The effect of cross-sectional geometry on the high-speed narrow open channel flows: An updated Reynolds stress model study

Abstract

This numerical study investigates the effect of the channel cross-sectional geometries, namely archway, circular, and horseshoe on the mean velocity fields, secondary currents, turbulence characteristics, and bed shear stress distributions in supercritical narrow open channel flows. Six uniform flow simulations, combining two filling ratios comparable to sediment bypass tunnel flows, were performed in OpenFOAM. An updated Speziale-Sarkar-Gatski Reynolds stress model was used, which was validated with experimental data for a rectangular channel flow. Near the bottom corner, the sidewall curvature increment alters the verticality of secondary flows, distances the secondary velocity isovels, and bulges the longitudinal velocity isovels toward the boundaries which increases the local bed shear stress. It also restricts the vertical growth of the developing intermediate vortex and the lateral growth of the bottom vortex, which are attributed to the reductions of turbulence anisotropy gradient at the corner zone. Furthermore, it minimizes the converging of the contour lines of primary Reynolds shear stress as the sidewall curvature modifies the near sidewall longitudinal velocity gradient. Circular cross-sections produced 1.7% – 2.3% higher laterally averaged shear velocities U*l than archway, which are insignificant to be regarded as shear stress concentration. At the top corner, the curved sidewall distorts the flow property contour lines and influences the inner secondary vortex. The aspect ratio reduction swells the bottom vortex and decreases U*l. Overall, a horseshoe cross-section is the suitable choice for sediment carrying channels as it can provide sufficiently wide invert while minimizing the low-momentum fluid zones and the bed shear stress undulation.