A numerical study of resistance in a rough walled channel flow where the ratio of roughness length scale to the depth of flow varies over a wide range
Numerical calculations were performed over a variety of two-dimensional rib roughness configurations in which the ratio of flow depth to roughness height was varied from 1.1 to 40. Periodically fully developed flow was achieved by employing periodic boundary conditions and the effect of turbulence was accounted for by a two-layer model. These calculations were used to test the hypothesis that any rough wall resistance may be reduced to an equivalent wall shear stress located on a plane wall. The position of the plane wall is determined by a novel method of prediction obtained by consideration of strearnwise force moments. The resistance is then determined by three dynamically significant length scales: the first (yo) specifies the position of the equivalent plane wall, the second is the depth of flow h and the third is similar to Nikuradse's sand grain roughness k,,. The latter length scale is however depth dependent and a universal relationship is postulated: ks y,, -,= F/Tk where ksw is the asymptotic value of ks at very large flow depths. For the calculation of friction factor, a resistance equation is proposed of the form typical of fully rough flows. These postulates are supported by the numerical model results though further work including physical experiments is required to confirm them. Before applying the two-layer model to this problem it was tested on smooth rectangular duct flows and Schlichting's (1936) long angle roughness experiments. The opportunity was taken to further explore these flows, and in addition calculations were carried out for Grass et al's (1991) open channel rib roughness experiments. The periodic boundary conditions were also applied to a larninar counter-flow plate-fin heat exchanger. A novel source-sink arrangement for heat flux was developed in order to implement these boundary conditions.