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Flow–acoustic resonance in a cavity covered by a perforated plate

Published online by Cambridge University Press:  03 December 2019

Xiwen Dai Open the ORCID record for Xiwen Dai [Opens in a new window]
Xiwen Dai*
Affiliation:
School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai200240, PR China
*
†Email address for correspondence: xiwen.dai@sjtu.edu.cn
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Abstract

To explain the large-scale hydrodynamic instability along a cavity-backed perforated plate in a flow duct, a two-dimensional multimodal analysis of flow disturbances is performed. First, a hole-by-hole description of the perforated plate shows a spatially growing wave with a wavelength close to the plate length, but much larger than the period of perforation. To better understand this problem and also cavity flow oscillations, we then combine the travelling mode and global mode analyses of the flow where the plate is represented by a homogeneous impedance. The spatially growing wave is, from a homogeneous point of view, essentially a Kelvin–Helmholtz instability wave, strongly distorted by evanescent acoustic waves near the cavity downstream edge. The phase difference of the unstable hydrodynamic mode at the two edges is found to be a bit larger than $2\unicode[STIX]{x03C0}$, whereas the upstream-travelling evanescent waves reduce the total phase change around the feedback loop, so that the phase condition of the global mode can still be satisfied. This particular case indicates the significant effects of those evanescent waves on both the amplitude and phase of cavity flow disturbances. The criterion of the global instability is discussed: the loop gain being larger or smaller than unity determines whether the global mode is unstable or stable. A global mode in the stable regime, which has so far received little attention, is explored by investigating the system response to external forcing. It is shown that sound can be produced when a lightly damped flow–acoustic resonance is excited by a vortical wave.

JFM classification

Acoustics: Aeroacoustics Wakes/Jets: Shear layers Instability: Instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 884 , 10 February 2020 , A4
Copyright
© 2019 Cambridge University Press

