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Acoustic resonances and trapped modes in pipes and tunnels

Published online by Cambridge University Press:  23 May 2008

STEFAN HEIN  and
WERNER KOCH
STEFAN HEIN
Affiliation:
Institute of Aerodynamics and Flow Technology, DLR Göttingen, Germany
WERNER KOCH
Affiliation:
Institute of Aerodynamics and Flow Technology, DLR Göttingen, Germany
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Abstract

Acoustic resonances of simple three-dimensional finite-length structures in an infinitely long cylindrical pipe are investigated numerically by solving an eigenvalue problem. To avoid unphysical reflections at the finite grid boundaries placed in the uniform cross-sections of the pipe, perfectly matched layer absorbing boundary conditions are applied in the form of the complex scaling method of atomic and molecular physics. Examples of the structures investigated are sound-hard spheres, cylinders, cavities and closed side branches. Several truly trapped modes with zero radiation loss are identified for frequencies below the first cutoff frequency of the pipe. Such trapped modes can be excited aerodynamically by coherent vortices if the frequency of the shed vortices is close to a resonant frequency. Furthermore, numerical evidence is presented for the existence of isolated embedded trapped modes for annular cavities above the first cutoff frequency and for closed side branches below the first cutoff frequency. As applications of engineering interest, the acoustic resonances are computed for a ball-type valve and around a simple model of a high-speed train in an infinitely long tunnel.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 605 , 25 June 2008 , pp. 401 - 428
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Aguilar, J. & Combes, J. M. 1971 A class of analytic perturbations for one-body Schrödinger Hamiltonians. Commun. Math. Phys. 22, 269–279.CrossRefGoogle Scholar
Annino, G., Yashiro, H., Cassettari, M. & Martinelli, M. 2006 Properties of trapped electromagnetic modes in coupled waveguides. Phys. Rev. B 73, 125308-1–125308-8.CrossRefGoogle Scholar
Aslanyan, A., Parnovski, L. & Vassiliev, D. 2000 Complex resonances in acoustic waveguides. Q. J. Mech. Appl. Maths 53, 429–447.CrossRefGoogle Scholar
Baslev, E. & Combes, J. M. 1971 Spectral properties of many body Schrödinger operators with dilation analytic interactions. Commun. Math. Phys. 22, 280–294.CrossRefGoogle Scholar
Bearman, P. W. 1984 Vortex shedding from oscillating bluff bodies. Annu. Rev. Fluid Mech. 16, 195–222.CrossRefGoogle Scholar
Bérenger, J. P. 1994 A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114, 185–200.CrossRefGoogle Scholar
Callan, M., Linton, C. M. & Evans, D. V. 1991 Trapped modes in two-dimensional waveguides. J. Fluid Mech. 229, 51–64.CrossRefGoogle Scholar
Camp, T. R. 1999 A study of acoustic resonance in a low-speed multistage compressor. Trans. ASME: J. Turbomachinery 121, 36–43.Google Scholar
Chew, W. C. & Weedon, W. H. 1994 A 3-D perfectly matched medium from modified Maxwell's equation with stretched coordinates. Microwave Optical Technol. Lett. 7 (13), 599–604.CrossRefGoogle Scholar
Collino, F. & Monk, P. 1998 The perfectly matched layer in curvilinear coordinates. SIAM J. Sci. Comput. 19, 2061–2090.CrossRefGoogle Scholar
Dequand, S., Hulshoff, S. J. & Hirschberg, A. 2003 Self-sustained oscillations in a closed side branch system. J. Sound Vib. 265, 359–386.CrossRefGoogle Scholar
Diedrichs, B., Krajnović, S. & Berg, M. 2008 On the aerodynamics of car body vibrations of high-speed trains cruising inside tunnels. Engng. Appl. Comput. Fluid Mech. 2, 51–75.Google Scholar
Duan, Y., Koch, W., Linton, C. M. & McIver, M. 2007 Complex resonances and trapped modes in ducted domains. J. Fluid Mech. 571, 119–147.CrossRefGoogle Scholar
Duan, Y. & McIver, M. 2004 Rotational acoustic resonances in cylindrical waveguides. Wave Motion 39, 261–274.CrossRefGoogle Scholar
Duclos, P., Exner, P. & Šťovíček, P. 1995 Curvature-induced resonances in a two-dimensional Dirichlet tube. Ann. Inst. Henri Poincaré A62, 81–101.Google Scholar
Evans, D. V. & Linton, C. M. 1991 Trapped modes in open channels. J. Fluid Mech. 225, 153–175.CrossRefGoogle Scholar
Evans, D. V. & Porter, R. 1998 Trapped modes embedded in the continuous spectrum. Q. J. Mech. Appl. Maths 52, 263–274.CrossRefGoogle Scholar
Harari, I., Patlashenko, I. & Givoli, D. 1998 Dirichlet-to-Neumann maps for unbounded wave guides. J. Comput. Phys. 143, 200–223.CrossRefGoogle Scholar
Hein, S., Hohage, T. & Koch, W. 2004 On resonances in open systems. J. Fluid Mech. 506, 255–284.CrossRefGoogle Scholar
