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arXiv 2201.06005physics.flu-dyn
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液滴碰撞中的分叉

Bifurcations in droplet collisions

A. Dubey, K. Gustavsson, G. Bewley, B. Mehlig

摘要:

Saffman和Turner(1957)认为,湍流中液滴的碰撞率随着湍流应变率的增加而增加。但Dhanasekaran等人(2021)在稳态应变流中的数值模拟表明,Saffman-Turner模型过于简化,因为它忽略了液滴-液滴相互作用。这些结果在一个复杂的依赖性的碰撞率的应变速率和差分沉降速度。在这里,我们表明,这种依赖性是由碰撞动力学中的分叉序列来解释的。我们计算的分叉图时,应变与重力对齐,并表明它产生重要的见解碰撞动力学。首先,稳态碰撞率在极限Kn $\to0$中保持非零,这与碰撞率在该极限中趋于零的常见假设相反(Kn是空气的平均自由程的无量纲度量)。其次,非单调依赖的碰撞速率的差分沉降速度解释了掠分岔。第三,分叉分析解释了为什么所谓的“闭合轨迹”出现和消失。第四,我们的分析预测,在某些鞍点附近,应变和差异沉降的影响相互抵消,

英文摘要:

Saffman and Turner (1957) argued that the collision rate for droplets in turbulence increases as the turbulent strain rate increases. But the numerical simulations of Dhanasekaran et al. (2021) in a steady straining flow show that the Saffman-Turner model is oversimplified because it neglects droplet-droplet interactions. These result in a complex dependence of the collision rate on the strain rate and on the differential settling speed. Here we show that this dependence is explained by a sequence of bifurcations in the collision dynamics. We compute the bifurcation diagram when strain is aligned with gravity, and show that it yields important insights into the collision dynamics. First, the steady-state collision rate remains non-zero in the limit Kn $\to0$, contrary to the common assumption that the collision rate tends to zero in this limit (Kn is a non-dimensional measure of the mean free path of air). Second, the non-monotonic dependence of the collision rate on the differential settling speed is explained by a grazing bifurcation. Third, the bifurcation analysis explains why so-called "closed trajectories" appear and disappear. Fourth, our analysis predicts strong spatial clustering near certain saddle points, where the effects of strain and differential settling cancel

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