Skin Friction from Surface Pressure Visualizations

This chapter discusses extraction of a skin friction field from a surface pressure field, which is particularly relevant to global surface pressure diagnostics with pressure sensitive paint (PSP). First, the exact relation between skin friction and surface pressure is derived from the Navier-Stokes (NS) equations for a compressible flow on a curved surface. The physical meanings of the relevant terms in this on-wall relation are discussed, including the boundary enstrophy flux (BEF) and the effects of the surface curvature. Then, the variational method is developed to determine a skin friction field from a surface pressure field in the first-order approximation where the BEF is modeled (approximated). Further, the approximate method is applied to reconstruction of the elemental structures of separated flows and extraction of the skin friction topology in incident and swept shock-wave/boundary-layer interactions.