Semi-analytical unsteady aerodynamic modeling of a flexible thin airfoil in arbitrary motion

A semi-analytical formulation based on conformal mapping is presented to predict the unsteady aerodynamic loads on a thin airfoil undergoing arbitrary rigid-body motion and chordwise deformation. Stemming from a previous modeling for a flat plate, a generalized conformal map is introduced to include airfoil flexibility. The unsteady flow is described by means of a complex potential, and a novel point vortex method is proposed to model wake shedding from the airfoil trailing edge.The aerodynamic loads on the section are evaluated analytically, which gives insight into effects of flexibility and free wake. The formulation is specialized to particular choices of the conformal map order, which fixes the degrees of freedom to represent chordwise deformation, and implemented to simulate a flexible airfoil in large-amplitude imposed motion.