Theoretical Aerodynamic Properties of Vanishing Aspect Ratio Harmonically Oscillating Rigid Airfoils in a Compressible Medium

Abstract

Theoretical solutions are given in terms of tabulated Mathieu functions for the aerodynamic properties of rigid vanishing aspect ratio harmonically oscillating airfoils in a compressible medium for the complete range of reduced frequencies. The significant variable introduced in defining the oscillatory coefficients when the flow is compressible is the single entity, kQM, and Mach Number variations enter only through this quantity. Numerical coefficients are tabulated for use in evaluating the expressions for lift, pitching, and rolling moment for the rectangular and triangular plan forms. Comparisons of the oscillatory coefficients based on compressible and incompressible flow indicate that, for the range of reduced frequencies applicable for flutter, the effects of compressibility can be considered negligible.