Data-driven identification of unsteady-aerodynamics phenomena in flapping airfoils

Abstract

This work presents a data-driven approach for the identification of relevant flow features and the breakdown of their contributions to unsteady forces in flapping airfoils. The method exploits the correlation between simultaneous flow-field and force measurements. The Extended Proper Orthogonal Decomposition of flow fields and force is employed to identify relevant flow features and to ascertain their contribution on unsteady aerodynamic loads. The analysis is performed in the wing-fixed non-inertial reference frame to avoid moving boundary effects in the decomposition and to accurately track flow features around the wing. This study discloses new insight into large-oscillation force modelling, allowing linking it to classic unsteady potential theories based on the small oscillations hypothesis. From modal analysis, the force is found to be related to large-scale spatio-temporal structures that model the flow behaviour in the proximity of the wing. Flow features in the mid-far wake are shown to have a negligible effect on the aerodynamic force. Two main spatio-temporal structures are found to be correlated with the loads on the wing. The bulk of chord-normal force oscillations is ascribed to the vorticity production and shedding which models the periodic variation of the circulation around the wing and its release in the wake. An alternating release of vorticity from both sides of the airfoil contributes to the determination of Leading and Trailing Edge Vortices and affects mostly the chord-wise force oscillations. The model retrieved through this approach is closely related to the potential aerodynamic-force models by Theodorsen and Garrick. Chord-normal force can be modelled as a quasi-steady circulatory contribution. The chord-wise force component is modelled by a term that can be assimilated to a non-circulatory force, which is linearly correlated to the airfoil kinematics, and by a term that can be assimilated to the Leading Edge Vortex suction.