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

The mean wall shear stress, (tau) over bar (w), is a fundamental variable for characterizing turbulent boundary layers. Ideally, (tau) over bar (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 (tau) over bar (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) x 1 m (spanwise). These dimensions ensure a strong measurement signal, while any error associated with an integral measurement of (tau) over bar (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 (tau) over bar (w)/q(infinity), follow a Coles-Fernholz relation C-f = [1/kappa ln (Re-theta) + C](-2) to within 3 % (kappa = 0.38 and C = 3.7) for a momentum thickness-based Reynolds number, Re-theta > 15,000. The agreement improves for higher Reynolds numbers to <1 % deviation for Re-theta > 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, for which the wall-drag indicates the anticipated trend from the transitionally to the fully rough regime.