The Effect of the Step Height on Energy Dissipation in Stepped Spillways Using Numerical Simulation

From 1970s, studies have been conducted on the hydraulic design of stepped spillways and many empirical formulas were developed. Despite the simple geometry of these spillways, their hydraulic behavior is complicated. As a result, for many cases, the physical models are studied to verify the design. Numerical simulation is considered as a tool to reduce the laboratory tests, in order to save time and money. Furthermore, the parameters which are not investigated or measured in physical models could be evaluated. In this paper, the results of numerical simulations are compared with the results of physical models and empirical formulas for the spillway of Renwick dam studied in a 1/8 scale model by Hunt and Kadavy (World Environmental and Water Resources Congress. ASCE, Great Rivers, pp. 3061–3071, 2009). Numerical simulation of flow is achieved by a mixture multi-phase flow model and a realizable k-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon}$$\end{document} turbulence model proposed by Qian et al. (Sci China Ser E-Tech Sci 52(7), 1958–1965, 2009). Grid sensitivity is accomplished and the size of mesh is reduced in locations where a high gradient of certain parameters exists or a higher precision is required. The numerical simulation results conform to the physical model tests. The velocity profile, energy dissipation, and the location of inception point where air entrainment in the flow is guaranteed, are investigated and compared to the scale model results. Also, thanks to this satisfaction, we could obtain the parameters such as pressure field which are not measured in the physical model.