Turbulence dynamics in drag-reducing polymer solutions

The addition of few parts per million of long chain polymers in an otherwise Newtonian fluid changes quite dramatically the physical behaviour of the resulting fluid. Among the many observed differences, the one that has so far attracted the greater attention is the large reduction of the viscous drag in wall turbulent flows. This phenomenon, together with a significant modification of the turbulent strcture, is quite robust though the polymers are substantially smaller than the typical scales of turbulence. This suggests that their effect should be explained in terms of matching characteristic time scales, rather than lengths. Even in homogeneous isotropic turbulence the energy flux intercepted by the stretched polymers is accumulated in the microstructure as elastic energy and dissipated by the relative friction between polymers and solvent to the point that a substantial depletion of the classical Richardson cascade of turbulent kinetic energy occurs. Clearly, near a solid wall, where the phenomena of interest for drag-reduction are occurring, the physics is more complex. Typically the classical mean velocity profile is substantially modified, showing a alteration of the logarithmic layer. This observation together with the related modification of turbulence still deserves a detailed description for a full comprehension of the subject. In the present contribution such a complex scenario will be discussed through the discussion of the results of a Direct Numerical Simulation, where an appropriate, though simplified, model for dilute numerical solutions is adopted. A generalized form of scale-energy budget able to discriminate between the different kinds of energy fluxes which occur either in physical and scale space will be shown as an instrumental tool for the evaluation of the interaction of polymers with the near-wall environment.