时间发散冲击流的线性稳定性分析
Linear stability analysis of a time-divergent slamming flow
AI总结：
本研究通过开尔文-亥姆霍兹型线性稳定性分析，揭示了时间发散冲击流中液-气界面的稳定性特性，发现长波长显著稳定，并预测了经典分析中缺失的边际稳定波长，同时探讨了气体粘性和压缩性的影响。
摘要：
当液体撞击固体时，中间的气体在接近撞击瞬间被以发散的速度挤出。尽管有越来越多的实验证据表明，在这种事件期间液体界面上会形成不稳定性，但对这些不稳定性本质的理解仍然有限。因此，本研究探讨了具有表面张力的液-气界面的稳定性，该界面受到气相中发散流动的影响，其中液相和气相均被视为势流体。我们对表面进行了开尔文-亥姆霍兹型线性模态稳定性分析，以获得振幅方程，随后对该方程进行了详细分析，并将其应用于两个与冲击问题相关的感兴趣情形，即波浪平行撞击垂直壁面，以及水平板撞击液体表面。在这两种情形中，我们发现与基于经典知识（即界面受到恒定气流作用时的稳定性）所预期的情况相比，长波长被显著稳定。在前一种情形中，这导致预测出一个在经典分析中完全缺失的边际稳定波长。对于后一种情形，我们发现与经典情形有许多相似之处，但含义是对于较小的圆盘尺寸，不稳定性被抑制。研究最后讨论了气体粘性和气体可压缩性对各自稳定性图的影响。
英文摘要：
When a liquid slams into a solid, the intermediate gas is squeezed out at a speed that diverges when approaching the moment of impact. Although there is mounting experimental evidence that instabilities form on the liquid interface during such an event, understanding of the nature of these instabilities is limited. This study therefore addresses the stability of a liquid-gas interface with surface tension, subject to a diverging flow in the gas phase, where the liquid and the gas phase are both represented as potential fluids. We perform a Kelvin-Helmholtz-type linear modal stability analysis of the surface to obtain an amplitude equation that is subsequently analysed in detail and applied to two cases of interest for impact problems, namely, the parallel impact of a wave onto a vertical wall, and the impact of a horizontal plate onto a liquid surface. In both cases we find that long wavelengths are stabilised considerably in comparison to what may be expected based upon classical knowledge of the stability of interfaces subject to a constant gas flow. In the former case, this leads to the prediction of a marginally stable wavelength that is completely absent in the classical analysis. For the latter we find much resemblance to the classical case, with the connotation that the instability is suppressed for smaller disk sizes. The study ends with a discussion of the influence of gas viscosity and gas compressibility on the respective stability diagrams.
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