zbMATH — the first resource for mathematics

A classification of duct modes based on surface waves. (English) Zbl 1163.74431
Summary: For the relatively high frequencies relevant in a turbofan engine duct, the modes of a lined section may be classified in two categories: genuine acoustic 3D duct modes resulting from the finiteness of the duct geometry, and 2D surface waves that exist only near the wall surface in a way essentially independent of the rest of the duct. Per frequency and circumferential order there are at most four surface waves. They occur in two kinds: two acoustic surface waves that exist with and without mean flow, and two hydrodynamic surface waves that exist only with mean flow. The number and location of the surface waves depends on the wall impedance \(Z\) and mean flow Mach number. When \(Z\) is varied, an acoustic mode may change via small transition zones into a surface waves and vice versa.
Compared to the acoustic modes, the surface waves behave – for example as a function of the wall impedance – rather differently as they have their own dynamics. They are therefore more difficult to find. A method is described to trace all modes by continuation in \(Z\) from the hard-wall values, by starting in an area of the complex \(Z\)-plane without surface waves.

76Q05 Hydro- and aero-acoustics
76B99 Incompressible inviscid fluids
Full Text: DOI
[1] Tyler, J.M.; Sofrin, T.G., Axial flow compressor noise studies, Trans. soc. automot. eng., 70, 309-332, (1962)
[2] W.E. Zorumski, Acoustic theory of axisymmetric multi-sectioned ducts, NASA TR R-419, 1974.
[3] Tester, B.J., The optimization of modal sound attenuation in ducts, in the absence of Mean flow, J. sound vib., 27, 4, 477-513, (1973) · Zbl 0272.76048
[4] Tester, B.J., The propagation and attenuation of sound in ducts containing uniform or “plug” flow, J. sound vib., 28, 2, 151-203, (1973) · Zbl 0258.76057
[5] Tester, B.J., Some aspects of sound attenuation in lined ducts containing inviscid Mean flows with boundary layers, J. sound vib., 28, 2, 217-245, (1973) · Zbl 0255.76094
[6] Koch, W.; Möhring, W., Eigensolutions for liners in uniform Mean flow ducts, Aiaa j., 21, 200-213, (1983) · Zbl 0526.76081
[7] S.W. Rienstra, The acoustics of a lined duct with flow, NLR TR 87002 U, 1987.
[8] E.R. Rademakers, Experimental validation of the lined duct acoustics model LINDA, NLR CR 89236L, 1989.
[9] Rienstra, S.W., Sound transmission in slowly varying circular and annular ducts with flow, J. fluid mech., 380, 279-296, (1999) · Zbl 0946.76088
[10] Rienstra, S.W.; Eversman, W., A numerical comparison between multiple-scales and FEM solution for sound propagation in lined flow ducts, J. fluid mech., 437, 367-384, (2001) · Zbl 0982.76077
[11] Ingard, K.U., Influence of fluid motion past a plane boundary on sound reflection, absorption, and transmission, J. acoust. soc. am., 31, 7, 1035-1036, (1959)
[12] Myers, M.K., On the acoustic boundary condition in the presence of flow, J. sound vib., 71, 3, 429-434, (1980) · Zbl 0448.76065
[13] M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Dover, New York, 1964. · Zbl 0171.38503
[14] Quinn, M.C.; Howe, M.S., On the production and absorption of sound by lossless liners in the presence of Mean flow, J. sound vib., 97, 1, 1-9, (1984)
[15] S.W. Rienstra, Hydrodynamic instabilities and surface waves in a flow over an impedance wall, in: G. Comte-Bellot, J.E. Ffowcs Williams (Eds.), Proceedings of the IUTAM Symposium ‘Aero- and Hydro-Acoustics’, 1985, Lyon, Springer, Heidelberg, 1986, pp. 483-490.
[16] Jones, D.S.; Morgan, J.D., The instability of a vortex sheet on a subsonic stream under acoustic radiation, Proc. camb. phil. soc., 72, 465-488, (1972) · Zbl 0251.76036
[17] Crighton, D.G.; Leppington, F.G., Radiation properties of the semi-infinite vortex sheet: the initial-value problem, J. fluid mech., 64, 2, 393-414, (1974) · Zbl 0298.76045
[18] F.W.J. Olver, Asymptotics and Special Functions, Academic Press, New York, 1974. · Zbl 0303.41035
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.