Analysis Validation and Design of Doubly Tuned Flow Reversal Muffler for Wide Band Transmission Loss

Abstract

An ideal exhaust muffler would have high insertion loss (IL) / transmission loss (TL), low back pressure, be smaller in size, have spark arresting capability, minimum break-out noise, sufficiently low flow-generated noise within the muffler element and at the tailpipe, etc. Keeping this in mind, researchers have been developing the mufflers using various computational models, right from 1-D plane wave theory, Transfer matrix method (TMM), and Integrated transfer matrix method (ITM) to modern-day techniques such as 3-D FEM and CFD analysis. Development of the muffler began with a simple expansion chamber (SEC) whose TL is characterized by periodic domes and sharp troughs occurring at the integral multiples of and#960; . To overcome this, a doubly tuned extended tube chamber muffler was developed that was successful in tuning out the first three of the four troughs of the TL Curve, thereby yielding wide band TL as well as Insertion Loss by making use of the 1-D plane wave analysis and the 3-D Finite Element Analysis of the muffler. The TL spectra of this doubly tunned extended tube chamber muffler stand a few dB higher compared to its corresponding SEC muffler. However, these features can only be explained in detail by deriving an analytical expression for the TL curve of a tuned muffler arranged in a form similar to that of the SEC muffler. newlineHence, the first objective of this research work is to attempt to derive this closed-form expression of TL for the doubly-tuned muffler. An analytical expression has been derived for the TL curve of a tuned side-inlet axial-outlet (SIAO) muffler by means of electroacoustic analogies and the transfer matrix method. This expression explains why the base TL curve of the tuned chamber is similar to that of the corresponding SEC with effective length reduced to half and area ratio increased to double. Consequently, one dome of the tuned chamber spans over two domes of the SEC-TL curve and stands 6 dB higher than the TL-domes of the corresponding SEC. However, this SIAO muffler cannot be d