key: cord-0910692-cjy1su5j
authors: Mirzaei, P.A.; Moshfeghi, M.; Motamedi, H.; Sheikhnejad, Y.; Bordbar, H.
title: A simplified tempo-spatial model to predict airborne pathogen release risk in enclosed spaces: An Eulerian-Lagrangian CFD approach
date: 2021-10-13
journal: Build Environ
DOI: 10.1016/j.buildenv.2021.108428
sha: 72f64148e5ad477fe905b723878b9ab8ae5d5eac
doc_id: 910692
cord_uid: cjy1su5j

COVID19 pathogens are primarily transmitted via airborne respiratory droplets expelled from infected bio-sources. However, there is a lack of simplified accurate source models that can represent the airborne release to be utilized in the safe-social distancing measures and ventilation design of buildings. Although computational fluid dynamics (CFD) can provide accurate models of airborne disease transmissions, they are computationally expensive. Thus, this study proposes an innovative framework that benefits from a series of relatively accurate CFD simulations to first generate a dataset of respiratory events and then develop a simplified source model. The dataset has been generated based on key clinical parameters (i.e., the velocity of droplet release) and environmental factors (i.e., room temperature and relative humidity) in the droplet release modes. An Eulerian CFD model is first validated against experimental data and is then interlinked with a Lagrangian CFD model to simulate trajectory and evaporation of numerous droplets in various sizes (0.1 μm–700 μm). A risk assessment model previously developed by the authors is then applied to the simulation cases to identify the horizontal and vertical spread lengths (risk cloud) of viruses in each case within an exposure time. Eventually, an artificial neural network-based model is fitted to the spread lengths to develop the simplified predictive source model. The results identify three main regimes of risk clouds, which can be fairly predicted by the ANN model.

The primary transmission mode of COVID19, as a rapidly spreading airborne disease, is 34 understood to be in-person exposure to infected people's respiratory secretions and bioaerosols 35 expelled in various sizes (1). Before reaching an effective vaccine, social distancing remains the 36 inevitable defensive measure during pandemics. Maintaining a physical distance between people, 37 as one of the means of social distancing, is enforced by many governments worldwide, while the 38 essence of such stipulated measures is adapted from early evidence regarding the release and 39 environmental persistence of SARS-CoV2 (2). 40

From fluid dynamics perspectives, COVID19 transmission mode via respiratory bioaerosols 41 requires a thorough investigation of droplets' number, size, and density distribution as well as 42 their initial velocities (3). It is widely agreed that heavy droplets will deposit within less than a 43 meter (4), while micron-size airborne droplets could travel to a much longer distance following the 44 air stream (5). Nonetheless, the effectiveness of such physical distance policies is controversial 45 on many occasions as the bioaerosol release mechanisms from respiration, sneeze, and coughs 46 are chronically underestimated in past studies. 47 Spatial profile of exhalation [-] (12, 13) 10 With or without facial mask [with or without] (11) 11 Gender [-] Man, Woman (14) 12 Age [year] 19 -50

The place of disagreement in contradictory findings associated with the disease transmission are 49 in numerous strands, including carriage process of pathogens with droplets and aerosols from an 50 infected person to a new host (16), drying and evaporation processes of exhaled bioaerosols 51 following with its properties (e.g., size, mucus), environmental conditions (e.g., relative humidity) 52 (6, 17) , and number and size of released bioaerosols in each activity mode (i.e., respiration, 53 sneeze, and coughs) (8, 18, 19) . As it has been broadly discussed in previous studies, one should 54 add the importance of demographical characteristics (age, gender, ethnicity, etc.) on the 55 J o u r n a l P r e -p r o o f bioaerosol release mode. Some of these understandings are summarized as 12 pivotal factors in 56 Table 1 . These are the effective parameters that may influence bioaerosol release and 57 dispersion. Many of these parameters ultimately alter the volume and speed of respiratory 58 droplets release and therefore can be represented by the velocity of two-phase respiratory flow 59 at the mouth. Hence, in this study, the effective parameters are shortlisted to three major ones 60 to lower the computational costs and carry out the calculations in a practical timeline. 61

