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In this paper, the acoustic impedance of a liner is educed by a novel semi-analytical inverse technique. The liner sample is placed flush with the solid walls in a rectangular duct with grazing flow. The technique uses complex acoustic pressure measured at four positions at the wall of the duct, upstream and downstream of the lined section, and educes the impedance with a mode-matching method. Previous studies neglected grazing flow nonuniformity and the pressure discontinuity that appears at the liner-wall boundary caused by the discontinuity of the acoustic particle velocity into the wall. In the present paper, the mode-matching formulation is rederived in terms of pressure instead of velocity potential which is found to be more numerically stable. Moreover, the proposed methodology is validated with benchmark data from an experiment performed by NASA. First, the ability of the code to reproduce the pressure field for a given impedance is tested. Second, the ability to educe the correct impedance for a given pressure distribution is tested. The results of the mode-matching code are in very good agreement with the experimental data. The effect of shear flow is investigated and it can be concluded that the assumption of uniform flow is appropriate for the chosen liner, duct size, and frequency range of interest. DOI: 10.2514/1.41647

A three-dimensional linearized Euler model is developed for the interaction and scattering of unsteady incident disturbances by an annular cascade of unloaded blades. The model is first used to examine the validity of the popular two-dimensional strip theory for three-dimensional annular cascades at frequencies relevant to fan engine noise. It is then applied to investigate three methods of passive control for turbofan tonal noise, namely, blade lean, blade sweep, and mean flow acceleration. Because blade lean and sweep generally enhance the blade upwash radial phase variation, an analysis is carried out to examine the effects of the radial modulation of the incident disturbances on the annular cascade sectional lift and the modal acoustic response. Noise control by blade lean and sweep is then investigated for typical fans. The results show that blade lean or sweep can be designed to be effective noise reduction mechanisms; however, their effectiveness depends on the characteristics of the incident disturbances and the number of propagating duct modes. Converging ducts are also shown to be effective sound reduction mechanisms.