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The noise reduction of a liner placed in the nacelle of a turbofan engine is still difficult to predict due to the lack of knowledge of its acoustic impedance that depends on grazing flow profile, mode order, and sound pressure level. An eduction method, based on a Bayesian approach, is presented here to adjust an impedance model of the liner from sound pressures measured in a rectangular treated duct under multimodal propagation and flow. The cost function is regularized with prior information provided by Guess's [J. Sound Vib. 40, 119-137 (1975)] impedance of a perforated plate. The multi-parameter optimization is achieved with an Evolutionary-Markov-Chain-Monte-Carlo algorithm.

An indirect technique for educing the homogenized acoustic impedance of a liner mounted on the wall of a barrel is presented. It is based on measurements and computational simulations of the multimodal scattering matrix of this lined duct. Measurements are performed with a multisource method and the use of an anechoic duct termination. The numerical computation of the scattering matrix relies on a finite element model, and assume that the duct is axisymmetric and uniformly covered by a locally reacting material. The impedance is educed by minimizing the difference between the theoretical and experimental acoustic power dissipations, which are deduced from the scattering matrix. The source is an incoming pressure field generated at one end of the duct only and composed of all cut-on modes. This technique was tested on a cylindrical barrel whose wall was partially lined with a realistic, locally reacting material made of honeycomb cells and a perforated facing sheet. Results for the acoustic impedance are compared with those deduced from semiempirical models and the experimental two microphone method. The best agreement with the indirect method is found with the semiempirical impedance results when the difference between the acoustic power dissipated by the actual lined barrel and the reference barrel is chosen as the cost function of the minimizing procedure.

An analytical three dimensional bicylindrical model is developed in order to take into account the effects of the saddle-shaped area for the interface of a n-Herschel-Quincke tube system with the main duct. Results for the scattering matrix of this system deduced from this model are compared, in the plane wave frequency domain, versus experimental and numerical data and a one dimensional model with and without tube length correction. The results are performed with a two-Herschel-Quincke tube configuration having the same diameter as the main duct. In spite of strong assumptions on the acoustic continuity conditions at the interfaces, this model is shown to improve the nonperiodic amplitude variations and the frequency localization of the minima of the transmission and reflection coefficients with respect to one dimensional model with length correction and a three dimensional model.

A flow duct acoustic facility was developed to measure liner efficiency in attenuating higher order acoustic duct modes propagation conditions with mean air flow. The method is based on measurement, upstream and downstream of a liner, of the acoustic power produced by a periodic source. Directly measured total or modal acoustic powers are deduced from the local measurement, in both cross sections, of acoustic pressure, axial acoustic particle velocity, and axial mean flow velocity which are supplied by a probe made of a microphone and a single hot film. In this paper, the equipment, signal processing, and the data treatment process of this facility are first described. Then, information on the accuracy of the methodology is provided by a validation test performed with a rigid wall duct section. Finally, the results of an experiment carried out with a locally reacting liner and a mean flow velocity of 20 m/s will be presented. Measurements of the main attenuation frequency and of the main total acoustic power dissipated agree with the values for which the liner was designed. These results point out the limitations of the method presented to sources with high-level periodic sounds to provide a sufficient signal-to-noise ratio, the noise being produced by fluctuations of the turbulent flow.