The identified parameters in Table 1 are supported by careful experimental and observational 62 studies from various methodological perspectives, including medicine, statistics, fluid dynamics, 63 etc. For example, the National Institute for Occupational Safety and Health (20) constructed a 64 cough aerosol simulator that produces a humanlike cough in a controlled environment based on 65 coughs recorded from influenza patients. The total aerosol volume expelled during each cough 66 was monitored to be 68 µL using aerosol generated from a cell culture medium. As another PIV 67 study to measure coughing velocity, Kwon et al. (12) obtained the average initial coughing velocity 68 of 15.3 m/s for males and 10.6 m/s for females while the average initial speaking velocity was 69 measured around 4.07 m/s and 2.31 m/s, respectively; the angle of the exhaled air from coughing 70 was reported around 38° for the males and 32° for the females while that of the exhaled air from 71 speaking was around 49° and 78°, respectively. In another conditioned indoor environment, 72 Zhang et al. (8) reported the distribution of generated aerosol from a horizontal coughing mode 73 using a manikin in the presence of 16 diffusers mounted on walls. In another study, an 74 experimental cough aerosol detection via laser diffraction system from 45 healthy people 75 presented a demographic statistical analysis of bioaerosol size by sex and age (15). 76

Respiration, speech, sneeze, and cough (RSSC) flows carry bioaerosols, the size of which 77 significantly varies through the particles' path line. Larger droplets (>50-100 µm) are mainly 78 governed by gravity. The intermediate (10-100µm) and small (<5-10 µm) droplets are more 79 affected by airflow and ventilation streams and may travel much further. At the same time, the 80 evaporation process changes the intermediate size droplets of RSSC to become airborne and 81 stay floating in the air, which particularly highlights the role of ventilation and air humidity. For 82 instance, the drying times for 50μm and 100μm droplets at a 50% relative humidity are reported 83 to be 0.3 and 1.3s, respectively (36). Even after complete evaporation, the small dried aerosol 84 particles can potentially carry viruses as the usual size of viral pathogens is 25 nm to 5 μm (5). 85

For small droplets with a low Stokes number (St≪1), the sedimentation time is longer than the 86 displacement ventilated room. Authors showed that for short separation distances, the interaction 122 between breaths is a key factor in the airborne cross-infection. Li et al. (31) studied the 123 evaporation and dispersion of cough droplets by Lagrangian-Eulerian model in quiescent air, 124 considering inhomogeneous humidity field, and demonstrated that evaporation-generated vapor 125 and super-saturated wet air exhaled from the respiratory tracks forms a vapor plume in front of 126 the respiratory tract opening. Interestingly, due to the droplet size reduction induced by 127 evaporation, both the number density of airborne droplets and mass concentration of inhalable 128 pathogens remarkably increased, which may increase the risk of infection. Moreover, the physics 129 of aerosol and droplet dispersion and distribution of droplet aerosols were investigated from 130 mouth coughing and nose breathing using LES by (5) and (8). It is reported that the typical size 131 range of speech and cough originated droplets (d 20 µm) can linger in the air for hours so that 132 they could be inhaled and rapid drying process of even large droplets, up to sizes O(100 µm), into 133 droplet nuclei/aerosols was observed. Another critical parameter in the time-dependent 134 dispersion of cough droplets, namely the effect of the human body by a 3D thermal manikin was, 135 investigated by (32) while due to the buoyancy-driven thermal flow, both the vertical velocity and 136 displacement of small droplets (≤20 μm) were completely reversed from descending to ascending. 137 Also, another recent experimental and numerical study on the transport of droplet aerosols in a 138 fever clinic showed that the best ventilation performance appeared for a patient sitting and 139 coughing while the case of a patient lying and talking was the worst case (31). In another clinical 140 experiment, the size of droplets were measured in an indoor environment, with an air temperature 141 of 18 o C and relative humidity of 50%, the horizontal range of large respiratory droplets (diameter 142 120 μm-200 μm) in speaking were between 0.16 m to 0.68 m, in coughing, between 0.58 m to 143 1.09 m, and in sneezing between 1.34 m to 2.76 m. (32). Also, results from comparative studies 144 on transport characteristics of contamination dispersion in a passengers' local environments 145 revealed significant increases of residence times (up to 50%) and extended travel distances of 146 contaminants up to 200 μm after considering cough flow, whereas contaminants travel 147 displacements still remained similar (33). 148

