SU Cai-hong, ZHOU Heng. Stability Analysis and Transition Prediction of Hypersonic Boundary Layer Over a Blunt Cone With Small Nose Bluntness at Zero Angle of Attack[J]. Applied Mathematics and Mechanics, 2007, 28(5): 505-513.
 Citation: SU Cai-hong, ZHOU Heng. Stability Analysis and Transition Prediction of Hypersonic Boundary Layer Over a Blunt Cone With Small Nose Bluntness at Zero Angle of Attack[J]. Applied Mathematics and Mechanics, 2007, 28(5): 505-513.

# Stability Analysis and Transition Prediction of Hypersonic Boundary Layer Over a Blunt Cone With Small Nose Bluntness at Zero Angle of Attack

• Rev Recd Date: 2007-03-09
• Publish Date: 2007-05-15
• Stability and transition prediction of hypersonic boundary layer on a blunt cone with small nose bluntness at zero angle of attack had been investigated.The nose radius of the cone is 0.5 mm;the cone half-angle is 5 degree,and the Mach number of the oncoming flow is 6.The base flow of the blunt cone was obtained by direct numerical simulation.The linear stability theory was applied for the analysis of the first mode and the second mode unstable waves under both isothermal and adiabatic wall condition,and e-N method was used for the prediction of transition location.The N factor was tentatively taken as 10,as no experimentally confirmed value was available.It is found that the wall temperature condition has a great effect on the transition location.For adiabatic wall,transition would take place more rearward than those for isothermal wall.And despite that for high Mach number flows,the maximum amplification rate of the second mode wave is far bigger than the maximum amplification rate of the first mode wave.The transition location of the boundary layer with adiabatic wall is controlled by the growth of first mode unstable waves.The methods employed are expected to be also applicable to the transition prediction for the three dimensional boundary layers on cones with angle of attack.
•  [1] Stentson K F, Rushton G H.Shock tunnel investigation of Boundary-Layer transition at M=5.5[J].AIAA Journal,1967,5(5):899-905. doi: 10.2514/3.4098 [2] Stentson K F. Hypersonic Boundary Layer Transition Experiments[R]. AFSC Wright-Patterson Air Force Base, AFWAL-TR- 80-3062, Ohio, Air Force Wright Aeronautical Laboratories, 1980. [3] Schneider S P. Laminar-Turbulent Transition in High-Speed Compressible Boundary Layer: Continuation of Elliptic-Cone Experiments[R]. School of Aeronautics and Astronautics of Purdue University, Lafayett, Indiana, AFRL-SR-BL-TR, ADA874373, 2000. [4] Malik M R, Balakumar P.Instability and Transition in Three-Dimensional Supersonic Boundary Layers[R]. Orlando FL: AIAA International Aerospace Planes Conference 4 th, 1992. [5] Muir J F, Trujillo A A.Experimental Investigation of the Effects of Nose Bluntness, Freestream Reynold Number, and Angle of Attack on Cone Boundary Layer Transition at a Mach Number of 6[R]. AIAA Paper,72-216，1972. [6] Holden M, Bower D, Chadwick K. Measurements of Boundary Layer Transition on Cones at Angle of Attack for Mach Numbers from 11 to 13[R]. AIAA Paper,95-2294,1995. [7] Cebeci T, Stewartson K. On stability and transition in three-dimensional flows[J].AIAA Journal,1980,18(4):398-405. doi: 10.2514/3.50772 [8] Cebeci T, Shao J P, Chen H H,et al. The Preferred Approach for Calculating Transition by Stability Theory[A].Institute for Numerical Computation and Analysis.In:Proceeding of International Conference on Boundary and Interior Layers[C].France:Toulouse,2004. [9] Crouch, J D, Kosorygin V S, Ng L L. Modeling the effects of steps on boundary-layer transition[A].IUTAM.In:Proceedings of the sixth IUTAM Symposium on Laminar-Turbulent Transition[C].India:Bangalore,2004. [10] Sousa J M M, Silva L M G. Transition prediction in infinite swept wings using Navier-Stokes computations and linear stability theory[J].Computers and Structures,2004,82(17/19):1551-1560. [11] 周恒，赵耕夫.流动稳定性[M].北京：国防工业出版社，2004. [12] Lingwood R J. On the application of en-methods to three-dimensional boundary-layer flows[J].European Journal of Mechanics-B/Fluids,1999,18(4): 581-620. [13] Mack L M. Stability of three dimensional boundary layers on swept wings at transonic speeds[A].In:Proc IUTAM Symposium Ⅲ[C].Gottingen:Springer, 1988. [14] Mack L M.Boundary Layer Linear Stability Theory[R]. Jet Propulsion Laboratories, California Institute of Tech, Pasadena, In:Special course on stability and transition of laminar flow, AGARD Report,709.1984,1-81 [15] Stetson K F, Kimmel R L. On Hypersonic Boundary Layer Stability[R]. AIAA paper,92-0737,1992. [16] ZHONG Xiao-lin,Tatineni M.Stable High-Order Schemes and DNS of Boundary-Layer Stability on a Blunt Cone at Mach 8[R]. AIAA Paper,1-0437,2001. [17] ZHONG Xiao-lin,MA Yan-bao.Numerical Simulation of Leading Edge Receptivity of Stetson's Mach 8 Blunt Cone Stability Experiments[R]. AIAA paper,113,2003. [18] Bountin D A, Sidorenko A A, Shiplyuk A N. Development of natural disturbances in a hypersonic boundary layer on a sharp cone[J].Journal of Applied Mechanics and Technical Physics,2001,42(1):57-62. [19] Malik M R. Prediction and control of transition in supersonic and hypersonic boundary layers[J].AIAA Journal,1989,27(11):1487-1493. doi: 10.2514/3.10292 [20] 黄章峰，曹伟，周恒.超音速平板边界层转捩中层流突变为湍流的机理[J].中国科学G辑，2005，35（5）：537-547.

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