The unsteady wall shear stress vector of a high Reynolds number turbulent pipe flow obtained with multi-aperture defocusing microscopic particle tracking

Kurzfassung

This study presents the first unsteady measurement of the wall shear stress (WSS) vector in a turbulent pipe flow up to Re_tau = 28400 using a single-camera, 3d-3c multi-aperture microscopic particle tracking velocimetry (MA-µPTV) system. By illuminating tracer particles from the side, the setup achieves higher scattering efficiency and reduces light scattering from window inclusions compared to backscattering configurations, doubling the number of successfully reconstructed particle triplets. This enables a spatial resolution of binaveraged statistics of 8 µm - approximately half the smallest viscous length scale - allowing direct access to the viscous sublayer and capturing near-wall turbulence with unprecedented fidelity. Velocity statistics up to the fourth moment are resolved at wall distances up to 600 µm. The probability density functions (PDFs) and joint PDFs of the WSS and its rate of change exhibit strong Reynolds number independence, indicating self-similar near-wall dynamics governed by local viscous scaling. While streamwise WSS fluctuations follow expected scaling, the spanwise component tau_z,rms remains significantly underestimated compared to flat plate turbulent boundary layer (TBL) correlations, even after extrapolation to y+ = 0. In contrast, the spanwise component agrees with pipe flow direct numerical simulation (DNS) data within measurement uncertainty, likely due to geometric confinement and suppression of large-scale spanwise coherent structures compared to flat plate flow. These results contribute to establishing a new experimental benchmark for high-Reynolds-number wall-bounded turbulence.