标题： 雷诺数对各向同性湍流中惯性粒子动力学的影响。 第二部分：考虑重力效应的模拟 显示英文标题

标题： The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part II: Simulations with gravitational effects

摘要： 在本研究的第一部分中，我们使用直接数值模拟（DNS）分析了无重力作用下惯性粒子在各向同性湍流中的运动。 在此，第二部分中，我们引入重力，并研究其在广泛范围的流动雷诺数、弗劳德数和粒子斯托克斯数下的影响。 我们发现，重力使粒子更均匀地采样流动，并减少了粒子与底层湍流相互作用的时间。 我们还发现，重力倾向于增加惯性粒子的加速度，并提出一个模型来解释这一效应。 随后，我们分析了粒子的相对速度和径向分布函数（RDF），这些通常在低至中等科莫戈罗夫尺度斯托克斯数$St$时与雷诺数无关。 我们发现，重力导致粒子相对速度降低，且在有重力的情况下，相对速度具有更高的标度指数。 我们观察到，重力对聚类有非平凡的影响，在低$St$时减少聚类，在高$St$时增加聚类。 通过考虑重力对Zaichik & Alipchenkov（New J. Phys., 11:103018, 2009）理论中描述的聚类机制的影响，我们对此非平凡的重力效应提供了解释。 我们还表明，当在Zaichik & Alipchenkov的理论中考虑重力的影响时，结果与DNS相符。 在小分离距离下，相对速度和RDF表现出显著的各向异性，并使用球谐函数对其进行量化。 我们利用相对速度和RDF计算粒子碰撞核，发现碰撞核与无重力情况下的结果相同，即对于低至中等$St$，几乎与雷诺数无关。 显示英文摘要

摘要： In Part I of this study, we analyzed the motion of inertial particles in isotropic turbulence in the absence of gravity using direct numerical simulation (DNS). Here, in Part II, we introduce gravity and study its effect over a wide range of flow Reynolds numbers, Froude numbers, and particle Stokes numbers. We see that gravity causes particles to sample the flow more uniformly and reduces the time particles can spend interacting with the underlying turbulence. We also find that gravity tends to increase inertial particle accelerations, and we introduce a model to explain that effect. We then analyze the particle relative velocities and radial distribution functions (RDFs), which are generally seen to be independent of Reynolds number for low and moderate Kolmogorov-scale Stokes numbers $St$. We see that gravity causes particle relative velocities to decrease, and that the relative velocities have higher scaling exponents with gravity. We observe that gravity has a non-trivial effect on clustering, acting to decrease clustering at low $St$ and to increase clustering at high $St$. By considering the effect of gravity on the clustering mechanisms described in the theory of Zaichik & Alipchenkov (New J. Phys., 11:103018, 2009), we provide an explanation for this non-trivial effect of gravity. We also show that when the effects of gravity are accounted for in the theory of Zaichik & Alipchenkov, the results compare favorably with DNS. The relative velocities and RDFs exhibit considerable anisotropy at small separations, and this anisotropy is quantified using spherical harmonic functions. We use the relative velocities and the RDFs to compute the particle collision kernels, and find that the collision kernel remains as it was for the case without gravity, namely nearly independent of Reynolds number for low and moderate $St$.