On Turbulence in Compressible Fluids

  • M. Y. Hussaini
  • G. Erlebacher
  • S. Sarkar
Conference paper

Abstract

There is no prospect of a comprehensive theory of turbulence, especially compressible turbulence. At best there would be hypotheses based on intuition and empiricism, scaling laws based on similarity methods, analogy and dimensional analysis, and physical and mathematical models which partially explain some turbulence phenomena. An example of a hypothesis is that due to Morkovin (1964) who enunciated that the compressibility effects on turbulence structure are negligible if the root-mean-square density fluctuations are small relative to the absolute density. This was based on the empirical data which was then available, and the implicit assumption was that the pressure fluctuations and total temperature fluctuations were both small. In his excellent review article on compressible turbulent shear flows, Bradshaw (1977) discusses the compressibility effects on turbulence when these assumptions are not satisfied as, for instance, in the case of boundary layers and wakes for Mach numbers beyond 5.

Keywords

Entropy Convection Vorticity Autocorrelation Compressibility 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bardina, J.; Ferziger, J.H.; and Reynolds, W.C. 1983 — Improved Turbulence Models Based on Large-Eddy Simulation of Homogeneous, Incompressible Turbulent Flows. Stanford University Technical Report, TF-19.Google Scholar
  2. Barnwell, D. 1989 — A skin friction law for compressible turbulent flows. AIAA Paper No. 89-1864, to appear in AIAA J., 1991.Google Scholar
  3. Bradshaw, P. 1977 — Compressible Turbulent Shear Flows. Ann. Rev. Fluid Mech. 9, edited by M. Van Dyck, J.V. Wehausen and J.L. Lumley (Annual Reviews Inc., Palo Alto, 1977), 33.Google Scholar
  4. Canuto, C.; Hussaini, M. Y.; Quarteroni, A.; and Zang, T. A. 1988 — Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin.MATHGoogle Scholar
  5. Cebeci, T.; and Smith, A.M.O. 1974 — Analysis of Turbulent Boundary Layers. New York: Academic Press.MATHGoogle Scholar
  6. Chandrasekhar, S. 1951 — Density fluctuations in isotropic turbulence. Proc. Roy. Soc. London, 211A, 18–24.MathSciNetGoogle Scholar
  7. Chu, B.T.; and Kovasznay, L.S.G. 1958 — Nonlinear Interactions in a Viscous Heat-Conducting Compressible Gas. J. Fluid Mech. 3, 494.MathSciNetCrossRefGoogle Scholar
  8. Dussauge, J.P.; and Quine, C. 1988 — A Second-Order Closure for Supersonic Turbulent Flows: Application to the Supersonic Mixing. Workshop on the Physics of Compressible Turbulent Mixing, Princeton.Google Scholar
  9. Erlebacher, G.; Hussaini, M.Y.; Speziale, C.G.; and Zang, T.A. 1987 — Toward the Large-Eddy Simulation of Compressible Turbulent FLows. ICASE Report No. 87-20.Google Scholar
  10. Erlebacher, G.; Hussaini, M.Y.; Kreiss, H.O.; and Sarkar, S. 1990 — The Analysis and Simulation of Compressible Turbulence. Theor. and Comput. Fluid Dyn. 2, 73–95.MATHGoogle Scholar
  11. Erlebacher, G.; Hussaini, M.Y.; Speziale, C.G.; and Zang, T.A. 1990 — On the large-eddy simulation of compressible turbulence. Proceedings of the 12th International Conference of Numerical Methods in Fluid Dynamics, University of Oxford.Google Scholar
  12. Feiereisen, W. J.; Reynolds, W. C. and Ferziger, J. H. 1981 — Numerical Simulation of Compressible, Homogeneous, Turbulent Shear Flow. Report TF-13, Dept. Mech. Eng., Stanford University.Google Scholar
  13. Ferziger, J.H. 1984 — Large Eddy Simulation: Its Role in Turbulence Research. In Theoretical Approaches to Turbulence edited by D.L. Dwyer, M.Y. Hussaini, and R.G. Voigt (springer, New York).Google Scholar
  14. Kadomtsev, B.B.; and Petviashvili, V.I. 1973 — Acoustic Turbulence. Sov. Phys. Dokl. 18, 115.Google Scholar
  15. Kline, S.J.; Cantwell, B.J.; and Lilley, G.M. 1982 — 1980–81, AFSOR — HTTM-Stanford Conference, Vol. 1, Stanford University Press, California, 368.Google Scholar
  16. Kolmogorov, A.N. 1941a — Local structure of turbulence in an incompressible fluid at very high Reynolds numbers. Doklady AN SSSR, 30, No. 4, 299–303.Google Scholar
  17. Kovasznay, L.S.G. 1953 — Turbulence in Supersonic Flows. J. Aero. Sciences 20, No. 10, 657–682.MATHGoogle Scholar
  18. Kreiss, H.O.; Lorenz; and Naughton, M., 1990 — Convergence of the Solutions of the Compressible to the Solution of the Incompressible Navier-Stokes Equations. To appear in Advances in Applied Mathematics.Google Scholar
