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 C Ar depending on the position of the maximum velocity (ξ dip ). ξ dip 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.
NomenclatureAr Aspect ratio Ar = b/h b Free surface width (m)
Sheet cavitation on a foil section and, in particular, its unsteady characteristics leading to cloud cavitation, were experimentally investigated using high-speed visualizations and fluctuating pressure measurements. Two sources of sheet cavitation instability were evidenced, the re-entrant jet and small interfacial waves. The dynamics of the re-entrant jet was studied using surface electrical probes. Its mean velocity at different distances from the leading edge was determined and its role in promoting the unsteadiness of the sheet cavitation and generating large cloud shedding was demonstrated. The effect of gravity on the dynamics of the re-entrant jet and the development of interfacial perturbations were examined and interpreted. Finally, control of cloud cavitation using various means, such as positioning a tiny obstacle (barrier) on the foil surface or performing air injection through a slit situated in the vicinity of the leading edge, was investigated. It was shown that these were very effective methods for decreasing the amplitude of the instabilities and even eliminating them.
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