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.
Turbulent drag reduction of viscoelastic wormlike micellar gels
