Reynolds Stress Model Study Comparing the Secondary Currents and Turbulent Flow Characteristics in High-Speed Narrow Open Channel and Duct Flows

This study numerically investigates and compares the secondary currents, velocity dips, turbulence properties, and boundary shear stresses in supercritical narrow open channel flows (OCFs) and in narrow duct flows (DFs) using an updated Launder-Reece-Rodi Reynolds stress model in OpenFOAM, which was validated previously for supercritical flows using experimental data. Six steady state simulations were performed at a bulk velocity of 2.31 m=s covering Reynolds numbers from 3.08 × 10⁵ to 6.16 × 10⁵ and aspect ratios (width to flow depth) of 1.0. 1.25, and 2.0, which in combination with the observed Froude numbers from 1.65 to 2.33 for OCFs are comparable to sediment bypass tunnel flows. Although free surface produces greater maximum secondary flows, the top wall in DFs creates stronger bulging of the longitudinal velocity above the velocity dips, which generates marginally higher maximum longitudinal velocity and significantly higher velocity fluctuations compared to OCFs. Two pairs of corner vortices are observed in each half width for DFs. However, such vortices differ in OCFs, in which the reduction of aspect ratio develops intermediate vortices. Such differences in the secondary currents are interrelated to the observed variations in the distributions of longitudinal velocity and Reynolds stresses. Higher average bed and sidewall shear stresses are obtained for DFs than for OCFs. The bottom vortices undulate the bed shear stress distributions. Similarly, the sidewall corner vortices (for DFs) or intermediate vortices and inner secondary vortices (for OCFs) undulate the wall shear stress distributions. These undulations are further influenced by the aspect ratio. Moreover, the flow characteristics below the mid depth observed for OCFs are comparable to those obtained for DFs, especially for the square cross sections with aspect ratio of 1.0.