Experimental Determination of a Reflective Muffler Scattering Matrix for Single-Mode Excitation
Abstract
The aim of the paper is to experimentally determine the scattering matrix S of an example reflective muffler of cylindrical geometry for Helmholtz number exceeding the plane wave propagation. Determining the scattering matrix of an acoustic systems is a new and increasingly used approach in the assessment of reduction of noise propagating inside duct-like elements of heating, ventilation and air conditioning systems (HVAC). The scattering matrix of an acoustic system provides all necessary information on the propagation of wave through it. In case of the analysed reflective silencer, considered as a two-port system, the noise reduction was determined by calculating the transmission loss parameter (TL) based on the scattering matrix (S). Measurements were carried out in two planes of the cross-section of pipes connected to the muffler. The paper presents results of the scattering matrix evaluation for the wave composed of the plane wave (mode (0,0)) and the first radial mode (0,1), each of which was generated separately using the self-designed and constructed single-mode generator. The gain of proceeding measurements for single modes stems from the fact that theoretically, calculation of the S-matrix does not require, as will be presented in the paper, calculation of the measurement data inverse matrix. Moreover, if single mode sound fields are well determined, it ensures error minimization. The presented measurement results refer to an example of a duct like system with a reflective muffler for which the scattering matrix S was determined. The acoustic phenomena inside such a system can be scaled by the parameter ka.Keywords:
cylindrical duct, reflective muffler, single-mode generation, multi-port method, scattering matrixReferences
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24. Snakowska A., Jurkiewicz J., Gorazd Ł. (2017) A hybrid method for determination of the acoustic impedance of an unflanged cylindrical duct for multimode wave, Journal of Sound and Vibration, 396: 325–339, https://doi.org/10.1016/j.jsv.2017.02.040
25. Song B. H., Bolton J. S. (2000) A transfer-matrix approach for estimating the characteristic impedance and wave numbers of limp and rigid porous materials, The Journal of the Acoustical Society of America, 107(3): 1131–1152, https://doi.org/10.1121/1.428404
26. Su J., Rupp J., Garmory A., Carrotte J.F. (2015), Measurements and computational fluid dynamics predictions of the acoustic impedance of orifices, Journal of Sound and Vibration, 352: 174–191, https://doi.org/10.1016/j.jsv.2015.05.009
27. Zorumski W.E. (1973), Generalized radiation impedances and reflection coefficients of circular and annular ducts, The Journal of the Acoustical Society of America, 54(6): 1667–1673, https://doi.org/10.1121/1.1914466
2. Abom M., Karlsson M. (2010), Can acoustic multi-port models be used to predict whistling, 16th AIAA/CEAS Aeroacoustics Conference, 5: 4285–4292.
3. Atig M., Dalmont J.P., Gilbert J. (2004), Termination of open-end cylindrical tubes at high sound pressure level, Computes Rendus Mecanique, 332(4): 299–304, https://doi.org/10.1016/j.crme.2004.02.008
4. Auger J.M., Ville J.M. (1990), Measurement of linear impedance based on the determination of duct eigenvalues by a Fourier-Lommel's transform, The Journal of the Acoustical Society of America, 88(1): 19–22, https://doi.org/10.1121/1.399942
5. Auregan Y., Farooqui M., Groby J.P. (2016), Low frequency sound attenuation in a flow duct using a thin slow sound material, The Journal of the Acoustical Society of America, 139(5): 149–153, https://doi.org/10.1121/1.4951028
6. Chen X.X., Zhang X., Morfey C.L., Nelson P.A. (2004) A numerical method for computation of sound radiation from an unflanged duct, Journal of Sound and Vibration, 270(3): 573–586, https://doi.org/10.1016/j.jsv.2003.09.055
7. Dalmont J.P., Nederveen C.J., Joly N. (2001), Radiation impedance of tubes with different flanges: numerical and experimental investigations, Journal of Sound and Vibration, 244(3): 505–534, https://doi.org/10.1006/jsvi.2000.3487
8. Gerges S.N.Y., Jordan R., Thieme F.A., Bento Coelho J.L., Arenas J.P. (2005), Muffler modeling by transfer matrix method and experimental verification, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 27(2): 132–140, https://doi.org/10.1590/S1678-58782005000200005 .
