Enabling instantaneous measurements of wall-shear stress in aerodynamic flows

Accurately measuring the instantaneous wall-shear stress in wall-bounded turbulent air flows is notoriously difficult. While conventional off-the-shelf flush-mounted hot-film sensors can be calibrated to acquire the time-averaged wall-shear stress, the instantaneous fluctuations are substantially underestimated as heat from the hot film is transferred into the substrate. To address this, nonlinear regression (NLR) is used to calibrate a flush-mounted hot film to enable accurate measurements of instantaneous wall-shear stress in turbulent boundary layers in a wind tunnel. During NLR calibration, the first four moments of wall-shear stress are acquired from either laser Doppler velocimetry (LDV), by linear fitting the streamwise velocity profile from within the viscous sublayer, or from direct numerical simulations matched to experiments by the Reynolds number based on the momentum thickness. The instantaneous wall-shear stress measured by the hot film is recovered with excellent agreement with that measured by LDV placed directly above the sensor. Direct numerical simulations show that the moments of wall-shear stress approach constant values for measurements taken below y Superscript plus Baseline equals 2 y + = 2 $y^+=2$ . Further investigation across different Reynolds numbers shows that all the second to fourth moments follow similar logarithmic trends. Inspired by this result, the sensor can be calibrated using only the first moment obtained in the same flow, while higher moments are estimated as functions of the Reynolds number. The versatility of the NLR approach is demonstrated through two case studies, showing that a posteriori NLR calibration can convert both new hot-film and historical near-wall hot-wire datasets into high-fidelity measurements of instantaneous wall-shear stress and reveal previously inaccessible physical signatures.