Modeling the effect of temperature and relative humidity on exposure to SARS‐CoV‐2 in a mechanically ventilated room

Abstract Computational fluid dynamics models have been developed to predict airborne exposure to the SARS‐CoV‐2 virus from a coughing person in a mechanically ventilated room. The models were run with three typical indoor air temperatures and relative humidities (RH). Quantile regression was used to indicate whether these have a statistically significant effect on the airborne exposure. Results suggest that evaporation is an important effect. Evaporation leads to respiratory particles, particularly those with initial diameters between 20 and 100 μm, remaining airborne for longer, traveling extended distances and carrying more viruses than expected from their final diameter. In a mechanically ventilated room, with all of the associated complex air movement and turbulence, increasing the RH may result in reduced airborne exposure. However, this effect may be so small that other factors, such as a small change in proximity to the infected person, could rapidly counter the effect. The effect of temperature on the exposure was more complex, with both positive and negative correlations. Therefore, within the range of conditions studied here, there is no clear guidance on how the temperature should be controlled to reduce exposure. The results highlight the importance of ventilation, face coverings and maintaining social distancing for reducing exposure.

tically significant effect on the airborne exposure. Results suggest that evaporation is an important effect. Evaporation leads to respiratory particles, particularly those with initial diameters between 20 and 100 μm, remaining airborne for longer, traveling extended distances and carrying more viruses than expected from their final diameter.
In a mechanically ventilated room, with all of the associated complex air movement and turbulence, increasing the RH may result in reduced airborne exposure. However, this effect may be so small that other factors, such as a small change in proximity to the infected person, could rapidly counter the effect. The effect of temperature on the exposure was more complex, with both positive and negative correlations.
Therefore, within the range of conditions studied here, there is no clear guidance on how the temperature should be controlled to reduce exposure. The results highlight the importance of ventilation, face coverings and maintaining social distancing for reducing exposure.

K E Y W O R D S
aerosol, computational fluid dynamics, cough, COVID-19, exhalation, exposure

