Propagation of Acoustic Waves in Ducts with Flow Using the Multimodal Formulation

This paper presents a multimodal method for the computation of the acoustic field in an axisymmetric varying duct with or without liner and in the presence of mean flow. The original three-dimensional equations are rearranged into a set of coupled one-dimensional equations by projecting the acoustic field over transverse basis functions. To maintain the computational efficiency of the original multimodal method (applicable without flow), only the leading-order effects of the mean flow are modeled using a multiple-scales approach. A matching procedure is also given to deal with liner discontinuities in such a duct. Two different transverse bases are used: one is based on Fourier–Bessel functions to evaluate the effect of modal scattering and the other is based on Fourier–Chebyshev polynomials to improve the method efficiency. The formulation is evaluated against analytical models based on the Wentzel–Kramers–Brillouin technique and against finite-element solutions. It is shown to give consistent results for minor computational cost for modes propagating in ducts with or without acoustic liners. This method can be easily adapted to take into account more complex flows and geometries.