The design and construction of a novel pipe flow apparatus for exploring polymer drag reduction

Abstract

Turbulent flows are inherently less efficient than their laminar counterparts, and this additional dissipation results in the waste of a substantial amount of energy in any turbulent fluid system. It has long been known that the addition of a small amount of high molecular weight polymer to a turbulent flow can greatly increase flow efficiency - improvements of 70 % or more are not uncommon. While the mechanism behind this so-called polymer drag reduction - also known as the Toms Effect - is not yet well understood, it has been asserted that the redistribution of energy in the turbulent flow structure via molecular stretching and transport is essential to the increased flow efficiency. This implies that the relevant dimensionless parameter is the ratio of the polymer time scale - the relaxation time - to the relevant flow time scale - the diffusion time. This ratio is known as the Weissenberg Number, and the role it plays in polymer drag reduction has not been explored experimentally in a systematic way. It has been known for some time that the slimes produced by fishes are effective drag reducing agents per unit weight; the slime of the Pacific Hagfish (Eptatretus stout), in particular, contains both long, flexible fibers and high molecular weight mucin polymer chains.

(cont.) It has been demonstrated both numerically and experimentally that small quantities of fibers can be used to achieve a drag reducing effect similar that of polymers, although less dramatic, while being less susceptible to the degradation and subsequent loss of drag reducing effectiveness that is characteristic of polymers in turbulent flow. It has been tentatively shown that polymers and fibers behave synergistically when combined in turbulent flow to achieve higher levels of drag reduction with less susceptibility to degradation than polymers alone. It is therefore suspected that the slime of the hagfish would be a remarkably effective drag reducing agent, in addition to being non-toxic and biodegradable. In order to evaluate the drag reducing effectiveness of hagfish slime, and to explore the effect of the Weissenberg number on drag reduction, a simple, reliable, adaptable, and low-cost pipe flow apparatus was designed and constructed. The apparatus utilizes a gravity driven flow, and can be used to access a range of Reynolds numbers by adjusting the vertical drop and using tubes of different diameters. In addition, the ability to use tubes of different diameters allows the flow diffusion time to be changed drastically while the polymer relaxation time is held constant, thus exploring the effect of the Weissenberg number on polymer drag reduction.

(cont.) In order to establish the accuracy of measurements made with the apparatus, the turbulent drag of a pure water flow and of a solution of 100 ppm polyacrylamide in tap water were measured for Reynolds numbers from 500 to 10,000 and compared with an empirical relationship and previous experimental results, respectively. Measurements made with the apparatus were in good agreement with predictions - generally within 1 % - and in qualitative agreement with previous results. The effect of molecule stiffness on drag reducing effectiveness was explored by testing two dilute solutions of partially hydrolyzed polyacrylamide - 100 ppm in tap water and 100 ppm in synthetic saltwater - and it was found that drag reducing effectiveness generally increases with molecule flexibility. The drag reducing effectiveness of solutions of 1.0 ppm hagfish slime mucin proteins in saltwater and of 3.6 ppm whole hagfish slime (containing both mucin proteins and fibers) in saltwater were evaluated. It was found that hagfish slime has little effect on flow turbulence at such low concentrations, and both solutions exhibited near-Newtonian behavior.

(cont.) It is expected that hagfish slime may be an effective drag reducer at higher concentrations, but the quantity of slime available for the present study was too small to allow for this to be tested. It was found that in all polymer flow cases, changing the tube diameter led to drastically different drag reduction behavior, implying that the Weissenberg number is in fact a key parameter for polymer drag reduction.