Accurate measurement of wall skin friction by single-pixel ensemble correlation

The present work deals with accurately estimating wall-skin friction from near-wall mean velocity by means of PIV measurement. The estimation accuracy relies on the spatial resolution and the precision of the resolved velocity profile inside the viscous sublayer, which is a big challenge for conventional window-based correlation method (Kahler C J, et al. Exp Fluids, 2012, 52: 1641-1656). With the help of single-pixel ensemble correlation, the ensemble-averaged velocity vector can be resolved at significant spatial resolution, thus improving the measurement accuracy. To demonstrate the feasibility of this single-pixel ensemble correlation method, we first study the velocity estimation precision in a case of steady near-wall flow. Synthetic particle images are used to investigate the effect of different image parameters. It is found that the velocity RMS-uncertainty level of the single-pixel ensemble correlation method can be equivalent to the conventional window correlation method once the effective particle number used for the ensemble correlation is large enough. Furthermore, a canonical turbulent boundary layer is synthetically simulated based on velocity statistics resolved by previous Direct Numerical Simulation (DNS) work (Schlatter P, et al. J Fluid Mech, 2010, 659: 116-126). The relative error of wall skin friction coefficient is shown to be one-order smaller than that of the window correlation method. And the optimization strategy to further minimize the measurement uncertainty is discussed in the last part.