Abstract:
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(Tkwhere
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 ( 199 1) open channel rib roughness experiments.
The periodic boundary conditions were also applied to a larninar counter-flow plate-fin
heat exchanger.A novel source-sinka rrangemenfto r heat flux was developedi n order
to implement these boundary conditions.
