Abstract
In this study, we experimentally investigate the turbulent drag-reduction (DR) mechanism in flow through ducts of circular, rectangular and square cross-sections using two grades of polyacrylamide in aqueous solution having different molecular weights and various semidilute concentrations. Specifically, we explore the relationship between drag reduction and fluid elasticity, purposely exploiting the mechanical degradation of polymer molecules to vary their rheological properties. We also obtain time-resolved velocity data for various DR levels using particle image velocimetry and laser Doppler velocimetry. Elasticity is quantified via relaxation times determined from uniaxial extensional flow using a capillary breakup apparatus. A plot of DR against Weissenberg number ($Wi$) is found to approximately collapse the data, with the onset of DR occurring at $Wi\approx 0.5$ and the maximum drag-reduction asymptote being approached for $Wi\gtrsim 5$. Thus quantitative predictions of DR in a range of shear flows can be made from a single measurable material property of a polymer solution, at least for this particular flexible linear polymer.
Highlights
It is well known that long-chain flexible polymers of high molecular weight possess excellent drag-reduction capabilities in turbulent flow when added to a Newtonian solvent even at minute concentrations
Fluid samples were taken at different pumping times for viscosity and relaxation time measurements using an Anton Paar MCR302 controlled-stress torsional rheometer and a Capillary Breakup Extensional Rheometer (CaBER) respectively, in conjunction with pressure-drop measurements to estimate the level of drag reduction
The polymer solutions were subjected to various levels of degradation by recirculating through the experimental rigs, and their shear and extensional rheological properties were closely monitored
Summary
It is well known that long-chain flexible polymers of high molecular weight possess excellent drag-reduction capabilities in turbulent flow when added to a Newtonian solvent even at minute concentrations. This phenomenon, discovered by Toms (1948), has prompted a large number of studies to better understand the underlying mechanism, with researchers approaching the problem from theoretical, experimental and numerical perspectives. One approach has been to estimate polymer relaxation time from shear rheometric measurements but such experiments are challenging for dilute polymers, especially in aqueous solution (Lindner, Vermant & Bonn 2003; Zell et al 2010). We are able to obtain quantitative predictions for the degree of turbulent drag reduction in a given flow – at least for the polymer studied – as long as CaBER measurements are obtainable
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