Suspensions of DNA macromolecules (0.8 wppm, 60 kbp), modeled as finitely extensible nonlinear elastic dumbbells coupled to the Newtonian fluid, show drag reduction up to 27% at friction Reynolds number 180, saturating at the previously unachieved Weissenberg number $\simeq {10}^4$. At a large Weissenberg number, the drag reduction is entirely induced by the fully stretched polymers, as confirmed by the extensional viscosity field. The polymer extension is strongly non-Gaussian, in contrast to the assumptions of classical viscoelastic models.

Drag reduction induced by a polydisperse solution of polyethylene oxide is investigated by direct numerical simulations of the Navier–Stokes equations coupled with the Lagrangian evolution of the polymers, modelled as dumbbells. Simulation parameters are chosen to match the experimental conditions of Berman (1977), who measured the polymer molecular weight distribution. Drag reduction is induced only by the few high molecular weight polymers fully stretched by the turbulent flow, whilst the hundreds of parts per million of low molecular weight chains are ineffective.

Polymer chains in turbulent flows are generally modelled as dumbbells, i.e. two beads joined by a nonlinear spring. The dumbbell only maps a single spatial configuration, described by the polymer end-to-end vector, thus a multi-bead FENE (finitely extensible nonlinear elastic) chain seems a natural improvement for a more accurate characterisation of the polymer spatial conformation. At a large Weissenberg number, a comparison with the more accurate Kuhn chain reveals that the multi-bead FENE chain drastically overestimates the probability of folded configurations. Surprisingly, the dumbbell turns out to be the only meaningful bead-spring model to coarse-grain a polymer macromolecule in turbulent pipe flows.

The turbulence of a realistic dilute solution of DNA macromolecules is investigated through a hybrid Eulerian–Lagrangian approach that directly solves the incompressible Navier–Stokes equation alongside the evolution of ${10}^8$ polymers, modelled as finitely extensible nonlinear elastic (FENE) dumbbells. At a friction Reynolds number of 320 and a Weissenberg number of $2\times {10}^4$, the drag reduction is equal to 26%, which is similar to the one obtained at the lower Reynolds number of 180. The polymers induce an increase in the flow rate and the turbulent kinetic energy, whose axial contribution is predominantly augmented. The stress balance is analysed to investigate the causes of the drag reduction and eventually the effect of the friction Reynolds number on the probability distribution of the polymer configuration. Near the wall, the majority of the polymers are fully stretched and aligned along the streamwise direction, inducing an increase in the turbulence anisotropy.

Direct numerical simulation of a turbulent pipe flow of a realistic solution of \(10^8\) polymers, modelled as finitely extensible nonlinear elastic (FENE) dumbbells, and directly momentum coupled with the incompressible Navier–Stokes equations, are performed by means of an Eulerian-Lagrangian approach. Besides the drag reduction, the polymers significantly modify mean and turbulent kinetic energy budgets. The polymer backreaction to the solvent reduces the Reynolds stress and thus decreases the turbulent production and, at large Weissenberg number, the polymers act as a source of turbulent kinetic energy for \(y^+> 40\), leading to an increase in the dissipation. This effect is peculiar to large Weissenberg polymers and it is particularly apparent at a small Reynolds number. At a smaller Weissenberg number, the effect of the polymers remains confined in the buffer layer, with the kinetic energy budget not significantly altered elsewhere.