The Development of the VC-Ogee Relationship Which Incorporates Upstream 3-Dimensional Flow Conditions

The Development of the VC-Ogee Relationship Which Incorporates Upstream 3-Dimensional Flow Conditions

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.

 

Download the full technical paper.

Download

Recent Insights

June 2024
Estimating Shear Stress within a Clay Foundation Using the Burgers-Creep Model
May 2024
Knight Piésold: Ensuring African Excellence in the DRC
May 2024
Wild Coast N2 Highway Project Taking Shape
April 2024
Risk Mitigation through Design Optimization Utilizing Seasonal Effects under Arctic Conditions at the Amaruq Mine
April 2024
Synthetic Rock Mass Modeling of Progressive Unravelling and Overall Slope Stability Using the Discrete Element Method
April 2024
Operational Slope Stability Risk Management for Large Open Pits at the Mount Milligan Mine – A Case Study
April 2024
Risk and Informed Approach to TSF Design and Operation
February 2024
Empowerment and Resilience
January 2024
Balancing Act: Water Usage Management Vital for a Sustainable Future
January 2024
A Difficult Balance Between Engineering, Environmental, Social and Economic Aspects
November 2023
Knight Piésold Commences with the ESIA for Haib Copper
November 2023
Insights from the Compilation and Critical Assessment of Breach and Runout Characteristics from Historical Tailings Dam Failures: Implications for Numerical Modelling
November 2023
Earthquake-induced Deformation Analysis of a TSF Undergoing Tailings Reprocessing
November 2023
Case Study: Approach to Determining the Risk Mitigation Priority of a Historic TSF in North America
October 2023
Data Management and Insights for Effective Tailings Storage Facility Management
October 2023
The Role of Sensitivity Analysis in Selecting Dam Breach Parameters
October 2023
Influence of Increased Confining Stress on Undrained Behavior of Tailings: A Case History at the Candelaria Mine
October 2023
The Re-use of Existing Bituminous Stabilised Materials for the Rehabilitation of National Route 7 - Case Study
September 2023
Transición energética para gerentes de mina
August 2023
Interview: Guillermo Barreda, Gerente General, Knight Piésold Perú