Numerical Simulation of the Interface Instability Inducedby Shock in Initial Nonuniform Flows
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摘要: 流体力学界面不稳定性及其后期的界面混合现象，是一种十分复杂的多尺度非线性物理问题，在惯性约束聚变、天体物理以及水中爆炸等领域有着广泛的应用前景，对该问题的研究不仅具有很高的学术价值，而且对促进相关领域的发展具有重要意义.中国工程物理研究院流体物理研究所基于Euler有限体积方法，发展了适用于可压缩多介质黏性流动具有多亚格子尺度模型的大涡模拟程序MVFT，并评估分析了不同亚格子尺度模型对界面不稳定性及界面混合的模拟能力；提出了流场非均匀性对R-M不稳定性影响的问题，并在激波驱动轻重气体双模扰动R-M界面不稳定性实验中成功应用并解读了新的实验现象和规律，在此基础上进而开展了反射激波作用下两种初始非均匀流场界面不稳定性引起的界面混合数值模拟研究，探讨了流场非均匀性对激波反射后强非线性阶段界面不稳定性发展、演化规律的影响，近期还对非均匀流场R-M不稳定性的演化规律、初始流场非均匀性和初始扰动效应及其影响的物理机制进行了分析和研究.Abstract: Interface instability and turbulent mixing are complex multi-scale nonlinear physical problems, which have been found and utilized widely in man-made applications and natural phenomena such as inertial confinement fusion(ICF), high-speed combustion, and astrophysics (i.e. supernova explosions), so this problem has gained significant attention in science and technology. The Institute of Fluids Physics, China Academy of Engineering Physics has developed a large eddy simulation code MVFT (multi-viscous flow and turbulence)with different SGS models, based on Eulerian finite volune method. Meanwhile, the ability of different SGS models for simulating the interface instability and interface mixing has been evaluated in research. The effect of nonuniformity of flow field on the Richtmyer-Meshkov (R-M) instability was put forward, which has been successfully used to explain the related new experiment phenomenon and laws of the R-M instability. Given the found mechanism, the R-M instability and interface mixing in nonuniform flow were further studied and the effect of nonuniformity on the interface instability development in the strong nonlinear stage was discussed. Recently, the effects of initial perturbation on the R-M instability have been researched as well. Distinctive evolution mechanisms of R-M instability between the nonuniform flows and the uniform flows were analyzed in detail.
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图 2 TMZ宽度实验结果和数值模拟比较
Figure 2. TMZ width comprisons between experimental and numerical results
图 3 湍动能流向分布
Figure 3. Distributions of turbulent kinetic energy in streamwise direction for different SGS models at four different times
图 4 湍动能峰值的时间历程
Figure 4. Time histories of peak values of turbulent kinetic energy for different SGS models
图 5 湍动能峰值及其拟合结果
Figure 5. Peak values of turbulent kinetic energies and their fitted results
图 6 流向分布的亚格子湍耗散
Figure 6. Distributions of SGS turbulent dissipations in streamwise direction for different SGS models at four different times
图 8 密度为Gauss分布的非均匀流场、高低密度均匀流场中垂直方向密度分布图
Figure 8. Density profiles of nonuniform flows with a Gaussian function and uniform flows in vertical direction
图 9 初始非均匀流场中无扰动界面的密度云图(t=1 ms)
Figure 9. Density contour images of numerical simulation result in a nonuniform Gaussian function flow without initial perturbation on interface (t=1 ms)
图 10 相同时刻MVFT-2D计算和实验纹影图的比较
Figure 10. (Color online) Schlieren photography pictures and numerical simulation results by MVFT-2D at a certain time (sizes of the pictures are ones of the test windows [0.038 m, 0.25 m]×[0.0 m, 0.2 m])
图 11 t=1.0 ms时刻MVFT-2D两种计算结果和实验纹影图的比较
Figure 11. Differences of interface shape, location and shock front at t=1.0 ms in initial uniform and nonuniform flows and experiments
图 12 二维和三维计算结果以及与实验的比较
Figure 12. Comparisons of MVFT-2D, MVFT-3D and experimental results at three times
图 13 气泡和尖钉位置以及3条激波阵面观测线
Figure 13. Bubbles and spike locations in test window as well as three shock front line positions
图 14 3条测试线上不同时刻激波阵面位置
Figure 14. Shock front locations of experiment and calculated results on three test lines at different times
图 15 大小扰动振幅历程的理论、实验与数值计算结果比较(其中误差棒为实验值的10%)
Figure 15. Perturbation amplitudes history of experiment, numerical computing and comparison to Sadot model and Zhang-Sohn theory, B1-S1 corresponds to small perturbation amplitude, and B3-S3 corresponds to large one (error bars of this visual measurement are equal to ±10%)
图 16 均匀与非均匀流场中大小扰动振幅历程计算比较
Figure 16. Perturbation amplitudes history calculations of initial uniform and nonuniform flows in R-M instability
图 18 t=1 ms不同初始振幅组合下的流场密度云图(左列:低密度均匀流场; 中列:高密度均匀流场; 右列:非均匀流场)
