Slope effects on hydraulic characteristics and energy dissipation of stepped spillways with trapezoidal piers

Abstract

Stepped spillways provide excellent energy dissipation, which can considerably reduce the size of downstream stilling basins. Previous research has confirmed that installing roughness elements on stepped surfaces can further improve energy dissipation efficiency, which is highly sensitive to the chute slope and the geometry of the added elements. Aiming to clarify the unclear slope sensitivity of stepped spillways with trapezoidal piers, this work intends to systematically reveal how slope variation affects the hydraulic characteristics, pressure-aeration distribution, and energy dissipation mechanism of the spillway. Five slope cases were designed, and numerical simulations were carried out using the renormalization group k–ε turbulence model to compare flow patterns, velocity, pressure, air-concentration characteristics, and energy dissipation performance. Results show that a gentler slope increases the critical Reynolds number required for the development of fully skimming flow and reduces the velocity difference between the bottom and surface layers, resulting in a more uniform velocity distribution. Negative pressure mainly occurs at the convex corners of the steps, where relatively high air concentrations develop, effectively mitigating the risk of potential cavitation damage. The energy dissipation rate of all cases exceeds 65% and increases gradually as the slope decreases. Under steep-slope conditions, the energy dissipation rate responds strongly to slope variation; however, this sensitivity weakens noticeably as the slope becomes gentler. This study provides a theoretical basis and technical reference for the optimal design and performance enhancement of stepped spillways with trapezoidal piers, particularly for projects with stringent requirements for high energy dissipation and cavitation protection.