Wall-drag measurements of smooth- and rough-wall turbulent boundary layers using a floating element

AbstractThe mean wall shear stress, $$\overline{\tau }_w$$τ¯w, is a fundamental variable for characterizing turbulent boundary layers. Ideally, $$\overline{\tau }_w$$τ¯w is measured by a direct means and the use of floating elements has long been proposed. However, previous such devices have proven to be problematic due to low signal-to-noise ratios. In this paper, we present new direct measurements of $$\overline{\tau }_w$$τ¯w where high signal-to-noise ratios are achieved using a new design of a large-scale floating element with a surface area of 3 m (streamwise) × 1 m (spanwise). These dimensions ensure a strong measurement signal, while any error associated with an integral measurement of $$\overline{\tau }_w$$τ¯w is negligible in Melbourne’s large-scale turbulent boundary layer facility. Wall-drag induced by both smooth- and rough-wall zero-pressure-gradient flows are considered. Results for the smooth-wall friction coefficient, $$C_f \equiv \overline{\tau }_w/q_{\infty }$$Cf≡τ¯w/q∞, follow a Coles–Fernholz relation $$C_f = \left[ 1/\kappa \ln \left( Re_{\theta }\right) + C\right] ^{-2}$$Cf=1/κlnReθ+C-2 to within 3 % ($$\kappa = 0.38$$κ=0.38 and $$C = 3.7$$C=3.7) for a momentum thickness-based Reynolds number, $$Re_{\theta } > 15{,}000$$Reθ>15,000. The agreement improves for higher Reynolds numbers to <1 % deviation for $$Re_{\theta } > 38{,}000$$Reθ>38,000. This smooth-wall benchmark verification of the experimental apparatus is critical before attempting any rough-wall studies. For a rough-wall configuration with P36 grit sandpaper, measurements were performed for $$10{,}500< Re_{\theta } < 88{,}500$$10,500