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Finite-wavelength scattering of incident vorticity and acoustic waves at a shrouded-jet exit

Published online by Cambridge University Press:  10 October 2008

ARNAB SAMANTA  and
JONATHAN B. FREUND
ARNAB SAMANTA
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA
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
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Abstract

As the vortical disturbances of a shrouded jet pass the sharp edge of the shroud exit some of the energy is scattered into acoustic waves. Scattering into upstream-propagating acoustic modes is a potential mechanism for closing the resonance loop in the ‘howling’ resonances that have been observed in various shrouded jet configurations over the years. A model is developed for this interaction at the shroud exit. The jet is represented as a uniform flow separated by a cylindrical vortex sheet from a concentric co-flow within the cylindrical shroud. A second vortex sheet separates the co-flow from an ambient flow outside the shroud, downstream of its exit. The Wiener–Hopf technique is used to compute reflectivities at the shroud exit. For some conditions it appears that the reflection of finite-wavelength hydrodynamic vorticity modes on the vortex sheet defining the jet could be sufficient to reinforce the shroud acoustic modes to facilitate resonance. The analysis also gives the reflectivities for the shroud acoustic modes, which would also be important in establishing resonance conditions. Interestingly, it is also predicted that the shroud exit can be ‘transparent’ for ranges of Mach numbers, with no reflection into any upstream-propagating acoustic mode. This is phenomenologically consistent with observations that indicate a peculiar sensitivity of resonances of this kind to, say, jet Mach number.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 612 , 10 October 2008 , pp. 407 - 438
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Bechert, D. & Pfizenmaier, E. 1975 Optical compensation measurements on the unsteady exit condition at a nozzle discharge edge. J. Fluid Mech. 71, 123–144.CrossRefGoogle Scholar
Bradshaw, P., Flintoff, J. L. & Middleton, D. 1968 Unexplained scale effects in ejector shroud “howling”. J. Sound Vib. 7, 183–190.CrossRefGoogle Scholar
Carrier, G. 1956 Sound transmission from a tube with flow. Q. Appl. Maths 13, 457–461.CrossRefGoogle Scholar
Crighton, D. G. 1972 a Radiation properties of the semi-infinite vortex sheet. Proc. R. Soc. Lond. A 330, 185–198.Google Scholar
Crighton, D. G. 1972 b The excess noise fields of subsonic jets. J. Fluid Mech. 56, 683–694.CrossRefGoogle Scholar
Crighton, D. G. 1992 The jet edge-tone feedback cycle; linear theory for the operating stages. J. Fluid Mech. 234, 361–391.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, 393–414.CrossRefGoogle Scholar
Crow, S. C. & Champagne, F. H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48, 547–591.CrossRefGoogle Scholar
Demir, A. & Rienstra, S. W. 2007 Sound radiation from a buried nozzle with jet and bypass flow. ICSV14 Paper 449. Cairns.Google 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
Gaster, M., Kit, E. & Wygnanski, I. 1985 Large-scale structures in a forced turbulent mixing layer. J. Fluid Mech. 150, 23–39.CrossRefGoogle Scholar
Heaton, C. J. & Peake, N. 2005 Acoustic scattering in a duct with mean swirling flow. J. Fluid Mech. 540, 189–220.CrossRefGoogle Scholar
Homicz, G. F. & Lordi, J. A. 1975 A note on the radiative directivity patterns of duct acoustic modes. J. Sound Vib. 41, 283–290.CrossRefGoogle Scholar
Howe, M. S. 1979 Attenuation of sound in a low Mach number nozzle flow. J. Fluid Mech. 91, 209–229.CrossRefGoogle Scholar
Howe, M. S. 1987 Self-excited oscillation in jet engine test cells. J. Fluids Struct. 1, 121–148.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
Jones, R. R. III & Lazalier, G. R. 1992 The acoustic response of altitude test facility exhaust systems to axisymmetric and two-dimensional turbine engine exhaust plumes. In DGLR/AIAA 14th Aeroacoustics Conference, Eurogress Center, Auchen, Germany, DGLR-Bericht 92-03, vol. II.Google Scholar
Lee, B. H. K. & Jones, D. J. 1973 Transmission of upstream sound through a subsonic jet. AIAA Paper 73-630.CrossRefGoogle Scholar
Levine, H. & Schwinger, J. 1948 On the radiation of sound from an unflanged circular pipe. Phys. Rev. 73, 383–406.CrossRefGoogle Scholar
Mani, R. 1973 Refraction of acoustic duct waveguide modes by exhaust jets. Q. Appl. Maths 30, 501–520.CrossRefGoogle Scholar
Massey, K. C., Ahuja, K. K., Jones, R. R. III & Tam, C. K. W. 1994 Screech tones of supersonic heated free jets. AIAA Paper 93-0141.CrossRefGoogle Scholar
Morgan, J. D. 1974 The interaction of sound with a semi-infinite vortex sheet. Q. J. Mech. Appl. Maths 27, 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, 413–436.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, 167–181.CrossRefGoogle Scholar
Pinker, R. A. & Bryce, W. D. 1976 The radiation of plane wave duct noise from a jet exhaust, statically and in flight. AIAA Paper 76-581.Google Scholar
Ridders, C. J. F. 1982 Accurate computation of f′(x) and f′(x)f″(x). Adv. Engng Softw. 4, 75–76.CrossRefGoogle Scholar
Rienstra, S. W. 1983 A small Strouhal number analysis for acoustic wave-jet flow-pipe interaction. J. Sound Vib. 86, 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, 267–288.CrossRefGoogle Scholar
Rienstra, S. W. 2007 Acoustic scattering at a hard–soft lining transition in a flow duct. J. Engng Maths 59, 451–475.CrossRefGoogle Scholar
Samanta, A. 2008 Finite-wavelength scattering of incident vorticity and acoustic waves at a shrouded-jet exit. PhD thesis, University of Illinois at Urbana-Champaign.CrossRefGoogle Scholar
Savkar, S. D. 1975 Radiation of cylindrical duct acoustic modes with flow mismatch. J. Sound Vib. 42, 363–386.CrossRefGoogle Scholar
Sebourn, C. L. & Shope, F. L. 2005 Research summary on the AEDC ASTF C-2 aeroacoustic resonance phenomenon. AIAA Paper 2005-2932.CrossRefGoogle Scholar
Strange, P. J. R. & Crighton, D. G. 1983 Spinning modes on axisymmetric jets. Part 1. J. Fluid Mech. 134, 231–245.CrossRefGoogle Scholar
Suzuki, T. & Colonius, T. 2006 Instability waves in a subsonic round jet detected using a near-field phased microphone array. J. Fluid Mech. 565, 197–226.CrossRefGoogle Scholar
Tam, C. K. W., Ahuja, K. K. & Jones, R. R. III 1994 Screech tones from free and ducted supersonic jets. AIAA J. 32, 917–922.CrossRefGoogle Scholar
Taylor, M. V., Crighton, D. G. & Cargill, A. M. 1993 The low frequency aeroacoustics of buried nozzle systems. J. Sound Vib. 163, 493–526.CrossRefGoogle Scholar
Veitch, B. & Peake, N. 2007 Models for acoustic propagation through turbofan exhaust flows. AIAA Paper 2007-3543.CrossRefGoogle Scholar
Veitch, B. & Peake, N. 2008 Acoustic propagation and scattering in the exhaust flow from coaxial cylinders. J. Fluid Mech. (in press).CrossRefGoogle Scholar