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Wall temperature effects on the stability of leeward vortices of a blunt inclined cone

壁温比对钝锥背风流向涡稳定性影响分析

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Abstract

Streamwise vortex instability is one of the most potent mechanisms for the transition of the three-dimensional boundary layers. By using the global stability analysis methods, stability characteristics of the leeward vortex over a blunt cone with an angle of attack under a typical wind tunnel condition are studied and are compared to the case with a smaller wall temperature ratio (corresponding to a flight condition). The vortical structure features inward and outward vortices, similar to that in the flight condition. Unlike the flight condition, the outward vortices appear stronger than the inward vortices, resulting in stronger outer-mode instabilities. Although the inner mode is heavily stabilized compared to the flight condition, it can still radiate apparent acoustics. The acoustic sources are computed based on Lighthill’s acoustic analogy, showing that the entropy term measuring the deviation from the isentropic relation is dominant. While Mack second mode is shown to most likely trigger the transition in the flight condition, it is absent in the wind tunnel condition, and a shear-layer mode turns out to be the most dangerous instead. Moreover, the instability frequencies and growth rates of the wind tunnel case are much smaller than those of the flight case, indicating that wall heating may stabilize the leeward vortices.

摘要

流向涡失稳是导致三维边界层转捩的重要机制之一, 通过全局稳定性分析方法研究了风洞工况下带攻角钝锥背风面流向涡的稳定性特征, 并与壁温比较小的工况(对应飞行条件)进行了比较. 风洞工况和飞行工况的涡结构特征相似, 均具有内、外卷涡. 与飞行工况相比, 风洞工况的外卷涡更显著, 导致了更**的外模态不稳定性. 尽管风洞工况内模态更加稳定, 但它仍具有与飞行工况类似的声辐射特征. Lighthill声比拟理论计算表明熵源项是主导声源项. 在飞行工况下, Mack第二模态最有可能引起转捩, 但其在风洞工况中并未被发现, 取而代之的是流向涡剪切失稳模态. 此外, 风洞工况下的模态失稳频率和增长率远小于飞行工况, 表明壁面加热能够稳定流向涡.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 92052301). The authors are grateful to Dr. Shuaibin Han at CARDC for helpful discussions on acoustic radiation.

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Authors and Affiliations

  1. State Key Laboratory of Aerodynamics, Mianyang, 621000, China

    Ligeng Zhang  (张力耕), Bingbing Wan  (万兵兵), Siwei Dong  (董思卫), Jianqiang Chen  (陈坚**) & ** Chen  (陈曦)

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  1. Ligeng Zhang  (张力耕)
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  2. Bingbing Wan  (万兵兵)
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  3. Siwei Dong  (董思卫)
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  4. Jianqiang Chen  (陈坚**)
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Contributions

Author contributions Ligeng Zhang: Data curation, Formal analysis, Investigation, Methodology, Visualization, Writing – original draft, Writing – review & editing. Bingbing Wan: Data curation, Investigation, Resources, Software, Writing – review & editing. Siwei Dong: Data curation, Investigation, Resources, Software, Writing – review & editing. Jianqiang Chen: Conceptualization, Methodology, Resources, Writing – review & editing, Project administration, Funding acquisition. ** Chen: Conceptualization, Data curation, Investigation, Methodology, Resources, Software, Visualization, Writing – review & editing.

Corresponding authors

Correspondence to Jianqiang Chen  (陈坚**) or ** Chen  (陈曦).

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Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Zhang, L., Wan, B., Dong, S. et al. Wall temperature effects on the stability of leeward vortices of a blunt inclined cone. Acta Mech. Sin. 40, 123563 (2024). https://doi.org/10.1007/s10409-023-23563-x

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