Shear and Diffusion in a Large Boundary Layer Injected with Polymer Solution

Abstract

Experimental studies involving velocity profile measurements and polymer diffusion measurements were made in a plane boundary layer with length varying up to 40 feet, thickness varying up to 15 inches, and Reynolds number varying up to 8 x 10^7. Aqueous solutions of Polyox WSR-301 of 250 to 2000 ppm were injected tangentially at the boundary near the origin of a boundary layer having a stream velocity of 18 fps.

Diffusion of the polymer from the boundary up into the boundary layer was evaluated from profiles made by sampling with withdrawal tubes located at various stations along the flow axis. A fluorescent marker dye was used for the evaluation.

Velocity measurements served to define the profile and permitted profile extrapolation to the boundary for boundary shear evaluations.

The maximum drag reduction of 35 per cent over a 40-foot boundary length exposed to V = 18 fps occurred with an injection of 0.004 lb/sec of polymer per foot width, which resulted in a downstream wall concentration of about 30 ppm.

A flush-mounted hot-film sensor was calibrated for both water and polymer flows in a gravity-flow pipe facility. The calibration curve was influenced by the addition of polymer. Measurements of the zero crossings and frequency spectra of the turbulent fluctuations, as well as velocity profiles, were made for various polymer concentrations in the commercially rough pipe. Zero crossings were found to correlate with the square root of the wall shear stress.