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On the interaction between fundamental and subharmonic instability waves in a turbulent round jet

Published online by Cambridge University Press:  20 April 2006

Reda R. Mankbadi
Reda R. Mankbadi
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, NJ 08903
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Abstract

The spatial interactions between a fundamental instability wave and its subharmonics in a turbulent round jet are studied for ‘natural’ or forced exit conditions. Time-averaging and conditional-averaging techniques are used to split each flow component into a mean one, a random turbulence one and several wave-like coherent-structure components at fundamental and subharmonic frequencies. The energy equations for the flow components are derived and integrated across the jet. Shape assumptions regarding the radial distributions of each flow component are used to obtain a set of nonlinear ordinary differential equations representing the energy interactions between the coherent components, while interacting with the mean flow and with the background turbulence. Vortex pairing is viewed here as occurring when the subharmonic absorbs energy from the fundamental and from the mean flow and exceeds the fundamental's level to become the dominant instability component. At the proper initial phase difference between the subharmonic and fundamental only the first subharmonic was found to amplify if the fundamental Strouhal number based on diameter is in the range of 0.6–1.0. For higher Strouhal numbers, several subharmonics can amplify. The pairing location moves closer to the nozzle exit with increasing excitation Strouhal number. The time-averaged coherent Reynolds stresses exhibit regions of sign change, indicating a reversal in the direction of energy transfer between the mean flow and the coherent components.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 160 , November 1985 , pp. 385 - 419
Copyright
© 1985 Cambridge University Press

