Wall shear stress measurement by detecting viscous liquid surface deformation in a cavity in incompressible flow

This paper presents a method for measuring the wall shear stress of a flat plate in incompressible flow based on optical measurement of the viscous liquid surface deformation in a cylindrical cavity. The liquid surface deformation is measured by detecting the liquid-surface-deformation-induced displacement field of white dots randomly distributed on the dark bottom of the cavity in images taken by a camera viewing the cavity perpendicularly. Numerical simulations of the flow over a simplified surface model indicate that the liquid surface deformation is caused by the elevated dynamic pressure in the cavity. Further, an analysis based on the similarity law of velocity in a turbulent boundary layer shows there is a functional relationship between the wall shear stress and the light deflection angle charactering the liquid surface deformation. Subsequently, in experiments in a low-speed wind tunnel, the liquid surface deformation is measured using the background-oriented Schlieren (BOS) technique and local velocity profiles are obtained via hot-wire anemometry to infer the wall shear stress in a range of the incoming flow velocities. Therefore, the relationship between the wall shear stress and the light deflection angle induced by the liquid surface deformation is established. The potential error sources are discussed.