Wall shear stress measurement using a zero-displacement floating-element balance

Abstract

The floating-element (FE) principle, introduced nearly a century ago, remains one of the most versatile direct wall shear stress measurement methods. Yet, its intrinsic sources of systematic error, associated with the flow-exposed gap, off-axis load sensitivity, and calibration, have thus far limited its widespread application. In combination with the lack of standard designs and testing procedures, measurement reliability still hinges heavily on individual judgement and expertise. This paper presents a framework to curb these limitations, whereby the design and operation of a FE balance are leveraged by an analytical model that attempts to capture the behaviour and predict the relative contribution of the systematic sources of error. The design is based on a parallel-shift linkage and a zero-displacement force-feedback system. The FE has a surface area of 200×200\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$200\ imes 200\\,$$\\end{document} mm, and measurement sensitivity is adjustable depending on the surface condition and the Reynolds number. It is thus suitable for application in a wide range of low-speed, boundary-layer wind tunnels, small or large scale. Measurements of the skin friction coefficient over a smooth wall show a remarkable agreement with oil-film interferometry, especially for Reθ>1.3×104\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\rm Re}_{\ heta } > 1.3 \ imes 10^4$$\\end{document}. The discrepancy relative to the empirical Coles–Fernholz relation (κ=0.39\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa = 0.39$$\\end{document} and C=4.352\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C = 4.352$$\\end{document}) is within 0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.5\\,$$\\end{document}%, and the level of uncertainty is below 1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\,$$\\end{document}% for a confidence interval of 95\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$95\\,$$\\end{document}%.