Direct Solution of an Analytical Model to Investigate Duct Acoustic Treatments at Low and High Frequencies

• Analytical model for computing acoustic flow in a fan intake • Suitable for flutter bite and noise studies at low and high frequencies • Supports arbitrary number of acoustic treatments in the model • Well-conditioned formulation enables use of direct solvers • Application to the contribution of liners to fan flutter Acoustic treatments are used in modern aeroengines to reduce community noise. Recent studies have highlighted an acoustic-driven instability known as flutter bite. This phenomenon arises at frequencies lower than those associated with noise, where an upstream acoustic wave, generated by fan vibration, is reflected at the duct inlet, forming a feedback loop. To study acoustic behavior over a wide frequency range, we introduce a new model. It consists of an annular duct with an arbitrary number of sections, each potentially featuring different acoustic treatments. The acoustic wave propagation inside the intake is solved analytically, and a mode-matching technique is employed to handle transitions between sections. Unlike previous approaches, we formulate the problem to obtain a numerically well-conditioned linear system, enabling the use of direct solvers instead of iterative ones. We discuss the convergence with respect to the number of radial modes and improve it through an appropriate choice of projection functions, even for low impedance values. Two illustrative applications are presented: the analysis of flutter bite in a fan intake with a single liner, and a study of the effect of multiple acoustic treatments.