The problem of the transmission of sound in a duct with very thin shear layers at the walls is treated by an inner expansion method. The results show that the formulation of the problem of the transmission of sound in a duct with a shear layer at the wall converges, in the case of a vanishingly thin shear layer, to the formulation of the same problem when uniform flow is assumed and the wall boundary condition is that of continuity of particle displacement.

An explicit, analytical, multiple-scales solution for modal sound transmission through slowly varying ducts with mean flow and acoustic lining is tested against a numerical finite-element solution solving the same potential flow equations. The test geometry taken is representative of a high-bypass turbofan aircraft engine, with typical Mach numbers of 0.5-0.7, circumferential mode numbers m of 10-40, dimensionless wavenumbers of 10-50, and both hard and acoustically treated inlet walls of impedance Z = 2 − i. Of special interest is the presence of the spinner, which incorporates a geometrical complexity which could previously only be handled by fully numerical solutions. The results for predicted power attenuation loss show in general a very good agreement. The results for iso-pressure contour plots compare quite well in the cases where scattering into many higher radial modes can occur easily (high frequency, low angular mode), and again a very good agreement in the other cases.

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