Applied Mathematics and Mechanics

, Volume 40, Issue 2, pp 283–292 | Cite as

Transition control of Mach 6.5 hypersonic flat plate boundary layer

  • Yunchi ZhangEmail author
  • Chi Li


An artificial disturbance is introduced into the boundary layer over a flat plate to investigate the effect on the transition process in the Mach 6.5 wind tunnel at Peking University. A linear stability theory (LST) is utilized to predict the evolution of the eigenmodes, and the frequency of the artificial disturbance is chosen according to the LST results. The artificial disturbance is generated by glowing discharge on the surface of the plate close to the leading edge. The Rayleigh-scattering visualization and particle image velocimetry (PIV) measurements are performed. By comparing the experimental results with artificial disturbances with those under the natural condition (without artificial disturbances), the present paper shows that the second-mode instability waves are significantly stimulated by the artificial disturbances, and the boundary layer transition is effectively triggered.

Key words

hypersonic boundary layer transition control glowing discharge 



total temperature, K


total pressure, Pa


free-stream velocity, m/s


unit Reynolds number, m-1


streamwise location from the leading edge, mm


wall normal coordinate, mm


frequency, Hz


normalized streamwise wavenumber


normalized spanwise wavenumber


normalized frequency


propagation angle of the eigenmode, (°)


velocity amplitude of the eigenmode wave, m/s


phase velocity of the eigenmode, m/s


thickness of the boundary layer, mm.

