Fluid mechanics of air recycling and filtration for indoor airborne transmission

Abstract

We present a statistical framework to account for the effects of recycling and filtration in ventilation systems for the estimation of airborne droplet nuclei concentration in indoor spaces. We demonstrate the framework in a canonical room with a four-way cassette air-conditioning system.The flow field within the room is computed using large eddy simulations (LES) for varying values of air changes per hour (ACH), and statistical overloading is used for droplet nuclei, which are tracked with a Langevin model accounting for subgrid turbulence.A key element is to break up the path that a virus-laden droplet nucleus can take from the time it is ejected by the sick individual to the time it reaches the potential host into four separate elementary processes.This approach makes it possible to provide turbulence-informed and statistically-relevant pathogen concentrations at any location in the room from a source that can be located anywhere else in the room.Furthermore, the approach can handle any type of filtration and provides a correction function to be used in conjunction with the well-mixed model.The easy-to-implement correction function accounts for the separation distance between the sick and the susceptible individuals, an important feature that is inherently absent in the well-mixed model.The analysis shows that using proper filtration can increase the cumulative exposure time in typical classroom settings by up to four times and could allow visitations to nursing homes for up to 45 minutes.

Existence of a Nonzero Worst-Case ACH for Short-Term Exposure in Ventilated Indoor Spaces

“…However, this scenario is not realistic as most air conditioning systems recycle the air and do not perfectly filter the recycled air. In order to analyze the effect of filtration and recycling, we use the statistical framework that takes into consideration the effect of filtration [27]. The filtration efficiency of the air conditioning unit, η ef , is defined as the fraction of particles that do not get recycled…”

“…Improvement to the Well-Mixed Model. As shown in [26,27], the theory can provide really accurate predictions of the nucleus concentration at the room scale. However, the accuracy of the theory falls considerably when we consider the separation distance between the source and the sink.…”

“…The well-mixed assumption is rooted in the important fact that the flow within indoor spaces is turbulent and the turbulence promotes mixing of the airborne nuclei resulting in a wellmixed indoor environment. We leverage the statistical framework posited by Salinas et al [26] and Krishnaprasad et al [27] as the basis for this paper. The results presented here use their turbulence-informed statistical framework, developed entirely using computational methods, to act as an improvement on the well-mixed models.…”

“…Well-Mixed Model. The analysis in the statistical model [26,27] is based on the well-mixed model developed by Bazant and Bush [6]. According to the well-mixed model, the entry of an infected person into a room increases the room-averaged nucleus concentration steadily and eventually, and a steady state is reached where the rate of emission by the infected person is balanced by the rate at which the nuclei exit the room.…”

“…We would like to emphasize that the objectives and conclusions of our study are strictly limited to scenarios involving short occupancy times. Our findings are based on examining 25 million combinations of possible locations between a sick and a susceptible person in a canonical room of square plan form of size L × L × 0 32L [26,27]. This has been achieved in the context of high-fidelity large eddy simulations (LES), using a novel statistical overloading technique which has been presented in Methods.…”