Archives of Acoustics, 47, 4, pp. 491-499, 2022

Analytical and Computational Acoustic Modelling of Side Outlet Muffler and Its Extension in the Modelling of Tapered Side Outlet Muffler

Motilal Nehru National Institute of Technology Allahabad

Suryappa Jayappa PAWAR
Motilal Nehru National Institute of Technology Allahabad

Mufflers are popular in the suppression of noise levels coming from various machinery. The most common parameters for the evaluation of the performance of mufflers are transmission loss, noise level, and insertion loss. The transmission loss is evaluated for tapered side outlet muffler using finite element analysis without considering the fluid-structure interaction. This study includes analytical modelling and acoustic modelling of the side outlet muffler and transmission loss is in excellent agreement with the reference paper. The feasibility of the acoustic model is also verified with the experimental work on simple expansion chamber muffler. The same finite element analysis is extended for the tapered side outlet muffler. The transmission loss of the tapered side outlet muffler in the given frequency range is found 8.96 dB better than the side outlet muffler. The acoustic pressure level and sound pressure level contours for the tapered side outlet muffler give a clear picture of wave propagation inside the muffler. The effect of the cut-off frequency on the transmission loss of the tapered side outlet muffler can be seen from the contours. This study can be helpful in the determination of the performance of the mufflers in terms of transmission loss, the performance of mufflers above cut-off frequency, and design improvements in the muffler to avoid the higher-order modes of the sound wave.
Keywords: 1-D analysis; FEA; sound pressure level; transfer matrix; transmission loss
Full Text: PDF
Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).


Åbom M. (1990), Derivation of four pole parameters including higher order mode effects for expansion chamber mufflers with extended inlet and outlet, Journal of Sound and Vibration, 137(3): 403–418, doi: 10.1016/0022-460X(90)90807-C.

Banerjee S., Jacobi A.M. (2013), Transmission loss analysis of single-inlet/double-outlet (SIDO) and double-inlet/single-outlet (DISO) circular chamber mufflers by using Green’s function method, Applied Acoustics, 74(12): 1499–1510, doi: 10.1016/j.apacoust.2013.06.007.

Banerjee S., Jacobi A.M. (2015), Analytical prediction of transmission loss in distorted circular chamber mufflers with extended inlet/outlet ports by using a regular perturbation method, Journal of Vibration and Acoustics, 137(6): 061002, doi: 10.1115/1.4030717.

Barbieri R., Barbieri N. (2006), Finite element acoustic simulation based shape optimization of a muffler, Applied Acoustics, 67(4): 346–357, doi: 10.1016/j.apacoust.2005.06.007.

Bilawchuk S., Fyfe K.R. (2003), Comparison and implementation of the various numerical methods used for calculating transmission loss in silencer systems, Applied Acoustics, 64(9): 903–916, doi: 10.1016/S0003-682X(03)00046-X.

Craggs A. (1989), The application of the transfer matrix and matrix condensation methods with finite elements to duct acoustics, Journal of Sound and Vibration, 132(3): 393–402, doi: 10.1016/0022-460X(89)90633-0.

Chang Y.-C., Chiu M.-C. (2010), Optimization of multi-chamber mufflers with reverse-flow ducts by algorithm of simulated annealing, Archives of Acoustics, 35(1): 13–33.

Chang Y.-C., Chiu M.-C., Wu M.-R. (2018), Acoustical assessment of automotive mufflers using FEM, neural networks, and a genetic algorithm, Archives of Acoustics, 43(3): 517–529, doi: 10.24425/123923.

Chang Y.-C., Yeh L.-J., Chiu M.-C. (2004), GA optimization on single-chamber muffler hybridized with extended tube under space constraints, Archives of Acoustics, 29(4): 577–596.

Chiu M.-C. (2011), Optimization design of hybrid mufflers on broadband frequencies using the genetic algorithm, Archives of Acoustics, 36(4): 795–822, doi: 10.2478/v10168-011-0053-5.

Falin Z., Dehua L., Yuping Z. (2010), Effect of higher order modes on muffler performance, [in:] International Conference on Optoelectronics and Image Processing, pp. 468–472, Haikou, China, doi: 10.1109/ICOIP.2010.70.

Kagawa Y., Omote T. (1976), Finite element simulation of acoustic filters of arbitrary profile with circular cross-section, The Journal of the Acoustical Society of America, 60(5): 1003–1013, doi: 10.1121/1.381199.

Kani M. et al. (2019), Acoustic performance evaluation for ducts containing porous materials, Applied Acoustics, 147(1): 15–22, doi: 10.1016/j.apacoust.2018.08.002.

Keskar H., Venkatesham B. (2017), Transmission loss characteristics of an annular cavity with arbitrary port locations using Green’s function method, The Journal of the Acoustical Society of America, 142(3): 1350–1361, doi: 10.1121/1.5001492.

