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Inviscid spatial stability of a compressible mixing layer

Published online by Cambridge University Press:  26 April 2006

T. L. Jackson  and
C. E. Grosch
T. L. Jackson
Affiliation:
Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA
C. E. Grosch
Affiliation:
Department of Oceanography and Department of Computer Science, Old Dominion University, Norfolk, VA 23529, USA
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Abstract

We present the results of the inviscid spatial stability of a parallel compressible mixing layer. The parameters of this study are the Mach number of the moving stream, the ratio of the temperature of the stationary stream to that of the moving stream, the frequency, and the direction of propagation of the disturbance wave. Stability characteristics of the flow as a function of these parameters are given. It is shown that if the Mach number exceeds a critical value there are always two groups of unstable waves. One of these groups is fast with phase speeds greater than ½ and is supersonic with respect to the stationary stream. The other is slow with phase speeds less than ½ and supersonic with respect to the moving stream. Phase speeds for the neutral and unstable modes are given, as well as growth rates for the unstable modes. Finally, we show that three-dimensional modes have the same general behaviour as the two-dimensional modes but with higher growth rates over some range of propagation direction.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 208 , November 1989 , pp. 609 - 637
Copyright
© 1989 Cambridge University Press

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References

Blumen, W., Drazin, P. G. & Billings, D. F. 1975 Shear layer instability of an inviscid compressible fluid. Part 2. J. Fluid Mech. 71, 305–316.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
Chapman, D. R. 1950 Laminar mixing of a compressible fluid. NACA Rep. 958.Google Scholar
Chinzei, N., Masuya, G., Komuro, T., Murakami, A. & Kudou, D. 1986 Spreading of two-stream supersonic turbulent mixing layers. Phys. Fluids 29, 1345–1347.Google Scholar
Drazin, P. G. & Davey, A. 1977 Shear layer instability of an inviscid compressible fluid. Part 3. J. Fluid Mech. 82, 255–260.Google Scholar
Dunn, D. W. & Lin, C. C. 1955 On the stability of the laminar boundary in a compressible fluid. J. Aero. Sci. 22, 455–477.Google Scholar
Gill, A. E. 1965 Instabilities of ‘top-hat’ jets and wakes in compressible fluids. Phys. Fluids 8, 1428–1430.Google Scholar
Gropengiesser, H. 1969 On the stability of free shear layers in compressible flows (in German). Deutsche Luft. und Raumfahrt, FB 69–25, 123 pp. also, NASA Tech. Transl. NASA TT F-12,786.Google Scholar
Ho, C. M. & Huerre, P. 1984 Perturbed free shear layers. Ann. Rev. Fluid Mech. 16, 365–424.Google Scholar
Jackson, T. L. & Hussaini, M. Y. 1988 An asymptotic analysis of supersonic reacting mixing layers. Combust. Sci. Tech. 57, 129–140.Google Scholar
Kumar, A., Bushnell, D. M. & Hussaini, M. Y. 1987 A mixing augmentation technique for hypervelocity scramjets. AIAA Paper 87–1882.Google Scholar
Lees, L. & Lin, C. C. 1946 Investigation of the stability of the laminar boundary layer in a compressible fluid. NACA TN 1115.Google Scholar
Lessen, M., Fox, J. A. & Zien, H. M. 1965 On the inviscid stability of the laminar mixing of two parallel streams of a compressible fluid. J. Fluid Mech. 23, 355–367.Google Scholar
Lessen, M., Fox, J. A. & Zien, H. M. 1966 Stability of the laminar mixing of two parallel streams with respect to supersonic disturbances. J. Fluid Mech. 25, 737–742.Google Scholar
Lock, R. C. 1951 The velocity distribution in the laminar boundary layer between parallel streams. Q. J. Mech. Appl. Maths 4, 42–63.Google Scholar
Macaraeg, M. G., Streett, C. L. & Hussaini, M. Y. 1988 A spectral collocation solution to the compressible stability eigenvalue problem. NASA Tech. Paper 2858.Google Scholar
Mack, L. M. 1975 Linear stability theory and the problem of supersonic boundary-layer transition. AIAA J. 13, 278–289.Google Scholar
Mack, L. M. 1984 Boundary layer linear stability theory. In Special Course on Stability and Transition of Laminar Flow, AGARD Rep. R-709, pp. 3-1–3-81.Google Scholar
Mack, L. M. 1987 Review of linear compressible stability theory. In Stability of Time Dependent and Spatially Varying Flows (ed. D. L. Dwoyer & M. Y. Hussaini), pp. 164–187. Springer.
Mack, L. M. 1989 On the inviscid acoustic-mode instability of supersonic shear flows. Fourth Symp. on Numerical and Physical Aspects of Aerodynamic Flows, California State University, Long Beach, California.
Michalke, A. 1972 The instability of free shear layers. Prog. Aerospace Sci. 12, 213–239.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
Papamoschou, D. & Roshko, A. 1986 Observations of supersonic free-shear layers. AIAA Paper 86–0162.Google Scholar
Papamoschou, D. & Roshko, A. 1988 The compressible turbulent shear layer: an experimental study. J. Fluid Mech. 197, 453–477.Google Scholar
Ragab, S. A. 1988 Instabilities in the wake mixing-layer region of a splitter plate separating two supersonic streams. AIAA Paper 88–3677.Google Scholar
Ragab, S. A. & Wu, J. L. 1988 Instabilities in the free shear layer formed by two supersonic streams. AIAA Paper 88-0038.Google Scholar
Stewartson, K. 1964 The Theory of Laminar Boundary Layers in Compressible Fluids. Oxford University Press.
Tam, C. K. W. & Hu, F. Q. 1988 Instabilities of supersonic mixing layers inside a rectangular channel. AIAA Paper 88–3675.Google Scholar
Zhuang, M., Kubota, T. & Dimotakis, P. E. 1988 On the instability of inviscid, compressible free shear layers. AIAA Paper 88–3538.Google Scholar