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A cavity-by-cavity description of the aeroacoustic instability over a liner with a grazing flow

  • Xiwen Dai (a1) and Yves Aurégan (a2)

Abstract

This paper presents a two-dimensional (2-D) cavity-by-cavity description of a convective instability near a lined wall with low dissipation due to the coupling of hydrodynamic modes with resonance of the wall. For a liner consisting of an array of deep cavities periodically placed along a duct containing a mean shear flow, the acoustic and hydrodynamic disturbances are described by the linearized Euler equations. The Bloch modes and the scattering matrix of periodic cells are used to examine the instability over the liner. The unstable Bloch mode is due to the coupling of a hydrodynamic mode in the shear flow with the cavity resonance. It is demonstrated that even when all the transverse modes are stable in the duct–cavity system, i.e. when the Kelvin–Helmholtz instability of the shear flow over the cavities does not occur, such an instability over the liner can still exist. The unstable Bloch wave, excited by the incident sound wave at the upstream part of the liner, convectively grows along the liner, and regenerates sound near the downstream edge of the liner with a sound level higher than the incident sound level. It is shown that a homogenized approach, where the wall effect is described by a homogeneous impedance, can also explain the unstable behaviour above the liner. It reveals that a small wall resistance and a small and positive reactance are two necessary conditions for such an instability.

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Corresponding author

Email address for correspondence: xiwen.dai@sjtu.edu.cn

References

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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, 208224.
Aurégan, Y. & Leroux, M. 2008 Experimental evidence of an instability along an impedance wall with flow. J. Sound Vib. 317, 432439.
Aurégan, Y. & Singh, D. K. 2014 Experimental observation of a hydrodynamic mode in a flow duct with a porous material. J. Acoust. Soc. Am. 136, 567572.
Aurégan, Y., Starobinski, R. & Pagneux, V. 2001 Influence of grazing flow and dissipation effects on the acoustic boundary conditions at a lined wall. J. Acoust. Soc. Am. 109, 5964.
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. 451517. North-Holland.
Bradley, C. E. 1994 Time harmonic acoustic Bloch wave propagation in periodic waveguides. Part I. Theory. J. Acoust. Soc. Am. 96, 18441853.
Brambley, E. J. 2009 Fundamental problems with the model of uniform flow over acoustic linings. J. Sound Vib. 322, 10261037.
Brambley, E. J. 2011 A well-posed boundary condition for acoustic liners in straight ducts with flow. AIAA J. 49, 12721282.
Brambley, E. J., Darau, M. & Rienstra, S. W. 2012 The critical layer in linear-shear boundary layers over acoustic linings. J. Fluid Mech. 710, 545568.
Brambley, E. J. & Peake, N. 2006 Classification of aeroacoustically relevant surface modes in cylindrical lined ducts. Wave Motion 43, 301310.
Brandes, M. & Ronneberger, D.1995 Sound amplification in flow ducts lined with a periodic sequence of resonators. AIAA Paper 95-126.
Briggs, R. J. 1964 Electron–Stream Interaction with Plasmas. MIT.
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, 20472055.
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.
Gabard, G. 2013 A comparison of impedance boundary conditions for flow acoustics. J. Sound Vib. 332, 714724.
Golliard, J., Sanna, F., Violato, D. & Aurégan, Y.2016 Measured source term in corrugated pipes with flow. Effect of diameter on pulsation source. AIAA Paper 2016-2886.
Ingard, U. 1959 Influence of fluid motion past a plane boundary on sound reflection, absorption, and transmission. J. Acoust. Soc. Am. 31, 10351036.
Khamis, D. & Brambley, E. J. 2016 Acoustic boundary conditions at an impedance lining in inviscid shear flow. J. Fluid Mech. 796, 386416.
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, 489534.
Koch, W. & Mohring, W. 1983 Eigensolutions for liners in uniform mean flow ducts. AIAA J. 21, 200213.
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, 607626.
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, 902922.
Marx, D. & Aurégan, Y. 2013 Effect of turbulent eddy viscosity on the unstable surface mode above an acoustic liner. J. Sound Vib. 332, 38033820.
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, 37983812.
Myers, M. K. 1980 On the acoustic boundary condition in the presence of flow. J. Sound Vib. 71, 429434.
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, 78108.
Nakiboglu, G. & Hirschberg, A. 2012 Aeroacoustic power generated by multiple compact axisymmetric cavities: effect of hydrodynamic interference on the sound production. Phys. Fluids 24, 067101.
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, 163191.
Nennig, B., Renou, Y., Groby, J.-P. & Aurégan, Y. 2012 A mode matching approach for modeling two dimensional porous grating with infinitely rigid or soft inclusions. J. Acoust. Soc. Am. 131, 38413852.
Pascal, L., Piot, E. & Casalis, G. 2017 Global linear stability analysis of flow in a lined duct. J. Sound Vib. 410, 1934.
Pridmore-Brown, D. C. 1958 Sound propagation in a fluid flowing through an attenuating duct. J. Fluid Mech. 4, 393406.
Renou, Y. & Aurégan, Y. 2011 Failure of the Ingard–Myers boundary condition for a lined duct: an experimental investigation. J. Acoust. Soc. Am. 130, 5260.
Rienstra, S. W. 2003 A classification of duct modes based on surface waves. Wave Motion 37, 119135.
Rienstra, S. W. & Darau, M. 2011 Boundary-layer thickness effects on the hydrodynamic instability along an impedance wall. J. Fluid Mech. 671, 559573.
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. 73106. Universitätsverlag Göttingen.
Schmid, P. J. & Henningson, D. S. 2000 Stability and Transition in Shear Flows. Springer.
Schmid, P. J., de Pando, M. F. & Peake, N. 2017 Stability analysis for n-periodic array of fluid systems. Phys. Rev. Fluids 2, 113902.
Spillere, A. M. N., Cordioli, J. A. & Bodén, H.2017 On the effect of boundary conditions on impedance eduction results. AIAA Paper 2017-3185.
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, 373399.
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, 28312854.
Tester, B. J. 1973 The propagation and attenuation of sound in lined ducts containing uniform or plug flow. J. Sound Vib. 28, 151203.
Weng, C., Schulz, A., Ronneberger, D., Enghardt, L. & Bake, F. 2018 Flow and viscous effects on impedance eduction. AIAA J. 56, 11181132.
Xin, B., Sun, D., Jing, X. & Sun, X. 2016 Numerical study of acoustic instability in a partly lined flow duct using the full linearized Navier–Stokes equations. J. Sound Vib. 373, 132146.
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, 134165.
Zhang, Q. & Bodony, D. J. 2012 Numerical investigation and modelling of acoustically excited flow through a circular orifice backed by a hexagonal cavity. J. Fluid Mech. 693, 367401.
Zhang, Q. & Bodony, D. J. 2016 Numerical investigation of a honeycomb liner grazed by laminar and turbulent boundary layers. J. Fluid Mech. 792, 936980.
Ziada, S. & Shine, S. 1999 Strouhal numbers of flow-excited acoustic resonance of closed side branches. J. Fluids Struct. 13, 127142.
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A cavity-by-cavity description of the aeroacoustic instability over a liner with a grazing flow

  • Xiwen Dai (a1) and Yves Aurégan (a2)

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