Unsteady Flow Around Thin Wings at High Mach Numbers

The perturbation velocity potential for unsteady flow around thin wings is expanded in a series of M~, taking into account linear and second-order terms in perturbation velocities. The first terms for the pressure are seen to be in agreement with those predicted by the Hayes-Lighthill piston theory. Additional terms provided by the present theory give improved accuracy for moderately high Mach Numbers and also take into account some effects of three-dimensionality, such as moderate leading-edge sweep and spanwise downwash variations. Comparison with previous solutions suggests that the present theory is sufficiently accurate for practical purposes down to M = 2. A calculation performed for the simple case of two-dimensional bending-torsion flutter shows good agreement with results obtained from the exact linearized theory for Mach Numbers above 1.5.