arXiv 2202.083222022-02physics.flu-dyn

尘埃涡旋的不稳定性

Instability of a dusty vortex

Shuai Shuai, Darish Jeswin Dhas, Anubhab Roy, M. Houssem Kasbaoui

DOI：: 10.1017/jfm.2022.687

摘要：

本文研究了半稀释尘埃流中，有限半径圆片中的惯性粒子对二维朗肯涡稳定性的影响。与不存在不稳定模式的无粒子情况不同，我们表明来自粒子的反馈力触发了一种新的不稳定性。使用弱惯性粒子的线性稳定性分析来表征驱动不稳定性的机制，并通过欧拉-拉格朗日模拟进一步验证。结果表明，当质量载荷为$M>0$时，颗粒涡总是不稳定的。令人惊讶的是，即使是非惯性粒子不稳定的旋涡的机制类似的离心瑞利-泰勒不稳定性的径向分层涡密度跳跃。我们确定了一个临界质量负载以上的本征模式$m$变得不稳定。随着m的增加，临界质量载荷下降到零。当粒子是惯性的，低于临界质量负载的模式变得不稳定，而在它上面的模式保持不稳定，但与非惯性的情况下相比，具有较低的增长率。与欧拉-拉格朗日模拟的比较表明，从模拟计算的增长率匹配以及理论预测。经过线性阶段，我们观察到高波数模式的出现，这些模式变成从核心发出的集中粒子的螺旋臂，而无粒子流的区域则被向内吸入。涡度场也表现出相似的模式，导致初始朗肯结构的破裂。这种新的不稳定性的尘埃涡突出了如何从分散相的反馈力可以引起故障，否则弹性的旋涡结构。

英文摘要：

We investigate the effect of inertial particles dispersed in a circular patch of finite radius on the stability of a two-dimensional Rankine vortex in semi-dilute dusty flows. Unlike the particle-free case where no unstable modes exist, we show that the feedback force from the particles triggers a novel instability. The mechanisms driving the instability are characterized using linear stability analysis for weakly inertial particles and further validated against Eulerian-Lagrangian simulations. We show that the particle-laden vortex is always unstable if the mass loading $M>0$. Surprisingly, even non-inertial particles destabilize the vortex by a mechanism analogous to the centrifugal Rayleigh-Taylor instability in radially stratified vortex with density jump. We identify a critical mass loading above which an eigenmode $m$ becomes unstable. This critical mass loading drops to zero as m increases. When particles are inertial, modes that fall below the critical mass loading become unstable, whereas, modes above it remain unstable but with lower growth rates compared to the non-inertial case. Comparison with Eulerian-Lagrangian simulations shows that growth rates computed from simulations match well the theoretical predictions. Past the linear stage, we observe the emergence of high-wavenumber modes that turn into spiraling arms of concentrated particles emanating out of the core, while regions of particle-free flow are sucked inward. The vorticity field displays similar pattern which lead to the breakdown of the initial Rankine structure. This novel instability for a dusty vortex highlights how the feedback force from the disperse phase can induce the breakdown of an otherwise resilient vortical structure.

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