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A model supersonic buried-nozzle jet: instability and acoustic wave scattering and the far-field sound

Published online by Cambridge University Press:  30 July 2015

Arnab Samanta  and
Jonathan B. Freund
Arnab Samanta*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India
Jonathan B. Freund
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA
*
†Email address for correspondence: samanta@aero.iisc.ernet.in
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Abstract

We consider sound source mechanisms involving the acoustic and instability modes of dual-stream isothermal supersonic jets with the inner nozzle buried within an outer shroud-like nozzle. A particular focus is scattering into radiating sound waves at the shroud lip. For such jets, several families of acoustically coupled instability waves exist, beyond the regular vortical Kelvin–Helmholtz mode, with different shapes and propagation characteristics, which can therefore affect the character of the radiated sound. In our model, the coaxial shear layers are vortex sheets while the incident acoustic disturbances are the propagating shroud modes. The Wiener–Hopf method is used to compute their scattering at the sharp shroud edge to obtain the far-field radiation. The resulting far-field directivity quantifies the acoustic efficiency of different mechanisms, which is particularly important in the upstream direction, where the results show that the scattered sound is more intense than that radiated directly by the shear-layer modes.

JFM classification

Acoustics: Acoustics Acoustics: Aeroacoustics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 778 , 10 September 2015 , pp. 189 - 215
Copyright
© 2015 Cambridge University Press 

