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Results of Jet Instability Theory

  • Conference paper
Recent Advances in Aerodynamics

Summary

Theoretical results concerning the instability of axisymmetric jets are reviewed. For inviscid parallel jet flow the various parameters affecting jet instability as shear layer thickness, Mach number, temperature ratio, and external flow velocity are discussed. Furthermore, viscous and nonlinear effects are considered. Finally, the influences of flow divergence and of nozzle-jet interaction are discussed.

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References

  1. Batchelor, G. K. and Gill, E. A. “Analysis of the Stability of Axisymmetric Jets,” J. Fluid Mech. 14 (1962), 529–551.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Bechert, D. “Excited Waves in Shear Layers.” Deutsche Luft- und Raumfahrt, DLR-FB 82–83, 1982.

    Google Scholar 

  3. A Model of the Excitation of Large Scale Fluctuations in a Shear Layer. AIAA Paper 83–0724, 1983.

    Google Scholar 

  4. Bechert, D. and Michel, U. “The Control of a Thin Free Shear Layer With and Without a Semi-Infinite Plate by a Pulsating Flow Field.” Acoustica 33 (1975), 287–307.

    ADS  MATH  Google Scholar 

  5. Blumen, W., Drazin, P. G., and Billings, D. F. “Shear Layer Instability of an Inviscid Compressible Fluid, Part 2.” J. Fluid Mech. 71 (1975), 305–316.

    Article  ADS  MATH  Google Scholar 

  6. Chan, Y. Y. “Spatial Waves in Turbulent Jets.” Physics of Fluids, 17 (1974), 46–53.

    Article  ADS  Google Scholar 

  7. Chan, Y. Y. and Leong, R. K. “Discrete Acoustic Radiation Generated by Jet Instability.” Canadian Acoustics and Space Institute Trans. 6 (1973), 65–72.

    Google Scholar 

  8. Crighton, D. G. “Acoustics as a Branch of Fluid Mechanics.” J. Fluid Mech. 106 (1981), 261–298.

    Article  ADS  MATH  Google Scholar 

  9. Crighton, D. G. and Gaster, M. “Stability of Slowly Diverging Jet Flow.” J. Fluid Mech. 77 (1976), 397–413.

    Article  ADS  MATH  Google Scholar 

  10. Crow, S. C. and Champagne, F. H. “Orderly Structure in Jet Turbulence.” J. Fluid Mech. 48 (1971), 547–591.

    Article  ADS  Google Scholar 

  11. Gaster, M. “A Note on the Relation Between Temporally-Increasing and Spatially-Increasing Disturbances in Hydrodynamic Stability.” Fluid Mech. 14 (1962), 222–24.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Gill, A. E. “Instabilities of ’Top-Hat’ Jets and Wakes in Compressible Fluid.” Physics of Fluid. 8 (1965), 1428–30.

    Article  Google Scholar 

  13. Gill, A. E. and Drazin, P. G. “Note on Instability of Compressible Jets and Wakes to Long-Wave Disturbances.” J. Fluid Mech. 22 (1965), 415.

    Article  MathSciNet  ADS  Google Scholar 

  14. Gropengießer, H. “Beitrag zur Stabilität freier Grenzschichten in kompressiblen Medien.” Deutsche Luft- und Raumfahrt, DLR-FB 69–25, 1969.

    Google Scholar 

  15. Haertig, J. “Theoretical and Experimental Study of Wavelike Disturbances in a Round Jet With Emphasis Being Placed on Orderly Structures.” In Mechanics of Sound Generation in Flows. Ed. E. A. Müller, New York: Springer Verlag, 1979, pp. 167–173.

    Google Scholar 

  16. Une Solution Analytique du Problème de l’instabilité d’un Jet Libre Rond Compressible. Institut Franco-Allemand de Recherche de Saint-Louis, ISL-R 119/81, 1981.

