Acquiring accurate measurements of instantaneous wall-shear stresses in wall-turbulent air flows in wind tunnel applications

Accurately measuring the instantaneous wall-shear stress in wall-bounded turbulent air flows is notoriously difficult. While conventional flush-mounted hot-film sensors can be calibrated by standard methods to acquire the mean wall-shear stress, the instantaneous fluctuations of wall-shear are significantly underestimated as heat from the hot-film probe is transferred into the sensor substrate. To address this issue, a new technique using non-linear regression (NLR) is used to calibrate a hot-film sensor to enable accurate measurements of instantaneous wall-shear stresses in turbulent boundary layers. During the NLR calibration process, the first four moments of wall-shear stress are acquired from either Laser Doppler Velocity (LDV), by linear fitting the velocity profile from within the viscous sublayer, or from Direct Numerical Simulation (DNS) data. As a result, the instantaneous wall-shear stress measured by the hot-film sensor matches excellently with the wall-shear stress measured by LDV placed directly above the sensor. Further investigation on different Reynolds numbers showed that the second-order moment is directly proportional to the first-order moment of the wall-shear stress, while the third-order and fourth-order moments are approximately constant over the Reynolds number range investigated. Inspired by this result, it was possible to calibrate the hot-film to accurately measure the instantaneous wall-shear stress with only the first-order moment of wall-shear stress.