有攻角圆锥边界层横流失稳分析

Crossflow instability analysis of boundary layer on a yawed cone

  • 摘要: 横流失稳是复杂三维边界层转捩的主要机制之一。本文针对马赫6条件下风洞实验工况的6°攻角尖锥边界层,利用二维全局稳定性分析(BiGlobal)和面推进抛物化稳定性方程(PSE3D)从多维稳定性分析的角度开展了横流失稳分析,并与一维稳定性分析(LST)和直接数值模拟(DNS)结果对比。结果显示,横流模态主要分布在背风面,但随着幅值的增长,模态扰动仍可显著影响迎风面区域;最不稳定非定常横流模态比准定常横流模态更不稳定,且波角更小;基于PSE3D得到的N值略低于基于Biglobal得到的N值,但两者主频相近,表明非平行效应削弱了横流扰动的增长,但并不改变扰动主频;基于LST的N值远大于全局稳定性分析得到的N值,这体现了两种方法对扰动增长定义的差异,另一方面也反映了三维效应的影响,因此不同的稳定性分析方法对确定转捩的N值影响显著。

     

    Abstract: The crossflow instability is one of the main transition mechanisms in complex three-dimensional boundary layers, yet is still far from being fully understood. In the present study, the two-dimensional global stability analysis (BiGlobal) and plane-marching parabolized stability equations (PSE3D) were employed for the crossflow instability in the boundary layer of a sharp cone at 6° angle of attack under the Mach 6 wind tunnel experimental conditions. The results were compared with those of the one-dimensional stability analysis (LST) and direct numerical simulation (DNS). It is shown that the crossflow mode is mainly distributed on the leeward side, yet can still remarkably affect the windward side as its amplitude increases downstream. The most unstable travelling crossflow mode is more amplified and has a smaller wave angle than the stationary crossflow mode. PSE3D obtains a slightly lower N factor than that obtained by BiGlobal, while the two have similar peak frequencies, indicating that the non-parallel effect weakens the growth of crossflow disturbance, without changing the peak frequency of disturbance. The N factor obtained by LST is significantly larger than those from global stability analyses, reflecting the difference in the definition of the growth rate between those two methods as well as the influence of three-dimensional effects. Therefore, different stability analysis methods have a significant impact on determining the transition N factor.

     

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