| INTRODUC TI ON
For COVID-19 and other respiratory diseases, indoor spaces may present a high-hazard environment when infection can be transmitted by exhaled, virus carrying, aerosol and droplets. Smaller aerosol particles present an ongoing hazard, as they can remain airborne for long periods of time. Larger aerosols and droplets can evaporate to smaller sizes and subsequently remain airborne, be inhaled directly, deposit onto mucous membranes, or onto exposed surfaces. Early in the COVID-19 pandemic, advice was being given to maintain social distancing and manage fomite (contaminated surface) risks through good hand hygiene. As knowledge of transmission developed, advice to ventilate spaces while avoiding air recirculation and to wear face coverings was an increasing focus. Advice on ventilation aimed to address the aerosol hazard, social distancing primarily the large droplet hazards, and face coverings the transmission risk from both. However, the behavior of aerosols and droplets released during exhalations is complex and more recent evidence shows that small aerosols are also important for close-range exposure. 1 Understanding this complexity, including the role of evaporation of respiratory aerosols and droplets under different indoor environmental conditions is important for explaining transmission mechanisms and providing effective public health advice.
The evaporation rate of aerosols and droplets is primarily dependent on the water content and chemical composition of the droplet (and subsequently the vapor pressure), the local temperature and relative humidity (RH) and other factors, such as the molecular diffusion coefficient of the vapor. A number of studies, discussed below, have looked at droplet evaporation and transport and the general conclusion is that lower temperature and/or higher relative humidity leads to a slower rate of evaporation and therefore larger droplets at a given time. These larger droplets will stay suspended in the air for less time and therefore present less of an airborne hazard.
The classic Wells evaporating-falling droplet curve 2 shows that falling droplets smaller than a critical diameter (around 100 -140 μm) will evaporate completely before they reach the ground. Wells hypothesized that this created "droplet nuclei", which were aerosols <5 μm diameter that could carry microorganisms in the air for long periods of time. Droplets larger than the critical diameter will reach the ground before they can evaporate significantly and do so increasingly rapidly with increasing initial diameter. Wells' work was revisited by Xie et al., 3  They found that there were three critical diameters. For droplets ≤40 μm diameter, an increase in RH resulted in the droplet moving further horizontally before evaporating; for droplets with diameters around 60 μm, this effect was reversed (i.e., an increase in RH resulted in droplets traveling less far before evaporation); and for droplets ≥80 μm there was almost no effect from a change in the RH. Neither Wells' nor Xie et al.'s droplets contained solids, so could evaporate completely, unlike real respiratory droplets.
Wang et al. 4 also considered evaporating droplets in an exhaled jet but did not consider the temperature difference between the ambient air and exhaled air or the radial velocity component. They did, however, reach the broadly supported conclusion (Xie et al. 3 ) that high RH results in slower evaporation and larger droplets deposit more quickly, which in turn reduces the airborne hazard. A more recent study of the evaporation of single droplets by Chen 5 showed that while for a stationary droplet, an increase in RH always results in an increase in droplet lifetime (note that this is for a stationary droplet, not a falling droplet), an increase in temperature does not always have the opposite effect. They reported that increased temperature only decreased the lifetime when the RH was below a critical threshold (37% in their case, where they consider 20 and 37°C).
A number of studies have used computational fluid dynamics (CFD) to examine the effect of temperature and RH on exhaled droplets. Li et al. 6 used a Reynolds averaged Navier-Stokes (RANS) approach to model water droplets with non-volatile cores in an unventilated room; their simulation ran for 30 s. They concluded that increased droplet evaporation could lead to the increased probability of infection. For the conditions, they considered (RH from 10% to 90% and temperature from 3 to 35°C; these upper and lower limits are outside comfortable indoor ranges), a change in RH was more important than a change in temperature when it came to evaporation (evaporation time or time to hit the floor).
Li et al. 7 also used a RANS approach in an outdoor environment and droplets where the vapor pressure was reduced as a result of the presence of salts. They concluded that for smaller droplets ( • Setting the humidity in a mechanically ventilated room to a high, but comfortable, level (50%-70% RH) may slightly reduce the inhaled dose.
• Ventilation should not be compromised to achieve higher RH and consideration should be given to the increase in the probability of fomite transmission.
• For the range of conditions studied here, there is no clear evidence that the temperature should be controlled in a normal indoor environment to reduce exposure, therefore, it can be set to a comfortable level. allows more realistic features to be included for example, complex ventilation airflow.
Yang et al. 8 modeled dispersion of exhaled droplets having nonvolatile cores within an air-conditioned bus, using RANS CFD. They showed that for 50 μm diameter droplets, increasing the RH from 35% to 95% (a very high RH for an air-conditioned space) resulted in the evaporation time (to the solid core) increasing from 1.8 to 7.0 s. However, the effect of RH on dispersion distance was not significant.
High-resolution CFD modeling of exhaled droplets has also been published. Chong et al. 9 carried out direct numerical simulation (DNS) of exhaled pure water droplets in a quiescent environment with a temperature of 20°C and RH between 50% and 90% (also a very high RH for an air-conditioned space). They reported an increase in droplet lifetimes (i.e., time to full evaporation) with an increase in RH.
Interestingly, they also reported that the exhaled puff could be sustained for longer distances when the ambient RH was higher.
There is also some empirical evidence to support the effect of RH on both airborne and surface deposited concentration. Parhizkar et al. 10 carried out experiments with subjects, who had been diagnosed with COVID-19, carrying out a range of activities in an exposure chamber. They reported that lower RH (over the range of 20%-70%) resulted in higher airborne and lower surface viral concentrations (as measured using polymerase chain reaction). However, their airborne concentration data does appear to be quite skewed by many high C T (cycle threshold) data (i.e., low viral concentration values).
In the current work reported here, a RANS CFD-based stochastic droplet transport model has been produced for a coughing person in a typical mechanically ventilated meeting room or office space.
Coughing was chosen over other types of exhalation as it is a particularly common symptom of COVID-19. However, it is recognized that speaking for an extended period of time might produce a larger volume of exhaled droplets than a single or even multiple coughs.
This work aims to show whether the temperature or RH effects reported for simpler models (analytical or more simplified CFD models) are still present when realistic room airflows are included and exposures are calculated over 5 min time-scales. The study is primarily focused on the fluid dynamics effects of a change in temperature and RH. It has already been demonstrated that temperature and RH can affect both the survival of airborne and surface-deposited viruses 11 and affect the physiology of both the infected and susceptible people, but these factors are not being considered here. By studying the fluid dynamics effects in isolation, the aim is to be able to show whether these need to be taken into account when choosing optimum parameters from a viral decay or physiological perspective.
The work builds on our CFD modeling in Coldrick et al., 12 where we validated the CFD methodology for exhaled droplet transport and deposition using experimental data for bacteria collected from speaking, singing and coughing human subjects in an exposure chamber. A statistical assessment of CFD model results has been used to see whether temperature and/or RH have a significant effect on the likely viral exposure. The statistical presentation of the results, that is, the possible range of the received exposures and the statistical significance of any correlations, make this work different from most previous work. Reporting the results in terms of viral exposure rather than droplet number or mass (as has been done in much of the previous work), enables overall risk to be estimated.

