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Applied Mathematics and Mechanics

, Volume 31, Issue 5, pp 535–544 | Cite as

Effect of disturbances at inlet on hypersonic boundary layer transition on a blunt cone at small angle of attack

  • Jian-xin Liu (刘建新)
  • Ji-sheng Luo (罗纪生)Email author
Article

Abstract

To investigate the effect of different disturbances in the upstream, we present numerical simulation of transition for a hypersonic boundary layer on a 5-degree half-angle blunt cone in a freestream with Mach number 6 at 1-degree angle of attack. Evolution of small disturbances is simulated to compare with the linear stability theory (LST), indicating that LST can provide a good prediction on the growth rate of the disturbance. The effect of different disturbances on transition is investigated. Transition onset distributions along the azimuthal direction are obtained with two groups of disturbances of different frequencies. It shows that transition onset is relevant to frequencies and amplitudes of the disturbances at the inlet, and is decided by the amplitudes of most unstable waves at the inlet. According to the characteristics of environmental disturbances in most wind tunnels, we explain why transition occurs leeside-forward and windside-aft over a circular cone at an angle of attack. Moreover, the indentation phenomenon in the transition curve on the leeward is also revealed.

Key words

transition blunt cone hypersonic 

Chinese Library Classification

O354.4 O357.41 

2000 Mathematics Subject Classification

76K05 76F06 

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References

  1. [1]
    Fischer, M. C. An Experimental Investigation of Boundary-Layer Transition on a 10° Half-angle Cone at Mach 6.9, NASA-TN-D-5766 (1970)Google Scholar
  2. [2]
    Martellucci, A., Neff, R. S., and True, W. H., III. An Experimental Investigation of Boundary Layer Transition on a Cone at Angle of Attack, SAMSO TR-69-383 (1969)Google Scholar
  3. [3]
    Muir, J. F. and Trujillo, A. A. Experimental investigation of the effects of nose bluntness, free-stream unit reynolds number, and angle of attack on cone boundary layer transition at a Mach number of 6. The 10th Aerospace Sciences Meeting of AIAA, AIAA-1972-216, San Diego, California, Jan. 17–19, 1972 (1972)Google Scholar
  4. [4]
    Stetson, K. F., Thompson, E. R., Donaldson, J. C., and Siler, L. G. Laminar boundary layer stability experiments on a cone at Mach 8. I — sharp cone. The 16th Fluid and Plasma Dynamics Conference of AIAA, AIAA-1983-1761, Danvers, MA, July 12–14, 1983 (1983)Google Scholar
  5. [5]
    Stetson, K. F., Thompson, E. R., Donaldson, J. C., and Siler, L. G. Laminar boundary layer stability experiments on a cone at Mach 8. III — sharp cone at angle of attack. The 23rd Aerospace Sciences Meeting of AIAA, AIAA-1985-492, Reno, NV, Jan. 14–17, 1985 (1985)Google Scholar
  6. [6]
    Stetson, K. F., Thompson, E. R., Donaldson, J. C., and Siler, L. G. Laminar boundary layer stability experiments on a cone at Mach 8. IV — on unit Reynolds number and environmental effects. The 4th Fluid Mechanics, Plasma Dynamics and Lasers Conference of AIAA and ASME, AIAA-1986-1087, Atlanta, GA, May 12–14, 1986 (1986)Google Scholar
  7. [7]
    Sakell, L. E. An Experimental Investigation of Boundary Layer Transition over Three Axially Symmetric Bodies at Mach 6, Ph. D. dissertation, New York University, New York (1972)Google Scholar
  8. [8]
    Schneider, S. P. Hypersonic laminar-turbulent transition on circular cones and scramjet forebodies. Progress in Aerospace Sciences 40(1–2), 1–50 (2004)CrossRefGoogle Scholar
  9. [9]
    Su, C. H. and Zhou, H. Transition prediction of a hypersonic boundary layer over a cone at small angle of attack with the improvement of eN-method. Science in China Series G 52(1), 115–123 (2009)CrossRefMathSciNetGoogle Scholar
  10. [10]
    Li, X. L., Fu, D. X., and Ma, Y. W. Direct numerical simulation of boundary layer transition of hypersonic flow over a blunt cone with angle of attack (in Chinese). Physics of Gases Theory and Applications 4(1), 33–44 (2009)Google Scholar
  11. [11]
    Mack, L. M. Boundary-Layer Linear Stability Theory, AGARD Report 709 (1984)Google Scholar
  12. [12]
    Balakumar, P. and Jeyasingham, S. Evolution of disturbances in three-dimensional boundary layers. The 38th Aerospace Sciences Meeting and Exhibit, AIAA-2000-145, Reno, NV, Jan. 10–13, 2000 (2000)Google Scholar
  13. [13]
    Dong, M., Luo, J. S., and Cao, W. Numerical investigation of the evolution of disturbances in supersonic sharp cone boundary layers. Applied Mathematics and Mechanics (English Edition) 27(6), 713–719 (2008) DOI 10.1007/s10483-006-0601-1CrossRefGoogle Scholar
  14. [14]
    Huang, Z. F. and Zhou, H. Evolution of a 2-D disturbance in a supersonic boundary layer and the generation of shocklets. Applied Mathematics and Mechanics (English Edition) 25(1), 1–9 (2004) DOI 10.1007/BF02437288zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jian-xin Liu (刘建新)
    • 1
  • Ji-sheng Luo (罗纪生)
    • 1
    Email author
  1. 1.Department of MechanicsTianjin UniversityTianjinP. R. China

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