Abstract:
This paper demonstrates extraction of linear models from a state-space free wake model by applying analytical linearization, extending the research presented in (Ref. 1). Two distinct Linear Time Invariant (LTI) models are developed: the first is a high-order LTI model derived from the direct conversion of the analytical Linear Time Periodic (LTP) model, and the second is a reduced-order LTI model generated by first applying the Proper Orthogonal Decomposition (POD) model order reduction technique to the LTP model, followed by conversion. In both cases, the LTP-to-LTI conversion is achieved using harmonic decomposition. A substantial reduction in the number of wake states, from 15552 to 4050, is accomplished while maintaining a similar degree of accuracy. The time domain responses of step and doublet inputs for rotor collective and cyclic pitch are analyzed by comparing the GENHEL rotor model coupled with the LTI wake against the non-linear free wake model. Good agreement is observed in the rotor forces and hub moments. The paper investigates the feasibility of converting the linearized wake model into a linear parameter-varying inflow model with radial and azimuthal basis functions representative of a Peters-He inflow model. A least squares mapping technique is used to derive equivalent Peters-He inflow coefficients which are shown to accurately model the inflow distribution over the rotor disk and the time variation in induced velocities when compared to the non-linear free wake model.