Supercritical flow characteristics in smooth open channels with different aspect ratios

Abstract

A transient numerical investigation is employed in this study to evaluate the influence of channel aspect ratio varying between 2.0 and 12.0 on the secondary currents and other flow characteristics in an open-channel turbulent flow at mildly supercritical Froude numbers. The transient three-dimensional Navier–Stokes equations are numerically solved using a finite volume approach with detached-eddy simulation as the turbulence model. The commonly used rigid-lid approximation to model the free surface is found to be unsatisfactory. A flat wave model linked with the volume of fluid method is used to simulate the free surface at the water–air interface to bring forth the realistic flow structures in the region below the free surface and the side walls. The size of the structures is dependent on the water column height rather than the channel aspect ratio. It is shown that the streamwise velocity profile across the channel has a strong dependence on the channel aspect ratio. This profile has two recognizable points of inflection for aspect ratios between 3.0 and 6.0, which move toward the sidewalls as the channel aspect ratio increases. A region of inviscid-like flow is seen about the channel central plane above a specific vertical location for a small channel aspect ratio only. The distribution of the contour patterns of the ratio of mean vertical and transverse secondary currents is similar for a wide range, and it does not depend on the channel aspect ratio. The transverse profiles of the Reynolds stresses are impacted by the channel aspect ratio and the vertical location from the channel bed. More waves form at the water–air interface in the narrower channel compared to the wider one, which indicates that the free-surface deformation is dependent on the channel aspect ratio. It is highly recommended that to study the fluid structure interaction problems in open channels, it is best to use a channel aspect ratio of 12 or greater.