Research paper Three-dimensional modelling of flow in sharp open-channel bends with vanes SANG SOO HAN, PhD, Research Assistant, Department of Building, Civil and Environmental Engineering, Concordia University, 1455 De Maisonneuve Boulevard W., Montreal, Quebec, Canada H3G 1M8. Email: hansangsoo@gmail.com (author for correspondence) PASCALE M. BIRON, Associate Professor , Department of Geography, Planning and Environment, Concordia University, Montreal, Quebec, Canada H3G 1M8. Email: pascale.biron@concordia.ca AMRUTHUR S. RAMAMURTHY, Professor , Department of Building, Civil and Environmental Engineering, Concordia University, Montreal, Quebec, Canada H3G 1M8. Email: ram@civil.concordia.ca ABSTRACT Flow around a sharp open-channel bend is highly three-dimensional (3D) due to the combined effects of secondary flow, a large free surface variation and flow separation along the inner wall. Continuous vanes often used in closed curved conduits to generate a more uniform downstream flow were tested in the open channel using a 3D finite-volume model with a Reynolds stress turbulence model and the volume of fluid method for free surface prediction. The velocity field, turbulent kinetic energy and the extent of the flow separation zone were successfully validated against laboratory measurements for the no-vane case. The 3D simulations for one-vane and three-vane configurations reveal that vertical vanes are effective to reduce the secondary flow intensity and flow separation along the inner wall. The energy loss for bends with vanes is further slightly reduced compared to the no-vane case. The three-vane configuration is particularly efficient at creating uniform downstream flow. Keywords: Flow separation, numerical simulation, open-channel bend, Reynolds stress model, secondary flow, turbulence model, water surface 1 Introduction In sharp bends of rectangular open channels, the main flow characteristics are secondary flow, large transverse water surface slope, flow separation along the inner wall and high turbulence caused by flow separation. Laboratory studies inves- tigated the bend flow characteristics (Reinauer and Hager 1997, Tominaga and Nagao 2000, Blanckaert and Graf 2001, Booij 2003, Roca et al. 2007). However, the cost and time require- ments of physical tests prompted investigators to explore the potential of numerical models as a more flexible and inexpensive tool to examine the flow behaviour subject to various geometries and boundary conditions. Fully three-dimensional (3D) models are required to accu- rately represent secondary flows in bends (De Vriend 1977, Demuren and Rodi 1986, Cheng and Farokhi 1992, Meselhe and Sotiropoulos 2000, Wu et al. 2000, Ferguson et al. 2003, Wilson et al. 2003, Zeng et al. 2008a, 2010). However, the common 3D models describing the flow dynamics and sediment transport in channel bends use the rigid-lid assumption (Demuren and Rodi 1986, Pezzinga 1994, Hodskinson 1996, Wu et al. 2000, Huang et al. 2001, Khosronejad et al. 2007, van Balen et al. 2009). If large free surface variations lead to static pressure much larger than kinetic pressure, an incorrect pressure field is substituted into the momentum equation with the rigid-lid assumption, leading to errors in predicting the flow field (Ouillon and Dartus 1997, Khosronejad et al. 2007). 3D models with a free surface kinematic equation overcome limitations of the rigid-lid assumption. However, they require considerable programming efforts and are computationally expensive (Li et al. 2000). The volume of fluid (VOF) method (Hirt and Nichols 1981) is a successful alternative to trace large free surface variations in numerical simulations without the limitations or requirements of other models (Hieu and Journal of Hydraulic Research Vol. 00, No. 0 (2010), pp. 1–9 doi:10.1080/00221686.2010.534275 # 2010 International Association for Hydro-Environment Engineering and Research Revision received 20 October 2010/Open for discussion until 31 August 2011. ISSN 0022-1686 print/ISSN 1814-2079 online http://www.informaworld.com 1