High frequency thin-airfoil theory for subsonic flow

A large parameter solution procedure of Schwartzschild and Landahl is adapted to the task of calculating closed-form approximate solutions for the pressure and lift of a flat-plate, infinite-span airfoil. Two general cases are treated: 1) the two-dimensional subsonic flow problem, in which the large parameter is the upwash frequency, and 2) the three-dimensional incompressible flow problem, in which the large parameter is the spanwise wavenumber of the upwash. For the first case, the four problems of a gust drifting with the freestream, a gust moving at other than the freestream velocity, a plunging motion, and a linear upwash are treated. For the second case, the two problems of a gust drifting with the freestream and a generalized gust moving at other than the freestream velocity are considered. Comparison of the solutions with available numerical results generally shows good agreement when the appropriate parameter is large. The solutions for the gust convecting with the freestream for both the two-dimensional compressible and the three-dimensional incompressible cases were derived previously by Adamczyk using the Wiener-Hopf technique.