Propagation of acoustic perturbations in non-uniform ducts with non-uniform mean flow using eigen analysis in general curvilinear coordinate systems

• Published in: Journal of sound and vibration Vol. 443; pp. 605 - 636
• Main Author: Wilson, Alexander G.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 17.03.2019; Elsevier Science Ltd
• Subjects: Acoustic propagation; Acoustics; Annular ducts; Coordinates; Curvilinear; Ducts; Eigenvalue; Eigenvalues; Eigenvector; Eigenvectors; Entropy; Euler; Euler-Lagrange equation; Fluid flow; Ideal gas; Iterative methods; Linearization; Non-orthogonal; Perturbation; Propagation; Reflected waves; Simulation; Eigenvalue; Euler; Perturbation; Curvilinear; Eigenvector; Non-orthogonal
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2018.11.023

A new framework, Eigen Analysis in General Curvilinear Coordinates (EAGCC), is presented for internal propagation of linear acoustic flow disturbances through irregular but smoothly varying duct geometries and non-uniform but smoothly varying mean flows. The framework is based on an eigen analysis of the linearised Euler equations for a perfect gas formulated in a general curvilinear coordinate system. A series of test cases are studied, from a simple uniform cylindrical annular duct with uniform mean flow to an axially and circumferentially non-uniform duct with non-uniform mean flow, which together validate the method for acoustic propagation through non-uniform annular ducts and non-uniform but irrotational and homentropic mean flow: although the framework provides for rotational and non-homentropic mean flow, and for modelling vortical and entropic flow perturbations, these features are not validated in this paper. Two propagation methods are presented. The first is a one-way “single sweep” calculation, in which only information travelling in the direction of propagation is retained. The second is an iterative “two-way sweep” method that accurately captures reflected waves and returns transmitted and reflected perturbations. Previous eigenvector analyses were subject to limitations on geometry and mean flow (for instance slowly-varying ducts) that are not required in the current method, for which the only limitations are that the duct and mean flow vary smoothly with position. This work extends the scope of the eigenvector approach to include acoustic problems previously limited to volumetric or surface-based methods.