Spectral Element Analysis of Sound hopagation in a Mu~er

Abstract

Abstract:~is paper is concerned with a Imt-squares specti element analysis of sound propagation in an expansion chamber muffler with and without a mean flow. The atgorithm is based on the least-squmes finite element methodology with spectral collocation discretization in space and three-time-level discretization in time to solve the Iintized acoustic field equations, Effects of the mean flow on the acoustic wave propagation in the muffler were tien into consideration. TRODUC~ON An accurate determination of acoustic wave propagation in a lined expansion duct is viti for noise connol and reduction in an engine exhaust system. The noise originating from the internal-combustion engine chamber flows with the burning gas through the exaust pipe and muffler and discharges into the ambient environment. The process of noise propagation in an engine piping system is quite complicated. Moreover, the pipe lining is often treated to dissipate acoustic energy for noise reduction, making the modeling of the acoustic waves in the engine exhaust system even more involved. Analytical solution of sound propagation in such a system generally is not possible; and hence most computations of acoustic modes in lined ducts are analyzed numerically by finite difference [e.g. This synopsis presents a least-squares spectral element method for sound wave propagation in a lined expansion chamber muffler. The method solves the first-order acoustic field equations derived from the full Navier-Stokes equations in a finite number of elements, which represent the muffler. Within each element we first approximate the solution to the acoustic field equations by a series of unknown coefficients with known basis functions, form the residual of the approximation, and then minimize the integral of the squares of the residual with respect to the unknown coefficients. The resultant system equations are written in a matrix form and discretized by the spectral element method for spatial derivatives and by the three-level time stepping for temporal derivatives. A similar approach was used by Chan [3] to develop an incompressible viscous flow solver to compute time accurate flows. Finally the discretized equations are solved for the unknown coefficients by the Jacobian preconditioned conjugate gradient method. Numerical results were presented for pressure contours of sound waves propagating at frequency of 1 Hz with and without flow effect, and at 1~Hz without flow effect. MA~MA~CAL MODEL~G Consider an expansion chamber muffler, as shown i