Two-dimensional incompressible unsteady airfoil theory—An overview

Two-dimensional unsteady airfoil theory has a history that dates back at least 75 years. Closed-form solutions have been obtained for airfoil loads due to step response (either to a pitch input or to a gust), due to airfoil oscillations in the frequency domain, and due to generalized airfoil motions in the Laplace domain. It has also been shown that the response of airloads to airfoil motions can be formulated in state space in terms of ordinary differential equations that approximate the airfoil and flow field response. The more recent of these models are hierarchical in that the states represent inflow shape functions that form a convergent series in a Ritz–Galerkin sense. A comparison of the various approaches with each other and with alternative computational approaches yields insight into both the methodologies and the solutions.