Implementation and Linearization of State-Space Free-Vortex Wake Models for Rotary- and Flapping-Wing Vehicles

Abstract

This article describes the implementation and linearization of free-vortex wake models in state-variable form as applied to rotary- and flapping-wing vehicles. More specifically, the wake models are implemented and tested for a UH-60 rotor in forward flight and for a hovering insect representative of a hawk moth. A periodic solution to each wake model is found by time marching the coupled rotor/wing and vortex wake dynamics. Next, linearized harmonic decomposition models are obtained and validated against nonlinear 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. This constitutes a first attempt to extend free-vortex wake methods in state-variable form, originally developed for rotary-wing applications, to flapping-wing flight.