Computational methods for sound transmission in nonuniform waveguides

The Method of Weighted Residuals in the form of a Modified Galerkin Method with boundary residuals and the Finite Element Method in a Galerkin implementation are developed for the study of the sound transmission in nonuniform axisymmetric ducts carrying a steady, compressible, flow. In this investigation the mean flow is modelled as essentially one-dimensional but with a kinematic modification to force tangency of the flow and the wall. The Method of Weighted Residuals uses trigonometric basis functions which are derived from an equivalent problem in a two­dimensional duct. The Finite Element Method formulation is based on a weighted residuals approach, and uses eight-node isoparametric rectangular elements. The two computational methods are developed through three stages : eigenproblem, no-flow case and flow case with designed testing cases or alternative checkouts. Data presented for various circular duct configurations include eigenvalues for uniform ducts, modal coefficients of transmitted and reflected waves, acoustic efficiencies and acoustic field for non­ uniform ducts. The quantitative results obtained by the two methods are of comparable accuracy for the eigenproblem and the no-flow transmission problem. For the flow case with moderate Mach numbers good agreements are achieved. When the flow attains the subsonic non­ linear regime the Finite Element Method suffers the difficulty of high dimensionality, however, correlations are still observed. Numerical simulations revealed no traces of the subsonic acoustic choking phenomenon