Direct numerical simulation of the turbulent flow generated during a violent expiratory event

Abstract

A main route for SARS-CoV-2 (severe acute respiratory syndrome coronavirus) transmission involves airborne droplets and aerosols generated when a person talks, coughs, or sneezes. The residence time and spatial extent of these virus-laden aerosols are mainly controlled by their size and the ability of the background flow to disperse them. Therefore, a better understanding of the role played by the flow driven by respiratory events is key in estimating the ability of pathogen-laden particles to spread the infection. Here, we numerically investigate the hydrodynamics produced by a violent expiratory event resembling a mild cough. Coughs can be split into an initial jet stage during which air is expelled through mouth and a dissipative phase over which turbulence intensity decays as the puff penetrates the environment. Time-varying exhaled velocity and buoyancy due to temperature differences between the cough and the ambient air affect the overall flow dynamics. The direct numerical simulation (DNS) of an idealized isolated cough is used to characterize the jet/puff dynamics using the trajectory of the leading turbulent vortex ring and extract its topology by fitting an ellipsoid to the exhaled fluid contour. The three-dimensional structure of the simulated cough shows that the assumption of a spheroidal puff front fails to capture the observed ellipsoidal shape. Numerical results suggest that, although analytical models provide reasonable estimates of the distance traveled by the puff, trajectory predictions exhibit larger deviations from the DNS. The fully resolved hydrodynamics presented here can be used to inform new analytical models, leading to improved prediction of cough-induced pathogen-laden aerosol dispersion.

Large eddy simulation of cough jet dynamics, droplet transport, and inhalability over a ten minute exposure

“…We do not describe in detail the turbulent mechanisms during a cough as this is well explained in the recent literature. 16,30,53,54 However, we note that the larger turbulent eddies that influence the particle transport are resolved through the LES approach which is transient. The particles are transported with the eddies with each small time step.…”

“…Vortex structures during the cough are characterized by the well-known vortex ring structures generated at the edge of the jet. 16,53 We note that expiratory events such as a cough are pulsatile; however, this study considered a cough as a single pulse. Figure 8 shows the droplet trajectories for each droplet found in the vortex ring structure at 1 s. The trajectories represent the individual droplet motion colored by velocity.…”

“…Studies applying LES include 12 which used a model containing 38 × 10 6 elements modeled for 10 s of physical time and showed that at a higher room temperature, the cough jet and droplet penetration is shorter; 13 investigated the cough jet development with and without the influence of co-flow air; 14 applied high-fidelity LES on a computational grid that was three orders of magnitude finer than most studies; and 15 modeled cough jet plume development in six ventilation cases and found that a vast majority of droplets remained suspended within the puff after the liquid evaporated. Studies using the DNS approach include 16 which detailed the initial jet stage and a dissipative phase over which turbulence intensity decayed; and 17 showed the effects of indoor ventilation and ambient conditions on the virus-laden droplet lifetime. These studies focused on the cough jet in detail, and the longest simulation time covered 10 s.…”

Estimates of the stochasticity of droplet dispersion by a cough

“…3,9 In subsequent direct numerical simulation (DNS) analyses, the ambient relative humidity was also found to significantly increase the droplet evaporation time, 25–27 especially those with a diameter below 30 μ m. 27 Rosti et al 26 found that turbulence increases the lifetime of the droplets, and an underestimation of 100% in droplet evaporation time was reported when the turbulence effects were filtered out. Although reasonable estimates of the horizontal displacement of the exhaled puff can be obtained from reduced-order models, 28,29 gas-phase only DNS of a cough 30 has shown that a large deviation from the predicted values could arise due to difficulties in predicting jet-to-puff transition effects and puff topology in such models, in addition to turbulence itself as discussed previously. Still, despite the in-depth physical insight obtained from DNS concerning small-scale interactions between liquid and gas phases, its significant computational cost hinders both the evaluation of long events and the quantification of event-to-event variations.…”

On the utility of a well-mixed model for predicting disease transmission on an urban bus

“… Talaat et al (2021) used steady Reynolds-Average Navier–Stokes (RANS) simulations to predict the flow field in the cabin of a Boeing 737 airplane to assess mitigation and safety of air travel. Several recent papers presented detailed analyses of the flow physics of a cough using direct numerical simulation ( Fabregat et al. , 2021 ; Monroe et al.…”