Turbulent velocity profile in fully-developed open channel flows |
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Authors: | Hossein Bonakdari Frédérique Larrarte Laurent Lassabatere Claude Joannis |
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Institution: | (1) Department of Civil Engineering, University of Razi, Kermanshah, Iran;(2) Water and Environment Division, LCPC, Route de Bouaye, BP 4129, 44341 Bouguenais Cedex, France |
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Abstract: | The determination of velocity profile in turbulent narrow open channels is a difficult task due to the significant effects
of the anisotropic turbulence that involve the Prandtl’s second type of secondary flow occurring in the cross section. With
these currents the maximum velocity appears below the free surface that is called dip phenomenon. The well-known logarithmic
law describes the velocity distribution in the inner region of the turbulent boundary layer but it is not adapted to define
the velocity profile in the outer region of narrow channels. This paper relies on an analysis of the Navier–Stokes equations
and yields a new formulation of the vertical velocity profile in the center region of steady, fully developed turbulent flows
in open channels. This formulation is able to predict time averaged primary velocity in the outer region of the turbulent
boundary layer for both narrow and wide open channels. The proposed law is based on the knowledge of the aspect ratio and
involves a parameter CAr depending on the position of the maximum velocity (ξdip). ξdip may be derived, either from measurements or from an empirical equation given in this paper. A wide range of longitudinal
velocity profile data for narrow open channels has been used for validating the model. The agreement between the measured
and the computed velocities is rather good, despite the simplification used. |
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Keywords: | Dip phenomenon Free surface flow Narrow channel Secondary current Velocity profile |
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