PSE在超音速边界层二次失稳问题中的应用  

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

作　　者：张永明[1] 周恒[1] 

机构地区：[1]天津大学力学系,天津300072

出　　处：《应用数学和力学》2008年第1期1-7,共7页Applied Mathematics and Mechanics

基　　金：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

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.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 incom- pressible 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 trustable second mode 2-D T-S wave. Consequently, secondary instability is unlikely the main cause leading to transition in supersonic boundary layers.

关 键 词：抛物化稳定性方程 二次失稳 基本扰动 亚谐波 

分 类 号：O357.41[理学—流体力学]