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横向矩形微槽抑制高超声速第二模态扰动波的参数化研究

刘勇 涂国华 向星皓 李晓虎 郭启龙 万兵兵

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横向矩形微槽抑制高超声速第二模态扰动波的参数化研究

刘勇, 涂国华, 向星皓, 李晓虎, 郭启龙, 万兵兵

Parametrization of suppressing hypersonic second-mode waves by transverse rectangular microgrooves

Liu Yong, Tu Guo-Hua, Xiang Xing-Hao, Li Xiao-Hu, Guo Qi-Long, Wan Bing-Bing
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  • 针对高超声速飞行器边界层转捩控制问题, 以马赫数6平板边界层的第二模态扰动波为研究对象, 采用线性稳定性理论(LST)和直接数值模拟(DNS)分别开展了离散模态的同步模式研究和大尺寸(0.4 mm宽)横向矩形微槽开槽位置对第二模态扰动波的控制作用研究. LST分析表明: 涡/熵波会导致Mack第二模态和“mode I”模态(通常来源于快声波)的分支类型发生改变. 通过DNS发现, 开槽表面对基本流的影响程度与边界层流向位置(或厚度)相关, 随着开槽位置后移(边界层厚度增加), 开槽表面对基本流动的影响程度减弱, 摩擦阻力系数和压差阻力系数也逐渐减小. DNS结果还表明, 位于快/慢模态同步区间之前的开槽工况对第二模态扰动波依然有抑制效果, 这与文献中关于小尺寸(微米量级)微孔隙位置对第二模态控制作用的结论不同, 同时发现, 当矩形微槽布置在最大增长率区间范围内或快/慢模态同步区间位置时, 对第二模态扰动的抑制效果最佳.
    Aiming at delaying boundary-layer transition of hypersonic vehicles, the second-mode wave in the boundary layer of a Mach 6 flat plate is studied. Linear stability theory (LST) and direct numerical simulations (DNS) are used to investigate the discrete modes and the relation between the suppressing effect of second-mode wave and the location of transverse rectangular micro-groove (0.4 mm in width), respectively. The LST results show that vortex/entropy waves cause the branch types of Mack’s second mode and “mode I” modes (usually derived from fast acoustic waves) to change. The DNS results show that the influence of the grooved surface on the base flow depends on the streamwise location (or boundary-layer thickness). As the grooved surface shifts backward (or thickness increases), the influence of intensity on the base flow decreases, and the friction resistance coefficient $ C{d_{\text{f}}} $, differential pressure resistance coefficient $ C{d_{\text{p}}} $ and total resistance coefficient $ C{d_x} $ of the grooved surface also decrease. It is found that the grooves located in front of the synchronization region of the fast mode and slow mode still have an inhibitory effect on the second-mode wave, which is different from the effect of small-sized (micrometer scale) micro-pores reported in the literature. It is also found that the suppression effect on the second-mode wave is best when the grooves are arranged in the vicinity of the maximum growth-rate point or at the location of the synchronization interval of the fast mode and slow mode.
      通信作者: 涂国华, ghtu@skla.cardc.cn
    • 基金项目: 国家自然科学基金(批准号: 92052301)资助的课题.
      Corresponding author: Tu Guo-Hua, ghtu@skla.cardc.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 92052301).
    [1]

    Richie G 1999 AIAA 4435

    [2]

    Bertin J J, Cummings R M 2006 Annu. Rev. Fluid Mech 38 129Google Scholar

    [3]

    Whitehead A 1989 AIAA 5013

    [4]

    Morkovin M V 1994 Bull. Am. Phys. Soc 39 1882

    [5]

    Fedorov A 2011 Annu. Rev. Fluid Mech 43 79Google Scholar

    [6]

    Malmuth N, Fedorov A, Shalaev V, Cole J, Khokhlov A, Hites M, Williams D 1998 Theoretical Fluid Mechanics Meeting Albuquerque, NM, USA, June 15–18, 1998 p2695

    [7]

    Fedorov A V, Malmuth N D, Rasheed A, Hornung H G 2001 AIAA J 39 605Google Scholar

    [8]

    Rasheed A, Hornung H G, Fedorov A V, Malmuth N D 2002 AIAA J 40 481Google Scholar

    [9]

    Chokani N, Bountin D A, Shiplyuk A N, Maslov A A 2005 AIAA J 43 149Google Scholar

    [10]

    Egorov I V, Fedorov A V, Soudakov V G 2008 J. Fluid Mech 601 165Google Scholar

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    Egorov I V, Fedorov A V, Novikov A V, Soudakov V G 2007 AIAA 948

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    Dong M, Li C 2021 AIAA J 59 2368Google Scholar

