Digital Holographic Microscopy Elucidates the Effects of Buffer Layer Flow Structures on Wall Shear Stress Distributions in a Turbulent Boundary Layer

Abstract

Digital holographic microscopy is used to measure the three-dimensional velocity distribution in the inner part of a turbulent boundary layer over a smooth wall. Velocity gradients within the viscous sublayer are then used for measuring the distributions of wall shear stresses. The measurements are performed in a square duct channel flow at Reynolds number based on half height of 50,000. The wall unit size is 17 μm, the sample volume is 90 × 145 × 90 wall units, and the spatial resolution of measurements is 3-8 wall units in streamwise and spanwise directions and one wall unit in the wall-normal direction. The uncertainty in velocity is better than 1 mm/s, less than 0.05% of the free stream velocity. Mean velocity profiles and distributions of Reynolds stresses agree with previously published data. The buffer layer 3-D flow is classified into three groups, the first containing a pair of counter-rotating inclined vortices and high streak-like shear stresses; the second group contains multiple streamwise vortices; and the third group has no buffer layer structures. Conditional sampling based on magnitude of wall shear stresses is used for identifying flow structures generating extreme maxima and minima in wall stresses. We show that inclined quasi–streamwise, counter-rotating vortex pairs, forming as spanwise vorticity lifts away from the wall and turns downstream, generate a stress minimum as the point of detachment, and maxima when these vortices entrain high momentum fluid. High wall stresses are also generated by other, isolated very slightly inclined streamwise vortices.