Skin Friction from Surface Temperature Visualizations

This chapter describes extraction of a skin friction field from a surface temperature field, which is particularly relevant to global surface temperature diagnostics with temperature-sensitive paint (TSP). First, the exact relation between skin friction and surface temperature is derived from the energy equation for a compressible flow on a curved surface, and the physical meanings of the relevant terms in this on-wall relation are discussed. Then, the variational method is developed to determine a skin friction field from a surface temperature field in the first-order approximation where the source term is modeled. Further, the approximate method is used to study the structure of turbulent wedges on a swept wing in a transonic flow and examine the classical Reynolds analogy from a general theoretical standpoint.