On the method of determining instantaneous wall shear stress from near-wall velocity measurements in wall turbulence

Abstract

The determination of the instantaneous wall shear stress (WSS) from near-wall velocity measurements has received considerable attention. However, the most appropriate procedure and the achievable accuracy remain open topics. The present work uses direct numerical simulation datasets of channel flow to investigate the influences of the wall-normal distribution of instantaneous velocity, the method for estimating the velocity gradient, and the wall-normal position of velocity vectors on the accuracy of the instantaneous WSS determined from near-wall velocity measurements. In general, the method of dividing instantaneous velocity vectors by their wall-normal positions performs better than the method of linearly fitting instantaneous velocity profiles for estimating the wall velocity gradients when the wall position is correctly determined. However, the nonlinear instantaneous velocity distribution within the viscous layer means that all methods introduce a negative mean bias error and non-negligible root mean square error for the instantaneous WSS and its statistics. The magnitudes of these errors increase with the wall-normal position of the velocity vectors. An empirical method for correcting the instantaneous WSS statistics is proposed based on the negligible Reynolds number dependence of the bias error of all statistics. The influence of the wall-normal position of the velocity vectors on the WSS statistics and the correction method are verified using experimental data from open channel flows. The verification results show that the correction method significantly improves the accuracy of the statistics of instantaneous WSS determined from near-wall velocity measurements under canonical wall turbulence.