| The room and scenarios
The effect of temperature and RH on exposure to the SARS-CoV-2 virus was studied in a representative mechanically ventilated meeting room/office space, based on a room studied in Foat et al. 13 The room, chosen as a generic example, was 13.0 long, 7.0 wide and 2.6 m high with a small cut-out in one corner. The room volume was approximately 237 m 3 and had mixing ventilation. The air was supplied through eight diffusers and extracted through four, which were all located on the ceiling. All ceiling diffusers were square, fourway diffusers (the effective air discharge area of each diffuser was 0.0446 m 2 ). It was assumed that the air change rate was 5 h −1 and that there was no recirculation. The room contained no furniture. A single coughing person was standing in the room, 3 m from one wall, and was facing along the long axis of the room, towards the centre of the room (see Figure 1).

F I G U R E 1
The coughing person standing in the meeting room. The extract vents are shown in red. Pathlines from the eight supply vents are shown, colored by velocity (m·s −1 ).
Nine models were run with all combinations of three temperatures and three relative humidities. The temperatures, 16, 20 and 28°C, were chosen to represent: the minimal permissible temperature, 14 a typical temperature for an air-conditioned room and an upper limit 15 respectively. The relative humidities: 30%, 50% and 70%, were chosen to represent likely ranges in mechanically ventilated offices. 30% is often given as a lower comfortable limit and 30%, 50% and 70% were used by Xie et al. 3

| The model
The CFD model used an unsteady RANS approach, with a two-way coupled Lagrangian phase for the exhaled droplets. This approach has been applied many times previously for similar studies. [6][7][8]16,17 Other studies have used large-eddy simulation 18 (LES) and even DNS 9 . While LES and DNS may be able to better resolve the details of the exhaled plume, it was not practical to use these highresolution approaches for the scenarios considered here, that is, whole room scale for 5 min.
The shear-stress transport (SST) turbulence model 19 was used, as it has been widely applied to indoor airflows and was used by Coldrick et al. 12 A coupled solver was used for the pressure-velocity coupling, second-order schemes were used for all the convection terms and a second-order implicit scheme was used for the temporal discretization. Buoyancy effects was modeled by solving the energy equation along with the incompressible ideal gas assumption. Only convective heat transfer was included. The simulations were carried out using ANSYS® Fluent® version 2019 R2.

