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Aeroacoustic power generated by a compact axisymmetric cavity: prediction of self-sustained oscillation and influence of the depth

Published online by Cambridge University Press:  12 June 2012

G. Nakı̇boğlu ,
H. B. M. Manders  and
A. Hirschberg
G. Nakı̇boğlu*
Affiliation:
Laboratory of Fluid Mechanics, Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
H. B. M. Manders
Affiliation:
Laboratory of Fluid Mechanics, Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
A. Hirschberg
Affiliation:
Laboratory of Fluid Mechanics, Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

Aeroacoustic power generation due to a self-sustained oscillation by an axisymmetric compact cavity exposed to a low-Mach-number grazing flow is studied both experimentally and numerically. The feedback effect is produced by the velocity fluctuations resulting from a coupling with acoustic standing waves in a coaxial pipe. A numerical methodology that combines incompressible flow simulations with vortex sound theory is used to predict the time-averaged acoustic source power generated by the cavity. The effect of cavity depth on the whistling is addressed. It is observed that the whistling occurs around a peak-whistling Strouhal number which depends on the cavity depth to width ratio. The proposed numerical method provides excellent predictions of the peak-whistling Strouhal number as a function of cavity depth. Given the oscillation amplitude, the numerical method predicts the time-averaged acoustic source power within a factor of two for moderate fluctuation amplitudes. For deep cavities the time-averaged acoustic source power appears to be independent of the cavity depth.

JFM classification

Acoustics: Aeroacoustics Acoustics: Hydrodynamic noise Vortex Flows: Vortex shedding
Type
Papers
Information
Journal of Fluid Mechanics , Volume 703 , 25 July 2012 , pp. 163 - 191
Copyright
Copyright © Cambridge University Press 2012