Kuskinen C., Riveros A., Floody S. (2010), Shape optimization of reactive-dissipative mufflers, The Journal of the Acoustical Society of America, 128(1): 2367, doi: 10.1121/1.3508404.

Lamancusa J. (1988), The transmission loss of double expansion chamber mufflers with unequal size chambers, Applied Acoustics, 24(1): 15–32, doi: 10.1016/0003-682X(88)90068-0.

Lee J.K., Oh K.S., Lee J.W. (2019), Methods for evaluating in-duct noise attenuation performance in a muffler design problem, Journal of Sound and Vibration, 464: 114982, doi: 10.1016/j.jsv.2019.114982.

Mechanical APDL: 2020 R1, Acoustics – Acoustic Fundamental (Ch. 8), ANSYS workbench help documentation, release 2020 R1, https://d.shikey.comdown/Ansys.Products.2020.R1.x64/install_docs/Ansys.Products.PDF.Docs.2020R1/v201/ANSYS_Mechanical_APDL_Theory_Reference.pdf (access: 28.08.2022).

Mimani A., Munjal M.L. (2012), 3-D acoustic analysis of elliptical chamber mufflers having an end-inlet and a side-outlet: An impedance matrix approach, Wave Motion, 49(2): 271–295, doi: 10.1016/j.wavemoti.2011.11.001.

Mimani A., Munjal M.L. (2016), Design of reactive rectangular expansion chambers for broadband acoustic attenuation performance based on optimal port location, Acoustics Australia, 44(2): 299–323, doi: 10.1007/s40857-016-0053-8.

Munjal M.L. (1975), Velocity ratio-cum-transfer matrix method for the evaluation of a muffler with mean flow, Journal of Sound and Vibration, 39(1): 105–119, doi: 10.1016/S0022-460X(75)80211-2.

Munjal M.L. (1987), Acoustics of duct and mufflers with application to exhaust and ventilation system, John Wiley and Sons, New York.

Perrey-Debain E., Marechal R., Ville J.M. (2014), Side-branch resonators modelling with Green’s function methods, Journal of Sound and Vibration, 333(19): 4458–4472, doi: 10.1016/j.jsv.2014.04.060.

Saharabudhe A.D., Ramu S.A., Munjal M.L. (1991), Matrix condensation and transfer matrix techniques in the 3-D analysis of expansion chamber mufflers, Journal of Sound and Vibration, 147(3): 371–394, doi: 10.1016/0022-460X(91)90487-5.

Selamet A., Ji Z.L. (1998), Acoustic attenuation performance of circular expansion chambers with offset inlet/outlet: I. Analytical approach, Journal of Sound and Vibration, 213(4): 601–617, doi: 10.1006/jsvi.1998.1514.

Seybert A.F., Cheng C.Y.R. (1987), Application of the boundary element method to acoustic cavity response and muffler analysis, Journal of Vibration, Acoustics, Stress, and Reliability in Design, 109(1): 15–21, doi: 10.1115/1.3269388.

Suwandi D., Middelberg J., Byrne K.P., Kessissoglou N.J. (2005), Predicting the performance of mufflers using transmission line theory, [in:] Proceedings of ACOUSTICS, pp. 181–187.

Tao Z., Seybert A.F. (2003), A review of current techniques for measuring muffler transmission loss, SAE Technical Paper Series, pp. 1–5, doi: 10.4271/2003-01-1653.

To C.W.S. (1984), The acoustic simulation and analysis of complicated reciprocating compressor piping systems, I: Analysis technique and parameter matrices of acoustic elements, Journal of Sound and Vibration, 96: 175–194, doi: 10.1016/0022-460X(84)90577-7.

Vishwakarma S.K., Pawar S.J. (2021), Simulation studies on the transition from simple expansion chamber muffler to tapered expansion chamber muffler, [in:] Advances in Fluid and Thermal Engineering, Sikarwar B.S., Sundén B., Wang Q. [Eds], pp. 389–398, Springer Nature Singapore, doi: 10.1007/978-981-16-0159-0_34.

Wu T.W., Wan G.C. (1996), Muffler performance studies using a direct mixed-body boundary element method and a three-point method for evaluating transmission loss, Journal of Vibration and Acoustics, 118(3): 479–484, doi: 10.1115/1.2888209.

Wu T.W., Zhang P., Cheng C.Y.R. (1998), Boundary element analysis of mufflers with an improved method for deriving the four-pole parameters, Journal of Sound and Vibration, 217(4): 767–779, doi: 10.1006/jsvi.1998.1800.

Young C.I.J., Crocker M.J. (1975), Prediction of transmission loss in mufflers by the finite element method, The Journal of the Acoustical Society of America, 57(1): 144–148, doi: 10.1121/1.380424.

Zhang L., Shi H.M., Zeng X.H., Zhuang Z. (2020), Theoretical and experimental study on the transmission loss of a side outlet muffler, Journal of Shock and Vibration, 6927574, doi: 10.1155/2020/6927574.

DOI: 10.24425/aoa.2022.142893