Hein, S., Hohage, T., Koch, W. & Schöberl, J. 2007 Acoustic resonances in a high lift configuration. J. Fluid Mech. 582, 179–202.CrossRefGoogle Scholar
Hislop, P. D. & Sigal, I. M. 1996 Introduction to Spectral Theory. Springer.CrossRefGoogle Scholar
Hu, F. Q. 2004 Absorbing boundary conditions. Intl. J. Comput. Fluid Dyn. 18, 513–522.CrossRefGoogle Scholar
Jungowski, W. M., Botros, K. K. & Studzinski, W. 1989 Cylindrical side-branch as tone generator. J. Sound Vib. 131, 265–285.CrossRefGoogle Scholar
Koch, W. 1983 Resonant acoustic frequencies of flat plate cascades. J. Sound Vib. 88, 233–242.CrossRefGoogle Scholar
Kriesels, P. C., Peters, M. C. A. M., Hirschberg, A., Wijnands, A. P. J., Iafrati, A., Riccardi, G., Piva, R. & Bruggeman, J. C. 1995 High amplitude vortex-induced pulsations in a gas transport system. J. Sound Vib. 184, 343–368.CrossRefGoogle Scholar
Lafon, P., Caillaud, S., Devos, J. P. & Lambert, C. 2003 Aeroacoustical coupling in a ducted shallow cavity and fluid/structure effects on a steam line. J. Fluids Struct. 18, 695–713.CrossRefGoogle Scholar
Levitin, M. & Marletta, M. 2006 A simple method of calculating eigenvalues and resonances in domains with regular ends. ArXiv preprint math.SP/0611237.Google Scholar
Li, Y. & Mei, C. C. 2006 Subharmonic resonance of a trapped wave near a vertical cylinder in a channel. J. Fluid Mech. 561, 391–416.CrossRefGoogle Scholar
Linton, C. M. & McIver, M. 1998 Trapped modes in cylindrical waveguides. Q. J. Mech. Appl. Maths 51, 389–412.CrossRefGoogle Scholar
Linton, C. M. & McIver, P. 2007 Embedded trapped modes in water waves and acoustics. Wave Motion 45, 16–29.CrossRefGoogle Scholar
Mittra, R. & Lee, S. W. 1971 Analytical Techniques in the Theory of Guided Waves. Macmillan.Google Scholar
Moiseyev, N. 1998 Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling. Phys. Rep. 302, 211–293.CrossRefGoogle Scholar
Nayfeh, A. H. & Huddleston, D. H. 1979 Resonant acoustic frequencies of parallel plates. AIAA Paper 79-1522.Google Scholar
Parker, R. 1966 Resonance effects in wake shedding from parallel plates: Some experimental observations. J. Sound Vib. 4, 62–72.CrossRefGoogle Scholar
Parker, R. 1967 a Resonance effects in wake shedding from compressor blading. J. Sound Vib. 6, 302–309.CrossRefGoogle Scholar
Parker, R. 1967 b Resonance effects in wake shedding from parallel plates: Calculation of resonant frequencies. J. Sound Vib. 5, 330–343.CrossRefGoogle Scholar
Parker, R. 1984 Acoustic resonances and blade vibration in axial flow compressors. J. Sound Vib. 92, 529–539.CrossRefGoogle Scholar
Parker, R. & Stoneman, S. A. T. 1989 The excitation and consequences of acoustic resonances in enclosed fluid flow around solid bodies. Proc. Inst. Mech. Engrs. 203, 9–19.CrossRefGoogle Scholar
Rockwell, D., Lin, J.-C., Oshkai, P., Reiss, M. & Pollack, M. 2003 Shallow cavity flow tone experiments: onset of locked-on states. J. Fluids Struct. 17, 381–414.CrossRefGoogle Scholar
Rockwell, D. & Naudascher, E. 1978 Review – Self-sustaining oscillations of flow past cavities. Trans. ASME: J. Fluids Engng. 100, 152–165.Google Scholar
Rockwell, D. & Naudascher, E. 1979 Self-sustained oscillations of impinging free shear layers. Annu. Rev. Fluid Mech. 11, 67–94.CrossRefGoogle Scholar
Schöberl, J. 1997 NETGEN An advancing front 2D/3D-mesh generator based on abstract rules. Computing and Visualization in Science 1, 41–52.Google Scholar
Schuhmann, R. & Weiland, T. 2000 Rigorous analysis of trapped modes in accelerating cavities. Phys. Rev. Special Topics—Accelerators and Beams 3, 122002.CrossRefGoogle Scholar
Simon, B. 1973 The theory of resonances for dilation analytic potentials and the foundations of time dependent perturbation theory. Ann. Maths 97, 247–274.CrossRefGoogle Scholar
Smith, B. A. W. & Luloff, B. V. 2000 The effect of seat geometry on gate valve noise. Trans. ASME: J. Pressure Vessel Technol. 122, 401–407.Google Scholar
Suzuki, M. 2004 An aerodynamic design of high-speed train for reducing flow-induced vibration in tunnel. In Proc. ECCOMAS 2004, Jyväskylä, Finland, July 24–28 (ed. Neittaanmäki, P., Rossi, T., Korotov, S., Oñate, E., Périaux, J. & Knörzer, D.).Google Scholar
Taylor, M. 1996 Partial Differential Equations II. Springer.CrossRefGoogle Scholar
Ursell, F. 1991 Trapped modes in a circular cylindrical acoustic waveguide. Proc. R. Soc. Lond. A 435, 575–589.Google Scholar
Ziada, S. & Bühlmann, E. T. 1992 Self-excited resonances of two side-branches in close proximity. J. Fluids Struct. 6, 583–601.CrossRefGoogle Scholar
Ziada, S. & Shine, S. 1999 Strouhal numbers of flow-excited acoustic resonance of closed side branches. J. Fluids Struct. 13, 127–142.CrossRefGoogle Scholar