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References

1. Abom, M. & Bodén, H. 1988 Error analysis of two-microphone measurements in ducts with flow. J. Acoust. Soc. Am. 83, 2429–2438.CrossRefGoogle Scholar
2. Allam, S. & A˚bom, M. 2006 Investigation of damping and radiation using full plane wave decomposition in ducts. J. Sound Vib. 292, 519–534.CrossRefGoogle Scholar
3. Binnie, A. M. 1961 Self-induced waves in a conduit with corrugated walls ii. Experiments with air in corrugated and finned tubes. Proc. R. Soc. Lond A 262, 179–191.Google Scholar
4. Blake, W. K. 1986 Mechanics of Flow-Induced Sound and Vibration: Vol 1 & Vol 2. Academic.Google Scholar
5. Blevins, R. D. 1977 Flow-induced Vibration. Van Nostrand Reinhold.Google Scholar
6. Bracewell, R. N. 1986 The Fourier Transform and its Applications. McGraw Hill.Google Scholar
7. Bruggeman, J. C., Hirschberg, A., vanDongen, M. E. H., Wijnands, A. P. J. & Gorter, J. 1991 Self-sustained aero-acoustic pulsations in gas transport systems: experimental study of the influence of closed side branches. J. Sound Vib. 150, 371–393.CrossRefGoogle Scholar
8. Cargill, A. M. 1971 Low frequency acoustic radiation from a jet pipe – a second order theory. J. Sound Vib. 83 (3), 339–354.CrossRefGoogle Scholar
9. Cargill, A. M. 1982 Low-frequency sound radiation and generation due to the interaction of unsteady flow with a jet pipe. J. Fluid Mech. 121, 59–105.CrossRefGoogle Scholar
10. Cebeci, T. 2004 Analysis of Turbulent Flows, 2nd edn. Elsevier.Google Scholar
11. Davies, P. O. A. L. 1981 Flow-acoustic coupling in ducts. J. Sound Vib. 77 (2), 191–209.CrossRefGoogle Scholar
12. Davies, P. O. A. L. 1988 Practical flow duct acoustics. J. Sound Vib. 124 (1), 91–115.CrossRefGoogle Scholar
13. Dequand, S., Hulshoff, S. J. & Hirschberg, A. 2003 Self-sustained oscillations in a closed side branch system. J. Sound Vib. 256, 359–386.CrossRefGoogle Scholar
14. Elder, S. A. 1980 Forced oscillations of a separated shear layer with application to cavity flow-tone effects. J. Acoust. Soc. Am. 67 (3), 774–781.CrossRefGoogle Scholar
15. English, E. J. & Holland, K. R. 2010 Aeroacoustic sound generation in simple expansion chambers. J. Acoust. Soc. Am. 128 (5), 2589–2595.CrossRefGoogle ScholarPubMed
16. Erdem, D., Rockwell, D., Oshkai, P. & Pollack, M. 2003 Flow tones in a pipeline-cavity system: effect of pipe asymmetry. J. Fluids Struct. 17, 511–523.CrossRefGoogle Scholar
17. Fletcher, J. C. 1979 Air flow and sound generation in musical wind instruments. Annu. Rev. Fluid Mech. 11, 95–121.CrossRefGoogle Scholar
18. Fluent 2006 Documentation. Canonsburg, PA.Google Scholar
19. Freymunt, P. 1966 On transition in a separated laminar boundary layer. J. Fluid Mech. 25, 683–704.CrossRefGoogle Scholar
20. Gates, R. S., Butler, C. B., Shaw, L. L. & Dix, R. E. 1987 Aeroacoustic effects of body blockage in cavity flow. In AIAA 11th Aeroacoustics Conference, Palo Alto, CA.CrossRefGoogle Scholar
21. Geveci, M., Oshkai, P., Rockwell, D., Lin, J. C. & Pollack, M. 2003 Imaging of the self-excited oscillation of flow past a cavity during generation of a flowtone. J. Fluids Struct. 18, 79–92.CrossRefGoogle Scholar
22. Gharib, M. & Roshko, A. 1987 The effect of flow oscillations on cavity drag. J. Fluid. Mech. 177, 501–530.CrossRefGoogle Scholar
23. Gloerfelt, X. 2009 Cavity Noise. von Kármán Lecture Notes on Aerodynamic Noise from Wall-bounded Flows , von Karman Institute for Fluid Dynamics, http://sin-web.paris.ensam.fr/squelettes/ref_biblio/Gloerfelt_VKI_2009a.pdf.Google Scholar
24. Golliard, J., Tonon, D. & Belfroid, S. P. C. 2010 Experimental investigation of the source locations for whistling short corrugated pipes. In Proceedings of ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting and 8th International Conference on Nanochannels, Microchannels and Minichannels, Montreal, Canada.Google Scholar
25. Hirschberg, A. & Rienstra, S. W. 2001 An introduction to acoustics, Report IWDE 01-03, Eindhoven University of Technology, http://www.win.tue.nl/~sjoerdr/papers/boek.pdf.Google Scholar
