Predicting Lift in Unsteady Separated Flows using Classical Aerodynamics

Large force transients produced during transverse wing-gust encounters can lead to permanent structural damage or catastrophic loss of control. Predicting these force transients is an important task that can aid in the development of effective and robust flight controllers. Despite its simplicity, Kussner's unsteady aerodynamics model has shown tremendous agreement with data for a wide range of gust ratios and gust profiles. This is a surprising result as large-amplitude gust encounters are known to possess substantial amounts of flow separation and the model was developed for wings under attached flow conditions. In this work we elucidate the mechanisms by which this potential flow model predicts the lift transients of separated flows. It is found that the bound circulation in Kussner's model approximates the circulation of the leading-edge vortex (LEV) - bound vortex pair in large-amplitude transverse gust experiments. Furthermore, it is found that for short-duration gusts, the LEV remains attached to the wing, thus permitting the model to capture the effective impulse of the flow. These findings make it possible to extend application of Kussner's model to large-amplitude, short-duration gusts, as well as offer perspective on its limitations and possible extensions.