| Modeling the droplets
The exhaled droplets were modeled as water droplets with a nonvolatile fraction, so their evaporation rate was based on the vapor pressure of pure water, and their size was reduced until only the solid non-volatile core remains. This is a simplification from real exhaled droplets, which consist of a complex mixture of salts, proteins and surfactants. 20 It has already been demonstrated that water droplets can evaporate more rapidly than saliva or saline droplets 21 and can follow different trajectories as a result. The vapor pressure of saliva droplets is lower than that of pure water and will decrease as the concentration of the salts in the droplet increases. 21 The nonvolatile mass fraction was set to 1.25%, based on the exhaled particle composition given by Stettler et al., 21 which is also close to that in Walker et al. 21 (2.1%). The results will be strongly dependent on the non-volatile mass fraction, with a lower mass fraction enabling droplets to evaporate further, so allowing larger initial diameter droplets, containing more virus, to stay airborne.
This simplification was made to reduce computing overhead with the rationale that all but the largest droplets evaporate to their equilibrium state quickly, whether they are water or saliva. Walker et al. 21 showed that the largest saliva droplets they considered, 200 μm diameter, reached their equilibrium in 60 s when exhaled into 20°C and 50% RH air and 100 μm droplets took less than 20 s. As the larger droplets sediment to the floor quickly (Xie et al. 3 showed that droplet with diameters ≥100 μm hit the ground in less than approximately 16 s), it was decided that this was a reasonable simplification to make.
The droplet transport and the mass and heat exchange between the droplets and the bulk phase was modeled as described by Coldrick et al., 12 with the exception that the work presented here treated the droplets as being composed of water with a non-volatile core, whereas Coldrick et al. treated them as a multi-component mixture. The particle force balance included the drag force and gravity only, with the drag force being determined from the mean and turbulent flow. The droplet transport used a discrete random walk (DRW) model. It is known that the DRW walk model, particularly when combined with an isotropic turbulence model (such as SST), can give poor predictions for deposition rates for certain scenarios and particles sizes 23 (specifically smaller particles). However, as the deposition of the virus will be dominated by sedimentation of the larger droplets, this was not expected to be an issue.
The secondary break-up was not considered due to the low Weber number of the droplets 24 (maximum of 1.5). The effects of Brownian motion were also not included. This is because it has been suggested 25 that the effect is only significant for particles with diameters ≤0.03 μm, which is smaller than the particles considered in the current study. The smallest droplet modeled in this work had an initial diameter of 0.25 μm and a final diameter, after evaporation, of 0.06 μm. The decay in the viability of the virus in droplets was not considered as part of this work.

| The computational geometry and mesh
The room and air supply and extract vents are described in Sections 2.1 and 2.2.3. The coughing person was represented by a simplified geometry, which was based on anthropometric data for a female. 26 They were 1.63 m tall, with their mouth centred on 1.43 m high. The mouth was represented by a circle with a diameter of 2.25 cm, based on the mouth opening area given by Gupta et al. 27 The geometry was meshed using unstructured tetrahedral cells in a region containing the person's head and upper body, with hexcore in the rest of the room, see Figure 2. The mesh was refined around the mouth and the exhaled jet and around the supply and extract vents. A mesh sensitivity study was conducted and the results of this are given in Section 2.6. The total cell count was 3.2 million, and the average y + (the non-dimensional near-wall cell distance) on the body surface was between 4.1 and 4.4 depending on the temperature and RH.

| Boundary conditions
The supply vents were defined as mass-flow inlets with the air entering the room at 30° to the horizontal, with 5% turbulent intensity and a length scale of 0.01 m. The temperature and RH of the incoming were set to match the conditions for the specific simulation. The extract vents were set as pressure outlets.
It was assumed that the person was fully clothed, so only their convective heat flux was modeled. This was applied as a surface heat flux of 25 W m −2 . This value is similar to that measured by Zhu et al. 28 for a resting subject and was used in Coldrick et al. 12 The heat flux was assumed to be the same for all the temperature and RH conditions. All walls, the floor and the ceiling were given adia- The mouth was a velocity inlet with a time-varying velocity profile and droplet source term as defined in the following section. The temperature and RH of the exhaled air were also specified at the mouth, see Table 1.

