Dispersion, dissipation and refraction of shock waves in acoustically treated turbofan inlets

This paper describes a numerical investigation of the effects of the inlet duct liner on the acoustics of a high-bypass ratio turbofan rotor operating at supersonic tip relative flow conditions. The near field of the blade row is then composed of periodic shocks that evolve spatially both because of the varying mean flow and because of the presence of acoustic treatment. The evolution of this shock system is studied using a Computational Fluid Dynamics-based method incorporating a wall impedance boundary condition. The configuration examined is representative of a fan operating near the takeoff condition. The behavior of the acoustic power and the associated waveforms reveal that significant dispersion occurs to the extent that there are no shocks in the perturbation field leaving the entrance plane of the duct. The effect of wave refraction due to the high degree of shear in the mean flow near the entrance plane of the inlet is examined, and numerical experiments are conducted to show that the incorporation of liners in this region can be highly beneficial. The implications of these results for the design of aircraft engine acoustic liners are discussed.