A multiscale approach for the detailed simulation of water droplets dispersed in a turbulent airflow is presented. The multiscale procedure combines a novel representative volume element (RVE) with the Pseudo Direct Numerical Simulation (P-DNS) method. The solution at the coarse-scale relies on a synthetic model, constructed using precomputed offline RVE simulations and an alternating digital tree, to characterize the non-linear dynamic response at the fine-scale. A set of numerical experiments for a wide range of volume fractions, particle distribution sizes, and external shear forces in the RVE are carried out. Quantitative results of the statistically stationary turbulent state are obtained, and the turbulence modulation phenomenon due to the presence of droplets is discussed. The developed synthetic model is then employed to solve global scale simulations of flows with airborne droplets via the P-DNS method. Improved predictions are obtained for flow conditions where turbulence modulation is noticeable.

提出了一种用于详细模拟分散在湍流中的水滴的多尺度方法。多尺度过程结合了一种新颖的代表性体积元素 (RVE) 与伪直接数值模拟 (P-DNS) 方法。粗尺度的解决方案依赖于使用预先计算的离线 RVE 模拟和交替数字树构建的合成模型，以表征细尺度的非线性动态响应。对 RVE 中的各种体积分数、颗粒分布尺寸和外部剪切力进行了一组数值实验。获得了统计静止湍流状态的定量结果，并讨论了由于液滴存在引起的湍流调制现象。然后使用开发的合成模型通过 P-DNS 方法求解带有空气中液滴的流动的全球规模模拟。对于湍流调制明显的流动条件，获得了改进的预测。