Abstract The modulation of turbulence by sub-Kolmogorov particles has been thoroughly characterized in the literature, showing either enhancement or reduction of kinetic energy at small or large scale depending on the Stokes number and the mass loading. However, the impact of a third parameter, the number density of particles, has not been independently investigated. In the present work, we perform direct numerical simulations of decaying Homogeneous Isotropic Turbulence loaded with monodisperse sub-Kolmogorov particles, varying independently the Stokes number, the mass loading and the number density of particles. Like previous investigators, crossover and modulations of the fluid energy spectra are observed consistently with the change in Stokes number and mass loading. Additionally, DNS results show a clear impact of the particle number density, promoting the energy at small scales while reducing the energy at large scales. For high particle number density, the turbulence statistics and spectra become insensitive to the increase of this parameter, presenting a two-way asymptotic behavior. Our investigation identifies the energy transfer mechanisms, and highlights the differences between the influence of a highly concentrated disperse phase (high particle number density, limit behavior) and that of heterogeneous concentration fields (low particle number density). In particular, a measure of this heterogeneity is proposed and discussed which allows to identify specific regimes in the evolution of turbulence statistics and spectra.

中文翻译：

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亚柯尔莫哥洛夫粒子对均匀和各向同性湍流的调制：粒子场异质性的影响

摘要 亚柯尔莫哥洛夫粒子对湍流的调制已在文献中得到彻底表征，显示出根据斯托克斯数和质量载荷在小尺度或大尺度上增强或减少动能。然而，尚未独立研究第三个参数，即粒子数密度的影响。在目前的工作中，我们对加载有单分散亚柯尔莫哥洛夫粒子的衰减均匀各向同性湍流进行直接数值模拟，独立地改变斯托克斯数、质量载荷和粒子数密度。像以前的研究人员一样，随着斯托克斯数和质量载荷的变化，观察到流体能谱的交叉和调制。此外，DNS 结果显示粒子数密度的明显影响，促进小尺度的能量，同时减少大尺度的能量。对于高粒子数密度，湍流统计和光谱对该参数的增加变得不敏感，呈现出双向渐近行为。我们的研究确定了能量转移机制，并强调了高浓度分散相（高粒子数密度、极限行为）和异质浓度场（低粒子数密度）的影响之间的差异。特别是，提出并讨论了这种异质性的度量，它允许识别湍流统计和光谱演变中的特定机制。湍流统计和光谱对该参数的增加变得不敏感，呈现出双向渐近行为。我们的研究确定了能量转移机制，并强调了高浓度分散相（高粒子数密度、极限行为）和异质浓度场（低粒子数密度）的影响之间的差异。特别是，提出并讨论了这种异质性的度量，它允许识别湍流统计和光谱演变中的特定机制。湍流统计和光谱对该参数的增加变得不敏感，呈现出双向渐近行为。我们的研究确定了能量转移机制，并强调了高浓度分散相（高粒子数密度、极限行为）和异质浓度场（低粒子数密度）的影响之间的差异。特别是，提出并讨论了这种异质性的度量，它允许识别湍流统计和光谱演变中的特定机制。极限行为）和异质浓度场（低粒子数密度）。特别是，提出并讨论了这种异质性的度量，它允许识别湍流统计和光谱演变中的特定机制。极限行为）和异质浓度场（低粒子数密度）。特别是，提出并讨论了这种异质性的度量，它允许识别湍流统计和光谱演变中的特定机制。