Propagation of Acoustic Waves in Ducts with Flow Using the Multimodal Formulation
This paper presents a multimodal method for the computation of the acoustic field in an axisymmetric varying duct with or without liner and in the presence of mean flow. The original three-dimensional equations are rearranged into a set of coupled one-dimensional equations by projecting the acoustic...
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| Veröffentlicht in: | AIAA journal 2023-06, Vol.61 (6), p.2721-2733 |
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| creator | Mangin, Bruno Daroukh, Majd Gabard, Gwénaël |
| description | This paper presents a multimodal method for the computation of the acoustic field in an axisymmetric varying duct with or without liner and in the presence of mean flow. The original three-dimensional equations are rearranged into a set of coupled one-dimensional equations by projecting the acoustic field over transverse basis functions. To maintain the computational efficiency of the original multimodal method (applicable without flow), only the leading-order effects of the mean flow are modeled using a multiple-scales approach. A matching procedure is also given to deal with liner discontinuities in such a duct. Two different transverse bases are used: one is based on Fourier–Bessel functions to evaluate the effect of modal scattering and the other is based on Fourier–Chebyshev polynomials to improve the method efficiency. The formulation is evaluated against analytical models based on the Wentzel–Kramers–Brillouin technique and against finite-element solutions. It is shown to give consistent results for minor computational cost for modes propagating in ducts with or without acoustic liners. This method can be easily adapted to take into account more complex flows and geometries. |
| doi_str_mv | 10.2514/1.J062659 |
| format | Article |
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The original three-dimensional equations are rearranged into a set of coupled one-dimensional equations by projecting the acoustic field over transverse basis functions. To maintain the computational efficiency of the original multimodal method (applicable without flow), only the leading-order effects of the mean flow are modeled using a multiple-scales approach. A matching procedure is also given to deal with liner discontinuities in such a duct. Two different transverse bases are used: one is based on Fourier–Bessel functions to evaluate the effect of modal scattering and the other is based on Fourier–Chebyshev polynomials to improve the method efficiency. The formulation is evaluated against analytical models based on the Wentzel–Kramers–Brillouin technique and against finite-element solutions. It is shown to give consistent results for minor computational cost for modes propagating in ducts with or without acoustic liners. This method can be easily adapted to take into account more complex flows and geometries.</description><identifier>ISSN: 0001-1452</identifier><identifier>ISSN: 0740-722X</identifier><identifier>EISSN: 1533-385X</identifier><identifier>DOI: 10.2514/1.J062659</identifier><language>eng</language><publisher>Virginia: American Institute of Aeronautics and Astronautics</publisher><subject>Acoustic liners ; Acoustic propagation ; Acoustic waves ; Acoustics ; Basis functions ; Bessel functions ; Chebyshev approximation ; Computational efficiency ; Computing costs ; Ducts ; Engineering Sciences ; Mathematical functions ; Mathematical models ; Physics ; Polynomials ; Propagation modes ; Scattering ; Sound fields ; Surface acoustic waves ; Three dimensional flow ; Wave propagation</subject><ispartof>AIAA journal, 2023-06, Vol.61 (6), p.2721-2733</ispartof><rights>Copyright © 2023 by Bruno Mangin, Majd Daroukh, Gwénaël Gabard. Published by the American Institute. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. All requests for copying and permission to reprint should be submitted to CCC at ; employ the eISSN to initiate your request. See also AIAA Rights and Permissions .</rights><rights>Copyright © 2023 by Bruno Mangin, Majd Daroukh, Gwénaël Gabard. Published by the American Institute. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. All requests for copying and permission to reprint should be submitted to CCC at www.copyright.com; employ the eISSN 1533-385X to initiate your request. 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| source | EZB-FREE-00999 freely available EZB journals; Alma/SFX Local Collection |
| subjects | Acoustic liners Acoustic propagation Acoustic waves Acoustics Basis functions Bessel functions Chebyshev approximation Computational efficiency Computing costs Ducts Engineering Sciences Mathematical functions Mathematical models Physics Polynomials Propagation modes Scattering Sound fields Surface acoustic waves Three dimensional flow Wave propagation |
| title | Propagation of Acoustic Waves in Ducts with Flow Using the Multimodal Formulation |
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