Design and validation of an air-bearing-based micro skin-friction balance for small area samples

Abstract

Skin friction, or wall shear stress is a fundamental parameter for characterizing turbulent boundary layer (TBL). Among various methods, the floating element (FE) method has long been advocated and developed. However, accurately measuring WSS for small-area samples remains challenging. This paper proposes air-bearing-based high-resolution micro skin-friction balance and a corresponding sliding-covering measurement method. As an extension of the traditional flush-mounted FE measurement method, it reduces errors caused by the edge gap and gap flow of the floating elements, and employs a clamping mechanism for high-precision assembly, thereby enhancing the measurement efficiency and accuracy for small-area samples. The error sources in balance calibration and measurement were carefully analyzed, with corresponding uncertainty calculated. The measurement range and resolution are $\pm 0.12N$ and $2.5\times 10^{-7}N$, respectively. For a smooth surface, assume the measured force is $1\times 10^{-4}N$, and the measurement precision is approximately $0.047\text{\%}$. The balance is validated using a smooth-wall zero-pressure-gradient TBL. The measured skin-friction coefficient, $C_f\equiv {\bar{\tau }}_w/q_{\infty }$, generally follows a Coles–Fernholz relation $C_f=2{\left(1/\kappa ln\left({\mathrm{Re}}_{\theta }\right)+C\right)}^{-2}$ within $3\text{\%}$ (with chosen constant of $\kappa =0.384$ and $C=4.12$) for a momentum-thickness-based Reynolds number ${\mathrm{Re}}_{\theta }=1050\sim 3361$. Additionally, the skin friction on the surfaces of two envelope materials (EMs) used for airships was measured using the sliding-covering method. The results were compared with those of a smooth surface, revealing that the outer surfaces of EMs exhibited a drag reduction effect at low Reynolds numbers, with further potential for improvement in a broader range of Reynolds numbers. The balance measured the skin-friction differences between samples and revealed that the roughness of the samples affected the precision of the measurements. As a direct measurement method, the results have higher reliability.