可压缩边界层稳定性问题特征值的分布  

Eigenvalue distribution of compressible boundary layer stability problem

作　　者：栾溟弋 张永明[1,2] 

机构地区：[1]天津大学机械工程学院,天津300072 [2]天津市现代工程力学重点实验室,天津300072

出　　处：《中国科技论文》2017年第5期500-506,共7页China Sciencepaper

基　　金：高等学校博士学科点专项科研基金资助项目(20120032120007);国家自然科学基金资助项目(11672204);国家重点研发计划资助项目(2016YFA0401200)

摘　　要：为了充分了解可压缩边界层中稳定的特征模态的信息,用Arnoldi方法研究了3种情况特征值的分布,即:亚音速边界层、超音速边界层第1模态和超音速边界层第2模态;比较上述3种情况以及不可压的情况。结果表明:亚音速的结果与不可压的结果类似,有2个离散模态分支A和C,以及1个连续模态分支B,但更多的模态出现在了稳定的离散模态分支C上;超音速边界层比亚音速边界层多出2个离散模态分支D和E,通过观察特征函数发现这2个分支中的模态代表边界层中的1个法向局部波包;而第2模态的结果与第1模态相比,C分支变短而D和E分支变得更长。In order to deeply understand the stable eigen modes of compressible boundary layer, Arnoldi method is applied to in-vestigate eigenvalue distribution of compressible boundary layer stability problem. Three cases are taken into consideration, i. e. subsonic boundary layer, first mode of supersonic boundary layer, and second mode of supersonic boundary layer. Comparing the above three modes and the situation of incompressible case, the results show that the eigenvalue distribution of subsonic boundary layer is similar to that of incompressible boundary layer, there are two district mode branches, branch A and C, and one continu-ous mode branch, branch B. However, there are more modes in the stable district mode branch C than those in incompressible boundary layer. For supersonic boundary layer, there are two more district mode branches, which are named as branch D and E. The eigenfunctions of the modes in the two new branches show that every mode in the two branches represents one wall-normal localized wave packet in boundary layer. In the case of second mode of supersonic boundary layer, branch C becomes shorter while branch D and E become longer, compared with those in the case of first mode.

关 键 词：流体力学 稳定性问题 可压缩边界层 特征值分布 Arnoldi方法 

分 类 号：V211[航空宇航科学与技术—航空宇航推进理论与工程]