    Google Scholar 

  17. Ho, C. M. and Huang, L. S. “Subharmonics and Vortex Merging in Mixing Layers.” J. Fluid Mech. 119 (1982), 443–473.

    Article  ADS  Google Scholar 

  18. Kambe, T. “The Stability of an Axisymmetric Jet With Parabolic Profile. J. Phys. Soc. Japan 26 (1969), 566–575.

    Article  ADS  Google Scholar 

  19. Kapur, S. S. and Morris, P. J. “A Model for the Orderly Structure of Turbulence in a Two-Dimensional Shear Layer.” In The Generation and Radiation of Supersonic Jet Noise. Ed. H. E. Plumblee. Marietta, Georgia: Lockheed-Georgia, 1974, I-76-I-83.

    Google Scholar 

  20. Kelly, R. E. “On the Instability of an Inviscid Shear Layer Which is Periodic in Space and Time.” J. Fluid Mech. 27 (1967), 657–689.

    Article  ADS  MATH  Google Scholar 

  21. Leconte, J. “On the Influence of Musical Sounds on the Flame of a Jet of Coal-Gas. Phil. Mag. 15 (1858), 235–239.

    Google Scholar 

  22. Lessen, M., Fox, J. A., and Zien, H. M. “The Instability of Inviscid Jets and Wakes in Compressible Fluid.” J. Fluid Mech. 21 (1965), 129–143.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. Lessen, M. and Singh, P. J. “The Stability of Axisymmetric Free Shear Layers.” J. Fluid Mech. 60 (1973), 443–457.

    ADS  Google Scholar 

  24. Maestrello, L. and Bayliss, A. “Flowfield and Far Field Acoustic Amplification Properties of Heated and Unheated Jets.” AIAA Journal, 20 (1982), 1539–46.

    Article  ADS  Google Scholar 

  25. Maslowe, S. A. and Kelly, R. E. “Inviscid Instability of an Unbounded Heterogeneous Shear Layer.” J. Fluid Mech. 48 (1971), 405–415

    Article  ADS  MATH  Google Scholar 

  26. Mattingly, G. E. and Chang, C. C. “Unstable Wave on an Axisymmetric Jet Column.” J. Fluid Mech. 65 (1974), 541–560.

    Article  ADS  MATH  Google Scholar 

  27. Michalke, A. “On Spatially Growing Disturbances in an Inviscid Shear Layer.” J. Fluid Mech. 28 (1965), 521–544.

    Article  MathSciNet  ADS  Google Scholar 

  28. “A Note on the Spatial Jet-Instability of the Compressible Cylindrical Vortex Sheet.” Deutsche Luftund Raumfahrt, DLR-FB 70–51, 1970.

    Google Scholar 

  29. “Instabilität eines kompressiblen runden Freistrahls unter Berücksichtigung des Einflusses der Strahlgrenzschichtdicke.” Z. Flugwiss. 19 (1971), 319–328. English translation NASA Tech. Memo. 75190, 1977.

    Google Scholar 

  30. “The Instability of Free Shear Layers—A Survey on the State of the Art.” Progr. Aerospace Sei. 12, 1972. Ed. D. Küchemann, New York: Pergamon Press, 213–239.

    Google Scholar 

  31. Michalke, A. and Freymuth, P. “The Instability and the Formation of Vortices in a Free Boundary Layer.” AGARD Conference Proc. No. 4, Separated Flows, Part II, 1966, 575–595.

    Google Scholar 

  32. Michalke, A. and Hermann, G. “On the Inviscid Instability of a Circular Jet With External Flow.” J. Fluid Mech. 114 (1982), 343–359.

    Article  ADS  MATH  Google Scholar 

  33. Michalke, A. and Schade, H. “Zur Stabilität von freien Grenzschichten.” Ing. Arch. 33 (1963), 1–23.

    Article  MATH  Google Scholar 

  34. Michel, U. and Michalke, A. “Prediction of Fly-Over Jet Noise Spectra.” ALAA Paper No. 81–2025, 1981.

    Google Scholar 

  35. Mollendorf, J. C. and Gebhart, B. “An Experimental and Numerical Study of the Viscous Stability of a Round Laminar Jet With and Without Thermal Bouyancy for Symmetric and Asymmetric Disturbances.” J. Fluid Mech. 61 (1973), 367–399.