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References

Acton, E. 1976 J. Fluid Mech. 76, 561.
Acton, E. 1980 J. Fluid Mech. 98, 1.
Ahuja, K. K., Lepicovsky, J. & Burrin, R. H. 1982 AIAA J. 20, 1700.
Abbey, H. & Ffowcs-Williams, J. E. 1984 AIAA Paper 84–2338.
Baltas, C. & Morris, P. J. 1984 AIAA Paper 84–2342.
Bradshaw, P., Ferris, D. H. & Johnson, R. F. 1964 J. Fluid Mech. 19, 591.
Browand, F. K. & Ho, C.-M. 1983 In Two-Dimensional Turbulence (J. Méc. Numéro Spécial), p. 99.
Browand, F. K. & Latigo, B. O. 1979 Phys. Fluids 22, 1011.
Browand, F. K. 1980 In Proc. 33rd Ann. Meeting Div. Fluid Dyn., APS.
Browand, F. K. & Weidman, P. D. 1976 J. Fluid Mech. 76, 127.
Brown, G. L. & Roshko, A. 1974 J. Fluid Mech. 64, 775.
Corcos, G. M. & Lin, S. J. 1984 J. Fluid Mech. 139, 29.
Corcos, G. M. & Sherman, F. S. 1976 J. Fluid Mech. 73, 241.
Crighton, D. G. & Gaster, M. 1976 J. Fluid Mech. 77, 397.
Crow, S. C. & Champagne, F. H. 1971 J. Fluid Mech. 48, 547.
Davies, P. O. A. L., Fisher, M. J. & Barratt, J. J. 1963 J. Fluid Mech. 15, 337.
Drubka, R. G. 1981 Ph.D. Thesis, Illinois Institute of Technology, Chicago.
Favre-Marinet, M. & Binder, G. 1979 J. Méc. 18, 356.
Freymuth, P. 1966 J. Fluid Mech. 25, 603.
Gutmark, E. & Ho, C. M. 1983 Phys. Fluids 26, 2932.
Hasan, M. A. Z. & Hussain, A. K. M. F. 1980 Internal Rep., Univ. Houston.
Hinze, J. O. 1975 Turbulence, pp. 489–495. McGraw-Hill.
Ho, C. M. & Huang, L. S. 1982 J. Fluid Mech. 119, 443.
Ho, C. M. & Huerre, P. 1984 Ann. Rev. Fluid Mech. 16, 365.
Huerre, P. 1980 Phil. Trans. R. Soc. Lond. A 293, 643.
Husain, Z. D. & Hussain, A. K. M. F. 1983 AIAA J. 21, 1512.
Hussain, A. K. M. F. & Reynolds, W. C. 1970 J. Fluid Mech. 41, 241.
Hussain, A. K. M. F. & Thompson, C. A. 1980 J. Fluid Mech. 100, 397.
Kelly, R. E. 1967 J. Fluid Mech. 27, 657.
Kendall, J. M. 1970 J. Fluid Mech. 41, 259.
Kibens, V. 1980 AIAA J. 18, 434.
Kibens, V. 1981 AIAA Paper 81–1960.
Knight, D. C. 1979 In Proc. 6th Symp. on Turbulence in Liquids, Univ. Missouri, Rolla, p. 167.
Ko, D. R. S., Kubota, T. & Lees, L. 1970 J. Fluid Mech. 40, 315.
Ko, N. W. M. & Davies, P. O. A. L. 1971 J. Fluid Mech. 50, 40.
Laufer, J. & Yen, T.-C. 1983 J. Fluid Mech. 134, 1.
Laufer, J. & Zhang, J. X. 1983 Phys. Fluids 26, 1740.
Liu, J. T. C. 1971 Phys. Fluids 14, 2251.
Liu, J. T. C. 1974 J. Fluid Mech. 62, 437.
Mankbadi, R. & Liu, J. T. C. 1981 Phil. Trans. R. Soc. Lond. A 298, 541.
Mankbadi, R. & Liu, J. T. C. 1984 Phil. Trans. R. Soc. Lond. A 311, 183.
Michalke, A. 1965 J. Fluid Mech. 23, 521.
Michalke, A. 1971 Z. Flugwiss. 19, 319.
Monkewitz, P. A. 1982 Internal Rep., Univ. California Los Angeles.
Moore, C. J. 1977 J. Fluid Mech. 80, 321.
Morris, P. J. 1976 J. Fluid Mech. 77, 511.
Oster, D. & Wygnanski, I. 1982 J. Fluid Mech. 123, 91.
Patnaik, P. A., Sherman, F. S. & Corcos, G. M. 1976 J. Fluid Mech. 73, 215.
Petersen, R. A., Kaplan, R. G. & Laufer, J. 1974 NASA Contractors Rep. 134733.
Plaschko, P. 1979 J. Fluid Mech. 92, 209.
Reynolds, W. C. & Bouchard, E. E. 1981 In Unsteady Turbulent Shear Flows (ed. R. Michel, J. Cousteix & R. Houdeville), p. 402. Springer.
Reynolds, W. C. & Hussain, A. K. M. F. 1972 J. Fluid Mech. 24, 263.
Riley, J. J. & Metcalfe, R. W. 1980 AIAA Paper 80–0274.
Stuart, J. T. 1958 J. Fluid Mech. 4, 1.
Stuart, J. T. 1960 J. Fluid Mech. 9, 353.
Stuart, J. T. 1965 Appl. Mech. Rev. 18, 523.
Strange, P. J. R. & Crighton, D. G. 1983 J. Fluid Mech. 134, 231.
Vlasov, Y. V. & Ginevsky, A. S. 1974 NASAT TF-15, 721.
Winant, C. D. & Browand, F. K. 1974 J. Fluid Mech. 63, 237.
Wlezien, R. W. & Kibens, V. 1984 AIAA paper presented at the Aerosp. Sci. Meeting, Reno, NV.
Zaman, K. B. M. Q. & Hussain, A. K. M. F. 1980 J. Fluid Mech. 101, 449.
Zaman, K. B. M. Q. & Hussain, A. K. M. F. 1981 J. Fluid Mech. 103, 133.
Zhang, Y.-Q., Ho., C.-M. & Monkewitz, P. A. 1984 In Proc. IUTAM Symp. on Laminar–Turbulent Transition, Novosibirsk.