| The exhalation
Each simulation consisted of five coughs, with each cough followed by 5 min of mixing. The particles from each cough were deleted at the end of the mixing period. This was done to enable the average effect of the five coughs to be calculated. A simulation was run to see whether the 5 min mixing period was sufficient to capture the bulk of the exposure for a person standing close to the infected person. This work is described in more detail in the Supplementary information S1. In summary, the exposures within 3 m in front of the infected person rise rapidly in the first minute and then continue to increase more slowly out to 5 min and beyond. Therefore, the results presented here do not show the full exposure that a person might receive if they were to stay in the room for 30 min.
Only the exhalation part of the cough was modeled, which was approximated as a triangular velocity profile having a duration of 0.4 s and a peak velocity of 15 m·s −1 at 0.08 s, based on Gupta et al. 27 The carrier flow velocity was specified over the mouth as defined by Gupta et al. 27 and as shown in Figure 3. The turbulence intensity and length scale were set to 10% and 0.01 m respectively. The flow properties for the cough are shown in Table 1. During the mixing period after each cough, there was no air movement from the mouth (i.e., no breathing).
As in Coldrick et al., 12 the bronchiolar, laryngeal and oral (BLO) model 29 was used to describe the distribution of exhaled droplets.
The BLO model describes the droplet size distribution for using a trimodal distribution fitted to experimental measurements of particles from coughing. The parameters for BLO droplet size distribution are given in Table 2.
The exhaled droplets were distributed across random locations over the mouth and at a random time point during the exhalation F I G U R E 2 Mesh on a vertical plane through the centre of the mouth. F I G U R E 3 Initial jet expansion angles for the cough, viewed from the front and side. 27 as described in Coldrick et al. 12 The number of droplets emitted during each time step was determined by the fraction of the total volume exhaled during that time interval. Over the duration of the exhalation, the sampled distribution approached the specified BLO distribution.

TA B L E 1 Flow properties for the cough exhalation
In Lagrangian particle tracking, each computational particle can represent a parcel of droplets. This is usually done to reduce the total number of particles that need to be simulated. However, for the BLO coughing model, only 310 droplets were exhaled per cough.
As this was not likely to provide a statistically significant number of droplets, ten times as many droplets were tracked per cough (3093 in total), with each droplet carrying one-tenth the viral RNA copies.

| Simulation strategy
The flow in the room was first solved as steady-state, then the model was run using an unsteady solver for 290 s with Δt = 1 and 10 s with To capture the dynamics of the cough and the initial droplet transport, the model was then run for 10 s with Δt = 0.01 s. The time step size was then reduced to 1 s from the remainder of the simulation. The sensitivity of the results to a change in Δt was assessed, and the findings are discussed in Section 2.6.  (1). 31 The number of droplets represented by each tracked parcel (one-tenth in this case) was also taken into account.

|
The SARS-CoV-2 viral load value used in this study was 2.76 × 10 9 cop-ies·ml −3 (2.76 × 10 15 copies·m −3 ). This figure represents an average of peak viral loads over time. 32 Details of how this figure was produced are given in the Supplementary Information S1. For this viral load, a droplet with an initial diameter of 8.8 μm will have an expected mean number of viral RNA copies equal to one and it will be increasingly likely that smaller droplets will contain no RNA as d 0 reduces.
This study has focused on the exposure to SARS-CoV-2 virus, but the relative effects predicted may be applied in principle to any respiratory virus with a viral load that is constant across the range of droplet sizes.
Exposures were calculated within sub-volumes (as a postprocessing step) using Equation (2).
where N is the number of droplets passing through the sub-volume, t (s) is the time each particle spends in the sub-volume and V (m 3 ) is the volume of the sub-volume. Published CFD studies use both the exposure-based approach applied here 33,34 and an explicit representation of a breathing

| Validation and model sensitivities
A number of tests were conducted to ensure that the simulations were conducted in a way that reduced the likelihood of producing an inaccurate or misleading solution. All tests used the distributions of exposure (e.g., see Figure 10) as the variable of interest.
For the mesh sensitivity study, the mesh was coarsened by in-  In addition to the validation outlined above, predictions for the dispersion of a tracer gas in the meeting room being studied here (see Section 2.1) were compared to data from an experiment described in Foat et al. 13 The model was run with the same settings as described at the start of Section 2.

