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Oscillations of an unstable mixing layer impinging upon an edge

Published online by Cambridge University Press:  20 April 2006

Samir Ziada  and
Donald Rockwell
Samir Ziada
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University. Bethlehem, PA 18015 Present address: Laboratory for vibrations and acoustics, Sulzer Bros, Winterthur, Switzerland.
Donald Rockwell
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University. Bethlehem, PA 18015
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Abstract

The central features of lihear and nonlinear disturbance growth in the unstable shear layer, mechanisms of impingement of the resultant vortices on the edge, induced force on the wedge, and upstream influence in the form of induced velocity fluctuations at separation are examined by simultaneous visualization, velocity, and force-measurement techniques.

The nature of the vortex–wedge interaction, and the associated force on the wedge, are directly related to the induced velocity at the upstream separation edge, thereby providing the essential ‘feedback’ for the self-sustained oscillation. Velocity fluctuations at the upper and lower sides of the separation edge tend to be π out of phase, a condition that is maintained along the outer boundaries of the downstream shear layer. Moreover, the phase between velocity fluctuations at separation and impingement satisfies the relation 2nπ, where n is an integer.

The shear layer downstream of the separation edge initially forms an asymmetric wake, which evolves into large-scale vortices, all of which have a circulation appropriate to the high-speed side. The disturbance amplification associated with the high-speed side dominates from the separation edge onwards, precluding development of instabilities associated with the low-speed side.

Regardless of the initial amplitude of the disturbance induced at the separation edge, the same saturation amplitude is attained in the downstream (nonlinear) region of the shear layer, underscoring the fact that variations in force amplitude at the wedge are dominated by the type of vortex–edge interaction mechanism. The sensitivity of this interaction to small offsets between the vortex centre and the leading edge entails that jumps in frequency of oscillation are also associated with jumps in the force amplitude.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 124 , November 1982 , pp. 307 - 334
Copyright
© 1982 Cambridge University Press

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References

Brown, G. B. 1937 The vortex motion causing edge tones. Proc. Phys. Soc. 49, 493–507.Google Scholar
Ffowcs Williams, J. E. 1969 Hydrodynamic noise. Ann. Rev. Fluid Mech. 1, 197–222.Google Scholar
Freymuth, P. 1966 On transition in a separated laminar boundary layer. J. Fluid Mech. 25, 683–704.Google Scholar
Hill, P. G. & Stenning, A. H. 1960 Laminar boundary layers in oscillatory flow. Trans. A.S.M.E. D: J. Basic Engng 82, 593–608.Google Scholar
Ho, C. & Nosseir, N. S. 1981 Dynamics of an impinging jet. Part 1. The feedback phenomenon. J. Fluid Mech. 105, 119–142.Google Scholar
Hussain, A. K. M. F. & Zaman, K. B. M. Q. 1978 The free shear layer tone phenomenon and probe interference. J. Fluid Mech. 87, 349–383.Google Scholar
Karamcheti, K., Bauer, A. B., Shields, W. C., Stegen, G. R. & Woolley, J. A. 1969 Some basic features of an edgetone flow field. Basic Aerodynamic Noise Research: Conf. at NASA Headquarters, Wash. D.C., 14–15 July. NASA-SP-207, p. 275.
Knisely, C. & Rockwell, D. 1982 Self-sustained low-frequency components in an impinging shear layer. J. Fluid Mech. 116, 157–186.Google Scholar
Mccartney, M. S. & Greber, I. 1973 An experimental and theoretical investigation of the edge-tone phenomenon. Case Western Reserve University Rep. FTAS/TR73–87.Google Scholar
Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23, 521–544.Google Scholar
Miksad, R. W. 1972 Experiments on the nonlinear stages of free-shear transition. J. Fluid Mech. 56, 695–719.Google Scholar
Powell, A. 1961 On the edgetone. J. Acoust. Soc. Am. 33, 395–409.Google Scholar
Richardson, E. G. 1931 Edge-tones. Proc. Phys. Soc. 43, 394–404.Google Scholar
Rockwell, D. & Naudascher, E. 1979 Self-sustained oscillations of impinging free shear layers. Ann. Rev. Fluid Mech. 11, 67–94.Google Scholar
Rockwell, D. & Schachenmann, A. 1982 Self-generation of organized waves in an impinging turbulent jet at low Mach number. J. Fluid Mech. 117, 425–441.Google Scholar
Rogler, H. L. 1974 A mechanism of vorticity segregation. Bull. Am. Phys. Soc. Ser. II 19, 1165.Google Scholar
Sarohia, V. 1977 Experimental investigation of oscillations in flows over shallow cavities. A.I.A.A. J. 15, 984–991.Google Scholar
Stuart, J. T. 1967 On finite amplitude oscillations in laminar mixing layers. J. Fluid Mech. 29, 417–440.Google Scholar
Ziada, S. 1981 Self-sustained oscillations of a mixing layer—wedge system. Ph.D. thesis, Dept of Mech. Engng and Mechanics, Lehigh University.
Ziada, S. & Rockwell, D. 1981a Vortex—leading-edge interaction. J. Fluid Mech. 118, 79–107.Google Scholar
Ziada, S. & Rockwell, D. 1982b Generation of higher harmonics in an unstable mixing layer—edge system. A.I.A.A. J. 20, 196–202.Google Scholar