On the high-frequency response of unsteady lift and circulation: A dynamical systems perspective

Abstract

In this paper, we consider the unsteady aerodynamics of a two-dimensional airfoil as a dynamical system whose input is the angle of attack (or airfoil motion) and output is the lift force. Based on this view, we discuss the evolution of lift and circulation from a purely dynamical perspective through step response, frequency response, transfer function, etc. In particular, we point to the relation between the high-frequency gain of the transfer function and the physics of the development of lift and circulation. Based on this view, we show that the circulatory lift dynamics is different from the circulation dynamics. That is, we show that the circulatory lift is not lift due to circulation. In fact, we show that the circulatory–non-circulatory classification is arbitrary. By comparing the steady and unsteady thin airfoil theory, we show that the circulatory lift possesses some acceleration (added-mass) effects. Finally, we perform simulations of Navier–Stokes equations to show that a non-circulatory maneuver in the absence of a free stream induces viscous circulation over the airfoil.