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三维曲面边界层的简化线性稳定性理论

涂国华 赵磊 万兵兵 陈曦 李晓虎 陈坚强

涂国华, 赵磊, 万兵兵, 等. 三维曲面边界层的简化线性稳定性理论[J]. 航空动力学报, 2023, 38(11):2583-2590 doi: 10.13224/j.cnki.jasp.20210378
引用本文: 涂国华, 赵磊, 万兵兵, 等. 三维曲面边界层的简化线性稳定性理论[J]. 航空动力学报, 2023, 38(11):2583-2590 doi: 10.13224/j.cnki.jasp.20210378
TU Guohua, ZHAO Lei, WAN Bingbing, et al. Simplified linear stability theory for boundary layer of three-dimensional curved surface[J]. Journal of Aerospace Power, 2023, 38(11):2583-2590 doi: 10.13224/j.cnki.jasp.20210378
Citation: TU Guohua, ZHAO Lei, WAN Bingbing, et al. Simplified linear stability theory for boundary layer of three-dimensional curved surface[J]. Journal of Aerospace Power, 2023, 38(11):2583-2590 doi: 10.13224/j.cnki.jasp.20210378

三维曲面边界层的简化线性稳定性理论

doi: 10.13224/j.cnki.jasp.20210378
详细信息
    作者简介:

    涂国华(1977-),男,研究员、博士生导师,博士,研究方向为流动稳定性与转捩、高阶精度格式和高超声速复杂流动模拟

    通讯作者:

    赵磊(1987-),男,副教授、博士生导师,博士,研究方向为流动稳定性与边界层转捩。E-mail:lei_zhao@tju.edu.cn

  • 中图分类号: V411.3;O354.4

Simplified linear stability theory for boundary layer of three-dimensional curved surface

  • 摘要:

    分析了贴体曲线正交坐标系下线性化小扰动方程(LPEs)中各曲率项的量级,结果显示大部分曲率项都是高阶小量。通过忽略这些高阶小量,得到了贴体曲线正交坐标系下的简化版小扰动方程。简化版小扰动方程不需要繁琐推导,可直接来源于笛卡儿坐标系下的小扰动方程的简单拓展,方便初学者使用。基于简化版的小扰动方程,发展出了能适用于三维曲面边界层的简洁形式的线性稳定性理论(LST)。针对亚声速后掠翼边界层的稳定性,简洁形式LST预测的横流失稳增长率与完整形式LST结果的绝对偏差小于4×10−5;针对高超声速尖锥边界层的稳定性,简洁形式LST精确预测了周向曲率对Mack模态中性曲线的影响。数值结果表明简洁形式的LST拥有与完整形式的LST几乎相同的精确度。

     

  • 图 1  翼型上表面的边界层厚度与曲率半径的比值

    Figure 1.  Ratio of boundary layer thickness to curvature radius for the upper surface of wing

    图 2  不同LST方程获得的横流扰动的增长率对比

    Figure 2.  Comparisons of growth rates of crossflow disturbances obtained by different LST equations

    图 3  距球头0.46 m处第一模态与第二模态T-S波的中性曲线

    Figure 3.  Neutral stability lines of first mode and second mode T-S wave at the location of 0.46 m away from the nose

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出版历程
  • 收稿日期:  2021-07-18
  • 网络出版日期:  2023-08-30

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