Optimum Acoustic Impedance for a Finite-Length Nacelle Liner of Turbofan Engine

The Cremer concept is an efficient analytical impedance-optimization method for an infinitelined duct, however which is invalid for a finite liner in practice, e.g., the aero-eigine nacelle liner with a short length to radius ratio L/R. Recently, the authors proposed an axial wave number merging design method (AWMDM) for a finite circular lined duct in the absence of flow, which achieves the optimum design for a not-too-short liner such as the automotive muffler and the ventilation system. Moreover, the Cremer concept is a particular case of the AWMDM at q=0, where q is the periodic number of the axial oscillations of the total cross-modal power. This paper is the first time to apply the proposed method to the front-nacelle liner of aero-engine, which faces the dual challenges of the mean flow and the short length. First, the AWMDM in the present of uniform flow is derived, in which the effect of flow is mainly reflected in the dispersion relation and the acoustic power expression. Then, taken the Fan-200 as an example, which is a low-speed fan test rig, the optimum impedances designed by the AWMDM of q=0 and1 are evaluated through both the in-duct transmission loss (TL) and far field noise reduction. For in-duct prediction, the finite element method is used to validate the correctness of the theoretical derivation, which assumes the single-mode incidence and non-reflecting terminations. For far-field prediction, the nonlinear harmonic (NLH) method is used for the computation of acoustic sources, and the boundary integral element method (BIEM) is for the acoustic prediction module. The in-duct result shows that the design of AWMDM q=1 consistently out performs the design of AWMDM q=0 in the liner length scope of L/R=0.5-1.5, although the extremely short liner length destroys the optimal condition for the total cross-modal power to reach the wave trough at the liner exit. In constract, the far-field result shows that the design of AWMDM q=0 is somewhat better than the design of AWMDM q=1, possibly due to the strong reflection from the fan inlet causing a difference in the mode matching at the liner exit compared to the case without reflection.