Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-05T06:06:59.129Z Has data issue: false hasContentIssue false
  • English
  • Français

Fluid mechanics of the flow-excited Helmholtz resonator

Published online by Cambridge University Press:  06 March 2009

RUOLONG MA ,
PAUL E. SLABOCH  and
SCOTT C. MORRIS
RUOLONG MA*
Affiliation:
Hessert Laboratory for Aerospace Research, Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
PAUL E. SLABOCH
Affiliation:
Hessert Laboratory for Aerospace Research, Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
SCOTT C. MORRIS
Affiliation:
Hessert Laboratory for Aerospace Research, Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
*
†Email address for correspondence: r.ma@nd.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A flow-excited Helmholtz resonator was investigated experimentally and theoretically. The analysis was focused on a simplified momentum balance integrated over the region of the orifice. The resulting expressions were used to guide an experimental programme designed to obtain measurements of the resonator pressure under flow excitation, as well as the dynamics of the shear layer in the orifice using particle image velocimetry (PIV). The pressure measurements indicated a number of distinctive features as the flow speed varied. The PIV results provided a detailed representation of the shear layer vorticity field, as well as the equivalent hydrodynamic forcing of the resonator. The forcing magnitude was found to be roughly constant over a range of flow speeds. A model was proposed that provides a prediction of the resonator pressure fluctuations based on the thickness of the approach boundary layer, the free stream speed and the acoustic properties of the resonator. The model was shown to provide an accurate representation of the resonating frequency as well as the magnitude of the resonance to within a few decibels.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 623 , 25 March 2009 , pp. 1 - 26
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Amandolèse, X., Hemon, P. & Regardin, C. 2004 An experimental study of the acoustic oscillations by flows over cavities. J. Vib. Acoust. 126, 190–195.CrossRefGoogle Scholar
Bruggeman, J. C. 1987 Flow induced pulsations in pipe system. PhD dissertation: Eindhoven University of Technology, Netherlands.Google Scholar
Bruggeman, J. C., Hirschberg, A., van Dongen, M. E. H. & Wijnands, A. P. 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
Chaterllier, L., Laumonier, J. & Gervais, Y. 2004 Theoretical and experimental investigations of low Mach number turbulent cavity flows. Exp. Fluids 36, 728–740.CrossRefGoogle Scholar
Crighton, D. G., Dowling, A. P., Ffowcs Williams, J. E., Heckl, M. & Leppington, F. G. 1992 Modern Methods in Analytical Acoustics. Springer.CrossRefGoogle Scholar
Crouse, B., Senthooran, S., Freed, D., Balasubramanian, G., Gleason, M., Puskarz, M., Lew, P. & Mongeau, L. 2006 Experimental and numerical investigation of a flow-induced cavity resonance with application to automobile buffeting. In 12th AIAA/CEAS Aeroacoustics Conf. Cambridge, MA, USA, 8–10, May 2006.Google Scholar
Dequand, S., Hulshoff, S., van Kuijk, H., Willems, J. & Hirschberg, A. 2003 Helmholtz-like resonator self-sustained oscillations. Part 2: detailed flow measurements and numerical simulations. AIAA J. 41, 416–423.CrossRefGoogle Scholar
Dequand, S., Luo, X., Willems, J. & Hirschberg, A. 2003 Helmholtz-like resonator self-sustained oscillations. Part 1: acoustical measurements and analytical models. AIAA J. 41, 408–415.CrossRefGoogle Scholar
Dequand, S., Hulshoff, S., van Kuijk, H., Willems, J. & Hirschberg, A. 2003 Helmholtz-like resonator self-sustained oscillations. Part 2: detailed flow measurements and numerical simulations. AIAA J. 41, 416–423.CrossRefGoogle Scholar