| Flow fields
The airflow into the room is illustrated in Figure 1. This effect is apparent in the droplet/particle tracks for two of the high-temperature cases (RH = 30% and 50%), but it is not clear whether this is due to the droplets evaporating more rapidly in these cases or simply due to the random nature of the flow and particle tracks in the room.
Due to the unsteadiness in the room airflow, the droplet/particle tracks from two coughs for the same temperature and RH conditions can look very different. Some exhaled droplets mix almost symmetrically across the room, while droplets/particles from another cough  It should be noted that all size bins did not contain the same number of droplets (see Supplementary Information S1 for the specific size bin diameters). Once a droplet has evaporated fully, the diameter of the resulting solid particle, d final , is 0.23 times d 0 . Xie et al. 3 showed that at 50% RH, 80 μm droplets evaporate completely (they did not contain any non-volatile components) in approximately 20 s and 50 μm droplets take 7.5 s. Figure 6 shows that droplets/particles with an initial diameter of ≥132 μm on average only travel between approximately 0.5 and 1.2 m from the infected person, and a reasonable proportion of this distance will be spent at a height below the breathing zone of a standing person. It is therefore likely to be relatively rare that these

| Exposure
This section shows exposure to viral RNA calculated according to is affected by temperature and RH. Following this, the distribution of exposures within three 1 m 3 volumes at increasing distances from the infected person (see Figure 9) under the different temperatures and RHs are shown. The data has then been analyzed using quantile regression to determine whether any changes due to distance from the person, temperature or RH are statistically significant.

| Contours
The contour plots in Figure 7 and  Therefore, for this mechanically ventilated room, mid-size droplets/ particles carrying large numbers of viruses have been shown to create a hazard region, which extends beyond the typical 2 m social distance spacing due to the airflows within the room.

F I G U R E 6
Distance traveled (before hitting the floor, walls or ceiling of the room) vs initial diameter, d 0 , plots for all temperature and RH conditions. The error bars show ± one standard deviation.
If it was practical to average data across more coughs, it is expected that the exposure contours would remain approximately the same shape, but the contour patterns would be smoother than illustrated in Figure 7.   A series of regression models were used to determine whether there were statistically significant differences between the variables of interest, including any possible interactions. Due to the nature of the data distributions, the RNA exposure was first transformed on a natural log scale. However, no sensible transformation of these data enabled a suitable linear regression model to be fitted. As a result, quantile regression models were fitted to the log RNA exposure.
All analysis was carried out in R Studio (V1.2.1335). Quantile regression models were created using the rq function from the quantreg package on the median log RNA exposure.

F I G U R E 7
Contour plots of viral RNA exposure on a horizontal plane at 1.4 m; for three size bins; d 0 < 20 μm (left), 20-100 μm (middle), >100 μm (right); at T = 28°C and RH = 30%. The 'X' indicates the location of the coughing person. 1 RNA copy·s·m −3 was added to all the data to allow it to be plotted on a logarithmic scale.

F I G U R E 8
Contour plots of viral RNA exposure on a horizontal plane at 1.4 m, for all temperature (shown in the side gray bars in °C) and RH (shown in the top gray as a percentage) conditions. Three particle bins are shown: d 0 ≤ 20 μm (upper), 20 μm < d 0 ≤ 100 μm (lower left), d 0 > 100 μm (lower right). The 'X' indicates the location of the coughing person. The exposure scale is different for the d 0 ≤ 20 μm image. 1 RNA copy·s·m −3 was added to all the data to allow it to be plotted on a logarithmic scale.
Analysis was initially carried out using the combined data from all three analysis volumes. However, a number of statistically significant interactions were found in the model selection process, highlighting the interdependency between temperature and RH, which was also found to vary between volumes. Additional quantile regression models were therefore formulated for each of the volume subsets, to better understand the interactions (see Supplementary Information S1 for the results of the chosen quantile regression models).

