Low Frequency Oscillations Of Thin Airfoils In Subsonic Compressible Flows

*† New and efficient analytical solutions are presented in this paper for the unsteady subsonic compressible flows past rigid and flexible airfoils executing low frequency oscillations. These solutions are obtained using a specially developed method based on velocity singularity associated with the airfoil leading edge and ridges (defined by the changes in the boundary conditions). Efficient analytical solutions in closed form are presented for the unsteady lift and pitching moment coefficients and for the chordwise distribution of the unsteady pressure difference coefficient in the general case of rigid or flexible airfoils executing oscillatory rotations and translations and flexural oscillations. A detailed analysis of the variations of these aerodynamic coefficients with the Mach number and with the reduced frequency of oscillations is also presented for the cases of oscillatory pitching rotations and normal-to-chord translations of rigid airfoils and for the flexural oscillations of flexible airfoils. The present solutions were found in very good agreement with previous incompressible flow results obtained in the limit case of incompressible flows by Theodorsen, Postel & Leppert and Mateescu & Abdo, and with previous compressible flow results.