Investigation of the unsteady responses of airfoils due to small-scale motion

Abstract

Unsteady pressures, forces, and pitching moments generated by foils experiencing vibratory motion in an incompressible, attached flow configuration are studied within this work. Specifically, two-dimensional, unsteady potential flow calculations are performed on Joukowski foils of varying thickness undergoing variable amplitude, small-scale, heaving or pitching motion over a range of reduced frequencies between 0.01 and 100. These calculated results are compared directly to predictions from implementing the Theodorsen model, which treats foils as infinitely thin flat plates that shed a planar sheet of vorticity. The effects of relaxing these seemingly strict assumptions of the Theodorsen model are explored, and focus is placed on results which show deviations from the Theodorsen model. These include altered unsteady responses for finitely thick foils and non-zero mean angle of attack conditions, non-linearity of the wake of shed vorticity, and analysis of the unsteady streamwise force. Further, within the potential flow framework the particular terms which control the unsteady responses are identified.