ZHANG Yong-ming, ZHOU Heng. PSE as Applied to Problems of Secondary Instability in Supersonic Boundary Layers[J]. Applied Mathematics and Mechanics, 2008, 29(1): 1-7.
Citation: ZHANG Yong-ming, ZHOU Heng. PSE as Applied to Problems of Secondary Instability in Supersonic Boundary Layers[J]. Applied Mathematics and Mechanics, 2008, 29(1): 1-7.

PSE as Applied to Problems of Secondary Instability in Supersonic Boundary Layers

  • Received Date: 2007-12-04
  • Rev Recd Date: 2007-12-19
  • Publish Date: 2008-01-15
  • Parabolized stability equations (PSE) approach is used to investigate problems of secondary instability in supersonic boundary layers. The results show that the mechanism of secondary instability does work, whether the 2-D fundamental disturbance is of the first mode or second mode T-S wave. The variation of the growth rates of the 3-D sub-harmonic wave against its span-wise wave number and the amplitude of the 2-D fundamental wave is found to be similar to those found in incompressible boundary layers. But even as the amplitude of the 2-D wave is as large as the order 2%, the maximum growth rate of the 3-D sub-harmonic is still much smaller than the growth rate of the most unstable second mode 2-D T-S wave. Consequently, secondary instability is unlikely the main cause leading to transition in supersonic boundary layers.
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  • [1]
    Herbert T h. Secondary instability of plane channel flow to subharmonic three-dimensional disturbances[J].Physics of Fluids,1983,26(4):871-874. doi: 10.1063/1.864226
    [2]
    Herbert T h. Subharmonic Three-Dimensional Disturbances in Unstable Plane Poiseuille Flows[R]. AIAA Paper,1983,1759.
    [3]
    Herbert T h.Analysis of Subharmonic Route to Transition in Boundary Layer[R]. AIAA Paper,1984,0009.
    [4]
    Saric W S, Kozlov V V,Levchenko V Ya. Forced and Unforced Sub-Harmonic Resonance in Boundary Layer Transition[R]. AIAA Paper,1984, 0007.
    [5]
    Thomas A S W. Experiments on secondary instability in boundary layers[A].In:Lamb J P Ed.Proc 10th US Natl Congr Appl Mech[C].Austin, Tex,US:ASME,1987,436-444.
    [6]
    Herbert T h.Secondary instability of boundary layers[J].Ann Rev Fluid Mech,1988,20(1):487-526. doi: 10.1146/annurev.fl.20.010188.002415
    [7]
    Spalart P R, Yang K S.Numerical Simulation of Boundary Layers: Part 2. Ribbon-Induced Transition in Blasius Flow[R]. NASA TM 88221,1986,24.
    [8]
    董亚妮,周恒.二维超音速边界层中三波共振和二次失稳机制的数值模拟研究[J].应用数学和力学,2006,27(2):127-133.
    [9]
    Bertolotti F P, Herbert T h.Analysis of the linear stability of compressible boundary layers using the PSE[J].Theoretical and Computational Fluid Dynamics,1991,3(1):117-124. doi: 10.1007/BF00271620
    [10]
    Bertolotti F P.Compressible boundary layer stability analyzed with the PSE equations[R]. AIAA Paper,1991,1637.
    [11]
    Chang C L, Malik M R,Erlebacher G,et al.Compressible Stability of Growing Boundary Layers Using Parabolized Stability Equations[R]. AIAA Paper,1991,1636.
    [12]
    张永明,周恒.抛物化稳定性方程在可压缩边界层中应用检验[J].应用数学和力学,2007,28(8):883-893.
    [13]
    Cebeci T, Shao J P, Chen H H,et al. The preferred approach for calculating transition by stability theory[A].In:An International Conference on Boundary and Interior Layers-Computational and Asymptotic Methods[C].July:ONERA,Toulouse,France,2004.
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