    [13]

    Long T H, Dong Y, Zhao R, Wen Z Y 2021 Phys. Fluids 33 054105Google Scholar

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    Brès G A, Colonius T, Fedorov A V 2010 AIAA J 48 267Google Scholar

    [15]

    Zhao R, Liu T, Wen C Y, Zhu J, Chen L 2018 AIAA J 56 2942Google Scholar

    [16]

    涂国华, 陈坚强, 袁先旭, 杨强, 张毅锋 2018 空气动力学报 36 273

    Tu G H, Chen J Q, Yuan X X, Yang Q, Zhang Y F 2018 Acta Aerodyn. Sin. 36 273 (in Chinese)

    [17]

    郭启龙, 涂国华, 陈坚强, 袁先旭, 万兵兵 2020 航空动力学报 35 135

    Guo Q L, Tu G H, Chen J Q, Yuan X X, Wan B B 2020 J. Aerosp. Power 35 135 (in Chinese)

    [18]

    Guo Q L, Li C, Tu G H, Chen J J, Wan B B, Liu Y 2021 Asia Conference on Mechanical and Aerospace Engineering, Athens, Greece, July 14–17, 2020 p012053

    [19]

    Wang X W, Zhong X L 2008 AIAA 4382

    [20]

    Wang X W, Zhong X L 2012 Phys. Fluids 24 1441

    [21]

    Lukashevich S V, Morozov S O, Shiplyuk A N 2016 J. Appl. Mech. Tech. Phys 57 873Google Scholar

    [22]

    Zhao R, Wen C Y, Long T H, Tian X D, Zhou L, Wu Y 2019 AIAA J 57 5061Google Scholar

    [23]

    孔维萱, 闫超, 赵瑞 2013 航空学报 34 2249

    Kong W X, Yan C, Zhao R 2013 Acta Aeronaut. Astronaut. Sin. 34 2249 (in Chinese)

    [24]

    Brès G A, Inkman M, Colonius T, Fedorov A V 2013 J. Fluid Mech 726 312Google Scholar

    [25]

    Zhao R, Liu T, Wen C Y, Zhu J, Chen L 2019 Phys. Rev. Appl 11 044015Google Scholar

    [26]

    Zhao R, Dong Y, Zhang X X, Wen Z Y, Long T H, Wu Y 2021 AIAA J 59 1893Google Scholar

    [27]

    Ma Y B, Zhong X L 2003 J. Fluid Mech 488 31Google Scholar

    [28]

    Tumin A, Wang X W, Zhong X L 2011 AIAA J 49 463Google Scholar

    [29]

    Liu Y, Guo Q L, Tu G H, Yang Q, Yuan X X, Wan B B 2021 International Conference on Mechanical Engineering and Automation Science, Seoul, South Korea, October 28–30, 2021 p132

    [30]

    Zhang H X, Zhang L P, Zhang S H, Li Q 2017 Comput. Fluids 154 371Google Scholar

    [31]

    Sandham N D, Lüdeke H 2009 AIAA 1288

    [32]

    Tullio N D, Sandham N D 2010 Phys. Fluids 22 094105Google Scholar

    [33]

    Zhao R, Wen C Y, Tian X D, Yuan W 2018 Int. J. Heat Mass Transfer 121 986Google Scholar

    [34]

    Wartemann V, Lüdeke H, Sandham N 2009 AIAA 7202

    [35]

    Fedorov A V, Tumin A 2010 AIAA 5003

    [36]

    Liu Z Y, Yu M 2017 AIAA 2247

    [37]

    Deng X G, Mao M L, Tu G H, Zhang H X, Zhang Y F 2012 Commun. Comput. Phys 11 1081Google Scholar

  • 图 1  增长率$ - {\alpha _{\text{i}}}$随频率${\omega _{\text{r}}}$的变化

    Fig. 1.  Growth rate $ - {\alpha _{\text{i}}}$ versus frequency ${\omega _{\text{r}}}$.

    图 2  马赫数6平板边界层离散模态的流向演化; (a) $ x = 50 $mm, (b) $ x = 200 $mm, (c) $ x = 1000 $mm

    Fig. 2.  Streamwise evolution of discrete modes of the Ma6 flat plate boundary layer: (a) $ x = 50 $mm, (b) $ x = 200 $mm, (c) $ x = $$ 1000 $mm.

    图 3  不同流向位置的离散谱和连续谱分 (a) $ x = 50 $mm; (b) $ x = 200 $mm; (c) $ x = 1000 $mm

    Fig. 3.  Discrete and continuum spectrum at different streamwise locations: (a) $ x = 50 $mm; (b) $ x = 200 $mm; (c) $ x = 1000 $mm.

