The upstream Froude number effect on the flow field of the U-shaped channel along the side weir in the supercritical flow regimes

The U-shaped channels are applied as transition cross-section from rectangular to circular in manholes. Also the U-shaped channels along the side weirs are used in the sewage networks, irrigation-drainage systems, flood protection and etc. The flow in the main channel along the side weir can be the supercritical conditions. In this study, the free surface flow in the supercritical regime has been simulated by FLOW-3D software, RNG model and volume of fluid (VOF) scheme in a U-shaped channel along the side weir. The comparison between the numerical and experimental results showed that the numerical simulation predicted the free surface flow with the reasonable accuracy. Generally, the flow depth decreases with distance from the upstream end of the side weir towards the downstream end in the U-shaped channel. The APE and RMSE of the water surface profile along the side weir have been computed 1.7% and 0.213%, respectively. Also, the APE and RMSE were respectively 3.8% and 0.0177% for the discharges over the side weir. In continue, the effects of the upstream Froude number on the flow pattern in the main channel were investigated. For all Froude numbers, because of entrance effects, a free surface drop occurred at the upstream end of the side weir and the water depth gradually reduced toward the downstream end. Then, a surface jump happened at the last fourth of the side weir length in vicinity of the inner bank. Unlike the potential energy, the kinetic energy increases along the surface jump. Also, a stagnation point is created at the end of the surface jump. The height of this stagnation point increases with increasing the Froude numbers. In addition, the dividing stream surface and stagnation zone were respectively produced near the inner and outer bank in the main channel along a side weir. The dividing stream surface reduces from channel bottom toward the side weir crest then increases to the flow surface. Also, the dimensions of the dividing stream surface and stagnation zone increased with increasing Froude number. The maximum lateral flow in the U-shaped channel occurs almost at the downstream end of the side weir. The transverse velocity increases at each cross-section of the main channel with increasing Froude number. The angle of the spilling jet was close to 90° at the upstream and downstream of the side weir crest and the pattern of spilling jet angle is similar for all Froude numbers. The minimum angle of the spilling happens approximately at the downstream of the side weir crest however, the minimum decreases with increasing Froude number. The pattern of the bed shear stress can be used to prediction of the areas of the scour and sedimentation in the alluvial channels. In the U-shaped channel along a side weir, the bed shear stress increases along the main channel axis form the beginning of the side weir toward the middle then decreases toward the downstream end. Generally, with increasing Froude number, the bed shear stress increases in the main channel along the side weir.