Acta Mechanica Sinica

, Volume 27, Issue 4, pp 488–493 | Cite as

Second mode unstable disturbance measurement of hypersonic boundary layer on cone by wavelet transform

  • Jian HanEmail author
  • Nan Jiang
  • Yan Tian
Research Paper


Experimental investigation of hypersonic boundary layer instability on a cone is performed at Mach number 6 in a hypersonic wind tunnel. Time series signals of instantaneous fluctuating surface-thermal-flux are measured by Pt-thin-film thermocouple temperature sensors mounted at 28 stations on the cone surface in the streamwise direction to investigate the development of the unstable disturbance. Wavelet transform is employed as a mathematical tool to obtain the multi-scale characteristics of fluctuating surface-thermal-flux both in the temporal and spectrum space. The conditional sampling algorithm using wavelet coefficient as an index is put forward to extract the unstable disturbance waveform from the fluctuating surface-thermal-flux signals. The generic waveform for the second mode unstable disturbance is obtained by a phase-averaging technique. The development of the unstable disturbance in the streamwise direction is assessed both in the temporal and spectrum space. Our study shows that the local unstable disturbance detection method based on wavelet transformation offers an alternative powerful tool in studying the hypersonic unstable mode of laminar-turbulent transition. It is demonstrated that, at hypersonic speeds, the dominant flow instability is the second mode, which governs the course of laminar-turbulent transition of sharp cone boundary layer.


Hypersonic boundary layer Sharp cone Instability Wavelet transform 


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  1. 1.
    Ferrier, M., Chokani, N.: Hypersonic transition detection with single point hot-wire measurements. AIAA paper, 2003-0063Google Scholar
  2. 2.
    Chokani, N.: VITA measurements of transition in transitional hypersonic boundary layer flows. Experiments in Fluids 38(4), 440–448 (2005)CrossRefGoogle Scholar
  3. 3.
    Gurley, K., Kijewski, T., Kareem, A.: First- and higher-order correlation detection using wavelet transforms. Journal of Engineering Mechanics 129(2), 188–201 (2003)CrossRefGoogle Scholar
  4. 4.
    Maslov, A.A., Shiplyuk, A.N., Bountin, D.A., et al.: Mach 6 boundary-layer stability experiments on sharp and blunted cones. Journal of Spacecraft and Rockets 43(1), 71–76 (2006)CrossRefGoogle Scholar
  5. 5.
    Demetriades, A.: New experiments on hypersonic boundary layer stability including wall temperature effects. In: Proc. Heat Transfer Fluid Mechanic Institute 26, 39–54 (1978)Google Scholar
  6. 6.
    Kendall, J.M.: Wind tunnel experiments relating to supersonic and hypersonic boundary layer transition. AIAA Journal 13, 290–299 (1975)CrossRefGoogle Scholar
  7. 7.
    Stetson, K.F., Thompson, E.R., Donaldson, J.C., et al.: Laminar boundary layer stability experiments on a cone at Mach 8. Part 1: Sharp cone. AIAA Paper 83-1761 (1983)Google Scholar
  8. 8.
    Kimmel, R.L., Demetriades, A., Donaldson, J.C.: Space-time correlation measurements in a hypersonic transitional boundary layer. AIAA Journal 34, 2484–2489 (1996)CrossRefGoogle Scholar
  9. 9.
    Lachowicz, J.T., Chokani, N., Wilkinson, S.P.: Boundary-layer stability measurements in a hypersonic quiet tunnel. AIAA Journal 34, 2496–2500 (1996)CrossRefGoogle Scholar
  10. 10.
    Doggett, G.P., Wilkinson, S.P., Chokani, N.: Effects of angle of attack on hypersonic boundary layer stability in a quiet wind tunnel. AIAA Journal 35(3), 464–470 (1997)CrossRefGoogle Scholar
  11. 11.
    Chokani, N.: Perspective: Stability experiments at hypersonic speeds in a quiet wind tunnel. AIAA Paper, 2001-0211Google Scholar
  12. 12.
    Chokani, N.: Nonlinear evolution of Mach modes in a hypersonic boundary layer. Physics of Fluids 17(1), 14102–14114 (2005)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Chokani, N.: Nonlinear spectral dynamics of hypersonic laminar boundary layer flow. Physics of Fluids 11(12), 3846–3851 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Norris, J.D., Chokani, N.: Transient nonlinear interactions in a hypersonic laminar boundary layer. AIAA Paper, 2002-0154Google Scholar
  15. 15.
    Jiang, N., Zhang, J.: Detecting multi-scale coherent eddy structures and intermittency in turbulent boundary layer by wavelet analysis. Chinese Physics Letters 22(8), 1968–1971 (2005)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Liu, J.H., Jiang, N.: Two phases of coherent structure motions in turbulent boundary layer. Chinese Physics Letters 24(9), 2617–2620 (2007)CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of MathematicsTianjin UniversityTianjinChina
  2. 2.Department of MechanicsTianjin UniversityTianjinChina
  3. 3.Tianjin Key Laboratory of Modern Engineering MechanicsTianjinChina
  4. 4.State Key Laboratory of Nonlinear Mechanics, Institute of MechanicsChinese Academy of SciencesBeijingChina

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