Classification of aeroacoustically relevant surface modes in cylindrical lined ducts

Wave modes in a straight cylindrical duct with a locally reacting boundary and a steady subsonic axial flow are investigated. The duct modes are separated into ordinary duct modes and surface modes confined to a neighbourhood of the boundary. Previous asymptotic results of Rienstra for the surface modes assume that the dimensionless frequency ω is large, and that the azimuthal order m ≪ ω. In this paper, these results are generalized to arbitrary values of m, as applicable to rotor-alone noise in aeroengines where m is a multiple of the number of blades and is typically O (ω). A dimensionless number λ is found to govern the surface modes’ behaviour, and qualitatively different behaviour is seen for λ in four distinct regions, separated by critical values depending only on the steady flow Mach number. For aeroacoustically relevant parameters, our generalized asymptotics are shown to provide a distinctly better approximation to the full equations than previous approximations.