Experimental and Numerical Study of Free-Surface Flows in a Corrugated Pipe

Abstract

A new discharge computational model is proposed on the basis of the integration of the velocity profile across the flow cross-section in an internally corrugated pipe flowing partially full. The model takes into account the velocity profiles in the pressurised pipe to predict the flow rate under free-surface flow conditions. The model was evaluated through new laboratory experiments as well as a literature datasets. The results show that flow depth and pipe slope may affect the model accuracy; nevertheless, a prediction error smaller than 20% is expected from the model. Experimental results reveal the influence of the pipe slope and flow depth on the friction factor and the stage-discharge curves: the friction factor may increase with pipe slope, while it reduces as flow depth increases. Hence, a notable change of pipe slope may lead to the variation of the stage-discharge curve. A part of this study deals with numerical simulation of the velocity profiles and the stage-discharge curves. Using the Reynolds-Averaged Navier-Stokes (RANS) equations, numerical solutions were obtained to simulate four experimental tests, obtaining enough accurate results as to velocity profiles and water depths. The results of the simulated flow velocity were used to estimate the flow discharge, confirming the potential of numerical techniques for the prediction of stage-discharge curves.Reference [4]. On the other hand, there are few studies on the friction factor and velocity profiles of corrugated pipes under free-surface flow conditions. The following paragraphs point to the previous studies on the hydraulics of corrugated pipes under free-surface flow conditions. An earlier study on flow resistance of three relatively large corrugated pipes under both full-pipe and free-surface flow conditions was performed by Webster and Metcalf [5]. The employed pipes were 3, 5, and 7 ft in diameter. That study mainly focused on the velocity profile and friction factor of the selected pipes under full-pipe flow conditions with less attention to the flow resistance of the pipes under free-surface flow. Nevertheless, the finding of Webster and Metcalf [5] about the value of Manning's n when the pipes convey the flow under free-surface conditions is quite interesting: they concluded that Manning's n for free-surface flow is almost independent of the flow depth and is around the value of 0.024 s/m 1/3 obtained for full-pipe flow conditions.Ead et al. [6] derived empirical equations to predict the flow velocity pattern within a steel corrugated pipe. The measurement of the velocity profiles was conducted at the pipe centreline axis as well as at the different lateral distances from the central vertical plane. Ead et al. [6] reported that the well-known Prandtl equation for the rough wall is valid to predict the velocity profile at a region near the corrugations, whereas, after a certain distance from the corrugations, there would be a deviation from the logarithmic line. The proposed equations by Ead et al. [6] may be used to predict the location w...

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