Implementation and Linearization of a State-Space Free-Vortex Wake Model for Flapping-Wing Flight

This paper describes the extension of a free-vortex wake method in state-variable form originally developed for rotary-wing applications to flapping-wing flight. Following a detailed mathematical description, the wake model is implemented for a hovering insect representative of a hawk moth. A periodic solution to the wake model is found at hover using a modified harmonic balance algorithm. Next, linearized harmonic decomposition models are obtained and validated against the nonlinear dynamics using simulations. Order reduction methods are explored to guide the development of linearized wake models that provide increased runtime performance compared to the nonlinear and linearized harmonic decomposition wake models while guaranteeing satisfactory prediction of the periodic response of the wake.