A lightweight vortex model for unsteady motion of airfoils

Abstract

A low-order vortex model has been developed for analysing the unsteady aerodynamics of airfoils. The model employs an infinitely thin vortex sheet in place of the attached boundary layer and a sheet of point vortices for the shed shear layer. The strength and direction of the vortex sheet shed at the airfoil trailing edge are determined by an unsteady Kutta condition. The roll-up of the ambient shear layer is represented by a unique point vortex, which is consistently fed circulation by the last point vortex of the free vortex sheet. The model's dimensionality is reduced by using three tuning parameters to balance representational accuracy and computational efficiency. The performance of the model is evaluated through experiments involving impulsively started and heaving and pitching airfoils. The model accurately captures the dynamics of the development and evolution of the shed vortical structure while requiring minimal computational resources. The validity of the model is confirmed through comparison with experimental force measurements and a baseline unsteady panel method that does not transfer circulation in the free vortex sheet.