Extended theodorsen function for an airfoil with a wake

Abstract

An extension of classical theories for a two-dimensional thin airfoil oscillating in an incompressible flow is achieved by assuming arbitrary and constant convection velocity of the wake vortices. The well-known Theodorsen function is replaced by different functions composed of the Theodorsen function and a new function. Their vector properties, which depend on the magnitude of the convection velocity of the wake vortices, are presented. The extended results include classical theories as special cases.