Theoretical solutions for unsteady compressible subsonic flows past oscillating rigid and flexible airfoils

Abstract

This paper presents simple and efficient analytical solutions for unsteady compressible subsonic flows past flexible airfoils executing low frequency oscillations. These analytical solutions are obtained with a method using velocity singularities related to 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 normal-to-chord translations and flexural oscillations. The method has been validated for the pitching and plunging oscillations of the rigid airfoils by comparison with results based on Jordan's data for compressible flows and by comparison with the solutions obtained by Theodorsen, Postel and Leppert and Mateescu and Abdo for the limit case of incompressible flows. A detailed analysis of the variations of the 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. Efficient analytical solutions are presented for the flexural oscillations of airfoils in compressible flows, which can be efficiently used in solving aeroelastic interaction problems.