Analytical And Experimental Aeroacoustic Studies Of Open-Ended 3-Duct Perforated Elements Used In Mufflers

Perforated element mufflers have been known to have good acousticp erformancew, henu sedo n automotive xhausst ystemsIn. thel astd ecadea nda half, plugm ufflersc, oncentrihc oler esonators, and three-ductc losed-endp erforatede lementsh ave been studied.T he presenti nvestigation concernso pen-endedt,h ree-ducpt erforatede lementsw, hich are knownt o combineh igh acoustic transmissiolno ss with low back pressuresT. he governinge quationsh ave been solved in the frequencyd omain,u singt he recouplinga pproacha longw ith appropriatbe oundaryc onditionst,o derivet he transferm atrixa ndt hent o calculaten oiser eductiona ndt ransmissiolno ss.T he predicted noiser eductionv aluesh aveb eens hownt o corroboratew ell with experimentallyo bservedv alues. Finally,p arametrics tudiesh aveb eend onet o draw designc urvesf or suchm ufflers.

Evaluation of noise attenuation due to exhaust mufflers

This paper deals with the evaluation of noise attenuation due to exhaust mufflers fitted to the conventional piston engines. A discussion of the existing methods for the purpose, reveals the undesirability of the assumptions and simplifications implied therein. An expression for the attenuation of a general muffler has been derived. The classical theory of "sound transmission in pipes" [1] has been exploited to evaluate this "expression" for mufflers of different geometry. The quantitative effects of atmospheric impedance, and the engine exhaust impedance on the attenuation curves of a specific muffler have been found for an automotive engine. Finally, attenuation curves of a number of mufflers have been drawn and compared to suggest certain design criteria.

Flow-Acoustic Performance of Perforated Element Mufflers With Application to Design

A fairly comprehensive computer program incorporating explicit expressions for the four-pole parameters of concentric-tube resonators, plug mufflers, and three-duct cross-flow perforated elements has been used for parametric studies. The parameters considered are hole diameter, the center-to-center distance between consecutive holes (which decides porosity), the incoming mean flow Mach number, the area expansion ratio, the number of partitions of chambers within a given overall shell length, and the relative lengths of these partitions or chambers, all normalized with respect to the exhaust pipe diameter. Transmission loss has been plotted as a function of a normalized frequency parameter. Additionally, the effect of the tail pipe length on insertion loss for an anechoic source has also been studied. These studies have been supplemented by empirical expressions for the normalized static pressure drop for different types of perforated-element mufflers developed from experimental observations.

Transverse plane wave analysis of short elliptical chamber mufflers: An analytical approach

Short elliptical chamber mufflers are used often in the modern day automotive exhaust systems. The acoustic analysis of such short chamber mufflers is facilitated by considering a transverse plane wave propagation model along the major axis up to the low frequency limit. The one dimensional differential equation governing the transverse plane wave propagation in such short chambers is solved using the segmentation approaches which are inherently numerical schemes, wherein the transfer matrix relating the upstream state variables to the downstream variables is obtained. Analytical solution of the transverse plane wave model used to analyze such short chambers has not been reported in the literature so far. This present work is thus an attempt to fill up this lacuna, whereby Frobenius solution of the differential equation governing the transverse plane wave propagation is obtained. By taking a sufficient number of terms of the infinite series, an approximate analytical solution so obtained shows good convergence up to about 1300 Hz and also covers most of the range of muffler dimensions used in practice. The transmission loss (TL) performance of the muffler configurations computed by this analytical approach agrees excellently with that computed by the Matrizant approach used earlier by the authors, thereby offering a faster and more elegant alternate method to analyze short elliptical muffler configurations. (C) 2010 Elsevier Ltd. All rights reserved.

Analysis of Lined Ducts With Mean Flow, With Application to Dissipative Mufflers

Mufflers with at least one acoustically absorptive duct are generally called dissipative mufflers. Generally, for want of systems approach, these mufflers are characterized by transmission loss of the lined duct with overriding corrections for the terminations, mean flow, etc. In this article, it is proposed that dissipative duct should be integrated with other muffler elements, source impedance and radiation impedance, by means of transfer matrix approach. Towards this end, the transfer matrix for rectangular duct with mean flow has been derived here, for the least attenuated mode. Mean flow introduces a coupling between transverse wave numbers and axial wave number, the evaluation of which therefore calls for simultaneous solution of two or three transcendental equations. This is done by means of a Newton-Raphson iteration scheme, which is illustrated here for square ducts lined with porous ceramic tiles.

