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6 - Multi-Modal Sound Propagation in Ducts

Published online by Cambridge University Press:  11 May 2021

Erkan Dokumacı
Erkan Dokumacı
Affiliation:
Dokuz Eylül University
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Summary

Chapter 6 introduces the three-dimensional analytic theory of sound propagation in ducts and presents acoustic models of hard-walled and lined uniform ducts. Also discussed are the effects of gradual cross-section non-uniformity, circular curvature of the duct axis, and sheared and vortical mean flows.

Keywords

transverse modesevanescent modesleast attenuated modecut-on frequencyspinning modeslined ductscurved ductsshear flow rotational flowtemperature gradient
Type
Chapter
Information
Duct Acoustics
Fundamentals and Applications to Mufflers and Silencers
 , pp. 238 - 325
Publisher: Cambridge University Press
Print publication year: 2021

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References

Weng, C., Boij, S. and Hanifi, A., The attenuation of sound by turbulence in internal flows, J. Acoust. Soc. Am. 133 (2013), 3764–3776.Google Scholar
Pridmore-Brown, D.C., Sound propagation in a fluid flowing through an attenuating duct, J. Fluid Mech. 4 (1958) 393–406.CrossRefGoogle Scholar
Schlichting, H., Boundary Layer Theory, (New York: McGraw-Hill, 1979).Google Scholar
Agarwal, N.K. and Bull, M.K., Acoustic wave propagation in a pipe with fully developed turbulent flow, J. Sound Vib. 132 (1989), 275–298.Google Scholar
Ingard, U., Influence of fluid motion past a plane boundary on sound reflection, absorption, and transmission, J. Acoust. Soc. Am. 31 (1959), 1035–1036.CrossRefGoogle Scholar
Myers, M.K., On the acoustic boundary condition in the presence of flow, J. Sound Vib. 71 (1980), 429–434.CrossRefGoogle Scholar
Eversman, W. and Beckemeyer, R.J., Transmission of sound in ducts with shear layers: Convergence to the uniform flow case, J. Acoust. Soc. Am. 52 (1972), 216–220.CrossRefGoogle Scholar
Nayfeh, A.H., Effect of acoustic boundary layer on the wave propagation in ducts, J. Acoust. Soc. Am. 54 (1973), 1737–1742.CrossRefGoogle Scholar
Auregan, Y., Starobinski, R. and Pagneux, V., Influence of grazing flow and dissipation effects on the acoustic boundary conditions at a lined wall, J. Acoust. Soc. Am. 109 (2001), 59–64.Google Scholar
Rienstra, S. and Darau, M., Boundary layer thickness effects of the hydrodynamic instability along an impedance wall, J. Fluid Mech. 671 (2011), 559–573.Google Scholar
Brambley, E.D., Well-posed boundary condition for acoustic liners in straight ducts with flow, AIAA J. 49 (2011), 1272–1282.Google Scholar
Khamis, D. and Brambley, E.J., Acoustic boundary conditions at an impedance lining in inviscid shear flow, J. Fluid Mech. 796 (2016) 386–416.Google Scholar
Drazin, P., Introduction to Hydraudynamic Instability, (Cambridge: Cambridge University Press, 2002).Google Scholar
Courant, R. and Hilbert, D., Methods of Mathematical Physics, Vol.1, (New York: Interscience, 1953).Google Scholar
Morfey, C.L., Sound transmission and generation in ducts with flow, J. Sound Vib. 14 (1971), 37–55.CrossRefGoogle Scholar
Farassat, F. and Myers, M.K., A graphical approach to wave propagation in a rigid duct, J. Sound Vib. 200 (1997), 729–735.CrossRefGoogle Scholar
Rice, E.J., Modal propagation angles in ducts with soft walls and their connection with suppressor performance, NASA-TM-79081, (1979).Google Scholar
Chapman, C.J., Sound radiation from a cylindrical duct: part I. Ray structure of the duct modes and the external field, J. Fluid Mech. 281 (1994), 293–311.CrossRefGoogle Scholar
Lowson, M.V. and Baskaran, S., Propagation of sound in elliptic ducts, J. Sound Vib. 38 (1975), 185–194.CrossRefGoogle Scholar
Willatzen, M. and Voon, L.C.L.Y., Theory of acoustic eigenmodes in parabolic cylindrical enclosures, J. Sound Vib. 286 (2005), 251–254.CrossRefGoogle Scholar
Reddy, J.N., An Introduction to the Finite Element Method, (New York: McGraw-Hill Inc., 1993).Google Scholar
