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Excitation of instability waves in free shear layers. Part 1. Theory

Published online by Cambridge University Press:  21 April 2006

D. W. Bechert
D. W. Bechert
Affiliation:
DFVLR, Abteilung Turbulenzforschung, Müller-Breslau-Straße 8, 1000 Berlin-West 12, West Germany
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Abstract

The generation of instability waves in free shear layers is investigated theoretically. The model assumes an infinitesimally thin shear layer shed from a semi-infinite plate which is exposed to sound excitation. For this model the forced instability waves are calculated. The shear-layer excitation by a source farther away from the plate edge in the downstream direction is very weak while upstream from the plate edge the excitation is relatively efficient. A special solution is given for the source at the plate edge. Any type of source farther away from the plate edge produces a parabolic pressure field near the edge. For this latter, fairly general case, a reference quantity is found for the magnitude of the excited instability waves. The theory is then extended to two streams, one on each side of the shear layer, having different velocities and densities. Furthermore, the excitation of a shear layer in a channel is calculated. The limitations to the theory and some aspects related to experiments are discussed. In particular, for a comparison with measurements, numerical computations of the velocity field outside the shear layer have been carried out.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 186 , January 1988 , pp. 47 - 62
Copyright
© 1988 Cambridge University Press

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References

Abramovitz, M. & Stegun, I. A. (ed.) 1970 Handbook of Mathematical Functions. Dover.
Bechert, D. W. 1980 Sound absorption caused by vorticity shedding, demonstrated with a jet flow. J. Sound Vib. 70, 389–405.Google Scholar
Bechert, D. W. 1982 Excited waves in shear layers. DFVLR-FB 82–23.
Bechert, D. W. 1985 Excitation of instability waves. Z. Flugwiss. Weltraumforsch. 9, 356–361.Google Scholar
Bechert, D. W. & Michel, U. 1974 The control of a thin free shear layer with and without a semi-infinite plate with a pulsating monopole or dipole. Some new closed form solutions. DFVLR-FB 74 22.Google Scholar
Bechert, D. W. & Michel, U. 1975 The control of a thin free shear layer with and without a semi-infinite plate by a pulsating flow field. Acustica 33, 287–307.Google Scholar
Bechert, D. W. & Pfizenmaier, E. 1975a On the amplification of broad band jet noise by a pure tone excitation. J. Sound Vib. 43, 581–587.Google Scholar
Bechert, D. W. & Pfizenmaier, E. 1975b Optical compensation meaurements on the unsteady exit condition at a nozzle discharge edge. J. Fluid Mech. 71, 123–144.Google Scholar
Bechert, D. W. & Stahl, B. 1988 Excitation of instability waves in free shear layers. Part 2. Experiments. J. Fluid Mech. 186, 63–84.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816.Google Scholar
Crighton, D. G. 1981 Acoustics as a branch of fluid mechanics. J. Fluid Mech. 106, 261–298.Google Scholar
Crighton, D. G. 1985 The Kutta condition in unsteady flow. Ann. Rev. Fluid Mech. 17, 411–445.Google 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.Google Scholar
Crow, S. C. & Champagne, F. H. 1971 Orderly structure in jet turbulence. J. Fluid Mech. 48, 547–591.Google Scholar
Deneuville, P. & Jaques, J. 1977 Jet noise amplification: a practically important problem. AIAA paper 77–1368.
Dziomba, B. & Fiedler, H. E. 1985 Effect of initial conditions on two-dimensional free shear layers. J. Fluid Mech. 152, 419–442.Google Scholar
Fiedler, H. E. & Mensing, P. 1985 The plane turbulent shear layer with periodic excitation. J. Fluid Mech. 150, 281–309.Google Scholar
Freymuth, P. 1966 On transition in a separated laminar boundary layer. J. Fluid Mech. 25, 683–703.Google Scholar
Hodge, C. G. & Tam, C. K. W. 1981 In Aerospace Highlights 1981. Astronautics and Aeronautics, Dec. 1981, pp. 28–29.
Howe, M. S. 1979 Attenuation of sound in a low Mach number nozzle flow. J. Fluid Mech. 91, 209–229.Google Scholar
Howe, M. S. 1980 The dissipation of sound at an edge. J. Sound Vib. 70, 407–411.Google Scholar
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151–168.Google Scholar
Koch, W. 1985 Local instability characteristics and frequency determination of self-excited wake flows. J. Sound Vib. 99, 53–83.Google Scholar
Mechel, F. & Ronneberger, D. 1965 Experimented Untersuchung der Schallausbreitung in luftdurchströmten Rohren mit Querschnittsveränderungen (Experimental investigation on the sound propagation in tubes with air flow and with changes in cross section). 5th Intl Congr. on Acoustics, Liège, 1965, paper K 23.
Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23, 521–544.Google Scholar
Möhring, W. 1975 On flows with vortex sheets and solid plates. J. Sound Vib. 38, 403–412.Google Scholar
Monkewitz, P. A. & Huerre, P. 1982 Influence of the velocity ratio on the spatial instability of mixing layers. Phys. Fluids 25, 1137–1143.Google Scholar
Moore, C. J. 1977 The role of shear-layer instability waves in jet exhaust noise. J. Fluid Mech. 80, 321–367.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.Google Scholar
Schmidt, C. 1978 Aerodynamic characterization of excited jets. J. Sound Vib. 61, 148–152.Google Scholar
Vasudevan, M. S., Nelson, P. A. & Howe, M. S. 1985 An experimental study of the influence of mean flow on acoustic dissipation by vorticity production at edges. Aero- and Hydro-Acoustics, IUTAM Symp. Lyon. Springer-Verlag.