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Acoustic modes in jet and wake stability

  • Eduardo Martini (a1), André V. G. Cavalieri (a1) and Peter Jordan (a2)

Abstract

Motivated by recent studies that have revealed the existence of trapped acoustic waves in subsonic jets (Towne et al., J. Fluid Mech., vol. 825, 2017, pp. 1113–1152), we undertake a more general exploration of the physics associated with acoustic modes in jets and wakes, using a double vortex-sheet model. These acoustic modes are associated with eigenvalues of the vortex-sheet dispersion relation; they are discrete modes, guided by the vortex sheet; they may be either propagative or evanescent; and under certain conditions they behave in the manner of acoustic-duct modes. By analysing these modes we show how jets and wakes may both behave as waveguides under certain conditions, emulating ducts with soft or hard walls, with the vortex-sheet impedance providing effective ‘wall’ conditions. We consider, in particular, the role that upstream-travelling acoustic modes play in the dispersion-relation saddle points that underpin the onset of absolute instability. The analysis illustrates how departure from duct-like behaviour is a necessary condition for absolute instability, and this provides a new perspective on the stabilising and destabilising effects of reverse flow, temperature ratio and compressibility; it also clarifies the differing symmetries of jet (symmetric) and wake (antisymmetric) instabilities. An energy balance, based on the vortex-sheet impedance, is used to determine stability conditions for the acoustic modes: these may become unstable in supersonic flow due to an energy influx through the shear layers. Finally, we construct the impulse response of flows with zero and finite shear-layer thickness. This allows us to show how the long-time wavepacket behaviour is indeed determined by interaction between Kelvin–Helmholtz and acoustic modes.

