Continuation Method for Calculation of Transonic Airfoil Flutter Boundaries

Abstract

Flutter boundaries, through variations in aerodynamic and structural dynamic parameters, are computed for a NACA 64A006 airfoil at transonic freestream Mach numbers with pitch-and-plunge structural coupling. These e utter boundaries are obtained with a new continuation algorithm that specie cally accounts for e utter onset. The algorithm, which is based on pseudoarclength continuation, solves an extended form of the Euler equations for the reduced velocity at e utter onset, the corresponding base-e ow solution, the destabilizing mode at e utter onset, and thecritical valueofa secondarystructural parameter, e.g., structural damping. Thealgorithm providesa relatively automated procedure for computing e utter boundaries directly, which avoids a trial-and-error, e utter-detection process typical of time-domain techniques. The current method is validated through comparison with independent e utter-boundary computations. Grid-sensitivity studies are carried out to assess the numerical accuracy of computed solutions.