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 ≈ 0.5 and the maximum drag-reduction asymptote being approached for Wi 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.

Previous experimental studies on turbulent square duct flow have focused mainly on high Reynolds numbers for which a turbulence-induced eight-vortex secondary flow pattern exists in the cross-sectional plane. More recently, direct numerical simulations (DNS) have revealed that the flow field at Reynolds numbers close to transition can be very different; the flow in this 'marginally turbulent' regime alternating between two states characterised by four vortices. In this study, we experimentally investigate the onset criteria for transition to turbulence in square ducts. In so doing, we highlight the potential importance of Coriolis effects on this process for low-Ekman-number flows. We also present experimental data on the mean flow properties and turbulence statistics in both marginally and fully turbulent flow at relatively low Reynolds numbers using laser Doppler velocimetry. Results for both flow categories show good agreement with DNS. The switching of the flow field between two flow states at marginally turbulent Reynolds numbers is confirmed by bimodal probability density functions of streamwise velocity at certain distances from the wall as well as joint probability density functions of streamwise and wall normal velocities which feature two peaks highlighting the two states.

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The results of direct numerical simulations to determine the critical conditions for self-sustained turbulence in wall-driven (Couette) square duct flow and its characteristics at relatively low turbulent Reynolds numbers are presented. We focus on the case in which a pair of opposite counter-moving walls translating with the same speed drives the flow. Stabilisation by the side walls is found to play a crucial role in the transition to turbulence, the minimum Reynolds number for maintaining a turbulent state (Rec ≈ 875) being much greater than that in a plane channel. At Reynolds numbers close to the critical, an alternation of the flow field, in time, between two states characterised by a four-vortex secondary flow pattern is observed, one being a mirror reflection of the other, and the flow remains approximately symmetrical about the common bisector of the moving walls. Due to the intermittency, large velocity fluctuations about the long-term mean are observed at different locations in the duct. These findings are consistent with results of previous studies on turbulent pressure-driven (Poiseuille) square duct flow at low Reynolds numbers; hence, the phenomenon is not unique to Poiseuille flows. Instantaneous flow field visualisations reveal the existence of coherent structures which are persistent over the length of the duct, thus indicating that the states are very stable in the streamwise direction. Quadrant analysis of the Reynolds shear stress shows that the secondary motions are closely related to the near-wall ejection and sweeping events.

Turbulent pipe flow is still an essentially open area of research, boosted in the last two decades by considerable progress achieved on both the experimental and numerical frontiers, mainly related to the identification and characterization of coherent structures as basic building blocks of turbulence. It has been a challenging task, however, to detect and visualize these coherent states. We address, by means of stereoscopic particle image velocimetry, that issue with the help of a large diameter (6 in.) pipe loop, which allowed us to probe for coherent states at various moderate Reynolds numbers (5300 < Re < 29 000) of the single-phase Newtonian flow. Although these states have been observed at flow regimes around laminar–turbulent transition (Re [Formula: see text] 2300) and also at high Reynolds number pipe flow (Re [Formula: see text] 35 000), at moderate Reynolds numbers, their existence had not been observed yet by experiment. By conditionally averaging the flow fields with respect to their dominant azimuthal wavenumber of streamwise velocity streaks, we have been able to uncover the existence of ten well-defined coherent flow patterns. It turns out, as a remarkable phenomenon, that their occurrence probabilities and the total number of dominant modes do not essentially change as the Reynolds number is varied. Their occurrence probabilities are noted to be reasonably well described by a Poisson distribution, which suggests that low-speed streaks are created as a Poisson process on the pipe circular geometry.