Despite the necessity to employ Lagrangian CFD models to trace the small particles, as explained 149 above, such models demand intensive computational resources, which hinder a comprehensive 150 investigation of the bioaerosol release process regarding its various affecting parameters. This 151 implies that Lagrangian simulations are costly choices to be directly applied to represent humans 152 as the source of bioaerosol release in many practical scenarios where multiple occupants interact 153 in mechanically or naturally ventilated environments. Nonetheless, developing a reliable 154 bioaerosol release source is vital for the design and control of ventilation design, space 155 management, and social distancing, especially during pandemics. Hence, similar to many other 156 simplified source term models of a human body such as the amount of heat or CO2 releases 157 widely used in buildings' design and control applications, a simplified airborne pathogen droplet 158 release model is necessary to be applied as a source term to other models. 159

To address this shortcoming in providing a deep insight related to virus-laden bioaerosol release 160 from human sources in indoor and outdoor spaces, this study proposes a framework to develop 161 a simplified model of droplets' release from respiratory events (here sneeze and cough). This 162 model encompasses a range of droplet release modes related to clinical (i.e., droplet release 163 velocity from the bio-source mouth) and environmental (i.e., room temperature and relative 164 humidity) distribution of bio-sources using an Eulerian-Lagrangian CFD model. The effective 165 parameters on droplet release from bio-sources are initially synthesized to define a series of 166 airborne pathogen release scenarios (35 cases). These scenarios are then simulated with a series 167 of computationally intensive Eulerian-Lagrangian CFD simulations to construct a repository 168 dataset. The dataset is then fed into a risk assessment model (RAM) previously developed by 169 authors (35) to account for the tempo-spatial risk analysis of the respiratory event rather than the 170 instantaneous release of droplets. In a later step, the tempo-spatial risk data is fitted to an artificial 171 neural network model capable of predicting the risk cloud expansion of a bio-source throughout 172 time. It should be noted that the background airflow of the studied enclosed space is assumed as 173 still air condition, so that the initial behavior of droplets' transport can be observed. The human 174 source is considered to have a fixed position in the room, and its movements are not taken into 175 account in this study. Nonetheless, the proposed framework demonstrates the flexibility to add 176 any complex background airflow that may be caused by bio-source movement, ventilation 177 systems, etc. 178

In addition, to develop artificial intelligence (AI) to predict numerical results of CFD simulation, the 179 powerful branch of AI, namely multi perceptron feedforward version of artificial neural network, is 180 adopted with deep learning to generate an accurate prediction for unseen conditions. Its code is 181 developed in Python program language, and the number of neurons, as well as other settings 182 such as learning rate, are tuned, and tailored for this specific work. 183

Regarding the structure of this paper, Section 2 describes the methods used to develop the 184

Eulerian-Lagrangian CFD model risk assessment model. It also briefly explains the risk 185 assessment model. Section 3 presents the scenarios designed to cover a range of airborne 186 pathogen release modes. Finally, Section 4 provides the results, followed by the discussions and 187 conclusion sections. 188 As stated before, comprehensive Eulerian and Lagrangian CFD modeling of airborne pathogen 3 respiratory aerosol release takes intensive computational cost even after using high-performance 4 and cluster computing resources. Furthermore, as addressed in Table 1 , the bioaerosol release 5 has been found to depend on several parameters. Thus, reaching a comprehensive model, 6 undertaking airborne pathogen respiratory droplets release rate of any individual, is an impractical 7 approach, following the existing methods in the literature. Hence, this study proposes an 8 innovative approach to substantially decrease the computational burdens while underpinning the 9 necessary complexities of such phenomena. The proposed framework benefits from different 10 tools to systematically develop a simplified model to be used for ventilation design or social 11 distancing control in spaces. 12 13

For this purpose, as depicted in the framework of Figure 2 , four steps are considered to generate 14 the simplified bio-source model. In

Step-1, an Eulerian CFD model is first developed to accurately 15 replicate the flow field in a room with a still background airflow field. While the buoyancy effect 16 due to the room temperature stratification and jet release temperature is taken into account, the 17 flow streams are successfully validated with an experimental study by (39). 18

