Numerical study of non-uniformity effect on Richtmyer-Meshkov instability induced by non-planar shock wave
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摘要:
基于Navier-Stokes方程组，采用可压缩多介质黏性流动和湍流大涡模拟程序MVFT (multi-viscous-flow and turbulence)，模拟了均匀流场与初始密度呈现高斯函数分布的非均匀流场中马赫数为1.25的非平面激波加载初始扰动air/SF6界面的Richtmyer-Meshkov (RM)不稳定性现象。数值模拟结果表明，初始流场非均匀性将会影响非平面激波诱导的RM不稳定性演化过程。反射激波加载前，非平面激波导致的界面扰动振幅随着流场非均匀性增强而增大；反射激波加载后，非均匀流场与均匀流场条件下的界面扰动振幅差异有所减小。进一步，定量分析流场中环量分布及脉动速度统计量揭示了前述规律的原因。此外，还与平面激波诱导的RM不稳定性进行了简单对比，发现由于非平面激波波阵面区域的涡量与激波冲击界面时产生的涡量的共同作用，使得非平面激波与平面激波诱导的界面失稳过程存在差异。
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关键词:
- Richtmyer-Meshkov不稳定性 /
- 非均匀流场 /
- 非平面激波 /
- 大涡模拟
Abstract:Based on the Navier-Stokes equations, the large-eddy simulation code MVFT (multi-viscous-flow and turbulence) was applied to numerically study the Richtmyer-Meshkov instability (i.e. RMI) for a perturbed interface, which is driven by a non-planar shock wave with Ma=1.25 in uniform and non-uniform flows with Gaussian distribution of the initial density. The simulation results show that the interface evolution of the RMI induced by non-planar shock wave is affected by the non-uniformity of the initial flows. Before reshock, the growth of the disturbed interface increases with the increasing of the non-uniformity flow field for either φ=0 or φ=π. However, these discrepancies are reduced as the flow enters the turbulent mixing. Further quantitative analysis of the circulations and high-order fluctuating velocity correlation in the flow field reveal the mechanisms for the aforementioned regulations. In addition, it is found that the interface evolution of the RMI induced by non-planar shock wave is different from that driven by planar shock wave. The mechanism for the difference is the influence of the initial vorticity of non-planar shock wave and the vorticity generated by the shock-interface.
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图 2 均匀流场及非均匀流场沿y方向的密度分布
Figure 2. Density distributions along y direction in uniform and non-uniform flows
图 7 沿x方向的脉动速度一点二阶相关量分布
Figure 7. Correlation distribution of fluctuating velocities along x direction
表 1 Air/SF6初始参数（20 ℃, 101.325 kPa）
Table 1. Properties of air and SF6 gases
Gas ρ/(kg·m−3) γ νl/(mm2·s−1) Prl D/(mm2·s−1) SF6 5.34 1.09 2.47 0.90 9.7 Air 1.29 1.40 15.7 0.71 20.4 
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表 2 正、负环量相对差值极大值
Table 2. Maximum values of relative difference for positive and negative circulations
φ Case Relative difference/% Before reshock Transition After reshock Γ + Γ − Γ + Γ − Γ + Γ − 0 Uni vs δ1=0.616 2 m 5.5 8.2 18.6 23.1 7.7 7.6 Uni vs δ2=0.496 1 m 8.3 13.1 25.0 31.4 7.3 5.1 π Uni vs δ1=0.616 2 m 5.7 6.1 40.1 46.9 6.0 7.8 Uni vs δ2=0.496 1 m 8.2 10.2 49.5 60.7 6.7 4.9
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