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Corresponding author

Email address for correspondence: emartini@ita.br

References

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Bers, A. 1975 Linear waves and instabilities. Plasma Physics–Les Houches 1972. Gordon and Breach Science Publishers.
Bogey, C. & Gojon, R. 2017 Feedback loop and upwind-propagating waves in ideally expanded supersonic impinging round jets. J. Fluid Mech. 823, 562591.10.1017/jfm.2017.334
Brès, G. A., Jordan, P., Jaunet, V., Le Rallic, M., Cavalieri, A. V. G., Towne, A., Lele, S. K., Colonius, T. & Schmidt, O. T. 2018 Importance of the nozzle-exit boundary-layer state in subsonic turbulent jets. J. Fluid Mech. 851, 83124.10.1017/jfm.2018.476
Briggs, R. J. 1964 Electron–Stream Interaction with Plasmas, Monograph 29. MIT Press.
Chomaz, J.-M., Huerre, P. & Redekopp, L. G. 1991 A frequency selection criterion in spatially developing flows. Stud. Appl. Maths 84 (2), 119144.10.1002/sapm1991842119
Gojon, R. & Bogey, C. 2017 Flow structure oscillations and tone production in underexpanded impinging round jets. AIAA J. 55 (6), 17921805.10.2514/1.J055618
Gojon, R., Bogey, C. & Marsden, O.2015 Large-eddy simulation of underexpanded round jets impinging on a flat plate 4 to 9 radii downstream from the nozzle. AIAA Paper 2210.
Goldstein, M. E. 1976 Aeroacoustics. p. 305. McGraw-Hill.
Healey, J. J. 2009 Destabilizing effects of confinement on homogeneous mixing layers. J. Fluid Mech. 623, 241271.10.1017/S0022112008005284
Huerre, P., Batchelor, G. K., Moffatt, H. K. & Worster, M. G. 2000 Open shear flow instabilities. Perspectives in Fluid Dynamics, pp. 159229. Cambridge University Press.
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151168.10.1017/S0022112085003147
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22 (1), 473537.10.1146/annurev.fl.22.010190.002353
Jendoubi, S. & Strykowski, P. J. 1994 Absolute and convective instability of axisymmetric jets with external flow. Phys. Fluids 6 (9), 30003009.10.1063/1.868126
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, 333358.10.1017/jfm.2018.566
Karamcheti, K.1956 Sound radiation from surface cutouts in high speed flow. PhD thesis, California Institute of Technology, Pasadena, CA.
Krothapalli, A. 1985 Discrete tones generated by an impinging underexpanded rectangular jet. AIAA J. 23 (12), 19101915.10.2514/3.9195
Krothapalli, A., Rajkuperan, E., Alvi, F. & Lourenco, L. 1999 Flow field and noise characteristics of a supersonic impinging jet. J. Fluid Mech. 392, 155181.10.1017/S0022112099005406
Lamb, H. 1945 Hydrodynamics, vol. 43. Dover.
Lessen, M., Fox, J. A. & Zien, H. M. 1965 The instability of inviscid jets and wakes in compressible fluid. J. Fluid Mech. 21 (1), 129143.10.1017/S0022112065000095
Lesshafft, L. & Huerre, P. 2007 Linear impulse response in hot round jets. Phys. Fluids 19 (2), 024102.10.1063/1.2437238
Monkewitz, P. & Sohn, K. 1988 Absolute instability in hot jets. AIAA J. 26 (8), 911916.10.2514/3.9990
Monkewitz, P. A. 1988 The absolute and convective nature of instability in two dimensional wakes at low reynolds numbers. Phys. Fluids 31 (5), 9991006.10.1063/1.866720
Monkewitz, P. A., Huerre, P. & Chomaz, J.-M. 1993 Global linear stability analysis of weakly non-parallel shear flows. J. Fluid Mech. 251, 120.10.1017/S0022112093003313
Noack, B. R. & Eckelmann, H. 1994 A global stability analysis of the steady and periodic cylinder wake. J. Fluid Mech. 270, 297330.10.1017/S0022112094004283
Ormonde, P. C., Cavalieri, A. V. G., da Silva, R. G. A. & Avelar, A. C. 2018 Passive control of coherent structures in a modified backwards-facing step flow. Exp. Fluids 59 (5), 88.10.1007/s00348-018-2543-y
Parras, L. & Le Dizès, S. 2010 Temporal instability modes of supersonic round jets. J. Fluid Mech. 662, 173196.10.1017/S0022112010003150
Pierce, A. 1981 Acoustics: An Introduction to its Physical Principles and Applications. McGraw-Hill.
Powell, A. 1953 The noise of choked jets. J. Acoust. Soc. Am. 25 (3), 385389.10.1121/1.1907052
Rienstra, S. W. & Hirschberg, A. 2018 An Introduction to Acoustics. Eindhoven University of Technology.
Rossiter, J. E.1964 Wind tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. Tech. Rep. no. 64037. RAE Farnborough.
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, 315346.10.1017/S0022112001007534
Schmidt, O. T., Towne, A., Colonius, T., Cavalieri, A. V. G., Jordan, P. & Brès, G. A. 2017 Wavepackets and trapped acoustic modes in a turbulent jet: coherent structure eduction and global stability. J. Fluid Mech. 825, 11531181.10.1017/jfm.2017.407
Siconolfi, L., Citro, V., Giannetti, F., Camarri, S. & Luchini, P. 2017 Towards a quantitative comparison between global and local stability analysis. J. Fluid Mech. 819, 147164.10.1017/jfm.2017.167
Tam, C. K. W. & Hu, F. Q. 1989a The instability and acoustic wave modes of supersonic mixing layers inside a rectangular channel. J. Fluid Mech. 203, 5176.10.1017/S0022112089001370
Tam, C. K. W. & Hu, F. Q. 1989b On the three families of instability waves of high-speed jets. J. Fluid Mech. 201, 447483.10.1017/S002211208900100X
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43, 319352.10.1146/annurev-fluid-122109-160705
Towne, A., Cavalieri, A. V. G., Jordan, P., Colonius, T., Schmidt, O., Jaunet, V. & Brès, G. A. 2017 Acoustic resonance in the potential core of subsonic jets. J. Fluid Mech. 825, 11131152.10.1017/jfm.2017.346
Yamouni, S., Mettot, C., Sipp, D. & Jacquin, L. 2013 Passive control of cavity flows. AerospaceLab (6), 17.
Yu, M.-H. & Monkewitz, P. A. 1990 The effect of nonuniform density on the absolute instability of two-dimensional inertial jets and wakes. Phys. Fluids A 2 (7), 11751181.10.1063/1.857618
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Acoustic modes in jet and wake stability

  • Eduardo Martini (a1), André V. G. Cavalieri (a1) and Peter Jordan (a2)

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