DNS of Drag Reduction by Dilute Polymer Solutions in a Turbulent Channel Flow

Abstract

Drag reduction by dilute polymer solutions is investigated by DNS. Computations were performed in turbulent channel flows at a base Reynolds number of Re ∼ 230 using a mixed Eulerian/Lagrangian scheme with a FENE-P dumb- bell model of the polymer. The full range of drag reduction from onset to Maximum Drag Reduction (MDR) is captured in DNS with realistic polymer parameters and concentrations. Investigation of the effect of polymer extensibility, relaxation time, and concentration on drag reduction shows the Weissenberg number (Weτ°) to be the most critical parameter in determining the magnitude of drag reduction, with the other parameters having only a secondary e3ect. Saturation with concentration, beyond which increasing the concentration has no added benefit, is observed at very dilute concentrations (β ≈ 0.95). A polymer of relaxation time is observed to suppress turbulent eddies of size l < O(λuτ). Virk's MDR asymptote is approached when l becomes comparable to the channel half width, or when Weτ° ∼ O(Reτ°).At even higher Weissenberg numbers, and in the absence of a background noise, the flow begins to relaminarize on viscous time scales. Introduction of an infinitesimal background noise on these relaminarized states re-triggers the production of turbulence and results in a flow with features in agreement with Virk's MDR asymptote. Drag reduction is initiated by suppression of turbulent eddies of size l < O(λuτ) Suppression of these eddies reduces the magnitude of the pressure-strain term, thus inhibiting the transfer of turbulence kinetic energy from the streamwise to the other components. This, in turn, leads to a drop in the Reynolds shear-stress in regions of high shear, reducing turbulence production and resulting in drag reduction.