(171d) Influence of Reynolds Number on Variations of Turbulent Statistics in Channel Flow of Dilute Polymer Solutions

The effects of Reynolds number on turbulent statistics in drag-reduced turbulent channel flows are investigated using direct numerical simulations in which the polymer-induced stresses are modeled by the FENE-P model. For drag reduction (DR) rates ranging from 18% to 71%, low and moderate Reynolds number flows (Re_τ = 125 and 395 based on friction velocity and channel half height) are investigated. Consistent with the experimental findings, the mean velocity profiles for low DR flows are simply shifted upward with the same slope in the log layer as for Newtonian flows, whereas the slope increases for high DR flows. Turbulent statistics such as turbulent intensities, Reynolds shear stress, and ejection event angles are affected in the entire wall-normal locations for both low and high DR flows at Re_τ = 125. However, at Re_τ = 395, the viscoelastic effects in the low DR regime are confined to the inner layer. The difference in the wall-normal extent affected by viscoelasticity between two Re flows was investigated in terms of the time scale of turbulent eddies. The probability density function of the eddy time scale, defined as the vortex swirling period, shows that the most probable eddy time scale in the outer layer is twice as large as that in the inner layer. Hence, coupling between the polymer and the outer eddies occurs only at relatively long polymer relaxation times. As the polymer relaxation time (λ) increases, longer time scale eddy structures interact with the polymer, and the outer layer modification becomes more pronounced. When the ratio of λ to an outer eddy time scale based on the channel half height and centerline velocity (h/U_c) is much greater than 1, the effect of the polymer encompasses the whole channel and DR approaches an asymptotic value. The distinction between inner and outer layer dynamics is not robustly captured by low Re simulations in which λU_c/h is O(1) even near the onset of DR, which is dictated by the ratio of polymer relaxation time to the wall time scale.