The effect of surface roughness on skin friction and turbulence in two dimensional flow

Abstract

This investigation is divided into two parts. Part I deals with the effect of roughness and pressure drop and skin friction, and Part II covers the effect of surface roughness and the turbulent velocity fluctuations, and the correlation between these fluctuations in the direction of the mean flow and those normal to the channel walls. The roughness for both investigations was the same, and consisted of corrugated paper glued to the inside walls of a channel of 4.9 cm. wide by 85 cm. (inside dimensions). The roughness was changed by removing every other one of the corrugations, as illustrated in Fig. 6. Pressure and velocity distribution measurements were made at various stations and the results compared to Karman’s equation, u/v* = Ar + B log y/k for rough walls, where u is the velocity in the channel, v* is the friction velocity = √τo/l, y = distance from wall, υ = the kinematic viscosity, k = the roughness height. Karman’s analysis showed B to be a universal constant independent of the wall roughness. Some investigators have given slightly different values to this constant. Their results were carried out in pipes or channels of near square cross section. These results appear to fall within 3% of those of Nikuradse as far as the value of B is concerned. However, a value of B a little less than 5.75 would fit the points better. These experiments were undertaken to add some information to this subject with flow in deep narrow channels and with other types of rough surfaces which had not been investigated. The turbulence measurements were determined with a hot-wire anemometer using a vibrating wire to calibrate it with. These results show that the correlation coefficient u'v'/(u')2 increases with speed for smooth walls and varies materially with the type of roughness with no definite systematic trend as to this change.