Surface Pressure from Skin Friction

This chapter describes extraction of surface pressure from skin friction in complex flows as an inverse problem, focusing on its application to global luminescent oil-film (GLOF) skin friction measurements. The relation between surface pressure and skin friction is the foundation of this method. A variational formulation is given, leading to the Euler-Lagrange equation that is a second-order elliptic-type partial differential equation with the variable coefficients where the Neumann condition is imposed. The numerical algorithm for solving the Euler-Lagrange equation is described, and then the approximate method with a constant boundary enstrophy flux (BEF) is proposed, which is particularly useful for its application to complex flows. The accuracy of this method is evaluated in the Falkner-Skan flow and the separated flow over a 70°-delta wing in simulations. Further, to obtain the normalized surface pressure fields, the approximate method is applied to the skin friction fields obtained by GLOF measurements in the separated flow over a 65°-delta wing and the square junction flow.