Brooks, C.J., Prediction and control of sound propagation in turbofan engine bypass ducts, PhD thesis, Institute of Sound and Vibration Research, University of Southampton, UK, (2007).Google Scholar
Tester, B.J., The propagation and attenuation of sound in lined ducts containing uniform or “plug” flow, J. Sound Vib. 28 (1973), 151–203.CrossRefGoogle Scholar
Eversman, W., Theoretical models for duct acoustic propagation and radiation, in Hubbard, H.H. (ed.), Aeroacoustics of Flight Vehicles: Theory and Practice, Vol. 2: Noise Control, NASA RP-1258, (Washington, DC: NASA, 1991), pp. 101–163.Google Scholar
Syed, A.A., On the prediction of sound attenuation in acoustically lined circular ducts, PhD thesis, Loughborough University, UK, (1980), available online at https://bit.ly/30rp5Kl.Google Scholar
Rienstra, S.W., A classification of duct modes based on surface waves, Wave Motion 37 (2003), 119–135.Google Scholar
Brambley, E.J. and Peake, N., Classification of aeroacoustically relevant surface modes in cylindrical lined ducts, Wave Motion 43 (2006) 301–310.Google Scholar
Redon, E., Bonnet-Ben Dhia, A.-S., Mercier, J. F. and Sari, S.P., Non-reflecting boundary conditions for acoustic propagation in ducts with acoustic treatment and mean flow, Int. J. Num. Meth. Engng. 86 (2011), 1360–1378.Google Scholar
Cremer, L., Theory regarding the attenuation of sound transmitted by air in a rectangular duct with an absorbing wall, and the maximum attenuation constant produced during this process, Acustica 3 (1953), 249–263.Google Scholar
Tester, B. J., The optimization of modal sound attenuation in ducts, in absence of mean flow, J.Sound Vib. 27 (1973), 477–513.CrossRefGoogle Scholar
Kabral, R., Du, L., Åbom, M., Optimum sound attenuation in flow ducts based on the exact Cremer impedance, Acta Acustica united with Acustica, 102 (2016), 851–860.CrossRefGoogle Scholar
Zhang, Z., Bodén, H. and Åbom, M., The Cremer impedance: An investigation of the low frequency behavior, J. Sound Vib. 549 (2019) 114844.Google Scholar
Gillespie, R.P., Partial Diffrentiation, (Edinburgh: Oliver and Boyd, 1954).Google Scholar
Law, T.R. and Dowling, A.P., Optimization of traditional and blown liners for a silent aircraft, 12th AIAA/CEAS Aeroacoustics Conference, Cambridge, Massachusettes, (2006), (AIAA paper 2006-2525).Google Scholar
Brambley, E.J., Davis, A.M.J. and Peake, N., Eigenmodes of lined flow ducts with rigid splices, J. Fluid Mech. 690 (2012), 388–425.Google Scholar
Regan, B. and Eaton, J., Modeling the influence of acoustic liner nonuniformities on duct modes, J. Sound Vib. 219 (1999), 859–879.Google Scholar
Wright, M. C. M. and McAlpine, A., Calculation of modes in azimuthally non-uniform lined ducts with uniform flow, J. Sound Vib. 302 (2007), 403–407.CrossRefGoogle Scholar
Watson, W. R., Circumferentially segmented duct liners optimized for axisymmetric and standing-wave sources, NASA Rep. No. 2075 (1982).Google Scholar
Campos, L. M. B. C. and Oliveira, J. M. G. S., On the acoustic modes in a cylindrical duct with an arbitrary wall impedance distribution, J. Acoust. Soc. Am. 116 (2004), 3336–3346.Google Scholar
Bi, W. P., Pagneux, V., Lafarge, D., and Aurégan, Y., Modelling of sound propagation in a non-uniform lined duct using a multi-modal propagation method, J. Sound Vib. 289 (2006) 1091–1111.Google Scholar
Bi, W.-P., Pagneux, V., Lafarge, D. and Auregan, Y., An improved multimodal method for sound propagation in nonuniform lined ducts, J. Acoust. Soc. Am. 122 (2007) 280–290.CrossRefGoogle ScholarPubMed
Brambley, E. J., Darau, M. and Rienstra, S. W., The critical layer in linear-shear boundary layers over acoustic linings, J. Fluid Mech. 710 (2012), 545–568.Google Scholar
Swinbanks, M.A., The sound field generated by a source distribution in a long duct carrying shear flow, J. Sound Vib. 40 (1975), 51–76.CrossRefGoogle Scholar
Nayfeh, A.H., Kaiser, J.E. and Telionis, D.P., Acoustics of aircraft engine-duct systems, AIAA Journal 13 (1975), 130–153.CrossRefGoogle Scholar
Oppeneer, M., Sound propagation in lined ducts with parallel flow, PhD thesis, Technische Universiteit Eindhoven, Eindhoven, the Netherlands, (2014).Google Scholar
