可压缩剪切层与边界层流动相互作用的稳定性研究

Linear Stability Studies on Interactional Compressible Shear and Boundary Layers

关键词:  可压缩边界层  可压缩剪切层  组合流动  线性稳定性理论

Key words:  Compressible boundary layer  Compressible shear layer  Confluent layers  Linear stability theory

摘要:

为了探究可压缩剪切层与边界层组合流动稳定性规律，采用线性稳定性理论对这种组合流动的线性稳定性问题进行研究。平均流动模型取双曲正切函数描述的可压缩剪切层与可压缩相似边界层速度剖面的直接叠加。采用整体数值方法(Global)求解组合流动线性稳定性方程，获得全部不稳定模态。结果表明，在这样的组合流动中，存在两个不稳定模态，一个与剪切层相关的不稳定模态，另一个是与边界层相关的不稳定模态。在此基础上，研究了剪切层与壁面之间的距离、扰动频率、雷诺数、马赫数、速度梯度、温度梯度对这种组合流动稳定性的影响。马赫数增大对不稳定模态起抑制作用，剪切层对边界层的不稳定模态的促进、抑制作用与马赫数、扰动频率有关，边界层对剪切层不稳定模态基本上起抑制作用。

Abstract:

In order to explore the stability laws of the confluent compressible shear and boundary layers，the linear stability of this confluent layers was studied through linear stability theory. The base flow model was composed by the hyperbolic tangent function described compressible shear layer and the similar velocity profile of compressible boundary layer directly. The linear stability equations were solved by the global numerical method and obtained all unstable modes eventually. The results indicate that there are two unstable modes in the confluent layers，and each layer has one unstable mode respectively. On this basis，the effects of the distance between the shear layer and the wall，disturbance frequency，Reynolds number，Mach number，velocity gradient and temperature gradient on the stability of the confluent layers were investigated in details. Increasing Mach number can reduce the growth rate of unstable modes，both for shear layer and boundary layer，the influence of shear layer on the unstable mode of boundary layer varies in Mach number and disturbance frequency，boundary layer can reduce the growth rate of the unstable mode in shear layer generally.