Analysis of Dependence of Multi-Mode Richtmyer-Meshkov Instability on Initial Conditions
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摘要: 利用可压缩多介质黏性流动和湍流大涡模拟程序MVFT，对多次冲击作用下的三维多模态Richtmyer-Meshkov(RM)不稳定性发展及其对初始扰动条件的依赖性进行了数值模拟分析。湍流混合区宽度在初始冲击后以幂次律增长，在反射冲击后和第一次反射稀疏波作用后，以具有不同增长因子的指数规律增长，在第一次反射压缩波作用后近似以线性规律增长; 而湍流混合区统计量则以类似的规律衰减。多模态RM不稳定性发展对初始扰动条件有很强的依赖性，主要体现在初始冲击后至反射冲击前和反射冲击后至第一次反射稀疏波作用前这两个阶段，即在第一次反射稀疏波作用后，湍流混合区的发展逐渐失去对初始扰动条件的记忆。
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关键词:
- 可压缩多介质黏性流动和湍流 /
- 大涡模拟 /
- Richtmyer-Meshkov不稳定性 /
- 湍流混合区
Abstract: Using the in-house large-eddy simulation code MVFT, we investigated the three-dimensional multi-mode Richtmyer-Meshkov (RM) instability under multiple impingements and its dependence on initial conditions.After the initial shock, the width of the turbulent mixing zone (TMZ) grows with time in power-law.After the reshock and the impingement of the first reflected rarefaction wave, the TMZ width grows with time in the exponential law but with different growth factors.After the impingement of the first reflected compression wave, it grows with time in an approximately linear fashion, and the statistical quantities in TMZ decay with time in a similar way.The evolution of multi-mode RM instability is greatly dependent on the initial conditions between the initial shock and the impingement of the first reflected rarefaction wave.After the impingement of the first reflected rarefaction wave, the evolution of the turbulent mixing zone has lost the memory of the effect exerted by the initial conditions. -
图 3 不同模型湍流混合区宽度随时间的增长历史
Figure 3. Time histories of growth of TMZ width (dTMZ) of different models
图 4 SF6的体积分数为0.1和0.9的等值面所显示的不同时刻湍流混合区图像
Figure 4. Images of TMZ visualized by the volume fraction isosurface of 0.1 and 0.9 for SF6 at different times
图 5 不同模型湍流混合区湍动能峰值时间历史
Figure 5. Time history of turbulent kinetic energy of different models in TMZ
图 6 不同模型湍流混合区湍动能耗散率峰值时间历史
Figure 6. Time histories of turbulent kinetic energy dissipation rate of different models in TMZ
图 7 不同模型湍流混合区拟涡能峰值时间历史
Figure 7. Time histories of enstrophy of different models in TMZ
表 1 气体初始参数
Table 1. Initial properties of air and SF6
Gas ρ/(kg/m3) p/(MPa) γ μlam/(μPa·s) D/(mm2/s) SF6 5.97 0.1 1.09 14.746 9.7 Air 1.18 0.1 1.40 18.526 20.4 
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表 2 模型参数
Table 2. Model parameters
Case η0/(mm) PS 1 0.07 0.035 2 0.14 0.070 3 0.28 0.140 4 0.56 0.280 5 1.12 0.560
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表 3 不同模型湍流混合区宽度的增长因子
Table 3. Growth factors of TMZ width of different models
Case θ t1*/(ms) t2*/(ms) 1 0.364 0.646 0.854 2 0.352 0.519 0.875 3 0.382 0.457 0.837 4 0.449 0.433 0.788 5 0.495 0.431 0.786
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