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<p>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 mode selection rule. In this sense, acoustic liners used in the nacelle walls are commonly used for noise control. In this work, an analytical investigation is proposed for the acoustic modes resulting from the rotor-stator interaction of lined ducts with mean flow. Despite the existence of analytical expression, these are not in closed form expression and require numerical methods for root-finding in transcendental governing equations, while also tracking their corresponding modes over a certain frequency band. This is used to construct the wave dispersion curve of the acoustic modes, i.e., their wavenumber as a function of the frequency, from which the attenuation performance of the liners can be investigated based on the cut-on frequency of acoustic modes 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 by using results from the literature. Then, three different models for liners are investigated, the <i>Tam and Auriault</i> model, 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.</p>

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An analytical investigation of acoustic waves in ducts with lined walls under mean flow

  • 期刊论文

  • 发表日期：

    2025年5月14日

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  • Guilherme A. D. da Silva,
  • Braulio G. Pimenta,
  • Roberto F. B. Miserda,
  • Adriano T. Fabro

摘要

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 mode selection rule. In this sense, acoustic liners used in the nacelle walls are commonly used for noise control. In this work, an analytical investigation is proposed for the acoustic modes resulting from the rotor-stator interaction of lined ducts with mean flow. Despite the existence of analytical expression, these are not in closed form expression and require numerical methods for root-finding in transcendental governing equations, while also tracking their corresponding modes over a certain frequency band. This is used to construct the wave dispersion curve of the acoustic modes, i.e., their wavenumber as a function of the frequency, from which the attenuation performance of the liners can be investigated based on the cut-on frequency of acoustic modes 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 by using results from the literature. Then, three different models for liners are investigated, the Tam and Auriault model, 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.