Turbulence modulation in particle-laden stationary homogeneous isotropic turbulence is investigated using One-Dimensional Turbulence (ODT), a low-dimensional stochastic flow simulation model. For this purpose, ODT is extended in two ways. First, a forcing scheme that maintains statistical stationarity is introduced. Unlike direct numerical simulation (DNS) of forced turbulence, the ODT framework accommodates forcing that is not directly coupled to the momentum equation. For given forcing the ODT energy dissipation rate is therefore the same in particle-laden cases as in the corresponding single-phase reference case. Second, previously implemented one-way-coupled particle phenomenology is extended to two-way coupling using the general ODT methodology for flow modulation through interaction with any specified energy and momentum sources and sinks. As in a DNS comparison case for $R{e}_{\lambda }=70$, turbulence modulation is diagnosed primarily on the basis of the fluid-phase kinetic-energy spectrum. Because ODT involves sub-processes with straightforward physical interpretations, the ODT mechanisms of particle-induced turbulence modulation are clearly identified and they are plausibly relevant to particle-laden Navier-Stokes turbulence. ODT results for the ratio of particle-phase and fluid-phase kinetic energies as a function of particle Stokes number and mass loading are reported for the purpose of testing these predictions in the future when these quantities are evaluated experimentally or using DNS.

中文翻译：

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使用一维湍流在满载粒子的均质各向同性湍流中进行湍流调制

利用一维湍流（ODT）（一种低维随机流动仿真模型）研究了满载颗粒的均质各向同性湍流中的湍流调制。为此，ODT有两种扩展方式。首先，介绍了一种保持统计平稳性的强制方案。与强制湍流的直接数值模拟（DNS）不同，ODT框架可容纳未直接与动量方程耦合的强迫。因此，对于给定的强迫，ODT的能量耗散率在充满粒子的情况下与相应的单相参考情况相同。其次，以前实现的单向耦合粒子现象学通过使用通用ODT方法通过与任何指定的能量，动量源和汇的交互作用进行流量调制，扩展为双向耦合。$\mathrm{[R}{Ë}_{\lambda }=70$湍流调制主要基于液相动能谱进行诊断。因为ODT涉及具有简单物理解释的子过程，所以可以清楚地识别出由粒子引起的湍流调制的ODT机制，并且它们与充满粒子的Navier-Stokes湍流有关。报告了ODT结果，表明相对于颗粒斯托克斯数和质荷的函数，颗粒相和流体相动能之比是为了在将来通过实验或使用DNS评估这些预测时测试这些预测的目的。