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Subharmonics and vortex merging in mixing layers

Published online by Cambridge University Press:  20 April 2006

Chih-Ming Ho  and
Lein-Saing Huang
Chih-Ming Ho
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, California 90007, U.S.A.
Lein-Saing Huang
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, California 90007, U.S.A.
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Abstract

In the present study, it is shown that the spreading rate of a mixing layer can be greatly manipulated at very low forcing level if the mixing layer is perturbed near a subharmonic of the most-amplified frequency. The subharmonic forcing technique is able to make several vortices merge simultaneously and hence increases the spreading rate dramatically. A new mechanism, ‘collective interaction’, was found which can bypass the sequential stages of vortex merging and make a large number of vortices (ten or more) coalesce.

A deeper physical insight into the evolution of the coherent structures is revealed through the investigation of a forced mixing layer. The stability and the forcing function play important roles in determining the initial formation of the vortices. The subharmonic starts to amplify at the location where the phase speed of the subharmonic matches that of the fundamental. The position where vortices are seen to align vertically coincides with the position where the measured subharmonic reaches its peak. This location is defined as the merging location, and it can be determined from the feedback equation (Ho & Nosseir 1981).

The spreading rate and the velocity profiles of the forced mixing layer are distinctly different from the unforced case. The data show that the initial condition has a longlasting effect on the development of the mixing layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 119 , June 1982 , pp. 443 - 473
Copyright
© 1982 Cambridge University Press

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References

Acton, E. 1976 J. Fluid Mech. 76, 651.
Ashurst, W. T. 1976 Bull. Am. Phys. Soc., Ser. II. 21, 1428.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Bechert, D. & Pfizenmaier, E. 1975 J. Fluid Mech. 72, 341.
Browand, F. K. & Weidman, P. D. 1976 J. Fluid Mech. 76, 127.
Brown, G. L. & Roshko, A. 1974 J. Fluid Mech. 64, 775.
Crow, S. C. & Champagne, F. H. 1971 J. Fluid Mech. 48, 567.
Corcos, G. M. & Sherman, F. S. 1976 J. Fluid Mech. 73, 241.
Crighton, D. G. & Gaster, M. 1976 J. Fluid Mech. 77, 397.
Dimotakis, P. E. & Brown, G. L. 1976 J. Fluid Mech. 78, 535.
Fiedler, H. E. 1980 Initiation, evolution and global consequences of coherent structures in turbulent shear flows. In Proc. Symp. on Coherent Structures, Madrid, Spain.
Freymuth, P. 1966 J. Fluid Mech. 25, 683.
Gutmark, E. & Ho, C.-M. 1980 Feedback mechanism in a free jet. Bull. Am. Phys. Soc., Ser. II. 25, 1102.
Ho, C.-M. 1981 Local and global dynamics of free shear layers. In Proc. Symp. on Numerical and Physical Aspects of Aerodynamic Flows. Springer.
Ho, C.-M. & Huang, L.-S. 1978 Bull. Am. Phys. Soc., Ser. II. 23, 1007.
Ho, C.-M. & Nosseir, N. S. 1981 J. Fluid Mech. 105, 119.
Ho, C.-M. & Zhang, Y. Q. 1981 On the manipulation of spreading rate of mixing layers. In Proc. 3rd Int. Symp. on Turbulent Shear Flows, University of California, Davis.
Huerre, P. 1980 Phil. Trans. R. Soc. Lond. A 293, 643.
Kelly, R. E. 1967 J. Fluid Mech. 27, 657.
Kibens, V. 1980 A.I.A.A. J. 18, 434.
Kim, H. T., Kline, S. J. & Reynolds, W. C. 1971 J. Fluid Mech. 50, 133.
Knight, D. D. 1979 Numerical investigation of large scale structures in the turbulent mixing layer. In Proc. 6th Biennial Symp. on Turbulence, University of Missouri, Rolla.
Kovasznay, L. S. G., Kibens, V. & Blackwelder, R. F. 1970 J. Fluid Mech. 41, 283.
Laufer, J. & Monkewitz, P. 1980 A.I.A.A. Paper no. 80–0962.
Merkine, L. & Liu, J. T. C. 1975 J. Fluid Mech. 70, 353.
Mcalister, K. W. & Carr, L. W. 1978 NASA TM-78446.
Michalke, A. 1965 J. Fluid Mech. 23, 521.
Miksad, R. W. 1972 J. Fluid Mech. 56, 695.
Monkewitz, P. & Huerre, P. 1982 The effect of the velocity ratio on the spatial stability of a 2-D mixing layer. Phys. Fluids. (to appear).
Oster, D., Wygnanski, I., Dziomba, B. & Fiedler, H. 1977 On the effect of initial conditions on the two dimensional turbulent mixing layer. In Proc. Symp. on Turbulent Flow, Berlin.
Pierrehumbert, R. T. & Widnall, S. E., 1982 The two- and three-dimensional instabilities of a spatially periodic shear layer. J. Fluid Mech. 114, 59.Google Scholar
Petersen, R. A. 1978 J. Fluid Mech. 89, 469.
Reynolds, W. C. & Bouchard, E. E. 1981 The effect of forcing on the mixing layer region of a circular jet. In Proc. IUTAM Symp. on Unsteady Turbulent Shear Flows. Springer.
Riley, J. J. & Metcalfe, R. W. 1980 A.I.A.A. Paper no. 80–0274.
Rockwell, D. O. 1972 A.S.M.E. Paper no. 72-WA/APM-21.
Tam, C. K. W. 1971 J. Fluid Mech. 46, 757.
Winant, C. D. & Browand, F. K. 1974 J. Fluid Mech. 63, 237.
Wygnanski, I. & Fiedler, H. E. 1970 J. Fluid Mech. 41, 327.
Wygnanski, I., Oster, D. & Fiedler, F. 1979 A forced plane turbulent mixing layer: a challenge for the predictor. In Proc. 2nd Symp. on Turbulent Shear Flow, Imperial College, London.