The Influence of Variable Flow Velocity on Unsteady Airfoil Behavior

Abstract

The importance of unsteady aerodynamics for prediction of rotor dynamics is unquestioned today. The purpose of unsteady aerodynamic models is to represent the effect of unsteady airfoil motion on the lift, moment and drag characteristics of a blade section. This includes unsteady motion (arbitrary motion) of the airfoil in angle of attack (pitch) and vertical movement (plunge), as well as the effects of an airfoil traveling through a vertical gust field. However, the additional degrees of freedom, namely the fore-aft motion and the unsteady freestream variations commonly are acknowledged, but neglected in virtually all analyses. Since the effect of unsteady freestream results in a stretching and compressing of the shed wake vorticity distribution behind an airfoil, it will have an effect on the airfoil characteristics. The subject of this thesis is to provide a review of the analytic and experimental work done in the area of unsteady freestream and unsteady fore-aft motion, to clarify the limits of the various theories, and to show the differences between them. This will be limited to the attached flow regime since all theories are based on the small disturbance assumption in incompressible flow. As far as possible the theories are compared with experimental data, however most of the available experimental data are confined to stalled flow conditions and are not useful here. In addition to the theories, a semiempirical mathematical model will be used based on the aerodynamics of indicial functions. The purpose is to show the differences of using the theories of unsteady airfoil motion in a constant flow, and those accounting for unsteady freestream flow. This will help to justify whether it is necessary to include the unsteady freestream effect in comprehensive rotor codes. Finally, a generalisation of Isaacs unsteady aerodynamic theory for an airfoil undergoing a frequency spectra in pitch and plunge in a freestream oscillating with the fundamental frequency is presented here for the first time. Therein the axis of rotation of the airfoil is a free parameter.