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

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. 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.

Keywords:

• Direct numerical simulation
• moist cough flow
• respiratory droplets
• liquid field approximation
• thermodynamics of phase change
• long-range pathogen transmission
• COVID-19

Acknowledgments

The present simulations have been carried out at the Supercomputer Education and Research Centre at the Indian Institute of Science, Bengaluru. SSD acknowledges support from Indian Institute of Science, Bengaluru, towards running the simulations. The authors thank anonymous referees whose suggestions have helped improve the quality of the paper.

Data availability statement

The data that support the findings of this study are available on request from the corresponding author.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

SR is supported through the Swedish Research Council [grant number 638-2013-9243].