Sánchez, J.R., Étude théorique et numérique des modes propres acoustiques dans un conduit avec écoulement et parois absorbantes. Modélisation et simulation, Doctorat de l’Université de Toulouse, Institut Supérieur de l’Aeronautique et de l’Espace, France, (2016).Google Scholar
Hilderbrand, F. B., Introduction to Numerical Analysis, (New York: McGraw-Hill, 1956).Google Scholar
Bender, C.M. and Orszag, S.A., Advanced Numerical Methods for Scientists and Engineers, (New York: Springer-Verlag, 1999).Google Scholar
Vilenski, G.G. and Rienstra, S.W., Numerical acoustic modes in a ducted shear flow, 11th AIAA/CEAS Aeroacoustics Conference, Monterey, CA, USA, (2005).Google Scholar
Nayfeh, A.H., Kaiser, J.E. and Shaker, B.S., Effect of mean-velocity profile shape on sound transmission through two dimensional ducts, J. Sound Vib. 34 (1974), 413–423.Google Scholar
Benedict, R.P., Fundamentals of Pipe Flow, (New York: John Wiley and Sons, 1980).Google Scholar
Gabard, G., A comparison of boundary conditions for flow acoustics, J. Sound Vib. 332 (2013), 714–724.CrossRefGoogle Scholar
Pagneux, V., Amir, N. and Kergomard, J., A study of wave propagation in varying cross-section waveguides by modal decomposition. Part I: Theory and validation, J. Acoust. Soc. Am. 100 (1996), 2034–2048.Google Scholar
Metchel, F.P., Modal analysis in lined wedge-shaped ducts, J. Sound Vib. 216 (1998), 673–696.Google Scholar
Nayfeh, A.H., Introduction to Perturbation Techniques, (John Wiley & Sons, 1981).Google Scholar
Rienstra, S.W., Sound transmission in slowly varying circular and annular lined ducts with flow, J. Fluid Mech. 380 (1999), 279–296.Google Scholar
Rienstra, S.W., Sound propagation in slowly varying lined flow ducts of arbitrary cross-section. J. Fluid Mech. 495 (2003), 157–173.Google Scholar
Cooper, A.J., Peake, N., Propagation of unsteady disturbances in a slowly varying duct with mean swirling flow, J. Fluid Mech. 445 (2001), 207–234.Google Scholar
Lloyd, A.E.D. and Peake, N., The propagation of acoustic waves in a slowly varying duct with radially sheared axial mean flow, J. Sound Vib. 332 (2013), 3937–3946.CrossRefGoogle Scholar
Brambley, E.J. and Peake, N., Sound transmission in strongly curved slowly varying cylindrical ducts with flow, J. Fluid Mech. 596 (2008), 387–412.Google Scholar
Rostafinski, W., Monograph on Propagation of Sound Waves in Curved Ducts, NASA Reference Publication 1248, (Washington, DC: NASA, 1991).Google Scholar
Felix, S. and Pagneux, V., Sound attenuation in lined bends, J. Acoust. Soc. Am. 116 (2004), 1921–1931.CrossRefGoogle Scholar
Furnell, G.D. and Bies, D.A., Characteristics of modal wave propagation within longitudinally curved acoustic waveguides, J. Sound Vib. 130 (1989), 405–423.Google Scholar
Capelli, A., The influence of flow on the acoustic characteristics of duct bend for highr order modes: A numerical study, J. Sound Vib. 82 (1982), 131–149.Google Scholar
Berger, S.A., Talbot, L. and Yao, L.-S., Flow in curved pipes, Ann. Rev. Fluid Mech. 15 (1983), 461–512.Google Scholar
Patankar, S.V., Pratap, V.S. and Spalding, D.B., Prediction of turbulent flow in curved pipes, J. Fluid Mech. 67 (1975), 583–595.Google Scholar
Kerrobrock, J.L., Small disturbances in turbomachine annuli with swirl, AIAA J. 15 (1977), 794–803.Google Scholar
Tam, C.K.W. and Auriault, L., The wave modes in ducted swirling with mean vortical swirling, J. Fluid Mech. 371 (1998), 1–20.Google Scholar
Nijboer, R.J., Eigenvalues and eigenfunctions of ducted swirling flows, National Aerospace Laboratory NLR, NLR-TP-2001-141, (2001), (also AIAA-2001-2178).CrossRefGoogle Scholar
Bergmann, P.G., The wave equation in a medium with a variable index of refraction, J. Acoust. Soc. Am. 17 (1946), 329–333.Google Scholar
Dokumaci, E., A simple approach for evaluation of cut-on condition of higher order modes in inhomogeneous uniform waveguides, J. Sound Vib. 440 (2019), 231–238.CrossRefGoogle Scholar
Abromovitch, M., Stegun, I.A., Handbook of Mathematical Functions, (Washington: National Bureau of Standards, Applied Mathematics Series 55, 1972).Google Scholar

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