Dowling, A. P. & Ffowcs Williams, J. E. 1983 Sound and Sources of Sound. Halsted.Google Scholar
Elder, S. A. 1978 Self-excited depth-mode resonance for a wall-mounted cavity in turbulent flow. J. Acoust. Soc. Am. 64, 877–890.CrossRefGoogle Scholar
Elder, S. A., Farabee, T. M. & DeMetz, F. C. 1982 Mechanisums of flow-excited cavity tones at low Mach number. J. Acoust. Soc. Am. 72, 532–549.CrossRefGoogle Scholar
Graf, H. R. & Durgin, W. W. 1993 Measurement of the nonsteady flow field in the opening of a resonating cavity excited by grazing flow. J. Fluids Struct. 7, 387–400.CrossRefGoogle Scholar
Hersh, A. S. & Walker, B. E. 1995 Acoustic behavior of Helmholtz resonators: part II. Effects of grazing flow. CEAS/AIAA 95-079, 595–604.Google Scholar
Howe, M. S. 1981 The influence of mean shear on unsteady aperture flow, with application to acoustical diffraction and self-sustained cavity oscillations. J. Fluid Mech. 109, 125–146.CrossRefGoogle Scholar
Howe, M. S. 1997 Low Strouhal number instabiliies of flow over apertures and wall cavities. J. Acoust. Soc. Am. 102, 772–780.CrossRefGoogle Scholar
Inagaki, M., Murata, O., Kondoh, T. & Abe, K. 2002 Numerical prediction of fluid-resonant oscillation at low Mach number. AIAA J. 40, 1823–1829.CrossRefGoogle Scholar
Ingard, U. & Ising, H. 1967 Acoustic nonlinearity of an orifice. J. Acoust. Soc. Am. 42, 6–17.CrossRefGoogle Scholar
Kinsler, L. E., Frey, A. R., Coppens, A. B. & Sanders, J. V. 2000 Fundamentals of Acoustics. Wiley.Google Scholar
Kook, H. 1997 Prediction and control of the interior presure fluctuations in a flow-exciated Helmholtz resonator. PhD dissertation: Purdue University, Lafayette, IN, USA.Google Scholar
Kook, H. & Mongeau, L. 2002 Analysis of the periodic pressure fluctuations induced by flow over a cavity. J. Sound Vib. 251, 823–846.CrossRefGoogle Scholar
Mallick, S., Shock, R. & Yakhot, V. 2003 Numerical simulation of the excitation of a Helmholtz resonator by a grazing flow. J. Acoust. Soc. Am. 114, 1833–1840.CrossRefGoogle ScholarPubMed
Mast, T. D. & Pierce, A. D. 1995 Describing-function theory for flow excited resonators. J. Acoust. Soc. Am. 97, 163–172.CrossRefGoogle Scholar
Meissner, M. 2005 The response of a Helmholtz resonator to external excitation. Part II: flow-induced resonance. Arch. Acoust. 30, 57–71.Google Scholar
Morris, S. C. & Foss, J. F. 2003 Turbulent boundary layer to single-stream shear layer: the transition region. J. Fluid Mech. 494, 187–221.CrossRefGoogle Scholar
Nelson, P. A., Halliwell, N. A. & Doak, P. E. 1981 Fluid dynamics of a flow excited resonance. Part I: experiment. J. Sound Vib. 78, 15–38.CrossRefGoogle Scholar
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
Panton, R. L. 1990 Effect of orifice geometry on Helmholtz resonator excitation by grazing flow. AIAA J. 28, 60–65.CrossRefGoogle Scholar
Panton, R. L. & Miller, J. M. 1975 Excitation of a Helmholtz resonator by turbulent boundary layer. J. Acoust. Soc. Am. 58, 800–806.CrossRefGoogle Scholar
Rockwell, D. & Naudascher, E. 1978 Review-Self-sustaining oscillations of flow past cavities. J. Fluids Engng 100, 152–165.CrossRefGoogle Scholar
Rowley, C. W. & Williams, D. R. 2006 Dynamics and control of high-Reynolds-number flow over open cavities. Annu. Rev. Fluid Mech. 38, 251–276.CrossRefGoogle Scholar
Rossiter, J. E. 1964 Wind tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. Tech Rep. 64037. RAE.Google Scholar
Walker, B. E. & Charwat, A. F. 1982 Correlation of the effects of grazing flow on the impedance of Helmholtz resonators. J. Acoust. Soc. Am. 72, 550–555.CrossRefGoogle Scholar