  19. Krzywoblocki, M.Z.E. 1951 — On the generalized fundamental equations of isotropic turbulence in compressible fluids and in hypersonics. Proc. 1st US Nat. Congr. Appl. Mech., Chicago, New York, 827–835.Google Scholar
  20. Leslie, D.C. 1973 — Developments in the Theory of Turbulence, Oxford University Press, Oxford.MATHGoogle Scholar
  21. L’vov V.S.; and Mikhailov, A.V.. 1978a — Sound and Hydrodynamic turbulence in a Compressible Liquid. Sov. Phys. J. Exp. Theor. Phys. 47, 756.Google Scholar
  22. L’vov, V.S.; and Mikhailov, A.V. 1978b — Scattering and Interaction of Sound with Sound in a Turbulent Medium. Sov. Phys. J. Exp. Theor. Phys. 47, 840.Google Scholar
  23. Marion, J-D. 1988 — Etude Spectrale d’une Turbulence Isotrope Compressible. Ph.D. Thesis, Ecole Centrale de Lyon, France.Google Scholar
  24. Moiseev, S.S.; Sagdeev, R.Z.; Tur, A.V.; and Yanovskii, V.V. 1977 — Structure of Acoustic-Vortical Turbulence. Sov. Phys. Dokl. 22, 582.MATHGoogle Scholar
  25. Monin, A.S.; and Yaglom, A.M. 1967 — Statistical Fluid Mechanics, 2, MIT Press, Cambridge, Massachusetts.Google Scholar
  26. Morkovin, M.V. 1964 — The Mechanics of Turbulence, edited by A. Favre (Gordon & Breach, New York), 367.Google Scholar
  27. Moyal, J.E. 1952 — The Spectra of Turbulence in a Compressible Fluid; Eddy Turbulence and Random Noise. Proc. of the Cambridge Phil. Soc., 48, part 1, 329–344.MathSciNetMATHCrossRefGoogle Scholar
  28. Obukhov, A.M. 1941 — Energy distribution in the spectrum of turbulent flow. Izvestiya AN SSSR, Ser. geogr. geofiz., No. 4–5, 453–466.Google Scholar
  29. Oh Y.H. 1974 — Analysis of Two-Dimensional Free Turbulent Mixing. AIAA Paper No. 74-594.Google Scholar
  30. Passot, T.; and Pouquet, A. 1987 — Numerical Simulation of Compressible Homogeneous Flows in the Turbulent Regime. J. Fluid Mech. 181 441–466.MATHCrossRefGoogle Scholar
  31. Saffman, P. G. 1977 — Problems and Progress in the Theory of Turbulence. Structures and Mechanisms of Turbulence II, Lecture Notes in Physics 76, edited by H. Fieldler, Springer-Verlag, Berlin, 273.Google Scholar
  32. Sarkar, S.; Erlebacher, G.; Hussaini, M.Y.; and Kreiss, H.O. 1989 — The Analysis and Modeling of Dilatational Terms in Compressible Turbulence. ICASE Report No. 89-79. Accepted for publication in J. Fluid Mech.Google Scholar
  33. Sarkar, S.; and Lakshmanan, B. 1990 — Application of a Reynolds stress turbulence model to the compressible shear layer. ICASE Report No. 90-18. Accepted for publication in AIAA Journal.Google Scholar
  34. Schlichting, H.; 1979 Boundary Layer Theory, McGraw-Hill, New York.MATHGoogle Scholar
  35. Speziale, C.G.; Erlebacher, G.; Zang, T.A.; and Hussaini, M.Y. 1988 — The subgrid scale modeling of compressible turbulence. Phys. Fluids 31, 940–942.CrossRefGoogle Scholar
  36. Tanuiti, T.; and Wei, C.C. 1968 Reductive Perturbation Method in Nonlinear Wave Propagation. I.J. Phys. Soc. of Japan, 24, No. 4, 941–946.CrossRefGoogle Scholar
  37. Tatsumi, T.; and Tokunaga, H. 1974 — One-Dimensional Shock-Turbulence in a Compressible Fluid. J. Fluid Mech. 65, 581.MathSciNetMATHCrossRefGoogle Scholar
  38. Tokunaga, H.; and Tatsumi, T. 1975 — Interaction of Plane Nonlinear Waves in a Compressible Fluid and Two-Dimensional Shock-Turbulence. J. Phys. Soc. Japan 38 1167.MathSciNetCrossRefGoogle Scholar
  39. Vandromme, D. 1983 — Contribution to the Modeling and Prediction of Variable Density Flows. Ph.D. Thesis, University of Science and Technology, Lille, France.Google Scholar
  40. Wilcox, D.C. 1989 — Hypersonic Turbulence Modeling without the Epsilon Equation. Seventh National Aero-Space Plane Technology Symposium.Google Scholar
  41. Yoshizawa, A. 1986 — Statistical Theory for Compressible Turbulent Shear Flows, with the Application to Subgrid Modeling, Phys. Fluids, 29, 2152–2164.MATHCrossRefGoogle Scholar
  42. Zakharov, V.E.; and Sagdeev, R.Z. 1970 — Spectrum of Acoustic Turbulence. Sov. Phys. Dokl. 15, 439.MATHGoogle Scholar
  43. Zeman, O. 1990 — Dilatational Dissipation: The Concept and Application in Modeling Compressible Mixing Layers. Phys. Fluids A 2, 178.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • M. Y. Hussaini
  • G. Erlebacher
  • S. Sarkar

There are no affiliations available

Personalised recommendations