AI 中文总结
该研究通过直接数值模拟（DNS），引入碰撞关联时间τ_cc与历史过滤方法，统一了湍流中聚并粒子系统与幽灵粒子系统的统计特性，重现了聚并系统的碰撞核与径向分布函数。
AI 中文摘要
本系列论文的首篇旨在理解湍流中聚并粒子的统计特性及其与无碰撞幽灵粒子的关联。我们在相同流动条件下开展三类直接数值模拟（DNS）：无相互作用的幽灵粒子；碰撞后聚并且单体在随机位置补充的粒子（CR）；具有相同碰撞-聚并动力学但无补充的粒子（CN）。所有分析均为单分散，仅关注单体。在斯托克斯数St=0.01至3.0范围内，幽灵粒子系统的碰撞核（K）及近接触处的径向分布函数（RDF，g(r)）均高于聚并系统。经速度过滤的RDF，即g_G^(-)(r)，可合理估计CR的接触RDF，即g_CR(d)。我们证明，g_G^(-)(d)与g_CR(d)之间、以及对应碰撞核之间的残差差异，源于幽灵粒子系统中连续碰撞间的关联。排除此类关联的经历史过滤的幽灵粒子碰撞核，可重现聚并系统的碰撞核。我们引入碰撞关联时间τ_cc以量化当前碰撞对未来事件的影响时长，发现其在研究的St范围内具有有限且狭窄的取值范围。过滤掉在与τ_cc相当的时间内发生碰撞的粒子，得到的经历史过滤的RDF可重现两类聚并系统的RDF。最后，涉及相同粒子的重复碰撞比例随St呈指数衰减。这些结果将聚并系统与幽灵粒子系统统一为历史过滤框架。
英文摘要
This is the first in a series of papers aimed at understanding the statistics of coalescing particles in turbulent flow and their relation to collisionless ghost particles. We perform three families of Direct Numerical Simulations (DNS) under identical flow conditions: ghost particles without mutual interactions; particles that coalesce upon collision with lost monomers replenished at random positions (CR); and particles with the same collision-coalescence kinetics without replenishment (CN). All analyses are monodisperse and concern only monomers. Across $St=0.01\text{-}3.0$, the ghost-particle system has higher collision kernels ($K$) and radial distribution functions (RDFs, $g(r)$) near contact than the coalescing systems. A velocity-filtered RDF, $g_{\mathrm{G}}^{(-)}(r)$, provides a reasonable estimate of the CR contact RDF, $g_{\mathrm{CR}}(d)$. We show that the residual discrepancy between $g_{\mathrm{G}}^{(-)}(d)$ and $g_{\mathrm{CR}}(d)$, and between the corresponding kernels, arises from correlations among successive collisions in the ghost-particle system. A history-filtered ghost-particle kernel, excluding such correlations, reproduces the coalescing-system kernel. We introduce a collision-correlation time $τ_{\mathrm{cc}}$ that quantifies how long current collisions influence future events and find that it has a finite, narrow range across the studied $St$. Filtering particles with collisions within a period comparable to $τ_{\mathrm{cc}}$ yields a history-filtered RDF that reproduces those of both coalescing systems. Finally, the fraction of repeated collisions involving identical particles decays exponentially with $St$. These results unify the coalescing and ghost-particle systems as a history-filtered framework.
Comments24 pages, 10 figures, 3 supplementary figures