    图 4  Mack模态的线性稳定性分析 (a) 中性曲线; (b) N值曲线

    Fig. 4.  Linear stability analysis of Mack modes: (a) Neutral curves; (b) N-value curves.

    图 5  扰动型函数 (a) 流向速度实部和虚部; (b) 温度实部和虚部

    Fig. 5.  Perturbation shape function: (a) Streamwise velocity real and imaginary parts; (b) temperature real and imaginary parts.

    图 6  400 kHz的Mack模态沿流向发展情况 (a) 增长率$ - {\alpha _{\text{i}}}$; (b) 相速度$c$

    Fig. 6.  Development of the 400 kHz Mack mode perturbation along the flow direction: (a) Growth rate $ - {\alpha _{\text{i}}}$; (b) phase velocity $c$.

    图 7  开槽位置

    Fig. 7.  Grooving locations.

    图 8  流向140 mm处基本流剖面 (a) 无量纲流向速度; (b) 无量纲温度

    Fig. 8.  Basic flow profile at the 140 mm streamwise location: (a) Dimensionless streamwise velocity; (b) dimensionless temperature.

    图 9  施加第二模态扰动后的瞬态压力云图 (a) 标准网格; (b) 加密网格

    Fig. 9.  Transient pressure contours after imposing the second-mode perturbation: (a) Standard grid; (b) fine grids.

    图 10  标准网格和加密网格上400 kHz第二模态扰动幅值沿流向演化.

    Fig. 10.  Evolution of the 400 kHz second-mode amplitude in the standard grid and the fine grid.

    图 11  基本流压力云图

    Fig. 11.  Pressure contours of the base flow.

    图 12  A1—A5工况基本流修正压力剖面分布 (a) 首槽中心线; (b) 尾槽中心线

    Fig. 12.  Pressure correction of the A1–A5 basic flow: (a) First groove centerline; (b) tail groove centerline.

    图 13  阻力系数($C{d_x}, C{d_{\text{f}}}, C{d_{\text{p}}}$)随开槽位置$ {x_{\text{l}}} $的变化

    Fig. 13.  Drag coefficients ($C{d_x}, C{d_{\text{f}}}, C{d_{\text{p}}}$) versus grooving locations $ {x_{\text{l}}} $.

    图 14  脉动压力云图 (a)—(f) A0—A5工况

    Fig. 14.  Pulsating pressure: (a)–(f) A0–A5 cases in turn.

    图 15  壁面脉动压力沿流向分布 (a)—(e) A1—A5工况壁面脉动压力

    Fig. 15.  Distributions of the wall pressure fluctuation: (a)–(e) The A1–A5 cases.

    图 16  400 kHz第二模态沿流向的发展 (a) A0—A5工况流向[100, 300] mm扰动幅值; (b) A0, A4, A5工况在加长区[300, 400] mm扰动幅值

    Fig. 16.  Development of the 400 kHz second mode along the streamwise direction: (a) A0–A5 cases flow direction[100, 300] mm disturbance amplitude; (b) A0, A4, and A5 cases in the extended area of [300, 400] mm.

    图 17  透射系数T 随开槽起始位置${x_{\text{l}}}$的变化

    Fig. 17.  Variation of transmission coefficient with grooving location.

    表 1  来流参数设置

    Table 1.  Free stream parameter setting.

    马赫数Ma单位
    雷诺数 Re/m
    壁温 Tw/K来流
    密度
    ρ/(kg·m3)
    来流
    温度 Te/K
    普朗
    特数 Pr
    比热比 γ
    6.0$1 \times {10^7}$$300{\text{ }}$$0.0184{\text{ }}$216.650.721.4
    下载: 导出CSV

    表 2  开槽位置参数

    Table 2.  Grooving location parameters.

    Cases开槽起始位置${x_{\text{l}}}/{L_0}$开槽区间
    A0
    A1120(120, 136)
    A2170(170, 186)
    A3200(200, 216)
    A4245(245, 261)
    A5270(270, 286)
    下载: 导出CSV
  • [1]

    Richie G 1999 AIAA 4435

    [2]

    Bertin J J, Cummings R M 2006 Annu. Rev. Fluid Mech 38 129Google Scholar

    [3]

    Whitehead A 1989 AIAA 5013

    [4]

    Morkovin M V 1994 Bull. Am. Phys. Soc 39 1882

    [5]

    Fedorov A 2011 Annu. Rev. Fluid Mech 43 79Google Scholar

    [6]

    Malmuth N, Fedorov A, Shalaev V, Cole J, Khokhlov A, Hites M, Williams D 1998 Theoretical Fluid Mechanics Meeting Albuquerque, NM, USA, June 15–18, 1998 p2695