F I G U R E 9
Layout of the three analysis volumes, with the sub-volume shown for the middle volume. The infected person is shown to the left of the image with the angle of the exhaled jet indicated by thick dashed lines.
F I G U R E 1 0 Box and whisker plots for exposure showing results for each simulation. Data is show for three breathing height analysis volumes at increasing distance from the person.
To highlight the effects of distance from the infected person, RH and temperature, data for these three variables is shown in Figures 11-13. These figures show violin plots overlaid on box and whisker plots. The violins have been used as they show the shape of the exposure distributions; they show the relative probability of a particular exposure being recorded in a sub-volume. In Figure 11 the data from all nine simulations have been combined in each analysis volume. In Figure 12, the data for all temperatures are combined to show the effect of RH and in Figure 13 the data from all RHs are combined to show the effect of temperature. The median and interquartile range values for these figures are given in the Supplementary Information S1.
Overall, a statistically significant decrease in exposure is found as the distance from the infected person is increased from 0-1 to 2-3 m (but not from 0-1 to 1-2 m) and as the RH is increased.
A statistically significant increase is observed as the temperature is increased from 16 to 28°C, but not from 16 to 20°C. However, when exploring interactions between covariates, it is clearly evident that the direction of change and magnitude of log RNA exposure is dependent upon the volume, temperature and RH (see Figure 10).
This highlights the need to further explore the effect of temperature and RH by volume.
The overall difference by volume is illustrated in Figure 11 There is a change in the shape of the distributions from the 0-1 m volume to the 1-2 m volume. So, even though the change in the median exposure is small, someone in the first volume is more likely to receive a high exposure (e.g., greater than 10 5 copies·s·m −3 ) than they are in the second volume.
This shows that, for two people standing face-to-face, 1 m social distancing would not have that much effect on the median exposure in absolute terms. The social distancing of 2 m or more would dramatically reduce the chance of receiving a high exposure from a coughing person. However, due to the unsteady airflow in the room and the stochastic nature of the particle transport, there are still potentially some locations within the 2-3 m volume where exposures are almost as high as the highest exposure in the nearer volumes (as also indicated in Figure 7). Out of all nine simulations, less than 0.1% of locations (3/(9 × 512)) in the 2-3 m volume had greater than 10% of the average highest exposure recorded in the 0-1 m volume, that is, greater than 2.2 × 10 5 copies·s·m −3 .
As stated earlier, people standing very close to the infected person could receive much higher exposures than indicated by the data shown here. This is because the exposure reported is a function of the sub-volume size when the droplets or particles are not uniformly distributed within the sub-volumes.
The overall difference by RH is illustrated in Figure 12. In the 0-1 m analysis, volume the median exposure reduced from 3095 to 2647 copies·s·m −3 as the RH increased from 30% to 70%. Similarly, in the 1-2 m analysis volume, the reduction in the median exposure was 4179-2488 copies·s·m −3 , for the same increase in RH.
In addition, in the 1-2 m analysis volume, RH was considered an important factor to control for in the model and the reduction in log RNA exposure from 30% to both 50% and 70% RH was statistically significant. However, in the 2-3 m analysis volume, there was minimal absolute change in the median exposure although the change from 30% to 70% RH (16-12 copies·s·m −3 ) was statistically significant.

F I G U R E 11
Violin plots (with added box and whisker) for exposure showing the effect of distance from the infected person. Data is shown for the three breathing height analysis volumes at increasing distance from the person.
The changes in median exposure due to RH in the 0-1 and 1-2 m volumes are larger than the reduction in exposure when moving from the 0 to 1 m volume to the 1-2 m volume. However, the reduction in exposure when moving from the 1-2 and 2-3 m volumes is much greater than any changes due to RH.
The overall difference according to temperature is shown in Figure 13. Although a statistically significant increase is observed as the temperature increases from 16 to 28°C overall, the magnitude and direction of this change vary between volumes. For example, in the 0-1 and 1-2 m volumes, the increase to 28°C is statistically significant. However, for the 2-3 m analysis volume data, compared to a temperature of 16°C, there was actually a statistically significant decrease in exposure at both 20 and 28°C.
It is not clear whether the large increase in the median exposure in the 0-1 m volume, as temperature increases, is a true reflection of the size of the temperature-driven effect. Figure 10 shows that the median exposures are low (less than 100 cop-

