Author(s): Wlodzimierz Czernuszenko
Linked Author(s):
Keywords: Open channel; Log-law; Rough flow
Abstract: The mean velocity distribution in an open channel flow over large relative roughness like gravel or pebble-bed is three-dimensional (3D) and is described mathematically by the Navier-Stokes equations. However, engineering community needs rather a simple estimation of the mean velocity distribution dependent on easy-measurable river characteristics instead of the 3D solution to these equations. A simple formulation of the 2D mean velocity profile is thus essential. Therefore, theoretical bases for building 2D equivalent velocity profile for turbulent flows over large relative roughness is presented. In order to define the equivalent velocity distribution and to smooth out the 3D flow irregularities, a special, spatial averaging operation is defined. The Reynolds equations are spatially averaged and the double-averaged momentum equation for primary component velocity is derived. The new hypotheses is proposed and some assumptions are introduced to solve this momentum equation. It results in a new version of logarithmic velocity distribution. To define this distribution, full reconstruction of the Nikuradse’s graph for flows over irregular gravel river bed is considered. It is based on very precise measurements of velocity as well as other hydraulic parameters for flows over large, artificial roughness elements as well as for more natural roughness surfaces. The artificial roughness elements used in the experimental work were cubes and spherical elements glued across of the bed of the channel at the required spacing. Also, three cases of beds comprising natural, river gravels with averaged sizes 20mm, 25mm and 35mm were examined. Results of these measurements (Mansour-Tehrani 1992, Koll 2002) are re-analyzed and the Nikuradse’s graph for flows over large roughness elements in an open channel is re-constructed.
Year: 2007