The Application of Wall Similarity Techniques to Determine Wall Shear Velocity in Smooth and Rough Wall Turbulent Boundary Layers

Abstract

Smooth and rough wall turbulent boundary layer profiles are frequently scaled using the wall shear velocity u*, thus it is important that u* is accurately known. This paper reviews and assesses several wall similarity techniques to determine u* and compares results with data from the total stress, Preston tube, and direct force methods. The performance of each method was investigated using experimental repeatability data of smooth and rough wall turbulent boundary layer profiles at Reθ of 3330 and 4840, respectively, obtained using laser Doppler velocimetry (LDV) in a recirculating water tunnel. To validate the results, an analysis was also performed on the direct numerical simulation (DNS) data of Jimenez et al. (2010, “Turbulent Boundary Layers and Channels at Moderate Reynolds Numbers,” J. Fluid Mech., 657, pp. 335–360) at Reθ = 1968. The inner layer similarity methods of Bradshaw had low experimental uncertainty and accurately determined u* and ε for the DNS data and are the recommended wall similarity methods for turbulent boundary layer profile analysis. The outer layer similarity methods did not perform well, due to the need to simultaneously solve for three parameters: u*, ε, and Π. It is strongly recommended that the u* values determined using wall similarity techniques are independently verified using another method such as the total stress or direct force methods.