The Mufflers Modeling by Transfer Matrix Method MIHAI BUGARU * , OVIDIU VASILE * , NICOLAE ENESCU * * Department of Mechanics University POLITEHNICA of Bucharest Splaiul Independentei 313, post code 060042, Bucharest ROMANIA Abstract: Mufflers are widely used for exhaust noise attenuation in vehicles, machinery and other industrial elements. Modeling procedures for accurate performance prediction had led to the development of new methods for practical muffler components in design. Plane wave based models such as the transfer matrix method (TMM) can offer fast initial prototype solutions for muffler designers. In the present paper the authors present an overview of the principles of TMM for predicting the transmission loss (TL) of a muffler. The predicted results agreed in some limits with the experimental data published in literature. Key-Words: Muffler modeling, transfer matrix method 1 Introduction Mufflers are commonly used in a wide variety of applications. Industrial flow ducts as well as internal combustion engines frequently make use of silencing elements to attenuate the noise levels carried by the fluids and radiated to the outside atmosphere by the exhausts. Design of a complete muffler system is, usually, a very complex task because each of its elements is selected by considering its particular acoustic performance and its interaction effects on the entire acoustic system performance. For the frequency analysis of the muffler, as can be seen from the references [1,3,5], it is very convenient to use the transfer matrix method. The present paper deals with the fundamentals of the Transfer Matrix Method (TMM) and the method is applied to a specific muffler configuration for the prediction of Transmission Loss. 2 Transfer Matrix Method Theory 2.1 Plane wave propagation [1,3,5] For plane wave propagation in a rigid straight pipe of length L, constant cross section S, and transporting a turbulent incompressible mean flow of velocity V (see Fig. 1), the sound pressure p and the volume velocity ν anywhere in the pipe element can be represented as the sum of left and right traveling waves. The plane wave propagation model is valid when the influence of higher order modes can be neglected. Using the impedance analogy, the sound pressure p and volume velocity ν at positions 1 (upstream end) and 2 (downstream end) in Fig. 1 (x = 0 and x =L, respectively) can be related by 2 2 1 ν B Ap p + = , (1) and 2 2 1 ν ν D Cp + = , (2) where A, B, C, and D are called the four-pole constants. Fig. 1. Plane wave propagation in a rigid straight pipe transporting a turbulent incompressible mean flow [3]. Munjal shows that the four-pole constants for non- viscous medium are L k L jMk A c c cos ) exp(− = , (3) L k L jMk S c j B c c sin ) exp( ) / ( − = ρ , (4) L k L jMk D c c cos ) exp(− = ,(5), (5) L k L jMk c S j C c c sin ) exp( ) / ( − = ρ , (6) where M=V/c is the mean flow Mach number (M<0.2), c is the speed of sound (m/s), k c =k/(1- M 2 ) is the convective wave-number (rad/m), k = ω/c is the acoustic Proceedings of the 10th WSEAS International Confenrence on APPLIED MATHEMATICS, Dallas, Texas, USA, November 1-3, 2006 476