Implementation and Linearization of a State-Space Free Wake Model with a Near-Wake Vortex Lattice Model

This paper describes the implementation and linearization of a state-space free-vortex wake model with a near-wake vortex lattice model as applied to a helicopter rotor. Following a detailed mathematical description, the wake model is implemented for a blade element model of a utility helicopter rotor and tested in multiple flight conditions including hover, forward flight, and vortex ring state (VRS), and for simple control inputs. The model is qualitatively verified against a Vortex Particle Method (VPM). Periodic solutions to the wake model are found by time marching the coupled rotor and vortex wake dynamics for the operating conditions mentioned above. 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.