9. Hocter S.T. (1999), Exact and approximate directivity patterns of the sound radiated from a cylindrical duct, Journal of Sound and Vibration, 227(2): 397–407, https://doi.org/10.1006/jsvi.1999.2351
10. Hocter S.T. (2000), Sound radiated from a cylindrical duct with Keller's geometrical theory, Journal of Sound and Vibration, 231(5): 1243–1256, https://doi.org/10.1006/jsvi.1999.2739
11. Joseph P., Morfey C.L. (1999) Multimode radiation from an unflanged, semi-infinite circular duct, The Journal of the Acoustical Society of America, 105(5): 2590–2600, https://doi.org/10.1121/1.426875
12. Jurkiewicz J., Snakowska A., Gorazd Ł. (2012), Experimental verification of the theoretical model of sound radiation from an unflanged duct with low mean flow, Archives of Acoustics, 37(2): 227–236, https://doi.org/10.2478/v10168-012-0030-7
13. Lavrentjev J., Abom M., Boden H. (1995), A measurement method for determining the source data of acoustic two-port sources, Journal of Sound and Vibration, 183(3): 517–531, https://doi.org/10.1006/jsvi.1995.0268
14. Lee J.K., Oh K.S., Lee J.W. (2020), Methods for evaluating in-duct noise attenuation performance in a muffler design problem, Journal of Sound and Vibration, 464: 114982, https://doi.org/10.1016/j.jsv.2019.114982
15. Lidoine S., Batard H., Troyes S., Delnevo A., Roger M. (2001) Acoustic radiation modelling of aeroengine intake comparison between analytical and numerical methods, 7th AIAA/CEAS Aeroacoustics Conference and Exhibit, Maastricht, https://doi.org/10.2514/6.2001-2140
16. Munjal M.L. (1987), Acoustics of Ducts and Mufflers with Application to Exhaust and Ventilation System Design, New York: John Wiley & Sons.
17. Sack S., Abom M., Efraimsson G. (2016), On acoustic multi-port characterisation including higher order modes, Acta Acustica United with Acustica, 102(5): 834–850, https://doi.org/10.3813/AAA.918998
18. Selamet A., Dickey N.S., Novak J.M. (1994), The Herschel-Quincke tube: A theoretical, computational, and experimental investigation, The Journal of the Acoustical Society of America, 96(5): 3177–3185, https://doi.org/10.1121/1.411255
19. Sinayoko S., Joseph P., McAlpine A. (2010), Multimode radiation from an unflanged, semi-infinite circular duct with uniform flow, The Journal of the Acoustical Society of America, 127(4): 2159–2168, https://doi.org/10.1121/1.3327814
20. Sitel A., Ville J. M., Foucart F. (2006), Multiload procedure to measure the acoustic scattering matrix of a duct discontinuity for higher order mode propagation conditions, The Journal of the Acoustical Society of America, 120, 5, 2478-2490, https://doi.org/10.1121/1.2354040
21. Snakowska A., Gorazd Ł., Jurkiewicz J., Kolber K. (2016), Generation of a single cylindrical duct mode using a mode synthesizer, Applied Acoustics, 114: 56–70, https://doi.org/10.1016/j.apacoust.2016.07.007
22. Snakowska A., Jurkiewicz J. (2010), Efficiency of energy radiation from an unflanged cylindrical duct in case of multimode excitation, Acta Acustica united with Acustica, 96(3): 416–424, https://doi.org/10.3813/AAA.918294
23. Snakowska A., Jurkiewicz J. (2021), A new approach to the theory of acoustic multi-port networks with multimode wave and its application to muffler analysis, Journal of Sound and Vibration, 490: 115722, https://doi.org/10.1016/j.jsv.2020.115722
24. Snakowska A., Jurkiewicz J., Gorazd Ł. (2017) A hybrid method for determination of the acoustic impedance of an unflanged cylindrical duct for multimode wave, Journal of Sound and Vibration, 396: 325–339, https://doi.org/10.1016/j.jsv.2017.02.040
25. Song B. H., Bolton J. S. (2000) A transfer-matrix approach for estimating the characteristic impedance and wave numbers of limp and rigid porous materials, The Journal of the Acoustical Society of America, 107(3): 1131–1152, https://doi.org/10.1121/1.428404
26. Su J., Rupp J., Garmory A., Carrotte J.F. (2015), Measurements and computational fluid dynamics predictions of the acoustic impedance of orifices, Journal of Sound and Vibration, 352: 174–191, https://doi.org/10.1016/j.jsv.2015.05.009
27. Zorumski W.E. (1973), Generalized radiation impedances and reflection coefficients of circular and annular ducts, The Journal of the Acoustical Society of America, 54(6): 1667–1673, https://doi.org/10.1121/1.1914466
