Influence of roughness height on the distribution of modeled turbulence statistics in non-aerated skimming flows in steep stepped spillways

Abstract

The stepped spillway design is widely used globally for its energy dissipation capabilities through its stepped design and air entrainment capacity, crucial for safe hydraulic structure operation. The most common condition found in stepped spillways is the skimming flow regime. This study numerically investigated the influence of the roughness height (KS) on the distribution of mean flow variables and modeled turbulence statistics in the non-aerated portion of a steep stepped spillway with a constant angle of 51.34°. Three roughness heights of 6.26, 3.13 and 1.57 cm were considered corresponding to a relation step height/horizontal length of 10/8, 5/4 and 2.5/2 (cm/cm), respectively. The results show that profiles of modeled turbulent kinetic energy (TKE) at different step edges can be collapsed into one single curve for relative roughness (Ks/h) smaller than 0.8. For larger ratios of roughness height to water depth, this behavior is not observed and for a given distance away from the wall, values of TKE show a broad range of values, with increasing values as boundary layer grows. A similar trend was obtained for the distribution of TKE along a water column that includes the cavity. The existence of an upper limit for the ratio between the roughness height and the water depth can now be incorporated in the hydraulic design of new steep stepped spillways.