Propagation of acoustic waves in axially varying ducts with potential flow using the multimodal formulation

Abstract

This paper presents a multimodal method applicable to the computation of the acoustic field in an axisymmetric duct with multiple-scales potential mean flow. The original threedimensional set of equations is rearranged into a set of coupled one-dimensional equations by using the Fourier transform of the sound disturbances in the azimuthal direction and a projection on shifted Chebyshev polynomials in the radial direction. To keep the computation resources identical to that of the standard multimodal formulation (without flow), only the leading order effects of the mean flow are encapsulated using a multiple-scales approach. The formulation is verified using a finite-element method and is shown to give consistent results for modes propagating inside ducts with or without acoustic liners and in the presence of potential flows. This method can be easily adapted to take into account more complex flows and geometries.