Mach number effect on the instability of a planar interface subjected to a rippled shock
Mach number effect on the instability of a planar interface subjected to a rippled shock
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DOI：
10.1103/physreve.98.043105
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发表时间：
2018-10
影响因子：
2.4
通讯作者：
Wenbin Zhang;Qiang Wu;L. Zou;Xian-xu Zheng;Xinzhu Li;Xisheng Luo;J. Ding
中科院分区：
文献类型：
--
作者：
Wenbin Zhang;Qiang Wu;L. Zou;Xian-xu Zheng;Xinzhu Li;Xisheng Luo;J. Ding
通过高阶可压缩多分量流体动力学模拟，研究了受到正弦波纹冲击的平面界面 (${\mathrm{N}}_{2}\ensuremath{-}{\mathrm{SF}}_{6}$) 的 Richtmyer-Meshkov (RM) 不稳定性，作为受到平面冲击冲击的正弦界面的变体。波纹激波是由平面激波穿过单模界面($\mathrm{He}\ensuremath{-}{\mathrm{N}}_{2}$)产生的，其传播特性与Bates的解析解相当吻合。研究发现，受波纹冲击影响的平坦接触面的演化在很大程度上取决于波纹冲击相位，并且可以通过脉冲扰动和连续扰动状态很好地解释。考虑了 1.15 至 1.80 范围内不同马赫数的各种波纹冲击。研究发现，对于不同阶段的波纹冲击，冲击强度对不稳定性增长的影响表现不同。在波纹激波振幅第一次消失时发生激波界面碰撞的情况下，随着激波强度的增加，脉冲扰动（即由脉冲激波冲击引起的振幅增长）在不稳定性增长中比连续摄动（即由激波后压力场扰动引起的振幅增长）起着越来越重要的作用。相反，在波纹冲击振幅第二次变为零时发生冲击的情况下，无论冲击强度如何，由脉冲扰动贡献的不稳定性发展占总不稳定性增长的一定百分比。脉冲扰动在单模框架内当前非标准 RM 不稳定性中的作用可以通过经验公式结合 Ishizaki 等人的模型来合理预测。 [物理。修订版 E 53，R5592 (1996)]。
The Richtmyer-Meshkov (RM) instability of a planar interface (${\mathrm{N}}_{2}\ensuremath{-}{\mathrm{SF}}_{6}$) subjected to a sinusoidal rippled shock, as the variant of a sinusoidal interface impinged by a planar shock, is investigated through high-order compressible multicomponent hydrodynamic simulations. The rippled shock is generated by a planar shock penetrating through a single-mode interface ($\mathrm{He}\ensuremath{-}{\mathrm{N}}_{2}$), and its propagation characteristic agrees reasonably with Bates' analytical solution. Evolution of the flat contact surface impacted by the rippled shock is found to be heavily dependent on the rippled shock phase, and it can be well explained by the impulsive perturbation and continuous perturbation regimes. Various rippled shocks with different Mach numbers ranging from 1.15 to 1.80 are considered. It is found that the influence of the shock strength on the instability growth behaves differently for rippled shocks at different phases. In the case that the shock-interface collision happens when the rippled shock amplitude vanishes for the first time, as the shock strength increases, the impulsive perturbation (i.e., amplitude growth caused by the impulsive shock impact) plays an increasingly more important role in the instability growth than the continuous perturbation (i.e., amplitude growth induced by the disturbed postshock pressure field). In contrast, in the case that the impingement occurs when the rippled shock amplitude becomes zero for the second time, the instability development contributed by the impulsive perturbation is a certain percentage of the total instability growth regardless of the shock strength. The role of the impulsive perturbation in the present nonstandard RM instability within the single-mode framework can be reasonably predicted by an empirical formula combined with the model of Ishizaki et al. [Phys. Rev. E 53, R5592 (1996)].