Implementation and Analytical Linearization of a Rotor Simulation with a Coupled Panel and Vortex Particle Method in State-Space Form

This article describes the implementation and analytical linearization of a dynamic rotor simulation with a coupled panel and vortex particle method in state-variable form. Panels are used to model the wing/blade surface as well as the near wake, whereas vortex particles are used to model the far wake. The coupled panel and vortex particle dynamics are formulated as a nonlinear time-periodic system of ODEs in the first-order form to be self-contained and inherently linearizable. Linearization of this coupled panel and vortex particle method is demonstrated via finite differencing and a novel analytical linearization technique to yield a linear time-periodic (LTP) representation. Harmonic decomposition is used to approximate the LTP dynamics with a linear time-invariant system so as to be suitable for time-invariant system analyses. The code is implemented in MATLAB® for a generic utility helicopter rotor blade and validated against an open-source vortex particle method. The linearized models are verified against the nonlinear dynamics both in time and frequency domains. Linearized models accurately represent the wake dynamics of the equilibrium condition for moderate amplitude and frequency forcing inputs. Analytical linearization is shown to abate the cost of linearization over perturbation methods by O(n2), where n is the total number of states of the system. Linearized models of the coupled panel and vortex particle dynamics have applications in the flight dynamics of rotary-wing vehicles, where these dynamics can be used to augment the rigid-body dynamics.