High-fidelity measurements in channel flow with polymer wall injection

Streamwise velocity profiles and their wall-normal derivatives were used to investigate the properties of turbulent channel flow in the low polymer drag reduction $(DR)$ regime ( $DR=6.5\,\%$ to $26\,\%$ ), as realized via polymer injection at the channel surface. Streamwise velocity data were obtained over a friction Reynolds number ranging from $650$ to $1800$ using the single-velocity-component version of molecular tagging velocimetry (1c-MTV). This adaptation of the MTV technique has the ability to accurately capture instantaneous profiles at very high spatial resolution ( ${\gtrsim}850$ data points per wall-normal profile), and thus generate well-resolved derivative information as well. Owing to this ability, the present study is able to build upon and extend the recent numerical simulation analysis of White et al. (J. Fluid Mech., vol. 834, 2018, pp. 409–433) that examined the mean dynamical structure of polymer drag-reduced channel flow at friction Reynolds numbers up to $1000$ . Consistently, the present mean velocity profiles indicate that the extent of the logarithmic region diminishes with increasing polymer concentration, while statistically significant increases in the logarithmic profile slope begin to occur for drag reductions less than $15\,\%$ . Profiles of the r.m.s. streamwise velocity indicate that the maximum moves farther from the wall and increases in magnitude with reductions in drag. Similarly, with increasing drag reduction, the profile of the combined Reynolds and polymer shear stress exhibits a decrease in its maximum value that also moves farther from the wall. Correlations are presented that estimate the location and value of the maximum r.m.s. streamwise velocity and combined Reynolds and polymer shear stress. Over the range of $DR$ investigated, these effects consistently exhibit approximately linear trends as a function of $DR$ . The present measurements allow reconstruction of the mean momentum balance (MMB) for channel flow, which provides further insights regarding the physics described in the study by White et al. In particular, the present findings support a physical scenario in which the self-similar properties on the inertial domain identified from the leading-order structure of the MMB begin to detectably and continuously vary for drag reductions less than $10\,\%$ .