A simple numerical method for three-dimensional analysis of simple expansion chamber mufflers of rectangular as well as circular cross-section with a stationary medium

Three-dimensional effects are a primary source of discrepancy between the measured values of automotive muffler performance and those predicted by the plane wave theory at higher frequencies. The basically exact method of (truncated) eigenfunction expansions for simple expansion chambers involves very complicated algebra, and the numerical finite element method requires large computation time and core storage. A simple numerical method is presented in this paper. It makes use of compatibility conditions for acoustic pressure and particle velocity at a number of equally spaced points in the planes of the junctions (or area discontinuities) to generate the required number of algebraic equations for evaluation of the relative amplitudes of the various modes (eigenfunctions), the total number of which is proportional to the area ratio. The method is demonstrated for evaluation of the four-pole parameters of rigid-walled, simple expansion chambers of rectangular as well as circular cross-section for the case of a stationary medium. Computed values of transmission loss are compared with those computed by means of the plane wave theory, in order to highlight the onset (cutting-on) of various higher order modes and the effect thereof on transmission loss of the muffler. These are also compared with predictions of the finite element methods (FEM) and the exact methods involving eigenfunction expansions, in order to demonstrate the accuracy of the simple method presented here.

On an Integrated Transfer Matrix method for multiply connected mufflers

The commercial automotive mufflers are generally of a complicated shape with multiply connected parts and complex acoustic elements. The analysis of such complex mufflers has always been a great challenge. In this paper, an Integrated Transfer Matrix method has been developed to analyze complex mufflers. Integrated transfer matrix relates the state variables across the entire cross-section of the muffler shell, as one moves along the axis of the muffler, and can be partitioned appropriately in order to relate the state variables of different tubes constituting the cross-section. The paper presents a generalized one-dimensional (1-D) approach, using the transfer matrices of simple acoustic elements, which are available from the literature. The present approach is robust and flexible owing to its capability to construct an overall matrix of the muffler with the transfer matrices of individual acoustic elements and boundary conditions, which can then be used to evaluate the transmission loss, insertion loss, etc. Results from the present approach have been validated through comparisons with the available experimental and three-dimensional finite element method (FEM) based results. The results show good agreement with both measurements and FEM analysis up to the cut-off frequency. (C) 2011 Elsevier Ltd. All rights reserved.

3-D acoustic analysis of elliptical chamber mufflers having an end-inlet and a side-outlet: An impedance matrix approach

The acoustical behavior of an elliptical chamber muffler having an end-inlet and side-outlet port is analyzed semi-analytically. A uniform piston source is assumed to model the 3-D acoustic field in the elliptical chamber cavity. Towards this end, we consider the modal expansion of acoustic pressure field in the elliptical cavity in terms of angular and radial Mathieu functions, subjected to rigid wall condition, whereupon under the assumption of a point source, Green's function is obtained. On integrating this function over piston area of the side or end port and dividing it by piston area, one obtains the acoustic field, whence one can find the impedance matrix parameters characterizing the 2-port system. The acoustic performance of these configurations is evaluated in terms of transmission loss (TL). The analytical results thus obtained are compared with 3-D HA carried on a commercial software for certain muffler configurations. These show excellent agreement, thereby validating the 3-D semi-analytical piston driven model. The influence of the chamber length as well as the angular and axial location of the end and side ports on TL performance is also discussed, thus providing useful guidelines to the muffler designer. (c) 2011 Elsevier B.V. All rights reserved.

On the Role of Higher-Order Evanescent Modes in End-Offset Inlet and End-Centered Outlet Elliptical Flow-Reversal Chamber Mufflers

This paper deals with the role of the higher-order evanescent modes generated at the area discontinuities in the acoustic attenuation characteristics of an elliptical end-chamber muffler with an end-offset inlet and end-centered outlet. It has been observed that with an increase in length, the muffler undergoes a transition from being acoustically short to acoustically long. Short end chambers and long end chambers are characterized by transverse plane waves and axial plane waves, respectively, in the low-frequency range. The nondimensional frequency limit k(0)(D-1/2) or k(0)R(0) as well as the chamber length to inlet/outlet pipe diameter ratio, i.e., L/d(0), up to which the muffler behaves like a short chamber and the corresponding limit beyond which the muffler is acoustically long are determined. The limits between which neither the transverse plane-wave model nor the conventional axial plane-wave model gives a satisfactory prediction have also been determined, the region being called the intermediate range. The end-correction expression for this muffler configuration in the acoustically long limit has been obtained using 3-D FEA carried on commercial software, covering most of the dimension range used in the design exercise. Development of a method of combining the transverse plane wave model with the axial plane wave model using the impedance Z] matrix is another noteworthy contribution of this work.

Flow resistance network analysis of the back-pressure of automotive mufflers

Complexity of mufflers generally introduces considerable pressure drop, which affects the engine performance adversely. Not much literature is available for pressure drop across perforates. In this paper, the stagnation pressure drop across perforated muffler elements has been measured experimentally and generalized expressions have been developed for the pressure loss across cross-flow expansion and cross-flow contraction elements. A flow resistance model available in the literature has been made use of to analytically determine the flow distribution and thereby the pressure drop of mufflers. A generalized expression has been derived here for evaluation of the equivalent flow resistance for parallel flow paths. Expressions for flow resistance across perforated elements, derived by means of flow experiments, have been implemented in the flow resistance network. The results have been validated with experimental data. Thus, the newly developed integrated flow resistance networks would enable us to determine the normalized stagnation pressure drop of commercial automotive mufflers, thus enabling an efficient flow-acoustic design of silencing systems.