An alternative floating element design for skin-friction measurement of turbulent wall flows

Abstract

Indirect methods to estimate surface shear stress are commonly used to characterise rough-wall boundary-layer flows. The uncertainty is typically large and often insufficient to carry out quantitative analysis, especially for surface roughness where established scaling and similarity laws may not hold. It is, thus, preferable to rely instead on independent measurement techniques to accurately measure skin friction. The floating element was one of the first to be introduced, and still is the most popular for its features. Although its fundamental principle has remained unchanged, different arrangements have been suggested to overcome its inherent limitations. In this paper, we review some of these designs and further present an alternative that is able to correct for extraneous loads into the drag measurement. Its architecture is based on the parallel-shift linkage, and it features custom-built force transducers and a data acquisition system designed to achieve high signal-to-noise ratios. The smooth-wall boundary-layer flow is used as a benchmark to assess the accuracy of this balance. Values of skin-friction coefficient show an agreement with hot-wire anemometry to within 2% for Re_{theta } = 4times 10^3 up to 10^4. A rough surface of staggered distributed cubes with large relative height, delta /hsimeq 10, is also investigated. Results indicate the flow reaches the fully rough regime, at the measurement location, for the entire range of Reynolds number. Furthermore, the values of skin friction agree with existing estimations from alternative methods.Graphical abstractDrawings of the floating-element (FE) balance and skin-friction measurements for a smooth-wall boundary layer. On top: slice along the X-Y plane and top view (left) next to their corresponding pictures (right). Colors highlight distinctsubsystems, namely, the floating frame for drag measurement (yellow), the pitching moment mechanism (red) and the acquisitionsystem (blue). Bottom left: smooth-wall setup and calibration system. The FE is flush mounted with the wind tunnel floor and thepulley is attached to a linear traverse which allows setting its position at different wall-normal locations. During calibration, a lid isremoved to make way for the pulley to move into the test section. A wire is then strung over to suspend the weights. Bottom right: Skin friction over a smooth wall. The inset indicates the relative discrepancy between the FE values (blue) and those inferred fromhot-wire anemometry of the boundary-layer profile (red).