Mean-Velocity Profile of Turbulent Boundary LayersApproaching Separation

Abstract

Turbulent boundary layers approaching separation are a common flow situation in many technical applications. Numerous theoretical, experimental, and numerical attempts have been made to find the proper scaling for the mean-velocity profile of this type of wall-bounded flow. However, none of these approaches seems to be completely satisfactory. New water-tunnel experiments of adverse-pressure-gradient turbulent boundary layers are presented that clearly show the breakdown of the logarithmic law. With these data and experimental results from several independent research groups, the classical scaling for zero-pressure-gradient turbulent boundary layers, the scaling by Castillo and George (Castillo, L., and George, W. K., Similarity Analysis for Turbulent Boundary Layer with Pressure Gradient: Outer Flow, AIAA Journal, Vol. 39, No. 1, 2001, pp. 41-47), and the scaling by Zagarola and Smits (Zagarola, M. V., and Smits, A. J., Mean-Flow Scaling of Turbulent Pipe Flow, Journal of Fluid Mechanics, Vol. 373,1998, pp. 33-79) are analyzed. Only the latter can be applied successfully for the outer region of the mean-velocity profile close to separation. It is shown that Zagarola and Smits's scaling is consistent with the classical two-layer approach and can be applied to collapse the different data. When the Reynolds shear stress is analyzed, George and Castillo's scaling shows a reasonably good collapse of the data in the outer region.