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References

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series, vol. 55. US Government Printing Office.Google Scholar
Bechert, D. 1980 Sound absorption caused by vorticity shedding, demonstrated with a jet flow. J. Sound Vib. 70 (3), 389–405.CrossRefGoogle Scholar
Brambley, E. J. 2009a Fundamental problems with the model of uniform flow over acoustic linings. J. Sound Vib. 322, 1026–1037.CrossRefGoogle Scholar
Brambley, E. J. 2009b Low-frequency acoustic reflection at a hard–soft lining transition in a cylindrical duct with uniform flow. J. Engng Maths 65 (4), 345–354.CrossRefGoogle Scholar
Chu, B. & Kovasznay, L. S. G. 1957 Nonlinear interactions in a viscous, heat-conducting, compressible gas. J. Fluid Mech. 3, 494–514.CrossRefGoogle Scholar
Crighton, D. G. & Huerre, P. 1990 Shear-layer pressure fluctuations and superdirective acoustic sources. J. Fluid Mech. 220, 355–368.CrossRefGoogle Scholar
Crighton, D. G. & Leppington, F. G. 1974 Radiation properties of the semi-infinite vortex sheet: the initial-value problem. J. Fluid Mech. 64 (2), 393–414.CrossRefGoogle Scholar
Gabard, G. & Astley, R. J. 2006 Theoretical model for sound radiation from annular jet pipes: far- and near-field solutions. J. Fluid Mech. 549, 315–341.CrossRefGoogle Scholar
Gill, A. E. 1965 Instabilities of top-hat jets and wakes in compressible fluids. Phys. Fluids 8, 1428–1430.CrossRefGoogle Scholar
Harper-Bourne, M. & Fisher, M. J. 1973 The noise from shock waves in supersonic jets. In Proceedings of the AGARD Conference on Noise Mechanisms, CP-131. AGARD, pp. 11,1–13.Google Scholar
Heaton, C. J. & Peake, N. 2006 Algebraic and exponential instability of inviscid swirling flow. J. Fluid Mech. 565, 279–318.CrossRefGoogle Scholar
Hirschberg, A. & Hoeijmakers, M. 2014 Comments on the low frequency radiation impedance of a duct exhausting a hot gas. J. Acoust. Soc. Am. 136 (2), EL84–EL89.CrossRefGoogle ScholarPubMed
Ho, C. M. & Huerre, P. 1984 Perturbed free shear layers. Annu. Rev. Fluid Mech. 16, 365–424.CrossRefGoogle Scholar
Jones, D. S. & Morgan, J. D. 1974 A linear model of a finite amplitude Helmholtz instability. Proc. R. Soc. Lond. A 338, 17–41.Google Scholar
Jordan, P. & Colonius, T. 2013 Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45, 173–195.CrossRefGoogle Scholar
Laufer, J. & Yen, T. 1983 Noise generation by a low-Mach number jet. J. Fluid Mech. 134, 1–31.CrossRefGoogle Scholar
Levine, H. & Schwinger, J. 1948 On the radiation of sound from an unflanged circular pipe. Phys. Rev. 73 (4), 383–406.CrossRefGoogle Scholar
Liu, J. T. C. 1981 Interaction between large-scale coherent structures and fine-grained turbulence in free shear flows. In Transition and Turbulence, Proceedings of the Symposium on Transition and Turbulence in Fluids, Madison, WI, October 13-15, 1980, pp. 167–214. Academic.CrossRefGoogle Scholar
Luo, K. H. & Sandham, N. D. 1997 Instability of vortical and acoustic modes in supersonic round jets. Phys. Fluids 9 (4), 1003–1013.CrossRefGoogle Scholar
Michalke, A. 1972 The instability of free shear layers. Prog. Aerosp. Sci. 12, 213–239.CrossRefGoogle Scholar
Miles, J. W. 1957 On the reflection of sound at an interface of relative motion. J. Acoust. Soc. Am. 29 (2), 226–228.CrossRefGoogle Scholar
Morgan, J. D. 1974 The interaction of sound with a semi-infinite vortex sheet. Q. J. Mech. Appl. Maths 27 (4), 465–487.CrossRefGoogle Scholar
Munt, R. M. 1977 The interaction of sound with 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: I. The cold jet reflection coefficient. J. Sound Vib. 142 (3), 413–436.CrossRefGoogle Scholar
Nichols, J. W. & Lele, S. K. 2011 Global modes and transient response of a cold supersonic jet. J. Fluid Mech. 669, 225–241.CrossRefGoogle Scholar
Noble, B. 1988 Methods Based on The Wiener–Hopf Technique, 2nd edn. Chelsea.Google Scholar
Orszag, S. A. & Crow, S. C. 1970 Instability of a vortex sheet leaving a semi-infinite plate. Stud. Appl. Maths 49 (2), 167–181.CrossRefGoogle Scholar
Papamoschou, D. & Debiasi, M. 2003 Conceptual development of quiet turbofan engines for supersonic aircraft. J. Propul. Power 19 (2), 161–169.CrossRefGoogle Scholar
Papamoschou, D. & Roshko, A. 1988 The compressible turbulent shear layer: an experimental study. J. Fluid Mech. 197, 453–477.CrossRefGoogle Scholar
Parras, L. & Dizes, S. L. 2010 Temporal instability modes of supersonic round jets. J. Fluid Mech. 662, 173–196.CrossRefGoogle Scholar
Peake, N. 1994 The viscous interaction between sound waves and the trailing edge of a supersonic splitter plate. J. Fluid Mech. 264, 321–342.CrossRefGoogle Scholar
Peake, N. & Parry, A. B. 2012 Modern challenges facing turbomachinery aeroacoustics. Annu. Rev. Fluid Mech. 44, 227–248.CrossRefGoogle Scholar
Powell, A. 1953 On the mechanism of choked jet noise. Proc. Phys. Soc. B 66, 1039–1056.CrossRefGoogle Scholar
Ribner, H. S. 1957 Reflection, transmission and amplification of sound by a moving medium. J. Acoust. Soc. Am. 29 (4), 435–441.CrossRefGoogle Scholar
Rienstra, S. W. 1983 A small Strouhal number analysis for acoustic wave-jet flow-pipe interaction. J. Sound Vib. 86 (4), 539–556.CrossRefGoogle Scholar
Rienstra, S. W. 1984 Acoustic radiation from a semi-infinite annular duct in a uniform subsonic mean flow. J. Sound Vib. 94 (2), 267–288.CrossRefGoogle Scholar
Rienstra, S. W. 2007 Acoustic scattering at a hard–soft lining transition in a flow duct. J. Engng Maths 59 (4), 451–475.CrossRefGoogle Scholar
Samanta, A.2009 Finite-wavelength scattering of incident vorticity and acoustic waves at a shrouded-jet exit. PhD thesis, University of Illinois at Urbana-Champaign.CrossRefGoogle Scholar
Samanta, A. & Freund, J. B. 2008 Finite-wavelength scattering of incident vorticity and acoustic waves at a shrouded-jet exit. J. Fluid Mech. 612, 407–438.CrossRefGoogle Scholar
Shen, H. & Tam, C. K. W. 2002 Three-dimensional numerical simulation of the jet screech phenomenon. AIAA J. 40 (1), 33–41.CrossRefGoogle Scholar
Smith, M. J. T. 2004 Aircraft Noise. Cambridge University Press.Google Scholar
Tam, C. K. W. 1995 Supersonic jet noise. Annu. Rev. Fluid Mech. 27, 17–43.CrossRefGoogle Scholar
Tam, C. K. W. 2009 Mach wave radiation from high-speed jets. AIAA J. 47 (10), 2440–2448.CrossRefGoogle Scholar
Tam, C. K. W., Golebiowski, M. & Seiner, J. M.1996 On the two components of turbulent mixing noise from supersonic jets. AIAA Paper 96-1716.CrossRefGoogle Scholar
Tam, C. K. W. & Hu, F. Q. 1989 On the three families of instability waves of high-speed jets. J. Fluid Mech. 201, 447–483.CrossRefGoogle Scholar
Tam, C. K. W., Parrish, S. A. & Viswanathan, K. 2014 Harmonics of jet screech tones. AIAA J. 52 (11), 2471–2479.CrossRefGoogle Scholar
Taylor, M. V., Crighton, D. G. & Cargill, A. M. 1993 The low frequency aeroacoustics of buried nozzle systems. J. Sound Vib. 163 (3), 493–526.CrossRefGoogle Scholar
Veitch, B. & Peake, N. 2008 Acoustic propagation and scattering in the exhaust flow from coaxial cylinders. J. Fluid Mech. 613, 275–307.CrossRefGoogle Scholar