26. Hourigan, K., Welsh, M. C., Thompson, M. C. & Stokes, A. N. 1990 Aerodynamic sources of acoustic resonance in a duct with baffles. J. Fluids Struct. 4, 345–370.CrossRefGoogle Scholar
27. Howe, M. S. 1975 Contributions to the theory of aerodynamic sound, with application to excess jet noise and the theory of the flute. J. Fluid Mech. 71, 625–673.CrossRefGoogle Scholar
28. Howe, M. S. 1984 On the absorption of sound by turbulence and other hydrodynamic flows. IMA J. Appl. Maths 32, 187–209.CrossRefGoogle Scholar
29. Howe, M. S. 1997 Edge, cavity and aperture tones at very low Mach numbers. J. Fluid Mech. 330, 61–84.CrossRefGoogle Scholar
30. Howe, M. S. 1998 Acoustics of Fluid-Structure Interactions. Cambridge Univesity Press.CrossRefGoogle Scholar
31. Huang, X. Y. & Weaver, S. 1991 On the active control of shear layer oscillations across a cavity in the presence of pipeline acoustic resonance. J. Fluids Struct. 5, 207–219.CrossRefGoogle Scholar
32. Keller, J. J. 1984 Non-linear self-excited acoustic oscillations in cavities. J. Sound Vib. 94, 397–409.CrossRefGoogle Scholar
33. Kergomard, J. 1985 Comments on wall ‘effects on sound propagation in tubes’. J. Sound Vib. 98, 149–153.CrossRefGoogle Scholar
34. Kirchhoff, G. 1868 Ueber den einfluss der wärmeleitung in einem gase auf die schallbewegung. Ann. Phys. 210 (6), 177–193.CrossRefGoogle Scholar
35. Knisely, C. & Rockwell, D. 1982 Self-sustained low-frequency components in an impinging shear layer. J. Fluid. Mech. 116, 157–186.CrossRefGoogle Scholar
36. Kooijman, G., Hirschberg, A. & Golliard, J. 2008 Acoustical response of orifices under grazing flow: effect of boundary layer profile and edge geometry. J. Sound Vib. 315, 849–874.CrossRefGoogle Scholar
37. Krishnamurty, K. 1955 Acoustic radiation from two-dimensional rectangular cutouts in aerodynamic surfaces. NACA Tech. Note 3487.Google Scholar
38. Kundu, P. K. 1990 Fluid Mechanics. Academic.Google Scholar
39. Martínez-Lera, P., Schram, C., Föller, S., Kaess, R. & Polifke, W. 2009 Identification of the aeroacoustic response of a low Mach number flow through a T-joint. J. Acoust. Soc. Am. 126 (2), 582–586.CrossRefGoogle ScholarPubMed
40. Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23 (3), 521–544.CrossRefGoogle Scholar
41. Morfey, C. L. 1971 Sound transmission and generation in ducts with flow. J. Sound Vib. 14, 37–55.CrossRefGoogle Scholar
42. Munt, R. M. 1977 The interaction of sound with a subsonic jet issuing from a semi-infinite cylindrical pipe. J. Fluid Mech. 83, 609–640.CrossRefGoogle Scholar
43. Munt, R. M. 1990 Acoustic transmission properties of a jet pipe with subsonic jet flow. I. The cold jet reflection coefficient. J. Sound Vib. 142, 413–436.CrossRefGoogle Scholar
44. Myers, M. K. 1986 An exact energy corollary for homentropic flow. J. Sound Vib. 109 (2), 277–284.CrossRefGoogle Scholar
45. Myers, M. K. 1991 Transport of energy by disturbances in arbitrary steady flows. J. Fluid Mech. 226, 383–400.CrossRefGoogle Scholar
46. Nakiboğlu, G., Belfroid, S. P. C., Golliard, J. & Hirschberg, A. 2011 On the whistling corrugated pipes: effect of pipe length and flow profile. J. Fluid Mech. 672, 78–108.CrossRefGoogle Scholar
47. Nakiboğlu, G., Belfroid, S. P. C., Willems, J. F. H & Hirschberg, A. 2010 Whistling behavior of periodic systems: corrugated pipes and multiple side branch system. Intl J. Mech. Sci. 52 (11), 1458–1470.CrossRefGoogle Scholar
48. Nakiboğlu, G. & Hirschberg, A. 2012 Aeroacoustic power generated by multiple compact axisymmetric cavities: effect of hydrodynamic interference on the sound production. Phys. Fluids (in press).CrossRefGoogle Scholar
49. Nakiboğlu, G., Rudenko, O. & Hirschberg, A. 2012 Aeroacoustics of the swinging corrugated tube: voice of the dragon. J. Acoust. Soc. Am. 131 (1), 749–765.CrossRefGoogle ScholarPubMed
50. Nelson, P. A., Halliwell, N. A. & Doak, P. E. 1983 Fluid dynamics of a flow excited resonance, part ii. Flow acoustic interaction. J. Sound Vib. 91, 375–402.CrossRefGoogle Scholar
