PSE在超音速边界层二次失稳问题中的应用

张永明; 周恒

PSE在超音速边界层二次失稳问题中的应用

张永明¹,
周恒^1,2

1.
天津大学力学系,天津 300072;2.南开大学天津大学刘徽应用数学中心,天津 300072

基金项目: 国家自然科学基金(重点)资助项目(10632050);国家自然科学基金(重大)研究计划资助项目(90716007);南开大学天津大学刘徽应用数学中心资助项目

详细信息

作者简介:
张永明(1979- ),男,云南人,博士生(Tel:+86-22-27403374;E-mail:yongmingzh@yahoo.com.cn);周恒(联系人.Tel:+86-22-27890533;Fax:+86-22-27407025;E-mail:hzhou1@tju.edu.cn).

中图分类号: O357.41
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- 文章访问数: 3212
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出版历程
- 收稿日期: 2007-12-04
- 修回日期: 2007-12-19
- 刊出日期: 2008-01-15

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

ZHANG Yong-ming¹,
ZHOU Heng^1,2

1.
Department of Mechanics, Tianjin University, Tianjin 300072, P. R. China;

摘要

摘要: 用抛物化稳定性方程（PSE）研究超音速边界层中的二次失稳问题．结果显示无论二维基本扰动是第一模态还是第二模态的T-S波，二次失稳机制都起作用．三维亚谐波的放大率随其展向波数和二维基本波幅值的变化关系与不可压缩边界层中所得类似．但是，即使二维波的幅值大到2％的量级，三维亚谐波的最大放大率仍远小于最不稳定的第二模态二维T-S波的放大率．因此，二次失稳应该不是导致超音速边界层转捩的主要因素．
- 抛物化稳定性方程 /
- 二次失稳 /
- 基本扰动 /
- 亚谐波
Abstract: 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.
- parabolized stability equations /
- secondary instability /
- fundamental disturbances /
- subharmonic waves

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参考文献(13)

[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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PSE在超音速边界层二次失稳问题中的应用

作者简介:
张永明(1979- ),男,云南人,博士生(Tel:+86-22-27403374;E-mail:yongmingzh@yahoo.com.cn);周恒(联系人.Tel:+86-22-27890533;Fax:+86-22-27407025;E-mail:hzhou1@tju.edu.cn).

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

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PSE在超音速边界层二次失稳问题中的应用

作者简介: 张永明(1979- ),男,云南人,博士生(Tel:+86-22-27403374;E-mail:yongmingzh@yahoo.com.cn);周恒(联系人.Tel:+86-22-27890533;Fax:+86-22-27407025;E-mail:hzhou1@tju.edu.cn).

计量

出版历程

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

计量

出版历程

目录

作者简介:
张永明(1979- ),男,云南人,博士生(Tel:+86-22-27403374;E-mail:yongmingzh@yahoo.com.cn);周恒(联系人.Tel:+86-22-27890533;Fax:+86-22-27407025;E-mail:hzhou1@tju.edu.cn).