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Inviscid instability of a skewed compressible mixing layer

Published online by Cambridge University Press:  26 April 2006

Ganyu Lu
Affiliation:
Also with the Department of Aeronautics and Astronautics, Stanford University.
Sanjiva K. Lele
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA Also with the Department of Aeronautics and Astronautics, Stanford University.

Abstract

In this paper we study the inviscid instability of a skewed compressible mixing layer between streams of different velocity magnitude and direction. The mean flow is governed by the three-dimensional laminar boundary-layer equations and can be reduced to a sum of a uniform flow and a two-dimensional shear flow. In the stability analysis, the amplification direction is assumed to be normal to the homogeneous direction of the mean flow. The results show that skewing enhances the instability by a factor of three for the incompressible mixing layer with velocity ratio 0.5 and uniform temperature. Under compressible conditions, skewing still increases the maximum amplification rate for a medium convective Mach number, but the enhancement is smaller. A scaling of the skewing effect is introduced which quantitatively explains the linear stability behaviour. Similarly, a suitably defined convective Mach number explains the compressibility effect.

Type
Research Article
Copyright
© 1993 Cambridge University Press

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References

Abramowich, G. N. 1963 The Theory of Turbulent Jets. MIT Press.
Bogdanoff, D. W. 1983 Compressibility effects in turbulent shear layers. AIAA J. 21, 926927.Google Scholar
Briggs, R. J. 1964 Electron-stream interaction with plasmas. Research Monograph 29. MIT Press.
Brown, G. L. 1974 The entrainment and large structure in turbulent mixing layers. In Proc. 5th Australian Conf. on Hydraulics and Fluid Mechanics (ed. D. Lindly & A. J. Sutherland), pp. 352359. University of Canterbury, Christchurch, New Zealand.
Brown, G. L. & Roshko, A. 1971 The effect of density difference on the turbulent mixing layer. AGARD-CP-93, pp. 23-123-12.
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775816.Google Scholar
Dimotakis, P. E. 1986 Two-dimensional shear-layer entrainment. AIAA J. 24, 17911796.Google Scholar
Dimotakis, P. E. 1991 Turbulent free shear layer mixing and combustion. GALCIT Rep. FM91-2.
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Gropengiesser, H. 1970 Study on the stability of boundary layers and compressible fluids. NASA Tech. Transl. NASA TT F-12, 786.Google Scholar
Grosch, C. E. & Jackson, T. L. 1991 Inviscid spatial stability of a three-dimensional compressible mixing layer. J. Fluid Mech. 231, 3550.Google Scholar
Gründel, H. & Fiedler, H. E. 1992 The mixing layer between non-parallel streams. In Fourth European Turbulence Conf. Abstracts, pp. 2729. Delft University of Technology, The Netherlands.
Hackett, J. E. & Cox, D. K. 1970 The three-dimensional mixing layer between two grazing perpendicular streams. J. Fluid Mech. 43, 7796.Google Scholar
Jackson, T. L. & Grosch, C. E. 1989 Inviscid spatial stability of a compressible mixing layer. J. Fluid Mech. 208, 609637.Google Scholar
Lees, L. & Lin, C. C. 1946 Investigation of the stability of the laminar boundary layer in a compressible fluid. NACA TN 1115.
Lele, S. K. 1989 Direct numerical simulation of compressible free shear flows. AIAA Paper, 89-0374.
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, 355367.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, 737742.Google Scholar
Macaraeg, M. G. 1991 Investigation of supersonic modes and three-dimensionality in bounded, free shear flows. Comput. Phys. Commun. 65, 201208.Google Scholar
Monkewitz, P. A. & Huerre, P. 1982 Influence of the velocity ratio on the spatial instability of mixing layers. Phys. Fluids 25, 11371143.Google Scholar
Nayfeh, A. H. 1980 Stability of three-dimensional boundary layers. AIAA J. 18, 406416.Google Scholar
Papamoschou, K. & Roshko, A. 1988 The compressible turbulent shear layer: an experimental study. J. Fluid Mech. 197, 453477.Google Scholar
Ragab, S. A. & Wu, J. L. 1988 Instabilities in the free shear layer formed by two supersonic streams. AIAA Paper 88-3677.
Sabin, C. M. 1965 An analytical and experimental investigation of the plane, incompressible, turbulent free-shear layer with arbitrary velocity ratio and pressure gradient. Trans. ASME D: J. Basic Engng 87, 421428.Google Scholar
Sandham, N. D. & Reynolds, W. C. 1989 A numerical investigation of the compressible mixing layer. Rep. TF-45. Department of Mechanical Engineering, Stanford University, Stanford, California.
Sandham, N. D. & Reynolds, W. C. 1990 Compressible mixing layer: linear theory and direct simulation. AIAA J. 28, 618624.Google Scholar
Schlichting, H. 1979 Boundary-Layer Theory, 7th edn. McGraw-Hill.
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