A numerical and experimental study of open-channel flow in a pipe of circular cross-section with a flat bed
Uniform open-channel flow in a pipe of circular cross-section with a flat bed, is studied by experiment and numerical modelling. A pipe of diameter D= 305 nun, and mild bed slopes So = 4.63 x 10-4and 9.27 x 10-4was, studied - the former slope only by experiment. The bed thicknesses( e), e/D = 0.141, and 0.285 were studied experimentally and numerically, with e/D = 0.020, studied only numerically. Five flow depths (Y. ) were studied; (Y. +e)/D = 0.3,0.4 (and 0.416), 0.5,0.667, and 0.751. A smooth bed and bed roughnessesd,5 o= 0.93,4.20, and 1.71 mm were also used. Mono-chromatic Laser Doppler Anemometry (ILDA) was used to measure the local mean longitudinal (primary), and vertical velocities, and their respective turbulence intensifies. The primary velocity contours display dipped maxima and bulging towards the comer. The inwardly-curving side-walls slightly modify these contours. In each channel half there is a surface cell and a bottom cell. These move high momentum fluid away from the centreline towards the comer zone. The primmy and secondary flows are largely similar to those in rectangular channels. The wall shear force ratios obtained by the Vanoni-Brooks separation technique follow the empirical trend from various channel types. Similarity laws for the longitudinal mean velocity in the comer-influenced zones are proposed. The numerical model is based on the SIMPLE technique, and computes the flow on a Cartesian grid, using a non-linear k-e turbulence model with wall functions. The model boundary conditions were modified to reflect the effects of the comers, the curved side-wall, and a roughened bed. Model predictions of the primary mean velocities, and centreline turbulence intensities, are close to the experimental and empirical distributions. Primary velocity predictions for e/D = 0.020 compare well to the case of a clear pipe flowing part-fiffl. The predicted secondary flows are largely similar to the experimental patterns. Usage of a small mesh size (e. g. when (YO + e)/D < 0.5) results in side-wall points lying within the larninar sublayer, leading to inaccurate secondary flow prediction by the k-e model. As in rectangular channels, the predicted local boundary shear stress decreases from the centreline along the bed and minimises at the comer. On the side-walls, the model overpredicts the local boundary shear stresses. Nonetheless, computed wall shear force ratio values follow the empirical trend.