Floating element measurements of wall-shear stress exerted by high-Reynolds-number turbulent boundary layers

Indirect methods to obtain the wall-shear stress $\tau_w$, such as the Clauser chart fit, necessitate inherent assumptions of the boundary layer. Therefore, direct methods are preferred to measure $\tau_w$ and subsequently obtain the friction velocity $U_{\tau} = \sqrt{\tau_w/\rho}$. Floating elements are genuinely small to obtain local wall-shear stress measurements, but cope with low signal-to-noise ratios since the signal scales with the surface area $(\propto l^2)$, where $l$ is the characteristic length, and the error forces scale with $hl$; $h$ represents the misalignment of the edges. Therefore, the capacious High Reynolds Number Boundary Layer Wind Tunnel at Melbourne incorporates a large floating element of 3m $\times$ 1m over which the changes in boundary layer parameters are negligible, and hence, local measurements of $U_{\tau}$ are made with high accuracy. Smooth-wall results follow the $U_{\infty}/U_{\tau} = 1/\kappa \ln \left({\rm Re}_{\theta}\right) + C$ trend within $\pm 1\%$ ($\kappa = 0.380$ and $C = 3.7$) for typical test conditions ranging from ${\rm Re}_{\theta} = 15,000$ to $45,000$. Moreover, the device is used to measure $U_{\tau}$ corresponding to rough walls, and boundary layers that are perturbed by flush-mounted control devices within the element.