Enabling instantaneous measurements of wall-shear stress in aerodynamic flows
File(s)
Author(s)
Type
Journal Article
Abstract
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+ =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.
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+ =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.
Date Issued
2026-09-10
Date Acceptance
2026-07-21
Citation
Journal of Fluid Mechanics, 2026, 1042
ISSN
0022-1120
Publisher
Cambridge University Press
Journal / Book Title
Journal of Fluid Mechanics
Volume
1042
Copyright Statement
© The Author(s), 2026. Published by Cambridge University Press This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
License URL
Publication Status
Published
Article Number
A29
Date Publish Online
2026-09-04