Direct numerical simulation of a moist cough flow using Eulerian approximation for liquid droplets

TL;DR

This study introduces a novel Eulerian computational method to simulate moist cough flows, accurately capturing key features and providing new insights into droplet evaporation and flow dynamics relevant for virus transmission.

Contribution

The paper presents a new Eulerian approach for simulating respiratory droplets in cough flows, enabling efficient long-range transmission studies and capturing features previously modeled with Lagrangian methods.

Findings

Droplet inertia is negligible for 10 μm droplets (Stokes number <<1).

Evaporation time for a mild cough is estimated.

A saturation-temperature diagram and vorticity-liquid field correlation are presented.

Abstract

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. Estimates of the Stokes number are provided, for the initial droplet size of $10 \mu$m, which are found to be <<1 thereby justifying the neglect of droplet inertia. Several of the 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 is particularly useful for studying the long-range transmission of virus-laden droplets.