Skin Friction Fields and Surface Dye Patterns on Delta Wings in Water Flows

Abstract

This paper discusses the relationship between skin friction fields and surface dye patterns in surface luminescent dye visualizations in water flows, providing a theoretical foundation for extraction of high-resolution skin friction fields. The limiting form of the mass diffusion equation at a wall is recast as an optical flow equation connecting skin friction with the luminescent dye intensity. Snapshot solutions are obtained from a time sequence of luminescent intensity images by solving the optical flow equation via the variational method, and then a normalized skin friction field is reconstructed by averaging the snapshot solutions. An error analysis is given to identify the major error sources and the limitations of the technique. To evaluate the feasibility of this technique, surface luminescent dye visualizations on a 65 deg delta wing and a 76/40 deg double-delta wing are conducted in a water tunnel. The extracted skin friction topology on the delta wings and the velocity fields obtained by using particle image velocimetry (PIV) are discussed.