一维惯性颗粒聚集的表征
Characterizing 1D Inertial Particle Clustering
AI总结：
本研究表征一维惯性颗粒聚集，提出测量体积需介于柯尔莫哥洛夫尺度与积分尺度10%之间，并开发修正偏差及区分湍流聚集与随机性的方法。
摘要：
聚集是含有惯性颗粒的湍流中的一个重要现象。尽管这一过程已被广泛研究，但在基础物理以及将不同观测结果统一为颗粒-湍流相互作用这一重要机制的连贯定量视图方面，仍存在未解决的问题。在本工作中，我们研究了将该现象投影到二维和一维（如实验中通常所做）的影响。特别是，探讨了一维投影中测量体积对检测到的聚集特性（如大小或浓度）的影响，以提供一种比较已发表/未来观测（来自实验或数值数据）的方法。结果表明，为了在广泛的实验条件下捕获平均聚集特性的准确值，测量体积需要大于柯尔莫哥洛夫长度尺度，并小于湍流积分长度尺度的大约百分之十。这种依赖性为考虑湍流特性进行优先浓度的一维测量提供了正确的标度。将表征聚集的结果与随机对聚集统计的贡献分开也至关重要，尤其是在一维中，因为Voronoi单元的原始概率密度函数不能提供关于聚集大小或局部浓度的无误差信息。我们提出了一种纠正这种测量偏差的方法，通过从一维中与随机泊松过程概率分布的比较中获得的聚集PDF解析模型，该模型似乎排除了聚集PDF中幂律的存在。我们开发了一种新的测试来区分湍流驱动的聚集与随机性，该测试通过分离每个聚集内的颗粒数量来补充聚集识别算法。
英文摘要：
Clustering is an important phenomenon in turbulent flows laden with inertial particles. Although this process has been studied extensively, there are still open questions about both the fundamental physics and the reconciliation of different observations into a coherent quantitative view of this important mechanism for particle-turbulence interaction. In this work, we study the effect of projecting this phenomenon onto 2D and 1D (as usually done in experiments). In particular, the effect of measurement volume in 1D projections on detected cluster properties, such as size or concentration, is explored to provide a method for comparison of published/future observations, from experimental or numerical data. The results demonstrate that, in order to capture accurate values of the mean cluster properties under a wide range of experimental conditions, the measurement volume needs to be larger than the Kolmogorov length scale, and smaller than about ten percent of the integral length scale of the turbulence. This dependency provides the correct scaling to carry out 1D measurements of preferential concentration, considering the turbulence characteristics. It is also critical to disentangle the cluster-characterizing results from random contributions to the cluster statistics, especially in 1D, as the raw probability density function of Voronoi cells does not provide error-free information on the clusters size or local concentration. We propose a methodology to correct for this measurement bias, with an analytical model of the cluster PDF obtained from comparison with a Random Poisson Process probability distribution in 1D, which appears to discard the existence of power laws in the cluster PDF. We develop a new test to discern between turbulence-driven clustering and randomness, that complements the cluster identification algorithm by segregating the number of particles inside each cluster.
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