Skin-Friction Drag Reduction by Dilute Polymer Solutions in Turbulent Channel Flow.

Abstract

Skin-friction drag reduction by dilute polymer solutions is investigated using results from direct numerical simulations (DNS) of homogeneous polymer solutions in turbulent channel flow. Simulations were preformed using a novel mixed Eulerian-Lagrangian scheme in a turbulent channel flow at a base Reynolds number of Re_{tau_b} approx 230 with a FENE-P dumbbell model of the polymer with realistic polymer parameters. The full range of drag reduction from onset to Maximum Drag Reduction (MDR) was reproduced in DNS, with statistics in good quantitative agreement with the available experimental data. Onset of drag reduction was found to be a function of both the polymer concentration and Weissenberg number, as originally suggested by de Gennes (1986). However, the onset criteria suggested by de Gennes (1986) were found to be several orders of magnitude higher than DNS data. A revised version of the theory of de Gennes (1986) has been developed, which gives good agreement with DNS results. The magnitude of drag reduction was found to be a universal function of beta, increasing monotonically with beta for 1.0 > beta > 0.98, and saturating at beta approx 0.98. The magnitude of drag reduction at saturation is a strong function of the Weissenberg number. A We_{tau} sim O (Re_{tau}/2) is needed to reach MDR. Investigation of the mechanism of drag reduction shows that the polymer suppresses the turbulence through an energetically insignificant but dynamically significant process, involving a reduction in the pressure-strain correlation at selected turbulent scales. When this reduction in the pressure-strain correlation is presented at the largest scales of turbulence, turbulence becomes highly anisotropic, and the Reynolds shear-stress and turbulence production are dramatically reduced and turbulence is suppressed. The above understanding of the mechanism of polymer drag reduction opens up new possibilities for skin-friction drag reduction in wall-bounded flows.