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References

Alomar, A. & Aurégan, Y. 2017 Particle image velocimetry measurement of an instability wave over a porous wall in a duct with flow. J. Sound Vib. 386, 208–224.CrossRefGoogle Scholar
Alvarez, J., Kerschen, E. & Tumin, A.2004 A theoretical model for cavity acoustic resonances in subsonic flow. AIAA Paper 2004-2845.CrossRefGoogle Scholar
Aurégan, Y. 2018 On the use of a stress–impedance model to describe sound propagation in a lined duct with grazing flow. J. Acoust. Soc. Am. 143, 2975–2979.CrossRefGoogle Scholar
Aurégan, Y. & Leroux, M. 2008 Experimental evidence of an instability along an impedance wall with flow. J. Sound Vib. 317, 432–439.CrossRefGoogle Scholar
Bers, A. 1983 Space–time evolution of plasma instabilities – absolute and convective. In Basic Plasma Physics, Handbook of Plasma Physics (ed. Galeev, A. A. & Sudan, R. N.), vol. 1, pp. 451–517. North-Holland.Google Scholar
Boujo, E., Bauerheim, M. & Noiray, N. 2018 Saturation of a turbulent mixing layer over a cavity: response to harmonic forcing around mean flows. J. Fluid Mech. 853, 386–418.CrossRefGoogle Scholar
Brambley, E. J., Darau, M. & Rienstra, S. W. 2012 The critical layer in linear-shear boundary layers over acoustic linings. J. Fluid Mech. 710, 545–568.CrossRefGoogle Scholar
Brandes, M. & Ronneberger, D.1995 Sound amplification in flow ducts lined with a periodic sequence of resonators. AIAA Paper 95-126, pp. 893–901.Google Scholar
Briggs, R. J. 1964 Electron–Stream Interaction with Plasmas. MIT.CrossRefGoogle 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. 151, 371–393.CrossRefGoogle Scholar
Celik, E. & Rockwell, D. 2002 Shear layer oscillation along a perforated surface: a self-excited large-scale instability. Phys. Fluids 14, 4444–4447.CrossRefGoogle Scholar
Celik, E. & Rockwell, D. 2004 Coupled oscillations of flow along a perforated plate. Phys. Fluids 16, 1714–1724.CrossRefGoogle Scholar
Coutant, A., Aurégan, Y. & Pagneux, V. 2019 Slow sound laser in lined flow ducts. J. Acoust. Soc. Am. 146, 2632–2644.CrossRefGoogle ScholarPubMed
Dai, X. & Aurégan, Y. 2016 Acoustic of a perforated liner with grazing flow: Floquet–Bloch periodical approach versus impedance continuous approach. J. Acoust. Soc. Am. 140, 2047–2055.CrossRefGoogle ScholarPubMed
Dai, X. & Aurégan, Y. 2018 A cavity-by-cavity description of the aeroacoustic instability over a liner with a grazing flow. J. Fluid Mech. 825, 126–145.CrossRefGoogle Scholar
Dai, X. & Aurégan, Y.2019 Hydrodynamic instability and sound amplification over a perforated plate backed by a cavity. AIAA Paper 2019-2703.CrossRefGoogle Scholar
Dai, X., Jing, X. & Sun, X. 2015 Flow-excited acoustic resonance of a Helmholtz resonator: discrete vortex model compared to experiments. Phys. Fluids 27, 057102.CrossRefGoogle 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
East, L. F. 1966 Aerodynamically induced resonance in rectangular cavities. J. Sound Vib. 3, 277–287.CrossRefGoogle Scholar
Ekmekci, A. & Rockwell, D. 2007 Oscillation of shallow flow past a cavity: resonant coupling with a gravity wave. J. Fluid. Struct. 23, 809–838.CrossRefGoogle Scholar
Evans, D. V., Levitin, M. & Vassiliev, D. 1994 Existence theorems for trapped modes. J. Fluid Mech. 261, 21–31.CrossRefGoogle Scholar
Gallaire, F. & Chomaz, J.-M. 2004 The role of boundary conditions in a simple model of incipient vortex breakdown. Phys. Fluids 16, 274–286.CrossRefGoogle Scholar
Gloerfelt, X. 2009 Cavity Noise, von Kármán Lecture Notes on Aerodynamic Noise from Wall-bounded Flows. von Karman Institute for Fluid Dynamics.Google Scholar
Guess, A. W. 1975 Calculation of perforated plate liner parameters from specified acoustic resistance and reactance. J. Sound Vib. 40, 119–137.CrossRefGoogle Scholar
Hein, S., Koch, W. & Nannen, L. 2010 Fano resonances in acoustics. J. Fluid Mech. 664, 238–264.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 179, 151–168.CrossRefGoogle Scholar
Illingworth, S. J., Morgans, A. S. & Rowley, C. W. 2012 Feedback control of cavity flow oscillations using simple linear models. J. Fluid Mech. 709, 223–248.CrossRefGoogle Scholar
Jordan, P., Jaunet, V., Towne, A., Cavalieri, A. V. G., Colonius, T., Schmidt, O. & Agarwal, A. 2018 Jet–flap interaction tones. J. Fluid Mech. 853, 333–358.CrossRefGoogle Scholar
Khamis, D. & Brambley, E. J. 2016 Acoustic boundary conditions at an impedance lining in inviscid shear flow. J. Fluid Mech. 796, 386–416.CrossRefGoogle Scholar
Khamis, D. & Brambley, E. J. 2017 Viscous effects on the acoustics and stability of a shear layer over an impedance wall. J. Fluid Mech. 810, 489–534.CrossRefGoogle Scholar
Koch, W. 2005 Acoustic resonances in rectangular open cavities. AIAA J. 43, 2342–2349.CrossRefGoogle Scholar
Kooijman, G., Hirschberg, A. & Aurégan, Y. 2010 Influence of mean flow profile and geometrical ratios on scattering of sound at a sudden area expansion in a duct. J. Sound Vib. 329, 607–626.CrossRefGoogle Scholar
Kooijman, G., Testud, P., Aurégan, Y. & Hirschberg, A. 2008 Multimodal method for scattering of sound at a sudden area expansion in a duct with subsonic flow. J. Sound Vib. 310, 902–922.CrossRefGoogle Scholar
