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On the whistling of corrugated pipes: effect of pipe length and flow profile

Published online by Cambridge University Press:  18 February 2011

G. NAKIBOĞLU ,
S. P. C. BELFROID ,
J. GOLLIARD  and
A. HIRSCHBERG
G. NAKIBOĞLU*
Affiliation:
Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
S. P. C. BELFROID
Affiliation:
TNO Science and Industry, 2600 AD Delft, The Netherlands
J. GOLLIARD
Affiliation:
TNO Science and Industry, 2600 AD Delft, The Netherlands
A. HIRSCHBERG
Affiliation:
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

Whistling behaviour of two geometrically periodic systems, namely corrugated pipes and multiple side branch systems, is investigated both experimentally and numerically. Tests are performed on corrugated pipes with various lengths and cavity geometries. Experiments show that the peak-whistling Strouhal number, where the maximum amplitude in pressure fluctuations is registered, is independent of the pipe length. Experimentally, a decrease of the peak-whistling Strouhal number by a factor of two is observed with increasing confinement ratio, i.e. the ratio of pipe diameter to cavity width. A numerical methodology that combines incompressible flow simulations with vortex sound theory is proposed to estimate the acoustic source power in periodic systems. The methodology successfully predicts the Strouhal number ranges of acoustic energy production/absorption and the nonlinear saturation mechanism responsible for the stabilization of the limit cycle oscillation. The methodology predicts peak-whistling Strouhal numbers in agreement with experiments and explains the dependence of the peak-whistling Strouhal number on the confinement ratio. Combined with an energy balance, the proposed methodology is used to estimate the acoustic fluctuation amplitudes.