    Article  ADS  MATH  Google Scholar 

  36. Morris, P. J. “The Spatial Viscous Instability of Axisymmetric Jets.” J. Fluid Mech. 77 (1976), 511–529.

    Article  ADS  MATH  Google Scholar 

  37. “Viscous Stability of Compressible Axisymmetric Jets.” AIAA Journal 21 (1983), 481–482.

    Google Scholar 

  38. Morris, P. J. and Tarn, C. K. “On the Radiation of Sound by Instability Waves of a Compressible Axisymmetric Jet.” In Mechanics of Sound Generation in Flows. Ed. E. A. Müller. New York: Springer Verlag, 1979, 55–61.

    Google Scholar 

  39. Neuwerth, G. “Theorie der Ausbreitung wellenförmiger Störungen entgegen der Strömungsrichtung in einem Unterschall-Freistrahl.” Deutsche Luft und Raumfahrt, DLR-FB 74–20, 1974.

    Google Scholar 

  40. Petersen, R. A. “Influence of Wave Dispersion on Vortex Pairing in a Jet.” J. Fluid Mech. 89 (1978), 469–495.

    Article  ADS  Google Scholar 

  41. Plaschko, P. “Helical Instabilities of Slowly Diverging Jets.” J. Fluid Mech. 92 (1979), 209–215.

    Article  ADS  MATH  Google Scholar 

  42. “Axial Coherence Functions of Circular Turbulent Jets Based on Inviscidly Calculated Damped Modes.” Submitted to Physics of Fluid, 1983.

    Google Scholar 

  43. Rayleigh, Lord. “On the Instability of Jets.” Proc. London Math. Soc. 10 (1879), 4–13.

    Article  MATH  Google Scholar 

  44. Schade, H. “Zur Stabilitätstheorie axialsymmetrischer Parallelströmungen.” Ing. Arch. 31 (1962), 301–316.

    Article  MathSciNet  MATH  Google Scholar 

  45. Tarn, C.K.W. “Supersonic Jet Noise Generated by Large Scale Disturbances.” J. Sound Vibr. 38 (1975), 51–79.

    Article  ADS  Google Scholar 

  46. Tyndall, J. “On the Action of Sonorous Vibrations on Gaseous and Liquid Jets.” Phil. Mag. 33 (1867), 375–391.

    Google Scholar 

  47. Watson, J. “On Spatially-Growing Finite Disturbances in a Plane Poiseuille Flow.” Fluid Mech. 14 (1962), 211–221.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  48. Wille, R. “Beiträge zur Phänomenologie der Freistrahlen.” Z. Flugwiss. 11 (1963), 222–233.

    Google Scholar 

  49. Woolley, J. P. and Karamcheti, K. A Study of Narrow Band Noise Generation by Flow Over Ventilated Walls in Transonic Wind Tunnels• Wright-Patterson Air Force Base, Ohio: Air Force Office of Scientific Research, AFOSR-TR-73–0503, 1973.

    Google Scholar 

  50. “Role of Jet Stability in Edgetone Generation.” AIAA Journal 12 (1974), 1457–58.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Hermann-Föttinger-Institut für Thermo- und Fluiddynamik, Technische Universität Berlin, Germany

    Alfons Michalke

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  1. Alfons Michalke
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Editors and Affiliations

  1. Department of Mechanical Engineering FAMU/FSU College of Engineering, The Florida State University, Tallahassee, FL, 32306, USA

    Anjaneyulu Krothapalli

  2. NASA Ames Research Center, Moffett Field, CA, 94035, USA

    Charles A. Smith

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© 1986 Springer-Verlag New York Inc.

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Michalke, A. (1986). Results of Jet Instability Theory. In: Krothapalli, A., Smith, C.A. (eds) Recent Advances in Aerodynamics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4972-6_7

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  • DOI: https://doi.org/10.1007/978-1-4612-4972-6_7

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-9379-8

  • Online ISBN: 978-1-4612-4972-6

  • eBook Packages: Springer Book Archive

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