On the numerical eigenmode analysis of acoustically lined ducts with uniform mean flow

Abstract The present work concerns the numerical eigenmode analysis of acoustically lined ducts of any constant cross-sectional shape in the presence of mean flow. The duct is lined with bulk-reactive porous material, which is separated from the flow channel by a perforated panel. A combined wave and finite element (WFE) method is introduced to investigate the effects of uniform mean flow on the eigenmodes and eigenvalues of the lined ducts. The proposed method is validated against analytical solutions for a simple case. A convergence rate of Se4 for eigenvalues can be reached for Mach number up to 0.8, with Se being the mesh size. In this study, the eigenmodes of a lined duct are divided into air-borne modes and lining-borne modes. The air-borne modes propagate mostly in the air domain, while the lining-borne modes can propagate in both air domain and porous domain. The effect of Mach number on the axial wavenumbers and mode shapes are analysed. It is found that, for air-borne modes, Mach number will strongly affect their wavenumbers, while its effect on the mode shape is marginal. On the contrary, for the lining-borne modes, Mach number has small effect on the wavenumber, but its effect on the mode shape is significant. Specifically, even the mode properties can be changed from a lining-borne mode to an air-borne mode for some left-travelling lining-borne mode. The transmission loss (TL) of a lined duct with three typical Mach numbers is calculated by the mode matching method. It is found that up-flow will generally increase TL of lined duct, compared with the case of no flow; while down-flow will generally decrease TL. In both situations, the peak frequency does not show significant change.