Chinese Library Classification


2010 Mathematics Subject Classification



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  1. [1]
    MORKOVIN, M. V., RESHOTKO, E., and HERBERT, T. Transition in open flow systems: a reassessment. Bulletin of American Physical Society, 39, 1–31 (1994)Google Scholar
  2. [2]
    FEDOROV, A. Transition and stability of high-speed boundary layers. Annual Review of Fluid Mechanics, 43, 79–95 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    JIANG, X. Y. and LEE, C. B. Review of research on the receptivity of hypersonic boundary layer (in Chinese). Journal of Experiments in Fluid Mechanics, 31, 1–11 (2017)Google Scholar
  4. [4]
    LEE, C. B. New features of CS solitons and the formation of vortices. Physics Letters A, 247, 397–402 (1998)CrossRefGoogle Scholar
  5. [5]
    LEE, C. B. and FU, S. On the formation of the chain of ring-like vortices in a transitional boundary layer. Experiments in Fluids, 30, 354–357 (2001)CrossRefGoogle Scholar
  6. [6]
    LEE, C. B. Possible universal transitional scenario in a flat plate boundary layer: measurement and visualization. Physical Review E, 62, 3659–3670 (2000)CrossRefGoogle Scholar
  7. [7]
    LEE, C. B., HONG, Z. X., KACHANOV, Y. S., BORODULIN, V. I., and GAPONENKO, V. V. A study in transitional flat plate boundary layers: measurement and visualization. Experiments in Fluids, 28, 243–251 (2000)CrossRefGoogle Scholar
  8. [8]
    LEE, C. B. and LI, R. Q. Dominant structure for turbulent production in a transitional boundary layer. Journal of Turbulence, 8, N55 (2007)CrossRefGoogle Scholar
  9. [9]
    LEE, C. B. and WU, J. Z. Transition in wall-bounded flows. Advances in Mechanics, 61, 683–695 (2008)Google Scholar
  10. [10]
    MACK, L. M. Linear stability theory and the problem of supersonic boundary-layer transition. AIAA Journal, 13, 278–289 (1975)CrossRefGoogle Scholar
  11. [11]
    STETSON, K., KIMMEL, R., DONALDSON, J., and SILER, L. A comparison of planar and conical boundary layer stability and transition at a Mach number of 8. 22nd Fluid Dynamics, Plasma Dynamics and Lasers Conference, AIAA, Honolulu, HI, U. S. A. (1991)Google Scholar
  12. [12]
    BOUNTIN, D. A., SIDORENKO, A. A., and SHIPLYUK, A. N. Development of natural disturbances in a hypersonic boundary layer on a sharp cone. Journal of Applied Mechanics and Technical Physics, 42, 57–62 (2001)CrossRefGoogle Scholar
  13. [13]
    CHEN, X., ZHU, Y. D., and LEE, C. B. Interactions between second mode and low-frequency waves in a hypersonic boundary layer. Journal of Fluid Mechanics, 820, 693–735 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    DEMETRIADES, A. An experiment on the stability of hypersonic laminar boundary layers. Journal of Fluid Mechanics, 7, 385–396 (1960)CrossRefzbMATHGoogle Scholar
  15. [15]
    KOSINOV, A. D., MASLOV, A. A., and SHEVELKOV, S. G. Experiments on the stability of supersonic laminar boundary layers. Journal of Fluid Mechanics, 219, 621–633 (1990)CrossRefGoogle Scholar
  16. [16]
    SEMIONOV, N. V., KOSINOV, A. D., and MASLOV, A. A. Transition control of supersonic boundary layer on flat plate. IUTAM Symposium on Mechanics of Passive and Active Flow Control, Springer, Berlin, 323–328 (1999)CrossRefGoogle Scholar
  17. [17]
    KASTELL, D. and SHIPLYUK, A. N. Experimental technique for the investigation of artificially generated disturbances in planar laminar hypersonic boundary layers. Aerospace Science and Technology, 3, 345–354 (1999)CrossRefzbMATHGoogle Scholar
  18. [18]
    SEMIONOV, N. V. and KOSINOV, A. D. Experimental study of supersonic boundary layer receptivity in controlled conditions. Laminar-Turbulent Transition, Springer, Berlin, 451–456 (2000)CrossRefGoogle Scholar
  19. [19]
    MASLOV, A. A., SHIPLYUK, A. N., SIDORENKO, A. A., and ARNAL, D. Leading-edge receptivity of a hypersonic boundary layer on a flat plate. Journal of Fluid Mechanics, 426, 73–94 (2001)CrossRefzbMATHGoogle Scholar
  20. [20]
    HUANG, Z. F., CAO, W., and ZHOU, H. The breakdown mechanism of laminar flow into turbulence in the transition process of supersonic boundary layer over a flat plate-temporal mode (in Chinese). Science China G, 35, 537–547 (2005)Google Scholar
  21. [21]
    LEE, C. B. and CHEN, S. Y. A review of recent progress in the study of transition in hypersonic boundary layer. National Science Review (2018) Scholar
  22. [22]
    LI, C. and ZHANG, Y. C. Effect of glow discharge on hypersonic flat plate boundary layer. Applied Mathematics and Mechanics (English Edition) (2019) Scholar
  23. [23]
    AUVITY, B., ETZ, M. R., and SMITS, A. J. Effects of transverse helium injection on hypersonic boundary layers. Physics of Fluids, 13, 3025–3032 (2001)CrossRefzbMATHGoogle Scholar
  24. [24]
    POGGIE, J., ERBLAND, P. J., SMITS, A. J., and MILES, R. B. Quantitative visualization of compressible turbulent shear flows using condensate-enhanced Rayleigh scattering. Experiments in Fluids, 37, 438–454 (2004)CrossRefGoogle Scholar
  25. [25]
    ZHU, Y. D., YUAN, H. J., ZHANG, C. H., and LEE, C. B. Image preprocessing method for nearwall particle image velocimetry (PIV) image interrogation with very large in-plane displacement. Measurement Science and Technology, 24, 125302 (2013)CrossRefGoogle Scholar
  26. [26]
    ZHANG, C. H., ZHU, Y. D., CHEN, X., YUAN, H. J., WU, J. Z., CHEN, S. Y., LEE, C. B., and GAD-EL-HAK, M. Transition in hypersonic boundary layers. AIP Advances, 5, 107137 (2015)CrossRefGoogle Scholar
  27. [27]
    TANG, Q., ZHU, Y. D., CHEN, X., and LEE, C. B. Development of second-mode instability in a Mach 6 flat plate boundary layer with two-dimensional roughness. Physics of Fluids, 27, 064105 (2015)CrossRefGoogle Scholar
  28. [28]
    ZHU, Y. D., ZHANG, C. H., CHEN, X., YUAN, H. J., WU, J. Z., CHEN, S. Y., LEE, C. B., and GAD-EL-HAK, M. Transition in hypersonic boundary layers: role of dilatational waves. AIAA Journal, 54, 3039–3049 (2016)CrossRefGoogle Scholar
  29. [29]
    ZHU, Y. D., CHEN, X., WU, J. Z., CHEN, S. Y., LEE, C. B., and GAD-EL-HAK, M. Aerodynamic heating in transitional hypersonic boundary layers: role of second-mode instability. Physics of Fluids, 30, 011701 (2018)CrossRefGoogle Scholar
  30. [30]
    JIA, L. C., ZHU, Y. D., JIA, Y. X., YUAN, H. J., and LEE, C. B. Image pre-processing method for near-wall PIV measurements over moving curved interfaces. Measurement Science and Technology, 28, 035201 (2017)CrossRefGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory for Turbulence and Complex SystemsPeking UniversityBeijingChina
  2. 2.Department of Aeronautics and Astronautics, College of EngineeringPeking UniversityBeijingChina

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