Wall-shear-stress measurements using volumetric µPTV

Abstract

Accurately determining the wall-shear-stress, tau _textrm{w}, experimentally is challenging due to small spatial scales and large velocity gradients present in the near-wall region of turbulent flows. To avoid these resolution requirements, several indirect iterative fitting methods, most notably the Clauser chart method, exist for determining overline{tau }_{w} by fitting the mean velocity profile further away from the near-wall region in the log-law layer. These methods often require proper selection of fitting constants, assumptions of a canonical flow state, and other empirical-based generalizations. To reduce the amount of ambiguity, determining the near-wall velocity gradient by assuming a linear relationship between the mean streamwise velocity and wall normal distance in the viscous sublayer can be used. However, this requires an accurate unbiased measurement of the near-wall velocity profile in the region below five viscous spatial units, which can be less than 50 µm for high Reynolds number flows. Therefore, in this study a method for a volumetric defocusing microparticle tracking velocimetry method is presented that is capable of resolving the flow in the viscous sublayer of a turbulent boundary layer up to U_{textrm{e}}=44.7,m/s (Re_{theta }=27250). This method allows for the measurement of the near-wall flow through a single optical access for illumination and imaging and serves as an excellent complement of larger scale measurements that require near-wall information. The overline{tau }_textrm{w} values determined from the defocusing approach were found to be in good agreement values obtained from a simultaneous parallax PTV measurement. Furthermore, analysis of the diagnostic plot and cumulative distribution of measured fluctuations in the near-wall region, showed that both methods are capable of accurately determining mean velocity and fluctuation profiles in the self-similar viscous sublayer region.