A technique to determine total shear stress and polymer stress profiles in drag reduced boundary layer flows

Two methods of recovering the entire total shear stress profile from incomplete velocity data in turbulent boundary layers are presented and validated for both DNS simulations and experimental measurements. The first method, an exponential–polynomial curve fit, recovers the whole total shear stress profile using the data from the outer part of the boundary layer (y/δ>0.3). However, while performing well, this curve fit is sensitive to the quality of the data. The second method, a new (1−y/δ) weighted straight line fit, which is very simple and accurate, has been applied to current experiments of drag reduction in zero pressure gradient turbulent boundary layers with and without polymer injection. The total shear stress profile obtained from this fit is used to estimate the contribution of the polymer stress to the total shear stress. It shows that the polymer stress is significant only in the inner part of the boundary layer and the magnitude of the polymer stress is not always proportional to the drag reduction.