Acoustic propagation in ducts with slowly varying elliptic cross-section

The propagation of acoustic waves along a duct of elliptic cross-section, t he eccentricity of which varies slowly along the axis, is considered as a m odel of the unsteady flow inside a realistic aeroengine nacelle. This is a development of recent work on a circular duct by Rienstra. The acoustic fie ld at each axial location is expanded in terms of the local even and odd Ma thieu modes, and the slow variation of the axial wavenumber and the modal a m plitude along the duct are determined as part of the solution. The duct e ccentricity is seen to have a very significant effect right across the rang e of practical azimuthal orders, and has different effects on the even and odd modes. For instance, the point at which a given mode changes from being cut-on to cut-off depends on the eccentricity; for even modes, and for the odd modes apart from at a very low frequency, the eccentricity makes modes more cut-on than in a circular duct. Even for cases in which a given mode is cut-on all along the duct according to standard circular duct theory, th e modal amplitude is seen to depend strongly on the cross-sectional eccentr icity. In a representative case the amplitude of a high order mode propagat ing upstream along a slowly varying elliptical duct is seen to be significa ntly levier than that of the equivalent mode propagating in a circular duct of the same cross-sectional area. (C) 2001 Academic Press.