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Numerical modeling of the disturbances of the separated flow in a rounded compression corner

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Abstract

Numerical modeling of the time-dependent supersonic flow over a compression corner with different roundness radii is performed on the basis of the solution of the two-dimensional Navier-Stokes equations in the regimes corresponding to local boundary layer separation. The development of unstable disturbances generated by local periodic injection/suction in the preseparated boundary layer is calculated. The results are compared with those of similar calculations for a flat plate. It is shown that the natural oscillations of the boundary-layer second mode stabilize in the separation zone and grow intensely downstream of the reattachment point. The acoustic modes excited within a separation bubble are studied using numerical calculations and an asymptotic analysis.

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References

  1. H. L. Reed, R. Kimmel, S. Schneider, and D. Arnal, “Drag prediction and transition in hypersonic flow,” AIAA Paper, No. 1818 (1997).

  2. S. A. Gaponov and A. A. Maslov, Disturbance Development in Compressible Flows [in Russian], Nauka, Novosibirsk (1980).

    Google Scholar 

  3. M. R. Maik, “Boundary layer transition prediction toolkit,” AIAA Paper, No. 1904 (1997).

  4. L. M. Mack, “Linear stability theory and the problem of supersonic boundary layer transition,” AIAA J., 13, 278 (1975).

    Article  ADS  Google Scholar 

  5. P. Balakumar, H. Zhao, and H. Atkins, “Stability of hypersonic boundary layers over a compression corner,” AIAA Paper, No. 2848 (2002).

  6. V. R. Gushchin and A. V. Fedorov, “Asymptotic analysis of inviscid disturbances in a supersonic boundary layer,” Zh. Prikl. Mekh. Tekhn. Fiz., No. 1, 69 (1989).

  7. V. R. Gushchin and A. V. Fedorov, “Excitation and development of unstable disturbances in a supersonic boundary layer,” Fluid Dynamics, 25, No. 3, 344 (1990).

    Article  MathSciNet  Google Scholar 

  8. M. V. Fedoryuk, Asymptotic Methods for Linear Ordinary Differential Equations [in Russian], Nauka, Moscow (1983).

    MATH  Google Scholar 

  9. I. V. Egorov, V. G. Sudakov, and A. V. Fedorov, “Numerical modeling of perturbation propagation in a supersonic boundary layer,” Fluid Dynamics, 39, No. 6, 874 (2004).

    Article  Google Scholar 

  10. N. A. Driscoll and S. A. Vavasis, “Numerical conformal mapping using cross ratios and Delaunay triangulation,” SIAM J. Sci. Comput., 19, 1783 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  11. V. Ya. Neiland, V. V. Bogolepov, G. N. Dudin, and I. I. Lipatov, Asymptotic Theory of Supersonic Viscous Flows [in Russian], Fizmatlit, Moscow (2004).

    Google Scholar 

  12. T. C. Adamson Jr. and A. F. Messiter, “Analysis of two-dimensional interactions between shock waves and boundary layers,” Annu. Rev. Fluid Mech., 12, 103 (1980).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  13. A. V. Fedorov and A. P. Khokhlov, “Excitation of unstable modes in a supersonic boundary layer by acoustic waves,” Fluid Dynamics, 26, No. 4, 531 (1991).

    Article  MATH  Google Scholar 

  14. I. V. Egorov, V. G. Sudakov, and A. V. Fedorov, “Numerical modeling of the receptivity of a supersonic boundary layer to acoustic disturbances,” Fluid Dynamics, 41, No. 1, 37 (2006).

    Article  Google Scholar 

  15. A. V. Fedorov and A. P. Khokhlov, “Prehistory of instability in a hypersonic boundary layer,” Theoret. Comput. Fluid Dynamics, 14, 359 (2001).

    Article  MATH  ADS  Google Scholar 

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Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, 2006, pp. 39–49.

Original Russian Text Copyright © 2006 by Egorov, Novikov, and Fedorov.

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Egorov, I.V., Novikov, A.V. & Fedorov, A.V. Numerical modeling of the disturbances of the separated flow in a rounded compression corner. Fluid Dyn 41, 521–530 (2006). https://doi.org/10.1007/s10697-006-0070-7

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  • DOI: https://doi.org/10.1007/s10697-006-0070-7

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