On turbulent kinetic energy production and dissipation in dilute polymer solutions

Abstract

Drag reduction by dilute polymer solutions is the most recognized phenomenon in wall-bounded turbulent flows, which is associated with large scales (e.g., velocity scales) in spite of a consensus that polymers act mainly on much smaller scales of velocity derivatives. We demonstrate that drag reduction is only one sort of polymers’ effect on a turbulent flow and show how turbulent velocity and velocity derivatives are altered in the presence of dilute polymers, irrespective of drag reduction phenomena. This is an experimental study on the interaction of dilute polymers with a complex three-dimensional turbulent flow with small mean velocity gradients. Lagrangian data (e.g., velocities and velocity gradients) of flow tracers were obtained by using three-dimensional particle tracking velocimetry in an observational volume in the turbulent bulk region, far from the boundaries. The focus is on aspects related to the turbulent kinetic energy (TKE) production, −⟨uiuj⟩Sij (ui is the fluctuating velocity, ⟨uiuj⟩ is the Reynolds stress tensor, and Sij is the mean rate-of-strain tensor), such as an anisotropy of Reynolds stresses and the alignment of the velocity vector field with respect to the eigenframe of Sij, among others. We base our study on the comparison of turbulent quantities in flows of water and of dilute polymer solution, forced in two distinct ways: frictional forcing by smooth rotating disks and inertial forcing by disks with baffles. The comparison of the results from the water and from the dilute polymer solution flows allows a critical examination of the influence of polymers on the TKE production, viscous dissipation, and the related turbulent properties. We conclude with (i) quantification of the direct effect of polymers on the small scales of velocity derivatives, (ii) evidence of an additional dissipation mechanism by the polymers, which is the main reason for the strong inhibition of the viscous dissipation, 2νs2, in a turbulent bulk, (iii) verification that TKE production does not change if the energy input to the flow is at the scales that are not affected by polymers (e.g., inertial forcing or a very rough wall), and last, (iv) evidence for qualitative modification of the turbulent structure, which is not exhausted by the additional dissipation mechanism.