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eN方法用于高超声速圆锥边界层转捩预测的可靠性

杨潇楠 苏彩虹

杨潇楠, 苏彩虹. eN方法用于高超声速圆锥边界层转捩预测的可靠性[J]. 气体物理, 2023, 8(2): 44-55. doi: 10.19527/j.cnki.2096-1642.0987
引用本文: 杨潇楠, 苏彩虹. eN方法用于高超声速圆锥边界层转捩预测的可靠性[J]. 气体物理, 2023, 8(2): 44-55. doi: 10.19527/j.cnki.2096-1642.0987
YANG Xiao-nan, SU Cai-hong. Reliability of the eN Method Applied to Hypersonic Blunt Cone Boundary Layers for Transition Prediction[J]. PHYSICS OF GASES, 2023, 8(2): 44-55. doi: 10.19527/j.cnki.2096-1642.0987
Citation: YANG Xiao-nan, SU Cai-hong. Reliability of the eN Method Applied to Hypersonic Blunt Cone Boundary Layers for Transition Prediction[J]. PHYSICS OF GASES, 2023, 8(2): 44-55. doi: 10.19527/j.cnki.2096-1642.0987

eN方法用于高超声速圆锥边界层转捩预测的可靠性

doi: 10.19527/j.cnki.2096-1642.0987
基金项目: 

国家自然科学基金 91952202

国家自然科学基金 12072231

详细信息
    作者简介:

    杨潇楠(1994-)男, 硕士, 主要研究方向为流动稳定性。E-mail: yang-xiaonan@qq.com

    通讯作者:

    苏彩虹(1979-)女, 教授, 主要研究方向为流动稳定性和转捩。E-mail: su_ch@tju.edu.cn

  • 中图分类号: O357.4

Reliability of the eN Method Applied to Hypersonic Blunt Cone Boundary Layers for Transition Prediction

  • 摘要: eN方法基于扰动在边界层中线性演化过程中的幅值增长程度来预测转捩。以来流Mach数为6、不同壁面温度条件下不同钝度圆锥为研究对象,结合直接数值模拟和抛物化稳定性方程,从eN方法是否能够准确描述扰动在上述边界层中线性增长的角度,分析了该方法预测转捩的可靠性。研究结果表明,在小钝度或高壁面温度情况下,扰动在向下游的演化过程中从第1模态转变为第2模态,基于线性稳定性理论的eN方法变得不再可靠。壁面温度相同,头部钝度越大,eN方法越可靠;同等钝度下,壁面温度越低,eN方法越可靠。由于存在模态转换时,线性稳定性理论总是低估扰动的增长,因而对于给定的转捩判据NT(可由某一工况实验标定给出),若钝度减小或壁面温度增加到一定程度,eN方法给出的转捩位置比实际情况更靠后。重新标定转捩判据时,钝度越小,壁面温度越高,NT的修正程度就越大。

     

  • 图  1  计算模型和坐标系示意图

    Figure  1.  Sketch of computational model and coordinate systems

    图  2  密度剖面与文献[26]结果的比较

    Figure  2.  Comparison of density profiles with the results in Ref.[26]

    图  3  定常基本流场的温度等值线

    Figure  3.  Temperature contour of steady base flow

    图  4  绝热壁下不同钝度圆锥的流动剖面

    Figure  4.  Profiles for adiabatic cones with different nose bluntness

    图  5  绝热壁和等温壁Tw=300 K工况下流动剖面的比较(Rn=2.54 mm)

    Figure  5.  Comparison of flow profiles between cones with adiabatic wall and isothermal wall of Tw=300 K (Rn=2.54 mm)

    图  6  不稳定模态的中性曲线

    Figure  6.  Neutral curves of instability modes

    图  7  DNS壁面压力脉动与PSE得到的幅值演化的比较

    Figure  7.  Wall pressure fluctuations of DNS compared with amplitude amplification obtained by PSE

    图  8  PSE和LST计算得到的不同频率不稳定波的N值曲线(粗实线和虚线分别为PSE和LST的N值包络线)

    Figure  8.  N factor curves of unstable modes with different frequencies obtained by PSE and LST(thick solid and dashed lines represent the envelope of N factor curves for PSE and LST, respectively)

    图  9  图 8(d)中PSE各曲线N值计算的起点下移至LST的中性点

    (粗实线和虚线分别为PSE和LST的N值包络线)

    Figure  9.  Result of moving the stating points of N factor curves by PSE in Fig. 8(d) down to the corresponding neutral points by LST

    (thick solid and dashed lines represent the envelope of N factor curves for PSE and LST, respectively)

    图  10  不同壁面温度条件下的中性曲线对比(Rn=0.79 mm)

    Figure  10.  Comparison of neutral curves under different wall temperature conditions(Rn=0.79 mm)

    图  11  PSE和eN方法的N值曲线对比(Rn=0.79 mm)

    Figure  11.  Comparison of N factor curves obtained by PSE and eN method(Rn=0.79 mm)

    表  1  PSE和eN方法给出的转捩位置的比较

    Table  1.   Comparison of predicted transition locations obtained by PSE and eN method

    Tw/K Rn/mm NT=4.5 NT=10
    PSE/m eN/m ΔξT/m PSE/m eN/m ΔξT/m
    adiabatic 0.025 4 0.09 0.16 0.07 0.28 0.51 0.23
    adiabatic 0.79 0.23 0.24 0.01 0.49 0.60 0.11
    adiabatic 2.54 0.60 0.60 0.00 0.95 0.95 0.00
    300 0.025 4 0.08 0.11 0.03 0.26 0.37 0.11
    300 0.79 0.19 0.19 0.00 0.39 0.40 0.01
    300 2.54 0.51 0.51 0.00 0.75 0.75 0.00
    下载: 导出CSV

    表  2  绝热壁下eN方法用于不同钝度工况所需的N值修正

    Table  2.   Modification of N factor in eN method for adiabatic cones with different nose bluntness

    Rn/mm NT=4.5 NT=10
    PSE: ξT/m eN: ΔN PSE: ξT/m eN: ΔN
    0.025 4 0.09 2.25 0.28 3.95
    0.79 0.23 0.35 0.49 1.25
    2.54 0.60 0.00 0.95 0.00
    下载: 导出CSV

    表  3  不同壁面温度下eN方法所需的N值修正(Rn=0.79 mm)

    Table  3.   Modification of N factor in eN method for cases with different wall temperatures (Rn=0.79 mm)

    Tw/K NT=4.5 NT=10
    PSE: ξT/m eN: ΔN PSE: ξT/m eN: ΔN
    300 0.19 0.00 0.39 0.25
    400 0.22 0.10 0.47 0.80
    adiabatic 0.23 0.35 0.49 1.25
    500 0.25 0.39 0.50 1.85
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-04-25
  • 修回日期:  2022-05-05
  • 刊出日期:  2023-03-20

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