    [7]

    Fedorov A V, Malmuth N D, Rasheed A, Hornung H G 2001 AIAA J 39 605Google Scholar

    [8]

    Rasheed A, Hornung H G, Fedorov A V, Malmuth N D 2002 AIAA J 40 481Google Scholar

    [9]

    Chokani N, Bountin D A, Shiplyuk A N, Maslov A A 2005 AIAA J 43 149Google Scholar

    [10]

    Egorov I V, Fedorov A V, Soudakov V G 2008 J. Fluid Mech 601 165Google Scholar

    [11]

    Egorov I V, Fedorov A V, Novikov A V, Soudakov V G 2007 AIAA 948

    [12]

    Dong M, Li C 2021 AIAA J 59 2368Google Scholar

    [13]

    Long T H, Dong Y, Zhao R, Wen Z Y 2021 Phys. Fluids 33 054105Google Scholar

    [14]

    Brès G A, Colonius T, Fedorov A V 2010 AIAA J 48 267Google Scholar

    [15]

    Zhao R, Liu T, Wen C Y, Zhu J, Chen L 2018 AIAA J 56 2942Google Scholar

    [16]

    涂国华, 陈坚强, 袁先旭, 杨强, 张毅锋 2018 空气动力学报 36 273

    Tu G H, Chen J Q, Yuan X X, Yang Q, Zhang Y F 2018 Acta Aerodyn. Sin. 36 273 (in Chinese)

    [17]

    郭启龙, 涂国华, 陈坚强, 袁先旭, 万兵兵 2020 航空动力学报 35 135

    Guo Q L, Tu G H, Chen J Q, Yuan X X, Wan B B 2020 J. Aerosp. Power 35 135 (in Chinese)

    [18]

    Guo Q L, Li C, Tu G H, Chen J J, Wan B B, Liu Y 2021 Asia Conference on Mechanical and Aerospace Engineering, Athens, Greece, July 14–17, 2020 p012053

    [19]

    Wang X W, Zhong X L 2008 AIAA 4382

    [20]

    Wang X W, Zhong X L 2012 Phys. Fluids 24 1441

    [21]

    Lukashevich S V, Morozov S O, Shiplyuk A N 2016 J. Appl. Mech. Tech. Phys 57 873Google Scholar

    [22]

    Zhao R, Wen C Y, Long T H, Tian X D, Zhou L, Wu Y 2019 AIAA J 57 5061Google Scholar

    [23]

    孔维萱, 闫超, 赵瑞 2013 航空学报 34 2249

    Kong W X, Yan C, Zhao R 2013 Acta Aeronaut. Astronaut. Sin. 34 2249 (in Chinese)

    [24]

    Brès G A, Inkman M, Colonius T, Fedorov A V 2013 J. Fluid Mech 726 312Google Scholar

    [25]

    Zhao R, Liu T, Wen C Y, Zhu J, Chen L 2019 Phys. Rev. Appl 11 044015Google Scholar

    [26]

    Zhao R, Dong Y, Zhang X X, Wen Z Y, Long T H, Wu Y 2021 AIAA J 59 1893Google Scholar

    [27]

    Ma Y B, Zhong X L 2003 J. Fluid Mech 488 31Google Scholar

    [28]

    Tumin A, Wang X W, Zhong X L 2011 AIAA J 49 463Google Scholar

    [29]

    Liu Y, Guo Q L, Tu G H, Yang Q, Yuan X X, Wan B B 2021 International Conference on Mechanical Engineering and Automation Science, Seoul, South Korea, October 28–30, 2021 p132

    [30]

    Zhang H X, Zhang L P, Zhang S H, Li Q 2017 Comput. Fluids 154 371Google Scholar

    [31]

    Sandham N D, Lüdeke H 2009 AIAA 1288

    [32]

    Tullio N D, Sandham N D 2010 Phys. Fluids 22 094105Google Scholar

    [33]

    Zhao R, Wen C Y, Tian X D, Yuan W 2018 Int. J. Heat Mass Transfer 121 986Google Scholar

    [34]

    Wartemann V, Lüdeke H, Sandham N 2009 AIAA 7202

    [35]

    Fedorov A V, Tumin A 2010 AIAA 5003

    [36]

    Liu Z Y, Yu M 2017 AIAA 2247

    [37]

    Deng X G, Mao M L, Tu G H, Zhang H X, Zhang Y F 2012 Commun. Comput. Phys 11 1081Google Scholar

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出版历程
  • 收稿日期:  2022-04-29
  • 修回日期:  2022-06-12
  • 上网日期:  2022-09-27
  • 刊出日期:  2022-10-05

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