A new approximation of the dispersion relations occurring in the sound-attenuation problem of turbofan aircraft engines

Abstract

The dispersion relations, appearing in the analysis of the stability of a gas flow in a straight acoustically-lined duct with respect to perturbations produced by a time harmonic source, beside the wave number and complex frequency contain the solution of a boundary value problem of the Pridmore-Brown equation depending on the wave number and frequency. For this reason, in practice the dispersion relations are rarely simple enough for carried out the zeros. The determination of zeros of these dispersion relations is crucial for the prediction of the perturbation attenuation or amplification. In this paper an approximation of the dispersion relations is given. Our approach preserves the general character of the mean flow, the general Pridmore-Brown equation and it's only in the shear flow that we replace the exact solution of the boundary value problem with its Taylor polynomial approximate. In this way new approximate dispersion relations are obtained which zero's can be found by computer.