Understanding Transmission Dynamics of COVID-19-Type Infections by Direct Numerical Simulations of Cough/Sneeze Flows

Abstract

The transmission dynamics of highly contagious respiratory diseases like COVID-19 (through coughing/sneezing) is an open problem in the epidemiological studies of such diseases (Bourouiba, JAMA. https://doi.org/10.1001/jama.2020.4756. 2020). The problem is basically the fluid dynamics of a transient turbulent jet/puff with buoyancy, laden with evaporating droplets carrying the pathogen. A turbulent flow of this nature does not lend itself to reliable estimates through modeling approaches such as RANS (Reynolds-Averaged Navier-Stokes equations) or other droplet-based models. However, direct numerical simulations (DNS) of what may be called "cough/sneeze flows" can play an important role in understanding the spread of the contagion. The objective of this work is to develop a DNS code for studying cough/sneeze flows by a suitable combination of the DNS codes available with the authors (developed to study cumulus cloud flows including thermodynamics of phase change and the dynamics of small water droplets) and to generate useful data on these flows. Recent results from the cumulus cloud simulations are included to highlight the effect of turbulent entrainment (which is one of the key processes in determining the spread of the expiratory flows) on the distribution of liquid water content in a moist plume. Furthermore, preliminary results on the temperature distribution in a "dry cough" (i.e., without inclusion of liquid droplets) are reported to illustrate the large spatial extent and time duration over which the cough flow can persist after the coughing has stopped. We believe that simulations of this kind can help to devise more accurate guidelines for separation distances between neighbors in a group, design better masks, and minimize the spread of respiratory diseases of the COVID-19 type.

Keywords: COVID-19 infections; Cough/sneeze flow; Direct numerical simulation; Droplet thermodynamics; Transmission dynamics; Turbulent jet/puff.

Fig. 1

The “cough cloud” captured from a human subject by superposing instantaneous images. The left picture shows droplet trajectories and the right picture shows a visualization of the cough cloud. Reprinted with permission from Cambridge University Press (Fig. 3e, f in Bourouiba et al. 2014)

Fig. 2

Comparison of natural clouds (left) with similar computed cumulus clouds (right) (Reprinted from Diwan et al. (2014); © American Meteorological Society. Used with permission)

Fig. 3

a Distribution of liquid water content in a moist plume computed using MEGHA-5 at a certain time instant, t*. b, c Respectively show the distribution of mass flux and entrainment coefficient with height (z) at t*. The mass flux profile is smoothed using the third-order Savitzky–Golay filter

Fig. 4

a Schematic of the computational domain for present simulations with typical dimensions specified. b Variation of flow rate during a typical single-cough event; data extracted from Gupta et al. (2009)

Fig. 5

Temperature distribution in a simulated “dry cough” flow at two time-instants from the start of the simulations. Note that the total duration of the cough is 0.53 s. The section corresponds to y = 0