Numerical Study of Shock Wave Impacting on the Double-Mode Interface in Nonuniform Flows
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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的二维计算程序MVFT-2D，针对初始非均匀流场密度为高斯分布、马赫数Ma=1.27激波作用下的双模态界面失稳现象，进行了数值模拟研究。数值模拟结果表明，处于非均匀流场中的双模态振幅耦合效应较弱，而且低密度区的初始大振幅界面扰动增长最快，高密度区的初始小振幅界面扰动增长最慢。通过进一步分析可知，在一定初始振幅范围内，非均匀流场低密度区的振幅增长率较高，混合区域更宽，湍动能较大，受初始振幅影响较大，导致该区域界面不稳定演化较快。其变化规律与均匀流场呈现相反趋势，说明非均匀流场界面不稳定性的发展规律与均匀流场存在较大差异。
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关键词:
- 密度非均匀流场 /
- Richtmyer-Meshkov不稳定性 /
- 初始扰动 /
- 数值模拟
Abstract: The double-mode Richtmyer-Meshkov (RM) instability, when the incident shock (Ma=1.27) impacting on several groups of initial double-mode cosine interface formed by different amplitudes in initially nonuniform flows whose density is Gaussian distribution, was numerically investigated using the large-eddy simulation code MVFT (multi-viscous-flow and turbulence).The numerical results show that the coupling effects between different amplitudes in the nonuniform flows are weak and the evolution of the interface with a large initial amplitude in the low density nonuniform area grows fastest, while that with a small initial amplitude in the high density nonuniform area grows slowly.Further analyses reveal that within a certain initial amplitude range, the amplitude growth rate and energy in the low density zone of nonuniform flows is larger than those in the high density zone, thus the influence of the initial amplitude on the low density zone is more obvious, which eventually leads to a faster evolution process of the RM instability.Moreover, the changing phenomena of uniform flows are opposite to nonuniform flows.Thus, it can be concluded that the evolution mechanisms of the RM instability between the nonuniform and uniform flows are distinctive. -
图 3 t=1 ms时非均匀流场无扰动界面的密度云图
Figure 3. Density images of nonuniform flow without perturbation on interface at t=1 ms
图 4 t=1 ms时不同初始振幅组合下的流场密度云图
Figure 4. Density images of uniform and nonuniform flows under different groups of initial amplitudes at t=1 ms
图 5 在A02不同情况下非均匀流场的振幅增长曲线
Figure 5. Perturbation amplitudes of nonuniform flows with 4 different amplitudes of A02
图 6 均匀流场与非均匀流场高、低密度区的振幅变化
Figure 6. Perturbation amplitudes of uniform flow and high and low density zone of nonuniform flow with different A0
图 7 不同初始扰动振幅下非均匀流场界面振幅增长率
Figure 7. Growth rate over time of nonuniform flows with 4 different amplitudes of A01
图 8 非均匀流场高、低密度区及均匀流场中界面振幅增长率
Figure 8. Growth rate over time in high-density and low-density nonuniform flows and uniform flows
图 9 初始均匀流场中不同初始振幅情况下的湍动能分布(实线：高密度；虚线：低密度)
Figure 9. Turbulent kinetic-energy profiles in high-density (solid line) and low-density (dashed line) uniform flows at various times under different initial amplitudes
图 10 初始非均匀流场中不同初始振幅情况下的湍动能分布(实线：高密度；虚线：低密度)
Figure 10. Turbulent kinetic-energy profiles in high-density (dashed line) and low-density (solid line) nonuniform flows at various times under different initial amplitudes
图 11 当A01=2.5 mm，A02=7.5 mm时初始均匀和非均匀流场中尖钉处的斜压涡量分布
Figure 11. Baroclinic vorticity in uniform and nonuniform flows with A01=2.5 mm, A02=7.5 mm at various times
表 1 气体参数
Table 1. Initial paramenters of air and SF6
Gas Density/(kg·m-3) γ η/(10-6 m2·s-1) Prl D/(cm2·s-1) Air 1.29 1.40 15.5 0.71 0.204 SF6 5.34 1.09 18.2 0.90 0.097 
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表 2 双模态界面的初始振幅
Table 2. Initial amplitudes of double-mode cosine interface
No. A01/mm A02/mm 1 5.0 7.5 2 7.5 5.0 3 2.5 7.5 4 7.5 2.5 5 7.5 7.5 6 7.5 10.0 7 10.0 7.5
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