JFM classification

Acoustics: Aeroacoustics Vortex Flows: Vortex shedding
Type
Papers
Information
Journal of Fluid Mechanics , Volume 672 , 10 April 2011 , pp. 78 - 108
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Åbom, M. & Bodén, H. 1988 Error analysis of two-microphone measurements in ducts with flow. J. Acoust. Soc. Am. 83, 2429–2438.CrossRefGoogle Scholar
Belfroid, S. P. C., Shatto, D. P. & Peters, R. M. 2007 Flow Induced Pulsation Caused by Corrugated Tubes. ASME Pressure Vessels and Piping Division, San Antonio, Texas.CrossRefGoogle Scholar
Binnie, A. M. 1960 Self-induced waves in a conduit with corrugated walls. I. Experiments with water in an open horizontal channel with vertically corrugated sides. Proc. R. Soc. Lond. A 259, 18–27.Google Scholar
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
Bruggeman, J. C., Hirschberg, A., van Dongen, 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
Bruggeman, J. C., Wijnands, P. J. & Gorter, J. 1986 Self-sustained low-frequency resonance in low-Mach-number gas flow through pipelines with side branch cavities. AIAA Paper 86-1924.CrossRefGoogle Scholar
Burstyn, W. 1922 Eine neue Pfeife (a new pipe). Z. Tech. Phys. 3, 179–180.Google Scholar
Cadwell, L. H. 1994 Singing corrugated pipes revisited. Am. J. Phys. 62, 224–227.CrossRefGoogle Scholar
Cermak, P. 1922 Über die Tonbildung bei Metallschläuchen mit eingedräcktem Spiralgang (On the sound generation in flexible metal hoses with spiraling grooves). Phys. Z. 23, 394–397.Google Scholar
Crawford, F. S. 1974 Singing corrugated pipes. Am. J. Phys. 62, 278–288.CrossRefGoogle Scholar
Curle, N. 1955 The influence of solid boundaries upon aerodynamic sound. Proc. R. Soc. Lond. A 231, 505–514.Google Scholar
Dequand, S., Hulshoff, S. J. & Hirschberg, A. 2003 a Self-sustained oscillations in a closed side branch system. J. Sound Vib. 265, 359–386.CrossRefGoogle Scholar
Dequand, S., Luo, X., Willems, J. F. H. & Hirschberg, A. 2003 b Helmholtz-like resonator self-sustained oscillations. Part 1. AIAA J. 41 (3), 408–415.CrossRefGoogle Scholar
Derks, M. M. G. & Hirschberg, A. 2004 Self-sustained oscillation of the flow along Helmholtz resonators in a tandem configuration. In Proc. 8th Intl Conf. on Flow-Induced Vibration (FIV2004), Paris, 6–9 July (ed. de Langre, E. & Axisa, F.), pp. 435–440. Polytechnique.Google Scholar
Eggels, J. G. M., Unger, F., Weiss, M. H., Westerwell, J., Adrian, R. J., Friedrich, R. & Nieuwstadt, F. T. M. 1994 Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J. Fluid Mech. 268, 175–209.CrossRefGoogle Scholar
Elder, S. A., Farabee, T. M. & DeMetz, F. C. 1982 Mechanisms of flow-excited cavity tones at low Mach number. J. Acoust. Soc. Am. 72 (2), 532–549.CrossRefGoogle Scholar
Elliott, J. W. 2005 Corrugated pipe flow. In Lecture Notes on the Mathematics of Acoustics (ed. Wright, M. C. M.), pp. 207–222. Imperial College Press.Google Scholar
Fletcher, J. C. 1979 Air flow and sound generation in musical wind instruments. Annu. Rev. Fluid Mech. 11, 95–121.CrossRefGoogle Scholar
Gloerfelt, X. 2009 Cavity Noise. von Karman Lecture Notes on Aerodynamic Noise from Wall-Bounded Flows. Von Karman Institute.Google Scholar
Golliard, J. 2002 Noise of Helmholtz-resonator like cavities excited by low Mach-number turbulent flows. PhD thesis, École Supérieure d'Ingénieurs de Poitiers, Poitiers, France.Google Scholar
Golliard, J., Tonon, D. & Belfroid, S. P. C. 2010 Experimental investigation of the source locations for whistling short corrugated pipes. In Proc. ASME 2010 3rd Joint US–European Fluids Engineering Summer Meeting and 8th Intl Conf. on Nanochannels, Microchannels and Minichannels, Montreal, Canada.Google Scholar
Goyder, H. 2009 On the Modelling of Noise Generation in Corrugated Pipes. ASME Pressure Vessels and Piping Division, Prague, Czech Republic.CrossRefGoogle Scholar
Gutin, L. 1948 On the sound field of a rotating propeller. (Original in Russian: Z. Tekh. Fiz. 1936; 12, 76–83.) NACA Tech. Memo. 1195.Google Scholar
Hofmans, G. C. 1998 Vortex sound in confined flows. PhD thesis, Eindhoven University of Technology, Eindhoven, the Netherlands.Google Scholar
Howe, M. S. 1980 The dissipation of sound at an edge. J. Sound Vib. 70, 407–411.CrossRefGoogle Scholar
Howe, M. S. 1998 Acoustics of Fluid–Structure Interactions. Cambridge University Press.CrossRefGoogle Scholar
Ingard, U. & Singhal, V. K. 1975 Effect of flow on the acoustic resonances of an open-ended duct. J. Acoust. Soc. Am. 58 (4), 788–793.CrossRefGoogle Scholar
Keller, J. J. 1984 Non-linear self-excited acoustic oscillations in cavities. J. Sound Vib. 94, 397–409.CrossRefGoogle Scholar
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
Kop'ev, V. F., Mironov, M. A. & Solntseva, V. S. 2008 Aeroacoustic interaction in a corrugated duct. Acoust. Phys. 54, 197–203.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
Kristiansen, U. R. & Wiik, G. A. 2007 Experiments on sound generation in corrugated pipes with flow. J. Acoust. Soc. Am. 121, 1337–1344.CrossRefGoogle ScholarPubMed
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
Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23 (3), 521–544.CrossRefGoogle Scholar
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
Munt, R. M. 1990 Acoustic transmission properties of a jet pipe with subsonic jet flow. Part I. The cold jet reflection coefficient. J. Sound Vib. 142, 413–436.CrossRefGoogle Scholar
Myers, M. K. 1986 An exact energy corollary for homentropic flow. J. Sound Vib. 109 (2), 277–284.CrossRefGoogle Scholar
Myers, M. K. 1991 Transport of energy by disturbances in arbitrary steady flows. J. Fluid Mech. 226, 383–400.CrossRefGoogle Scholar
Nakamura, Y. & Fukamachi, N. 1991 Sound generation in corrugated tubes. Fluid Dyn. Res. 7, 255–261.CrossRefGoogle Scholar
Nakiboğlu, G., Belfroid, S. P. C., Tonon, D., Willems, J. F. H. & Hirschberg, A. 2009 A Parametric Study on the Whistling of Multiple Side Branch System as a Model for Corrugated Pipes. ASME Pressure Vessels and Piping Division.CrossRefGoogle Scholar
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
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
Patankar, S. V. & Spalding, D. B. 1972 A calculation procedure for heat mass and momentum transfer in three-dimensional parabolic flows. Intl J. Heat Mass Transfer 15, 1787–1806.CrossRefGoogle Scholar
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
Petrie, A. M. & Huntley, I. D. 1980 The acoustic output produced by a steady airflow through a corrugated duct. J. Sound Vib. 70 (1), 1–9.CrossRefGoogle Scholar
Pierce, A. D. 1981 Acoustics. McGraw Hill.Google Scholar
Popescu, M. & Johansen, S. T. 2008 Acoustic wave propagation in low Mach flow pipe. AIAA Paper 2008-0063.CrossRefGoogle Scholar
Rayleigh, Lord 1945 Lecture Notes on the Mathematics of Acoustics. Dover.Google Scholar
Rockwell, D. 1983 Oscillations of impinging shear layers. AIAA J. 21, 645–664.CrossRefGoogle Scholar
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
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
Sarohia, V. 1977 Experimental investigation of oscillations in flow over shallow cavities. AIAA J. 15 (7), 984–991.CrossRefGoogle Scholar
Schlichting, H. 1979 Boundary Layer Theory. McGraw Hill.Google Scholar
Serafin, S. & Kojs, J. 2005 Computer models and compositional applications of plastic corrugated tubes. Organised Sound 10 (1), 67–73.CrossRefGoogle Scholar
Silverman, M. P. & Cushman, G. M. 1989 Voice of the dragon: the rotating corrugated resonator. Eur. J. Phys. 10, 298–304.CrossRefGoogle Scholar
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
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
Ziada, S. & Bühlmann, E. T. 1991 Flow-induced vibration in long corrugated pipes. In Intl Conf. on Flow-Induced Vibrations. IMechE, UK.Google Scholar
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
Ziada, S. & Shine, S. 1999 Strouhal numbers of flow-excited acoustic resonance of closed side branches. J. Fluids Struct. 13, 127–142.CrossRefGoogle Scholar