The effect of acoustic treatment on unsteady aerodynamic response of oscillating cascade in annular duct with finite extent

This paper develops a model to predict the unsteady aerodynamic response of an oscillating rotor cascade subject to the effect of acoustic treatment within a finite-length annular duct. In this model, the interaction between an oscillating rotor and a lined duct segment of locally reacting impedance is analysed by the transfer element method while the effect of acoustic liner is modelled as distributed monopole sources based on the equivalent surface source method. In an analytical way, the unsteady aerodynamic force distribution on rotor blade surfaces and the corresponding disturbances induced by initial small-amplitude blade oscillation are computed by using the three-dimensional lifting surface theory. Within the linear scope, the primary perturbations induced by initial cascade oscillation and the scattering fields resulted from the interactions between different duct components is superposed to give the total unsteady blade loadings, such that the flutter characteristics of oscillating rotor can be evaluated. It is noteworthy that, combined with a boundary integral approach, the present model considers implicitly the reflections at the duct openings, thus the behaviour of rotor in finite-length duct can be investigated. The numerical calculation reveals a noticeable impact of acoustic treatment on the cascade flutter characteristics.