Landau, L. D. & Lifshitz, E. M. 1981 Physical Kinetics. pp. 281–283. Pergamon Press.Google Scholar
Linton, M. C. & McIver, P. 2007 Embedded trapped modes in water waves and acoustics. Wave Motion 45, 16–29.CrossRefGoogle Scholar
Lyapina, A. A., Maksimov, D. N., Pilipchuk, A. S. & Sadreev, A. F. 2015 Bound states in the continuum in open acoustic resonators. J. Fluid Mech. 780, 370–387.CrossRefGoogle Scholar
Ma, R., Slaboch, P. E. & Morris, S. C. 2009 Fluid mechanics of the flow-excited Helmholtz resonator. J. Fluid Mech. 623, 1–26.CrossRefGoogle Scholar
Martini, E., Cavalieri, A. V. G. & Jordan, P. 2019 Acoustic modes in jet and wake stability. J. Fluid Mech. 867, 804–834.CrossRefGoogle Scholar
Marx, D. & Aurégan, Y. 2013 Effect of turbulent eddy viscosity on the unstable surface mode above an acoustic liner. J. Sound Vib. 332, 3803–3820.CrossRefGoogle Scholar
Marx, D., Aurégan, Y., Bailliet, H. & Valière, J.-C. 2010 PIV and LDV evidence of hydrodynamic instability over a liner in a duct with flow. J. Sound Vib. 329, 3798–3812.CrossRefGoogle Scholar
Masson, V., Mathews, J. R., Moreau, S., Posson, H. & Brambley, E. J. 2018 The impedance boundary condition for acoustics in swirling ducted flow. J. Fluid Mech. 848, 645–675.CrossRefGoogle Scholar
Mathews, J. R., Masson, V., Moreau, S. & Posson, H. 2018 The modified Myers boundary condition for swirling flow. J. Fluid Mech. 847, 868–906.CrossRefGoogle Scholar
Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23, 521–544.CrossRefGoogle Scholar
Nakiboglu, 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
Nakiboglu, G., Manders, H. B. M. & Hirschberg, A. 2012 Aeroacoustic power generated by a compact axisymmetric cavity: prediction of self-sustained oscillation and influence of the depth. J. Fluid Mech. 703, 163–191.CrossRefGoogle Scholar
Pagneux, V. 2013 Trapped modes and edge resonances in acoustics and elasticity. CISM Int. Cent. Mech. Sci 547, 181–223.CrossRefGoogle Scholar
Pascal, L., Piot, E. & Casalis, G. 2017 Global linear stability analysis of flow in a lined duct. J. Sound Vib. 410, 19–34.CrossRefGoogle Scholar
Powell, A. 1961 On the edgetone. J. Acoust. Soc. Am. 33, 395–409.CrossRefGoogle Scholar
Powell, A. 1995 Lord Rayleigh’s foundations of aeroacoustics. J. Acoust. Soc. Am. 98, 1839–1844.CrossRefGoogle Scholar
Pridmore-Brown, D. C. 1958 Sound propagation in a fluid flowing through an attenuating duct. J. Fluid Mech. 4, 393–406.CrossRefGoogle Scholar
Rienstra, S. W. & Hirschberg, A. 2018 An Introduction to Acoustics. Eindhoven University of Technology.Google Scholar
Rockwell, D. & Naudascher, E. 1978 Review self-sustaining oscillations of flow past cavities. J. Fluids Engng 100, 152.CrossRefGoogle Scholar
Ronneberger, D. & Jüschke, M. 2007 Sound absorption, sound amplification, and flow control in ducts with compliant walls. In Oscillations, Waves and Interactions (ed. Kurz, T., Parlitz, U. & Kaatze, U.), pp. 73–106. Universitätsverlag Göttingen.Google Scholar
Rossiter, J. E.1964 Wind-tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. Aero. Res. Counc. R&M, No. 3438.Google Scholar
Rowley, C. W., Colonius, T. & Basu, A. J. 2002 On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities. J. Fluid Mech. 455, 315–346.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
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
Schmid, P. J. & Henningson, D. S. 2000 Stability and Transition in Shear Flows. Springer.Google Scholar
Sever, C. & Rockwell, D. 2005 Oscillations of shear flow along a slotted plate: small- and large-scale structures. J. Fluid Mech. 530, 213–222.CrossRefGoogle Scholar
Sipp, D., Marquet, O., Meliga, P. & Barbagallo, A. 2010 Dynamics and control of global instabilities in open-flows: a linearized approach. Appl. Mech. Rev. 63, 030801.CrossRefGoogle Scholar
Tam, C. K. W. 1976 The acoustic modes of a two-dimensional rectangular cavity. J. Sound Vib. 49, 353–364.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
Tam, C. K. W., Pastouchenko, N. N., Jones, M. G. & Watson, W. R. 2014 Experimental validation of numerical simulations for an acoustic liner in grazing flow: self-noise and added drag. J. Sound Vib. 333, 2831–2854.CrossRefGoogle Scholar
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43, 319–352.CrossRefGoogle Scholar
Tuerke, F., Sciamarella, D., Pastur, L. R., Lusseyran, F. & Artana, G. 2015 Frequency-selection mechanism in incompressible open-cavity flows via reflected instability waves. Phys. Rev. E 91, 013005.Google ScholarPubMed
Xiong, L., Bi, W. & Aurégan, Y. 2016 Fano resonance scatterings in waveguides with impedance boundary conditions. J. Acoust. Soc. Am. 139, 764–772.CrossRefGoogle ScholarPubMed
Yamouni, S., Sipp, D. & Jacquin, L. 2013 Interaction between feedback aeroacoustic and acoustic resonance mechanisms in a cavity flow: a global stability analysis. J. Fluid Mech. 717, 134–165.CrossRefGoogle Scholar
Zhang, Q. & Bodony, D. J. 2016 Numerical investigation of a honeycomb liner grazed by laminar and turbulent boundary layers. J. Fluid Mech. 792, 936–980.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
Zoccola, P. J. 2004 Effect of opening obstructions on the flow-excited response of a Helmholtz resonator. J. Fluids Struct. 19, 1005–1025.CrossRefGoogle Scholar