| General discussion
The results from our CFD modeling support the finding of most rele- Only coughing has been considered in the current models and the direction of the cough (i.e., the exhaled jet of air) is below the horizontal. 27 If the coughed jet was horizontal or if the individual was sneezing, talking or breathing, the results may be different.
However, it is expected that the basic influence of temperature and RH driven on the evaporation rate would be the same, so the overall effect on exposure would likely be similar.
For sneezing, there may be considerably more droplets 38 and the force of the sneeze may project these droplets further into the room. 39 This would have a significant effect on the magnitude of the exposure and possibly a small effect on the spatial distribution of exposure.
Conversely, for breathing or quiet talking, the number of droplets and their initial momentum would be lower. Therefore, this is likely to reduce the magnitude of exposure as well as have some influence on the spatial distribution. As well as different types of exhalation, it would be interesting to study the effect of wearing a face covering. These may remove a high proportion of the larger droplets/particles, that is, those that are most affected by RH, so the overall effect of temperature and RH on exposure could be less than shown here for the no face covering case.
As the model was based on a real room, only one air change rate has been considered, along with one supply/extract vent layout and one location of the infected person relative to the vents. An increase in the air change rate will increase the turbulence and mixing in the room so will likely reduce any effect from temperature and RH. The opposite is likely to be true for a decrease in the air change rate.
The droplets used in the present work had a vapor pressure of pure water so will evaporate more quickly than saliva or saline droplets (the reasons for using the vapor pressure of pure water are discussed in Section 2.2.1). The slower the evaporation the smaller the effect that temperature and RH will have. Therefore, if these models were rerun with more realistic multicomponent droplets, it would be expected that any effect from a change in temperature and RH would be reduced. As stated in the introduction, only the fluid dynamics effects from a change in temperature and RH have been considered here.
The decay in the viability of the virus in droplets was not included.
While some of these effects could be included in a CFD model, it would be more effective to include others in a higher-level model, such as a quantitative microbiological risk assessment model. 41

| CON CLUS IONS
A series of RANS CFD models have been developed to predict the effect of temperature and RH on the airborne exposure to SARS-CoV-2 from a coughing person in a mechanically ventilated meeting room or office space.
The novelty of this work is the coupling of spatial distributions of viral exposures and statistical analysis to evaluate viral exposure due to different size exhaled droplets. The analysis was used to indicate whether the effects of temperature, RH and distance from the infected person have a statistically significant effect on the airborne exposure. The modeling demonstrates the importance of evaporation on exposure to respiratory aerosols and droplets. The results demonstrate that evaporation leads to mid-sized droplets reaching a size where they can often remain airborne over distances of more than 4 m. For a case where viral load [RNA copies·m −3 ] is independent of the initial droplet size, evaporation could result in exposure to particles that are less than or equal to 6 μm in diameter, which would not be mitigated through simple face masks, and could carry much higher amounts of the virus than the final particle size in the air suggests.
In the mechanically ventilated room studied, with all the associated complex air movement and turbulence, increasing the RH resulted in a statistically significant reduction in the exposure.
However, this effect may be so small in absolute terms that other factors, such as moving closer or to the side of the person or fluctuations in the airflows, could rapidly counter the effect.
The effect of temperature on the exposure was more complex, with a positive correlation shown up to 2 m from the infected person, but a negative correlation in a region from 2 to 3 m. In all instances, moving away from the infected person resulted in a decrease in exposure, but the reduction in the median exposure was very small when moving from a region located 0-1 m in front of the person compared to a region located 1-2 m from the person.
If no other parameters are important, then setting the RH in a mechanically ventilated room to a high but comfortable level may slightly reduce the inhaled dose. If the RH is increased to reduce airborne exposure, then consideration should be given to the increase in the probability of fomite transmission. The effect of temperature on the exposure was more complex, with both positive and negative correlations. Therefore, within the range of conditions studied here, there is no clear guidance on how the temperature should be controlled to reduce exposure. The effect of distance shows that applying social distancing of 2 m would generally reduce the likelihood of two people, standing face-to-face, receiving a high exposure, however, results suggest that in some cases this will not be sufficient to mitigate the highest concentration of virus. The ventilation rate should not be compromised to achieve a high RH or low temperature.

CO N FLI C T O F I NTE R E S T
No conflict of interest declared.

DATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.