Global Skin-Friction Diagnostics Based on Surface Mass-Transfer Visualizations

The theoretical foundations are formulated for extraction of skin-friction fields from surface mass-transfer visualizations with pressure-sensitive paint and sublimating coatings. The asymptotic form of the mass transport equation at a wall is expressed as the optical flow equation in the image plane. Then, a relative skin-friction field is obtained by solving the optical flow equation as an inverse problem via the variational method. For steady-state visualizations with pressure-sensitive paint and sublimating coatings, a relative skin-friction field can be obtained from a single normalized intensity image. Further, a superposition procedure of a snapshot solution and a variation solution associated with the unsteady effect is proposed to reconstruct an unsteady skin-friction field from a time sequence of pressure-sensitive paint visualization images. The capability of the proposed method is examined by applying it to pressure-sensitive paint visualizations in impinging nitrogen jets. This method is also used to extract skin-friction fields from sublimation visualization images on a delta wing in a low-speed flow and on a flat surface in fin shock/boundary-layer interaction at Mach 6. The skin-friction topology in these cases is revealed by using this method. In addition, the limitations of this method are discussed.