Fluid Dynamics

, Volume 39, Issue 6, pp 874–884 | Cite as

Numerical modeling of perturbation propagation in a supersonic boundary layer

  • I.V. Egorov
  • V.G. Sudakov
  • A.V. Fedorov
Article

Abstract

The growth of two-dimensional disturbances generated in a supersonic (M∞ = 6) boundary layer on a flat plate by a periodic perturbation of the injection/suction type is investigated on the basis of a numerical solution of the Navier-Stokes equations. For small initial perturbation amplitudes, the secondmode growth rate obtained from the numerical modeling coincides with the growth rate calculated using linear theory with account for the non-parallelism of the main flow. Calculations performed for large initial perturbation amplitudes reveal the nonlinear dynamics of the perturbation growth downstream, with rapid growth of the higher multiple harmonics.

Keywords

Navier-Stokes equations supersonic flow boundary layer perturbations numerical modeling 

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REFERENCES

  1. 1.
    T. C. Lin, W. R. Grabowsky, and K. E. Yelmgren,“The search for optimum configurations for re-entry vehicles,” J. Spacecraft and Rockets. 21, No. 2, 142–149(1984).ADSGoogle Scholar
  2. 2.
    P. V. Tartabini, R. A. Lepsch, J. J. Korte, and K. E. Wurster, “A multidisciplinary performance analysis of a liftingbody single-stage-to-orbit vehicle,” AIAA Paper No. 2000–1045(2000).Google Scholar
  3. 3.
    H. L. Reed, R. Kimmel, S. Schneider, and D. Arnal, “Drag prediction and transition in hypersonic flow,” AIAA Paper No. 97–1818(1997).Google Scholar
  4. 4.
    S. A. Gaponov and A. A. Maslov, Perturbation Development in Compressible Flows[in Russian], Nauka, Novosibirsk (1992).Google Scholar
  5. 5.
    M. Morkovin, “Bypass transition to turbulence and research desiderata,” Transition in turbulence: NASA, CP-2386, 161–199(1985).Google Scholar
  6. 6.
    N. A. Jaffe, T. T. Okamura, and A. M. O. Smith, “Determination of spatial amplification factors and their application to predicting transition,” AIAA J., 8, No. 2, 301–308(1970).CrossRefMATHGoogle Scholar
  7. 7.
    C. D. Pruett and C. L. Chang, “Spatial direct numerical simulation of high-speed boundary layer flows. Pt. II: Transition on a cone in Mach 8 flow,” Theoret. Comput. Fluid Dynamics, 7, No. 5, 397–424(1995).MATHADSGoogle Scholar
  8. 8.
    X. Zhong, “Direct numerical simulation of hypersonic boundary-layer transition over blunt leading edges. Pt I: A new numerical method and validation,” AIAA Paper No. 97–0755(1997).Google Scholar
  9. 9.
    S. H Hu and X. Zhong, “Linear stability of hypersonic flow over a parabolic leading edge,” AIAA Paper No. 97–2015(1997).Google Scholar
  10. 10.
    X. Zhong, “Receptivity of hypersonic boundary layers to free-stream disturbances,” AIAA Paper No. 2000–0531(2000).Google Scholar
  11. 11.
    Y. Ma and X. Zhong, “Direct numerical simulation of instability of nonequilibrium reacting hypersonic boundary layers,” AIAA Paper No. 2000–0539(2000).Google Scholar
  12. 12.
    Y. Ma and X. Zhong, “Numerical simulation of receptivity and stability of nonequilibrium reacting hypersonic boundary layers,”AIAA Paper No. 2001–0892(2001).Google Scholar
  13. 13.
    X. Zhong and Y.Ma, “Receptivity and linear stability of Stetson’sMach 8 blunt cone stability experiments,” AIAA Paper No. 2002–2849(2002).Google Scholar
  14. 14.
    K. F. Stetson, E. R. Thompson, J. C. Donaldson, and L. G. Siler, “Laminar boundary layer stability experiments on a cone at Mach 8. Pt 2: Blunt cone,” AIAA Paper No. 84–0006(1984).Google Scholar
  15. 15.
    K. F. Stetson and R. L. Kimmel, “On hypersonic boundary layer stability,” AIAA Paper No. 92–0737(1992).Google Scholar
  16. 16.
    S. K. Godunov, “Finite-differencemethod for the numerical calculation of discontinuous solutions of the equations of hydrodynamics,” Math. Sb., 47, No. 3, 271–306(1959).MathSciNetGoogle Scholar
  17. 17.
    V. P. Kolgan, “The application of the minimum-derivative principle to the construction of finite-difference schemes for the calculation of discontinuous solutions of the equations of gasdynamics,” Uchen. Zap. TsAGI, 3, No. 6, 68–77(1972).Google Scholar
  18. 18.
    P. L. Roe, “Approximate Riemann solvers, parameter vectors, and difference scheme,” J. Comput. Phys., 43, No. 2, 357–372(1981).MATHADSMathSciNetGoogle Scholar
  19. 19.
    I. U. Babaev, V. A. Bashkin, and I. V. Egorov, “Numerical solution of the Navier-Stokes equations using iterative methods of variational type,” Zh. Vych. Matem. Mat. Phys., 34, No. 11, 1693–1703(1994).MathSciNetGoogle Scholar
  20. 20.
    V. A. Bashkin, I. V. Egorov, and D. V. Ivanov, “The application of Newton’s method to the calculation of internal hypersonic separated flows,” Prikl. Matem. Tekh. Fiz., 38, No. 1, 30–42(1997).MATHGoogle Scholar
  21. 21.
    V. R. Gushchin and A.V. Fedorov, “Short-wave instability in the shock layer of a perfect gas,” Izv. Akad Nauk SSSR, Mekh. Zhidk. Gaza, 1, 10 (1989).MathSciNetGoogle Scholar
  22. 22.
    A. V. Fedorov and A. P. Khokhlov, “Prehistory of instability in a hypersonic boundary layer,” Theoret. Comput. Fluid Dynamics, 14, No. 6, 359–375(2001).MATHADSGoogle Scholar
  23. 23.
    A. V. Fedorov and A. P. Khokhlov, “Receptivity of hypersonic boundary layer to wall disturbances,” Theoret. Comput. Fluid Dynamics, 15, No. 4, 231–254(2002).MATHADSGoogle Scholar
  24. 24.
    S. A. Gaponov, “The flow non-parallelism effect on the development of perturbations in a hypersonic boundary layer,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 26 (1980).Google Scholar
  25. 25.
    C. D. Pruett and T. A. Zang, “Direct numerical simulation of laminar breakdown in high-speed, axisymmetric boundary layer,” AIAA Paper No. 92–0742(1992).Google Scholar
  26. 26.
    K. F. Stetson and R. L. Kimmel, “On the breakdown of a hypersonic boundary layer,” AIAA Paper No. 93–0896(1993).Google Scholar
  27. 27.
    A. N. Shiplyuk, A. A. Maslov, and N. D. Chokani, “Nonlinear interactions of second mode instability with natural and artificial disturbances,” AIAA Paper No. 2003–0787(2003).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • I.V. Egorov
  • V.G. Sudakov
  • A.V. Fedorov

There are no affiliations available

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