Direct Numerical Simulation of a Moist Cough Flow using Eulerian Approximation for Liquid Droplets

The COVID-19 pandemic has inspired several studies on the fluid dynamics of respiratory events. Here, we propose a computational approach in which respiratory droplets are coarse-grained into an Eulerian liquid field advected by the fluid streamlines. A direct numerical simulation is carried out for a moist cough using a closure model for space-time dependence of the evaporation time scale. Stokes-number estimates are provided, for the initial droplet size of 10 μm, which are found to be ≪1, thereby justifying the neglect of droplet inertia, over the duration of the simulation. Several important features of the moist-cough flow reported in the literature using Lagrangian tracking methods have been accurately captured using our scheme. Some new results are presented, including the evaporation time for a ‘mild’ cough, a saturation-temperature diagram and a favourable correlation between the vorticity and liquid fields. The present approach can be extended for studying the long-range transmission of virus-laden droplets.

新型冠状病毒肺炎（COVID-19）疫情催生了多项针对呼吸事件流体动力学的研究。本研究提出一种计算方法，将呼吸液滴粗粒化为由流体流线平流输运的欧拉（Eulerian）液相场。针对湿性咳嗽开展直接数值模拟，采用适配蒸发时间尺度时空依赖性的闭合模型。针对初始粒径为10 μm的液滴，本研究给出了斯托克斯数（Stokes number）的估算值，其结果远小于1，从而证明在模拟全程可忽略液滴惯性。过往文献中采用拉格朗日追踪法报道的湿性咳嗽流场多项关键特征，均可通过本研究方案得到精准复现。本研究还呈现多项全新结果，包括“轻度”咳嗽的蒸发时长、饱和温度分布图，以及涡量场与液相场间的显著相关关系。本研究方案可进一步拓展，用于研究载有病毒的液滴的远距离传播过程。