Fully developed turbulent flow in both smooth and rough-walled pipes is investigated for Reynolds numbers from 30,000 to 480,000. The values of mean velocity, root-mean-square values of the fluctuating velocity components, and cross-correlation values of the fluctuating velocities are presented for flow in a smooth pipe and two sand-roughened pipes, R/ε = 208 and R/ε = 26.4. The quantity R/ε is the ratio of the actual pipe radius to the average sand particle size. The experimental measurements for flow in smooth pipes are in good agreement with those of previous investigations throughout the Reynolds number range considered. Several of the rough pipe turbulence quantities show substantial deviations from the corresponding smooth pipe quantities. For rough pipes, the measured uv cross-correlation values approach those predicted empirically from the Reynolds equations for fully developed, axisymmetric flow as the flow approaches the hydraulically smooth case. However, as the Reynolds number is increased and the flow proceeds through the transition region from smooth to fully rough flow and to the fully rough flow region, the values of the uv cross correlation in rough pipes are significantly lower than the predicted values. This difference between predicted and measured data becomes more pronounced as the Reynolds number is further increased and the flow becomes fully rough. The difference between measured and predicted uv values, and other differences between smooth and rough pipe results, suggests that the accepted reduction of the Reynolds equations for flow in smooth pipes is not valid for flow in rough pipes. Thus, the Reynolds equations are re-examined for flow in rough pipes, and it is shown that these equations can be satisfied by the experimental data if secondary flows and angular variations in the mean velocity are postulated.
This paper presents the results of an experimental study of fully developed turbulent flow in rough pipes. The investigation was undertaken in an attempt to better understand some of the changes in turbulence structure which accompany a change in wall roughness, and the experimental results include energy spectra of the fluctuating velocities in each coordinate direction, as well as microscales and macroscales of turbulence. The results indicate that the turbulence structure in the central region of the pipe is relatively independent of surface roughness, while the structure near the wall is very much dependent on the nature of the solid boundary. For hydraulically smooth flow, the principal effect of the wall is to radially suppress the extent of the larger eddies in the flow field. In the transition regime, the longitudinal extent of both large and small eddies is disrupted by the roughness elements, and the dissipation eddies appear to be stretched radially as they intermesh with the sand grains. The large eddies are almost completely obliterated by the roughness particles in the fully rough flow regime, while a tendency toward isotropy of the small eddies is noted. Thus, very definite changes in the flow structure occur as wall roughness is varied, and it is postulated that these changes are due principally to the fact that the roughness elements occupy the space where the three-dimensional streaky structure originates in smooth pipe flow.
JANUARY 1972ENGINEERING NOTES and the turbulent Schoenherr law for no drag reduction 59 r 1/2 (10)The percentage of drag reduction, %D.R., is also plotted in Fig. 2 %D. R. = (11) where C F is the drag coefficient for polymer solutions and CV, 0 is the drag coefficient for no drag reduction at the same Reynolds number. The results are most favorable.It should be noted that the maximum drag reduction is predicted on the basis of a theoretical model. In practice highshear stresses will probably mechanically degrade the polymer molecules and diminish the drag reduction so that the maximum drag reduction may not be attained. The actual friction line lies then between the Schoenherr line of no drag reduction and the line of maximum reduction. This line may be determined by the method of Ref. 2.
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