Modification of the mean near-wall velocity profile of a high-Reynolds number turbulent boundary layer with the injection of drag-reducing polymer solutions

Abstract

The current study explores the influence of polymer drag reduction on the near-wall velocity distribution in a turbulent boundary layer (TBL) and its dependence on Reynolds number. Recent moderate Reynolds number direct numerical simulation and experimental studies presented in White et al. [Phys. Fluids 24, 021701 (2012)]10.1063/1.3681862 have challenged the classical representation of the logarithmic dependence of the velocity profile for drag-reduced flows, especially at drag reduction levels above 40%. In the present study, high Reynolds number data from a drag reduced TBL is presented and compared to the observations of White et al. [Phys. Fluids 24, 021701 (2012)]10.1063/1.3681862. Data presented here were acquired in the TBL flow on a 12.9-m-long flat plate at speeds to 20.3 m s−1, achieving momentum thickness based Reynolds number to 1.5 × 105, which is an order of magnitude greater than that available in the literature. Polyethylene oxide solutions with an average molecular weight of 3.9 × 106 g mol−1 were injected into the flow at various concentrations and volumetric fluxes to achieve a particular level of drag reduction. The resulting mean near-wall velocity profiles show distinctly different behavior depending on whether they fall in the low drag reduction (LDR) or the high drag reduction (HDR) regimes, which are nominally divided at 40% drag reduction. In the LDR regime, the classical view that the logarithmic slope remains constant at the Newtonian value and the intercept constant increases with increasing drag reduction appears to be valid. However, in the HDR regime the behavior is no longer universal. The intercept constant continues to increase linearly in proportion to the drag reduction level until a Reynolds-number-dependent threshold is achieved, at which point the intercept constant rapidly decreases to that predicted by the ultimate profile. The rapid decrease in the intercept constant is due to the corresponding increase in the profile slope in the HDR regime. There was significant scatter in the observed slope in the HDR regime, but the scatter did not appear to be Reynolds number dependent. Finally, the ultimate profiles for flows at maximum drag reduction were examined and did not exhibit a logarithmic functional relationship, which is the classical empirical relationship suggested by Virk [J. Am. Inst. Chem. Eng. 21, 625–656 (1975)]10.1002/aic.690210402.