Author: SJ van Vuuren, GL Coetzee
Conference: 84th Annual Meeting of International Commission on Large Dams
Date: May 15-20, 2016

ABSTRACT
The widely used Ogee relationship is one of the most studied hydraulic relationships in the world (Savage & Johnson, 2001). Various attempts were made to accurately describe the shape of the lower nappe of water flowing over a sharp-crested weir, known as the Ogee profile. The current Ogee profile relationship was formulated from 2-dimensional hydraulic assessments. Recent studies, which included varying upstream geometry layouts, have indicated that the 2-dimensional approach flow conditions may be insufficient and, that 3-dimensional flow should be considered (van Vuuren, et al., 2011). An accurate Ogee flow profile is hydraulically efficiency and minimizes the possible occurrence of sub-atmospheric pressures on the surface of the spillway. An asymmetrical and/or skew approach channel causes 3-dimensional flow over the Ogee spillway that may contribute to the separation of the lower nappe from the surface that was designed with a 2-dimensional flow relationship.

Based on the results obtained from physical model studies and numerical analyses the VC-Ogee relationship was developed to incorporate the upstream 3-dimensional flow conditions. The VC-Ogee relationship utilizes the Hager formula (1987) for the upstream quadrant and the power function of the WES profile for the downstream quadrant. These relationships were extended to include the upstream topography, asymmetricity of the approach channel, orientation of flow relative to the spillway as well as the curvature of the spillway. The VC-Ogee relationship, which incorporates the influence of 3-dimensional flow conditions, reduces the potential of sub-atmospheric pressures and provides a more realistic discharge  relationship.

INTRODUCTION
The Ogee profile is one of the most studied hydraulic relationships used for the design of spillways (Savage & Johnson, 2001) and due to its high discharge efficiency, the nappe-shaped profile is used for most spillway control crests (Khatsuria, 2005). The Ogee spillway can be divided into three regions: the upstream quadrant, the downstream quadrant, and the rear slope.

Improvements of the Ogee relationship continued throughout the 20th century using physical modelling and applying empirical and mathematical curves. The increased computational resources available in the 21st century introduced detailed numerical assessments by means of Computational Fluid Dynamics (CFD) modelling. Data obtained from a detailed physical model study and extensive CFD modelling (Van Vuuren & Coetzee (2015a)) provided a qualitative and quantitative comparison of the fluid flow over a sharp-crested weir (SCW). CFD models were extended to incorporate different upstream approach channel layout configurations for straight and curved spillways. The algorithms used to solve the 3-dimensional flow regime in the CFD model included turbulent flow -, aeration - and cavitation modules.

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