Author(s): Koeli Ghoshal, Manotosh Kumbhakar
Linked Author(s): Koeli Ghoshal
Keywords: Turbulent flow, RANS equation, mixing length, von Karman constant, mean velocity
Abstract: The vertical distribution of stream wise velocity of fluid in an open channel turbulent flow laden with sediment is of primary interest and a long standing topic of research. Generally, the velocity comes through the Reynolds-Averaged Navier-Stokes equation (RANS eqn. ) where the unknown Reynolds stresses are modeled by Prandtl's mixing length hypothesis. However, researchers pointed out that the mixing length model introduced by Prandtl is not really correct close to the bed. Present work makes use of a modified mixing length model that considers velocity fluctuations parallel and normal to the mean flow directions in different ways. On the other hand, in clear water turbulent flows the mean velocity profile is described in near bed region by the well-known logarithmic law whose shape is characterized by the von Karman parameter ? having a universal value 0. 41 for clear water flows. Further research suggests that ? is different from 0. 41 in the presence of sediment particles. Furthermore, previous study shows that the von Karman parameter in sediment-laden flow depends on a function called as damping factor. The damping factor is a function of the distance to the channel bed and depends on the velocity and concentration profiles as well as their gradients. Therefore, this study derives the mean velocity profile of turbulent flow starting from the RANS equation for a two-dimensional steady-uniform turbulent flow by taking into account the aforementioned important key factors of sediment-laden turbulent flow. The derived model is a first order non-linear differential equation which has been solved numerically and validated by comparing it with available experimental measurements. Present model shows good prediction accuracy throughout the water depth especially in the region close to the channel bed
Year: 2017