51. Oshkai, P., Rockwell, D. & Pollack, M. 2005 Shallow cavity flow tones: transformation from large- to small-scale modes. J. Sound Vib. 280, 777–813.CrossRefGoogle Scholar
52. Peters, M. C. A. M. 1993 Aeroacoustic sources in internal flows. PhD thesis, Technische Universiteit Eindhoven, Eindhoven, The Netherlands.Google Scholar
53. Peters, M. C. A. M., Hirschberg, A., Reijnen, A. J. & Wijnands, A. P. J. 1993 Damping and reflection coefficient measurements for an open pipe at low Mach and low Helmholtz numbers. J. Fluid Mech. 256, 499–534.CrossRefGoogle Scholar
54. Pierce, A. D. 1989 Acoustics, An Introduction to Its Physical Principles and Applications. Acoustical Society of America.Google Scholar
55. Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
56. Rayleigh, Lord 1896 The Theory of Sound – Volume I & II. Macmillan.Google Scholar
57. Rienstra, S. W. 1983 A small Strouhal number analysis for acoustic wave-jet flow-pipe interaction. J. Sound Vib. 86, 539–556.CrossRefGoogle Scholar
58. Rockwell, D. 1983 Oscillation of impinging shear layer. AIAA J. 21, 645–664.CrossRefGoogle Scholar
59. Rockwell, D. & Knisely, C. 1980 Vortex-edge interactions: mechanisms for generating low frequency components. Phys. Fluids. 23 (2), 239–340.CrossRefGoogle Scholar
60. Rockwell, D., Lin, C. J., 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
61. Rockwell, D. & Naudascher, E. 1978 Review:self-sustaining oscillations of flow past cavities. Trans. ASME: J. Fluids Engng 100, 152–165.Google Scholar
62. Rockwell, D. & Schachenmann, A. 1982 Self-generation of organized waves in an impinging turbulent jet at low Mach numbers. J. Fluid Mech. 117, 425–441.CrossRefGoogle Scholar
63. Ronneberger, D. & Ahrens, C. D. 1977 Wall shear stress caused by small amplitude perturbations of turbulent boundary-layer flow: an experimental investigation. J. Fluid Mech. 83 (3), 433–464.CrossRefGoogle Scholar
64. Roshko, A. 1955 Some measurements of flow in a rectangular cutout. NACA Tech. Note 3488.Google Scholar
65. Rowley, C. W., Williams, D. R., Colonius, T., Murray, R. M. & Macmynowski, D. G. 2006 Linear models for control of cavity flow oscillations. J. Fluid Mech. 547, 317–330.CrossRefGoogle Scholar
66. Rowley, C. W. & Williams, E. D. R. 2006 Dynamics and control of high-Reynolds-number flow over open cavities. Annu. Rev. Fluid Mech. 38, 251–276.CrossRefGoogle Scholar
67. Sahohia, V. 1975 Experimental and analytical investigation of oscillations in flows over cavities. PhD thesis, California Institute of Technology, Pasadena, California.Google Scholar
68. Schachenmann, A. & Rockwell, D. 1980 Self-sustained oscillations of turbulent pipe flow terminated by an axisymmetric cavity. J. Sound Vib. 73, 61–72.CrossRefGoogle Scholar
69. Schlichting, H. 1979 Boundary Layer Theory. McGraw Hill.Google Scholar
70. da Silva, A. R., Scavone, G. P. & Lefebvre, A. 2009 Sound reflection at the open end of axisymmetric ducts issuing a subsonic meanflow: a numerical study. J. Sound Vib. 327, 507–528.CrossRefGoogle Scholar
71. Tam, C. K. W. & Block, P. J. W. 1978 On the tones and pressure oscillations induced by flow over rectangular cavities. J. Fluid Mech. 89, 373–399.CrossRefGoogle Scholar
72. Tijdeman, H. 1975 On the propagation of sound waves in cylindrical tubes. J. Sound Vib. 39 (1), 1–33.CrossRefGoogle Scholar
73. Tonon, D., Landry, B. J. T., Belfroid, S. P. C., Willems, J. F. H, Hofmans, G. C. J. & Hirschberg, A. 2010 Whistling of a pipe system with multiple side branches: comparison with corrugated pipes. J. Sound Vib. 329, 1007–1024.CrossRefGoogle Scholar
74. Ziada, S., Ng, H. & Blake, C. E. 2003 Flow excited resonance of a confined shallow cavity in low Mach number flow and its control. J. Fluids Struct. 18, 79–92.CrossRefGoogle Scholar
75. Ziada, S. & Shine, S. 1999 Strouhal numbers of flow-excited acoustic resonance of closed side branches. J. Fluids Struct. 13, 127–142.CrossRefGoogle Scholar