stepped invert, respectively. The results showed that the height and width of the standing waves were significantly influenced by the wall convergence angle and by the macro-roughness of the invert, increasing with a larger wall deflection, and attenuated on the stepped chute. The numerical velocity and vorticity fields, along with the 3D recirculating vortices on the stepped invert, were in line with recent findings on constant width chutes.