Introducing one-dimensional model to estimate velocity distribution in narrow open-channels

Authors
H. Bonakdari
N. Binesh
Abstract
In open channels, the distribution of velocity, shear stress and other related quantities such as the diffusion and dispersion coefficients and thus all transport processes are three-dimensional, according to the three-dimensional convection and diffusion principles. Determining the velocity distribution- as a key parameter for estimating other hydraulic parameters- has always been the subject of attention. Velocity distribution in the inner region of the flow (y0.2D). The log-Wake law is of the most accepted laws for velocity distribution in wide open channels, this law modifies the logarithmic law by adding a Wake function; but in case of narrow open channels, the log-Wake law deviates from the measured data near the free surface. Because the profile by the log-Wake law depicts the velocity which increases with the increase of distance from the bed monotonically and is not able to show the velocity negative gradient near the free surface which happens in narrow open channels. In narrow open channels, the three dimensional structure of the flow and the transport momentum from the side walls to the central zone due to strong secondary currents, causes the maximum velocity to occur below the water surface which is called velocity-dip phenomenon. The velocity dip phenomenon was first reported more than a century ago. Since that time, numerous investigations have been conducted by many researchers in order to propose new models to be able to not only describe the dip phenomenon and negative gradient of velocity near the free surface, but also to predict the position of the maximum velocity accurately and fit the experimental data throughout the whole flow depth.
This paper introduces an analytical model based on Reynolds Averaged Navier Stokes (RANS) equations and an eddy viscosity distribution, to estimate velocity distribution in turbulent fully developed flows. The proposed model is suitable for both narrow and wide open channels, and is capable of predicting the dip phenomenon. The results by the model verified with data measured in several rectangular lab channels and data collected from an actual sewer channel. Since the proposed equation for velocity distribution is dependent of Coles Wake parameter (Π), the effect of this parameter on level of accuracy and description of velocity profile as well as prediction of dip phenomenon and location of maximum velocity has been studied. Many researchers proposed different values for Coles parameter, and it seems there is no universal constant value for this parameter. In this study, the value of Coles parameter was proposed by fitting the data from different channels, based on the least error calculated in predicting the velocity profiles by the proposed model. The results show that the profiles by the model agree well with experimental data and predict the velocity-dip phenomenon; also the model provides little errors compared to measured data in the channels, which is representative of high level of accuracy in defining velocity distribution profile of the flow. The value of Coles parameter estimated for channel-sewer was less than that for lab channels.

Keywords

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Modares Civil Engineering journal
Volume 16, Issue 5
November and December 2016
Pages 33-43