Numerical characterization of an axisymmetric lined duct with flow using the multimodal scattering matrix

• Autorzy: Taktak M. , Majdoub M. A. , Haddar M. , Bentahar M.

Warianty tytułu

PL

Numeryczna charakteryzacja wyściełanego przewodu osiowo-symetrycznego z przepływem za pomocą wielomodalnej macierzy rozpraszania

• Języki publikacji: EN

Abstrakty

EN

In this paper, the development of a numerical method to compute the multimodal scattering matrix of a lined duct in the presence of flow is presented. This method is based on the use of the convected Helmholtz equation and the addition of modal pressures at duct boundaries as additional degrees of freedom of the system. The boundary effects at the inlet and outlet of the finite waveguide are neglected. The choice of this matrix is justified by the fact that it represents an intrinsic characterization of a duct system. The validation of the proposed finite element is done by a comparison with the analytical formulation for simple cases of ducts. Then, the numerical coefficients of the scattering matrix of a lined duct and its acoustic power attenuation are computed for several flow velocities to evaluate the flow effect.

PL

W pracy zaprezentowano numeryczną metodę wyznaczania macierzy rozpraszania dla wyściełanego przewodu z uwzględnieniem wewnętrznego przepływu czynnika. Metodę oparto na zastosowaniu równania konwekcji Helmholtza z wprowadzeniem ciśnień modalnych na brzegach jako dodatkowych stopni swobody układu. Efekty brzegowe na wlocie i wylocie przewodu falowego o skończonej długości pominięto. Wybór macierzy rozpraszania uzasadniono faktem, że reprezentuje ona wewnętrzną charakterystykę analizowanego modelu. Zaproponowany element skończony zweryfikowano poprzez porównanie z istniejącymi rozwiązaniami analitycznymi dla prostych przypadków konfiguracji przewodu. Następnie numerycznie obliczono wartości elementów macierzy rozpraszania oraz współczynniki tłumienia akustycznego dla kilku prędkości przepływu w celu określenia, jak dalece wpływa on na badany układ.

Słowa kluczowe

EN

lined duct; scattering matrix; mean flow

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2013
• Tom: Vol. 51 nr 2
• Strony: 313--325
• Opis fizyczny: Bibliogr. 19 poz., rys.

Twórcy

autor

Taktak M.

• University of Sfax, National School of Engineers of Sfax, Unit of Mechanics, Modelling and Production, Sfax, Tunisia

autor

Majdoub M. A.

• University of Sfax, National School of Engineers of Sfax, Unit of Mechanics, Modelling and Production, Sfax, Tunisia

autor

Haddar M.

• University of Sfax, National School of Engineers of Sfax, Unit of Mechanics, Modelling and Production, Sfax, Tunisia

autor

Bentahar M.

• University of Technology of Compi`egne, Roberval Laboratory UMR UTC-CNRS no. 6253, Compi`egne Cedex, France

Bibliografia

• 1. Abom M., 1991,Measurement of the scattering matrix of acoustical two-ports, Mechanical Systems Signal Processing, 5, 2, 89-104
• 2. Akoum M., Ville J.M., 1998, Measurement of reflection matrix of a discontinuity in a duct, Journal of the Acoustical Society of America, 103, 5, 2463-2468
• 3. Aurègan Y., Starobinski R., 1998, Determination of acoustical energy dissipation/production potentiality from the acoustic transfer functions of a multiport, Acta Acustica United with Acustica, 85, 788-792
• 4. Bi W.P., Pagneux V., Lafarge D., Aurègan Y., 2006, Modelling of sound propagation in non-uniform lined duct using a Multi-Modal PropagationMethod, Journal of Sound and Vibration, 289, 1091-1111
• 5. Craggs, A., 1989, The application of the scattering matrix and matrix condensation methods with finite elements to ducts acoustics, Journal of Sound and Vibration, 132, 2, 393-402
• 6. Dhatt G., Touzot G., 1989, Presentation of the Finite Element Method, Maloine S.A. Editeur, Paris
• 7. Elnady T., Bodèn H., 2003, On semi-empirical liner impedance modeling with grazing flow, AIAA Paper, 2003-3304
• 8. Leroux M., Job S., Aurègan Y., Pagneux V., 2003, Acoustical propagation in lined duct with flow. Numerical simulations and measurements, 10th International Congress of Sound and Vibration, Stockholm, Sweden, 3255-3262
• 9. Lesueur L., 1988, Rayonnement acoustique des structures: Vibroacoustique et Interactions Fluide Structure, Editions Eyrolles, Paris
• 10. Lung T.Y., Doige A.G., 1983, A time-averaging transient testing method for acoustic properties of piping systems and mufflers with flow, Journal of the Acoustical Society of America, 73, 867-876
• 11. Munjal M.L., 1987, Acoustics of Ducts and Mufflers, Wiley-Interscience, New York
• 12. Peat K.S., 1988, The transfer matrix of a uniform duct with a linear temperature gradient, Journal of Sound and Vibration, 123, 1, 43-53
• 13. Pierce A.D., 1981, Acoustics: An Introduction to its Physical Principles and Applications, McGraw-Hill, New York
• 14. Sitel A., Ville J.M., Foucart F., 2003, An experimental facility for measurement of acoustic transmission matrix and acoustic power dissipation of a duct discontinuity in higher modes propagation conditions, Acta Acustica United with Acustica, 89, 586-594
• 15. Sitel A., Ville J.M., Foucart F., 2006, Multimodal procedure to measure the acoustic scattering matrix of a duct discontinuity for higher order mode propagation conditions, Journal of the Acoustical Society of America, 120, 5, 2478-2490
• 16. Taktak M., Ville J.M., Haddar M., Gabard G., Foucart F., 2010, An indirect method for the characterization of locally reacting liners, Journal of the Acoustical Society of America, 127, 6, 3548-3559
• 17. To C.W.S., Doige A.G., 1979, A transient testing technique for the determination of matrix parameters of acoustic systems, I: Theory and principles, Journal of Sound and Vibration, 62, 207-222
• 18. To C.W. S., Doige A.G., 1979, A transient testing technique for the determination of matrix parameters of acoustic systems, II: Experimental procedures and results, Journal of Sound and Vibration, 62, 223-233
• 19. Ville J.M., Foucart F., 2003, Experimental set up for measurement of acoustic power dissipation in lined ducts for higher order modes propagation with air mean flow conditions, Journal of the Acoustical Society of America, 114, 4, 1742-1748