Transonic Correction to Theodorsen's Theory for Oscillating Airfoil in Pitch and Plunge Toward Flutter

This paper presents a transonic correction method for an oscillating airfoil in pitch and plunge. The proposed method applies correction functions to the Theodorsen’s theory to capture the transonic nonlinear aero- dynamics. These correction functions apply necessary corrections to the amplitudes and the phase angles of the unsteady lift and pitching moment coefficients to account for transonic aerodynamics. The proposed method also postulates a correction for the motion of the aerodynamic center which could be induced by moving shocks. A series of unsteady RANS CFD simulations of the airfoil at the mean aerodynamic chord of the Transonic Truss-Braced Wing aircraft are conducted using FUN3D to provide data to construct these transonic correction functions. The computed responses of the unsteady lift and pitching moment coefficients using these transonic correction functions match the CFD simulation results very well even when the pitching moment coefficient is highly nonlinear. A flutter analysis of an airfoil in pitch and plunge illustrates the potential use of the proposed transonic correction method.