Numerical calculations of supersonic underexpanded jets in a cocurrent flow with the use of parabolized Navier-Stokes equations

  • A. P. MakashevaEmail author
  • A. Zh. Naimanova


Results of a numerical study of three-dimensional supersonic jets propagating in a cocurrent flow are described. Averaged parabolized Navier-Stokes equations are solved numerically on the basis of a developed scheme, which allows calculations in supersonic and subsonic flow regions to be performed in a single manner. A jet flow with a cocurrent flow Mach number 0.05 ⩽ M ⩽ 7.00 is studied, and its effect on the structure of the mixing layer is demonstrated. The calculated results are compared with available experimental and numerical data.

Key words

underexpanded supersonic jet cocurrent flow Navier-Stokes equations 


  1. 1.
    K. S. Abdol-Hamid and R. G. Wilmoth, “Multiscale turbulence effects in underexpanded supersonic jets,” AIAA J., 27, No. 3, 315–322 (1989).CrossRefADSGoogle Scholar
  2. 2.
    R. Ishii and Y. Umeda, “Numerical analysis of two-phase jets,” J. Thermophys. Heat Transfer, No. 1, 17–24 (1988).Google Scholar
  3. 3.
    E. Rathakrishnan, “A numerical approach to single and twin supersonic jet flows,” in: Scholar
  4. 4.
    V. S. Avduevskii, A. V. Ivanov, I. M. Karpman, et al., “Structure of turbulent underexpanded jets exhausting into the ambient space and cocurrent flow,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 15–29 (1972).Google Scholar
  5. 5.
    A. Mohamed, A. Hamed, and T. Lehnig, “Supersonic rectangular over-expanded jets of single and two-phase flows,” in: Scholar
  6. 6.
    V. I. Zapryagaev, N. P. Kiselev, and A. A. Pavlov, “Effect of streamline curvature on intensity of streamwise vortices in the mixing layer of supersonic jets,” J. Appl. Mech. Tech. Phys., 45, No. 3, 335–434 (2004).CrossRefADSGoogle Scholar
  7. 7.
    V. N. Vatsa, M. J. Werle, O. L. Anderson, and G. B. Hankins (Jr.), “Solutions for three-dimensional over-or underexpanded exhaust plumes,” AIAA J., 20, No. 9, 1188–1194 (1982).zbMATHCrossRefADSGoogle Scholar
  8. 8.
    D. Anderson, J. Tannehill, and R. Pletcher, Computational Fluid Mechanics and Heat Transfer, Hemisphere, New York (1984).zbMATHGoogle Scholar
  9. 9.
    N. D. Sinha and S. M. Dash, “Parabolized Navier-Stokes analysis of ducted supersonic combustion problems,” J. Propuls. Power, No. 5, 455–464 (1987).Google Scholar
  10. 10.
    Jungwoo Kim, Dongjoo Kim, and Haecheon Choi, “An immersed-boundary finite-volume method for simulations of flow in complex geometries,” J. Comput. Phys., No. 171, 132–150 (2001).Google Scholar
  11. 11.
    G. N. Abramovich, Theory of Turbulent Jets [in Russian], Nauka, Moscow (1984).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Institute of MathematicsMinistry of Education and Science of the Kazakhstan RepublicAlmatyKazakhstan

Personalised recommendations