AN ANALYTICAL INVESTIGATION OF THE ATTENUATION PERFORMANCE OF DUCTS UNDER MEAN FLOW AND LINED WALLS
Turbo machines; compressors; turbines.
Turbo machines such as fans, compressors and turbines are among the most important sources of aeroacoustic noise. Typically, the aeroacoustic interaction between the rotor and stator blades of aeronautical turbofan generates tonal noises that propagate along the nacelle duct and has great contribution in the total aeronautical noise generated by modern aircraft. The acoustic modes generated from this interaction depend on the number of blades of the rotor and the stator, known as the Tyler and Sofrin relationship. In this sense, acoustic liners used in the nacelle walls are commonly used for noise control, using the Helmholtz resonator mechanism for acoustic attenuation. In this work, an analytical investigation is proposed for the acoustic modes resulting from the rotor-stator iteration of lined ducts with mean flow. Despite of the existence of analytical expression, these are not in closed form expression and require numerical schemes for root-finding in transcendental equations while also tracking their corresponding modes over a certain frequency band. Subsequently, these results are used to construct the wave dispersion curve of the acoustic modes, i.e., their wavenumber as a function of the frequency. From these curves, the attenuation performance of the liners can be investigated based on the frequency of the cut-on mode and on the behaviour of the imaginary part of the wavenumber. First, a numerical validation of the implemented methodology, using the Muller’s method, is proposed using results from the literature. Then, three different models for liners are investigated, the Tam and Auriault model, and the single degree of freedom and the two degrees of freedom Helmholtz resonator models. The evolution of the radial mode shapes along the frequency is also shown and discussed. In addition, the physical interpretation of the obtained dispersion curves for the different liners’ models is discussed. It is shown that they present significant qualitative and quantitative differences in terms of attenuation performance and main attenuation mechanism. The proposed approach has the potential of being used as a low cost computational design methodology for acoustic attenuation in lined ducts.