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冲击加载下V形界面的失稳与湍流混合

李俊涛 孙宇涛 潘建华 任玉新

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冲击加载下V形界面的失稳与湍流混合

李俊涛, 孙宇涛, 潘建华, 任玉新

Instability and turbulent mixing of shocked V shaped interface

Li Jun-Tao, Sun Yu-Tao, Pan Jian-Hua, Ren Yu-Xin
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  • 采用多组分混合物质量分数模型和最小色散可控耗散格式的高分辨率有限体积方法,数值模拟了弱激波冲击不同角度的V形空气/SF6界面的Richtmyer-Meshkov不稳定性问题.激波冲击界面后,在界面附近沉积涡量,形成沿界面规则排列的旋涡结构,同时界面扰动发展形成气泡和尖钉结构.本文统计了界面左端移动速度和界面混合宽度增长率等特征量的演化规律,并与已有的实验结果进行了对比,两者符合较好.讨论了物质界面处的流体向湍流混合发展的过程,随着界面旋涡结构的演化,涡结构之间开始发生相互诱导、并对等现象,并逐渐聚集在几个区域,而多尺度结构也因旋涡的诱导作用在这些区域中产生.通过对由雷诺数定义的惯性尺度进行分析,发现了具有上下边界的惯性尺度区域的形成,对动能能谱的分析发现了-5/3对数率的出现,这同样说明了惯性尺度区域的形成.由于湍流混合转捩与惯性尺度区域的形成是一致的,界面附近流场将发展为湍流.
    Based on the mass fraction model of multicomponent mixture, the interactions between weak shock wave and V shaped air/SF6 interface with different vertex angles are numerical simulated. The numerical scheme used in the simulation is the high-resolution finite volume method with minimized dispersion and controllable dissipation scheme, in which the dissipation can be adjusted without affecting the already optimized dispersion property of the scheme. The grid sensitivity study is performed to guarantee that the resolution is sufficient in the numerical simulation. After the shock wave interacts with the interface, the baroclinic vorticity is deposited near the interface due to the misalignment of the density and pressure gradient, which is the manifestation of the Richtmyer-Meshkov instability, leading to the vortical structures forming along the interface. The interface perturbations lead to the bubbles and spikes appearing. The predicted leftmost interface displacement and interface width growth rate in the early stage of interface evolution agree well with the experimental results. The process of transition to turbulence at the material interface is studied in detail. The numerical results indicate that with the evolution of the interfacial vortical structure due to Kelvin-Helmholtz instability, the array of vortices begins to merge. As a result, the vortices accumulate in several distinct regions. It is in these regions that the multi-scale structures are generated because of the interaction between vortices. It is shown clearly that in the regions where vortices are accumulated, the fluctuation energy spectrum has many large and smallscale elements, which indicates there may be turbulent structures in these regions. To further examine if there is mixing transition in these regions, the characteristic length scales of the flow fields are calculated. The separation between the Lipemann-Taylor scale and inner viscous scale is observed based on the circulation-based Reynolds number, leading to the appearance of an uncoupled inertial range. The classical Kolmogorov -5/3 power law is also shown in the fluctuation energy spectrum, which means that the inertial range is developed. The appearing of this inertial range confirms that the mixing transition does occur, and the flow field near the material interface will develop into turbulence.
      通信作者: 孙宇涛, sun.yu.tao@qq.com
    • 基金项目: 国家自然科学基金(批准号:U1430235)资助的课题.
      Corresponding author: Sun Yu-Tao, sun.yu.tao@qq.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. U1430235).
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    Sun Z S, Ren Y X, Larricq C, Zhang S Y, Yang Y C 2011 J. Comput. Phys. 230 4616

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  • [1]

    Lindl J D, McCrory R L, Campbell E M 1992 Phys. Today 4532

    [2]

    Marble F E, Hendrics G J, Zukoski E E 1987 AIAA 871880

    [3]

    Luo X S, Zhai Z G, Si T, Yang J M 2014 Adv. Mech. 44 201407 (in Chinese)[罗喜胜, 翟志刚, 司廷, 杨基明2014力学进展 44 201407]

    [4]

    Rudinger G, Somers L M 1960 J. Fluid Mech. 7 161

    [5]

    Haas J F, Sturtevant B 1987 J. Fluid Mech. 181 41

    [6]

    Zhai Z, Si T, Luo X, Yang J M 2011 Phys. Fluids 23 084104

    [7]

    Bates K R, Nikiforakis N, Holder D 2007 Phys. Fluids 19 036101

    [8]

    Hoi D N, Hamid A, Kevin R B, Nikos N 2011 Commun. Nonlinear Sci. Numer. Simul. 16 4158

    [9]

    Zou L Y, Liu C L, Tan D W, Huang W B, Luo X S 2010 J. Vis. 13 347

    [10]

    Fan M R, Zhai Z G, Si T, Luo X S, Zou L Y, Tan D W 2012 Sci. China:Phys. Mech. Astron. 55 284

    [11]

    Sun Z S, Ren Y X, Larricq C, Zhang S Y, Yang Y C 2011 J. Comput. Phys. 230 4616

    [12]

    Wang Q J, Ren Y X, Sun Z S, Sun Y T 2013 Sci. China:Phys. Mech. Astron. 56 423

    [13]

    Wang T, Bai J S, Li P, Tao G, Jiang Y, Zhong M 2013 Chin. J. High Pressure Phys. 2 18(in Chinese)[王涛, 柏劲松, 李平, 陶钢, 姜洋, 钟敏2013高压物理学报 2 18]

    [14]

    Shyue K M 1998 J. Comput. Phys. 142 208

    [15]

    Luo X, Dong P, Si T, Zhai Z G 2016 J. Fluid Mech. 802 186

    [16]

    Rikanati A, Alon U, Shvarts D 2003 Phys. Fluids 15 3776

    [17]

    Miura A 1997 Phys. Plasmas 4 2871

    [18]

    Dimotakis P E 2000 J. Fluid Mech. 409 69

    [19]

    Zhou Y, Remington B A, Robey H F, Cook A W, Glendinning S G, Dimits A, Cabot W 2003 Phys. Plasmas 10 1883

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出版历程
  • 收稿日期:  2016-07-19
  • 修回日期:  2016-08-19
  • 刊出日期:  2016-12-05

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