On the Diameter Effect for Turbulent Flow of Drag-Reducing Surfactant Solutions

The friction coefficient was measured for developed flow of a drag-reducing surfactant solution in four tubes of 2 mm, 10 mm, 20 mm, and 52 mm diameter. The results are presented in terms of several different parameters to investigate the possibility of developing a simple empirical method for prediction and correlation of the pipe diameter effect on friction. With the exception of the tube with the smallest diameter (2 mm), we found that the drag reduction level expressed as a function of bulk fluid velocity is approximately independent of the tube diameter in the subcritical region (that without temporary fluid degradation), with the deviations being smaller than 7% over the range of diameters and velocities (0.5 to 10 m/s) covered. This diameter-invariant representation appears to correlate the data better than earlier approaches based on shear velocities, and explains why the solvent shear velocity approach was found to be more successful than the solution shear velocity approach, an empirical finding little-understood at the time. In the supercritical region, on the other hand, where wall shear stress affects significantly the drag-reducing ability of the fluid, the friction velocity may be a better parameter.