Proceedings of the Institution of Civil Engineers Water Management 163 June 2010 Issue WM6 Pages 289–295 doi: 10.1680/wama.2010.163.6.289 Paper 800091 Received 04/09/2008 Accepted 05/01/2010 Keywords: hydraulics & hydrodynamics/waterways & canals/ mathematical modelling Mohammad Reza Najafi Senior Research Engineer, Water Research Institute, Tehran Pars, Tehran, Iran Amir Reza Zarrati Professor, Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran Numerical simulation of air–water flow in gated tunnels M. R. Najafi MSc and A. R. Zarrati PhD Gated tunnels are among the important hydraulic structures which fulfil various functions. However, due to the high-velocity flow through these structures, critical flow conditions may occur. Generally, physical model studies are performed to optimise the design of these structures which are time consuming and also very expensive. In the present research work a three- dimensional numerical model was used to simulate complicated free-surface air–water flow in gated tunnels. The volume of fluid scheme was used together with the K – å turbulence model in this simulation. The flow rating curve and air demand downstream of the service gate were computed at different gate openings and were compared with experimental data with good agreement. In addition a comparison of the calculated pressure distribution and cavitation index in the gate chamber with physical measurements showed the accuracy of the computational fluid dynamics model. Furthermore, a comparison of flow pattern and rooster tail formation downstream of the gate with experimental observations showed the capability of the numerical model in simulating the complex air–water flow in high-speed gated tunnels. This study shows the application of numerical simulation as a powerful tool in the design of hydraulic structures. NOTATION F body sum of all the body forces per unit volume of the fluid Fr Froude number at vena contracta K kinematic turbulence energy per unit mixture fluid mass P a pressure P v water vapour pressure Q a air discharge Q w water flow discharge U cross-sectional mean flow velocity ~ v velocity vector Æ w water volume fraction Æ a air volume fraction â aeration ratio å turbulance dissipation rate ì e effective viscosity ì t eddy viscosity r mixture fluid density r w water density ó cavitation index 1. INTRODUCTION Gated tunnels are used for emergency drawdown of the reservoirs, regulating the reservoir water level and sometimes for sediment flushing (Vischer and Hager, 1997). In gated tunnels a high-speed flow issuing from the gate drags and entrains a lot of air. If air demand of the flow is not supplied, pressure reduction, vacuum and as a result, cavitation occur downstream of the gate (Toombes and Chanson, 2007). Usually an air vent is installed just downstream of the gate to supply enough air to the flow (Kavianpour, 2003). Aeration ratio in the tunnel is defined as â ¼ Q a Q w 1 where Q a is air discharge of the vent and Q w is water flow discharge. Various researchers have tried to introduce empirical relationships for predicting the aeration ratio. For a free surface flow, in a partially full conduit with no hydraulic jump, the US Army Corps of Engineers suggested the following relationship (USACE, 1964), based on field data â ¼ 0 : 03 Fr  1 ð Þ 106 2 where Fr is the Froude number at vena contracta. Wisner also suggested the following relationship (Wisner, 1965) â ¼ 0 : 024 Fr  1 ð Þ 14 3 As the empirical equations are not very accurate (Kavianpour et al., 2005), physical modelling of gated tunnels is essential in order to determine the aeration ratio, gate rating curve, pressures and cavitation index along the tunnel, and flow condition downstream of the gate. However, physical modelling is time-consuming and is very costly in comparison with analytical or numerical models. On the other hand, in recent years, with advances in computer technology, numerical modelling has widely been utilised in water-related problems. Many researchers have applied two-dimensional or three- Water Management 163 Issue WM6 Numerical simulation of air–water flow in gated tunnels Najafi • Zarrati 289