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Inviscid spatial stability of a compressible mixing layer. Part 3. Effect of thermodynamics

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 report the results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow. The models are (i) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity–temperature relation and a Prandtl number of one; (ii) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (iii) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity–temperature relation and arbitrary but constant Prandtl number. The purpose of this study was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the qualitative features of the stability characteristics are quite similar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, we show that the stability characteristics are sensitive to the value of the Prandtl number and to a particular value of the temperature ratio across the mixing layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 224 , March 1991 , pp. 159 - 175
Copyright
© 1991 Cambridge University Press

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References

Balsa, T. F. & Goldstein, M. E., 1990 On the instabilities of supersonic mixing layers: A high- Mach-number asymptotic theory. J. Fluid Mech. 216, 585–611.Google Scholar
Blumen, W.: 1970 Shear layer instability of an inviscid compressible fluid. J. Fluid Mech. 40, 769–781.Google Scholar
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, W. B.: 1962 Exact numerical solutions of the complete linearized equations for the stability of compressible boundary layers. Norair Rep. NOR-62–15, Northrop Aircraft Inc., Hawthorne, CA.
Chapman, D. R.: 1950 Laminar mixing of a compressible fluid. NACA Rep. 958.Google Scholar
Djordjevic, V. D. & Redekopp, L. G., 1988 Linear stability analysis of nonhomentropic, inviscid compressible flows. Phys. Fluids 31, 3239–3245.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
Drazin, P. G. & Reid, W. H., 1984 Hydrodynamic Stability Cambridge University Press.
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. Trans F-12,786.Google Scholar
Jackson, T. L. & Grosch, C. E., 1989 Inviscal spatial stability of a compressible mixing layer. J. Fluid Mech 208, 609–637.Google Scholar
Jackson, T. L. & Grosc, H. C. E. 1990a On the classification of unstable modes in bounded compressible mixing layers. In Instability and Transition (ed. M. Y. Hussaini & R. G. Voigt), pp. 187–198. Springer.
Jackson, T. L. & Grosch, C. E., 1990b Inviscid spatial stability of a compressible mixing layer. Part 2. The flame sheet model. J. Fluid Mech 217, 391–420.Google Scholar
Klemp, J. B. & Acrivos, A., 1972 A note on the laminar mixing of two uniform parallel semi-infinite streams. J. Fluid Mech 55, 25–30.Google Scholar
Lees, L. & Lin, C. C., 1946 Investigation of the stability of the laminar boundary layer in a compressible fluid. NACA Tech. Note 1115.Google Scholar
Lees, L. & Reshotko, E., 1962 Stability of the compressible laminar boundary layer. J. Fluid Mech 12, 555–590.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
Macaraeo, 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.: 1965 Computation of the stability of the laminar compressible boundary layer. In Methods in Computational Physics (ed. B. Alder, S. Fernbach & M. Rotenberg), vol. 4. pp. 247–299. Academic.
Mack, L. M.: 1984 Boundary layer linear stability theory. In Special Course on Stability and Transition of Laminar Flow. AGARD Rep R-709, 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. Numer. Phys. Aspects of Aerodyn. Flows California State University, Long Beach, California.
Ragab, S. A. & Wu, J. L., 1988 Instabilities in the free shear layer formed by two supersonic streams. A1AA Paper 88–0038.Google Scholar
Stewaktson, 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
Tam, C. K. W. & Hu, F. Q. 1989 The instability and acoustic wave modes of supersonic mixing layers inside a rectangular channel. J. Fluid Mech 203, 1 51–76.Google Scholar
Ting, L.: 1959 On the mixing of two parallel streams. J. Math. Phys. 28, 153–165.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