Linearized Models of the Coupled Rotorcraft Flight Dynamics and Acoustics for Real-Time Noise Prediction

This article demonstrates the linearization of the coupled rotorcraft flight dynamics and aeroacoustics to provide realtime acoustic predictions in generalized maneuvering flight. To demonstrate the methodology, the study makes use of a nonlinear simulation model of a generic utility helicopter (PSUHeloSim) that is coupled with an aeroacoustic solver based on a marching cubes algorithm. A periodic equilibrium of the coupled rotorcraft flight dynamics and acoustics is first found at a desired flight condition using a modified harmonic balance trim solution method. Next, the nonlinear time-periodic dynamics are linearized about that periodic equilibrium and transformed into an equivalent higher order linear time-invariant system in harmonic decomposition form. Composite aeroacoustic measures are included as an output of this system. To speed up runtime and make control design tractable, the order of these harmonic decomposition models is reduced via residualization to an 8-state model where the states are representative of the rigid-body dynamics of the aircraft. This 8-state model is shown to provide accurate acoustic response predictions for small-amplitude pilot inputs and to abate runtime by a factor of approximately 104, thus enabling acoustic predictions in generalized maneuvering flight that are significantly faster than real time. The 8-state model is subsequently used to demonstrate the use of linear system tools for the dynamic analysis of the coupled rotorcraft flight dynamics and acoustics.