Figure 18. Density contour images of numerical simulation results at t=1 ms under different groups of initial amplitudes (left column shows low-density uniform flows; middle column high-density uniform flows; and right columnnonuniform Gaussian function flows)
图 19 t=1.8 ms不同初始振幅组合下的流场密度云图(左列:低密度均匀流场; 中列:高密度均匀流场; 右列:非均匀流场)
Figure 19. Density contour images of numerical simulation result at t=1.8 ms under different groups of initial amplitudes (left column shows low density uniform flows; middle column high-density uniform flows; and right column nonuniform Gaussian function flows)
图 20 在4种不同初始流场的振幅扰动增长图
Figure 20. Perturbation amplitudes of A0=7.5 mm initial amplitude with four other initial amplitudes
图 21 非均匀和均匀流场的高低密度区振幅时间变化图
Figure 21. Perturbation amplitudes of four different initial amplitudes density zones in nonuniform and uniform flows
图 22 t=1 ms, S3非均匀流场低密度区的平均环量
Figure 22. Average vorticities of S3 (spike trough) in low-density zone of nonuniform flows with four different initial amplitudes at t=1 ms
图 23 t=1 ms, 不同初始扰动振幅下, 非均匀流场高密度区S3、低密度区S1、均匀流场高低密度区, 波谷处的涡量平均值分布图
Figure 23. Average vorticities of four conditions: the spike trough in low-density zone of nonuniform flows S3, the spike trough in high-density zone of nonuniform flows S1, and the spike trough in low-density uniform flows and high-density uniform flows with four initial amplitudes at t=1 ms
图 24 初始扰动振幅为分别为0, 2.5, 5, 7.5, 10 mm情况下, 非均匀流场低密度区、高密度区4/3波长面积内总环量时间图
Figure 24. Total circulations over time with four different initial amplitudes: 0.0, 2.5, 5, 7.5 and 10 mm in low-density zone and high-density zone of nonuniform flows
图 25 初始振幅为(a)7.5 mm情况下, 非均匀流场高低密度区、高低密度均匀流场区, 4/3波长面积内总环量、正环量、负环量时间图; 初始扰动振幅分别为: (b)2.5 mm, (c)5 mm, (d)7.5 mm, (e)10 mm情况下, 非均匀流场高低密度区、高低密度均匀流场区, 4/3波长面积内负环量时间图
Figure 25. Circulations over time in four conditions: low-density zone of nonuniform flows, high-density zone of nonuniform flows, low-density uniform flows, and high-density uniform flowsunder four initial amplitudes
图 26 密度云图和涡量云图(左列:均匀流场, 中列: δ1 Gauss分布的非均匀流场, 右列: δ2 Gauss分布的非均匀流场)
Figure 26. Density and vortex contour images of the numerical simulation results by MVFT at certain times (Left column, uniform initial conditions; middle column, δ1 nonuniform Gaussian function; and right column, δ2 nonuniform Gaussian function. Small arrow denotes the direction of propagation of the shock wave fronts before reshock of the interface)
图 27 初始均匀流场及Gauss分布δ1和δ2的非均匀流场, 界面不稳定性的混合区域宽度时间变化图
Figure 27. Mixing width history calculations of initial uniform and nonuniform flows in R-M instability
图 28 初始均匀流场及Gauss分布δ1, δ2的非均匀流场, 正负环量、总环量变化图
Figure 28. Positive circulation, negative circulationand total circulation evolutions over time of the flow field of the two elliptic gas cylinders
图 29 流场中正负环量之间的相对误差对比图
Figure 29. Relative errors between the flow field in the positive and negative circulations (The reshock times are 1.73, 1.70, and 1.70 ms, respectively, for the three graphs)
表 1 激波再加载前后不同SGS模型计算时湍动能衰减常数
Table 1. Decay constants of turbulent kinetic energies before and after reshock for different SGS models
models VM DSM SVM before reshock 0.076 99 0.100 78 0.083 18 after reshock 0.087 62 0.049 7 0.075 48 
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表 2 空气和SF6的物理参数
Table 2. Properties of air and SF6 gases
gases densities (g/cm3) specific ratios kinetic viscosities (10-6m2/s) Prandtl numbers diffusion coefficients in air (cm2/s) air 1.29 1.40 15.7 0.71 0.204 SF6 5.97 1.09 2.47 0.90 0.097
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表 3 振幅组合表
Table 3. Six groups of initial amplitudes
No. A01/mm A02/mm 1 5 7.5 2 7.5 5 3 2.5 7.5 4 7.5 2.5 5 5 10 6 10 5
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表 4 t=1 ms时, 初始振幅为2.5, 5, 7.5, 10 mm情况下, 均匀流场高低密度区、非均匀流场高低密度区4/3波长面积内环量对比表
Table 4. Negative circulations of five initial amplitudes in four flow field at t=1 ms
A0/mm Γ- in low-density of uniform flows /(m2·s-1) Γ- in high-density of uniform flows /(m2·s-1) Γ- in high-density of nonuniform flows /(m2·s-1) Γ- in low-density of nonuniform flows /(m2·s-1) 2.5 -1.02 -1.96 -2.94 -5.01 5 -2.72 -3.43 -4.93 -6.55 7.5 -5.37 -6.53 -7.07 -8.81 10 -6.91 -8.79 -9.23 -11.40 0.0 0.00 0.00 -0.35 -3.42
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