Step (2) is dedicated to accurately modeling large to small droplet movements via a Lagrangian 19 CFD model, which is then coupled with the Eulerian model to reproduce the velocity field at an 20 acceptable level while fast due to its low and yet precise enough number of cells. At this stage, 21 parameters of J o u r n a l P r e -p r o o f bio-source velocity, room temperature, and room RH). Thirty-five scenarios have been generated 1 to cover a wide range of rooms' conditions and bio-source release velocities related to sneeze 2 and cough modes. It should be noted that due to the extensive computational cost of a potential 3 high-resolution CFD model, a comprehensive study is firstly conducted to find a model with a 4 coarser mesh size, which can simultaneously provide a fair level of accurate results. 5

Step-3, a risk assessment model previously developed by authors (34) is implemented to 6 translate the CFD simulations to a time series of airborne pathogen disease transmission risk in 7 the vicinity of the bio-source. The RAM model, thus, provides the tempo-spatial risk of infection in 8 the studied room. This implies that the maximum horizontal and vertical distances from the 9 infected bio-source with a considerable level of risk calculated by RAM are assumed as the risk 10 cloud of that case study. 11

Eventually, in Step-4, the calculated maximum distances (risk clouds) of all case studies 12 generated in the previous step are used to train a simplified model using the artificial neural 13 network (ANN) technique. In this model, the release velocity, room temperature, and RH are the 14 inputs, and the tempo-spatial risk cloud is the output. 15

An Eulerian method is applied to model the unsteady incompressible flow field using Navier-17

Stokes as the governing equations for mass, momentum, and energy equations: 18 = 0

(1)

where ′ ′ ̅̅̅̅̅̅ is the Reynolds stress tensor, which is modeled by the Boussinesq hypothesis. SST 19 k-ω is also used as the turbulence model (40). 20

Particles are modeled based on a Lagrangian-Eulerian approach using SimcenterSTAR-22

CCM+Ver. 13.06.12 (double precision), where the conservation equations of mass, momentum, 23 and energy for the dispersed phase are derived for each particle in a Lagrangian form to calculate 1 their trajectories. 2

As a general method for particle, droplet, and bubble, the trajectories of discrete phases (i.e., 4 respiratory droplets) are resolved by integrating a force conservation equation on each particle, 5 written in a Lagrangian reference frame: 6

where "i" is the coordinate direction (i =x,y, or z), and subscript "p" represents particles. u and 7 are the fluid phase velocity and density, respectively. is the force per unit particle mass 8 (acceleration), and the term ( − )represents an additional acceleration (force per unit 9 particle mass) in which is calculated as: 10

where is the molecular viscosity of the fluid, and is the particle diameter. Also, is the 11 relative Reynolds number, which is calculated as: 12

Since the dispersed droplets are volatile, the mass transfer occurs between the phases 13 accompanied by an interphase heat transfer. Hence, heat transfer occurs because of the 14 interphase temperature differences, and the interphase mass transfer changes the sizes of the 15 droplets as described in the following sub-sections. 16

The equation related to the conservation of mass of a particle can be expressed as: 18

where denotes the mass of the particle, and ̇ represents the rate of mass transfer to the 19 particle. The latter is a non-zero value for the simulations, which include the evaporation process. 20

The multi-component droplet evaporation model used in this study assumes droplets to be 1 internally homogeneous, consisting of an ideal mixture of liquid components subject to 2 vaporization. Moreover, the model assumes inert components in both the droplet and the gas. 3

Regarding the evaporation of multi-component droplets, ̇ is defined as the rate of change of 4 mass of each transferred component due to quasi-steady evaporation: 5 6 where * represents the mass transfer conductance, and is known as the Spalding transfer 7 number. Also, "i" is the index of each component in the mixture, and represents the fractional 8 mass transfer rate for which the sum of all N components complies with the following equation: 9

As a basic assumption for material particles, one can assume that particles are internally 11 homogeneous. From a thermal point of view, this is equal to a low Biot number (<0.1). The 12 equation of conservation of energy will be: 13

where is the rate of convective heat transfer to the droplets from the continuous phase, 14

represents the rate of radiative heat transfer, and is related to other heat sources. 15

The computational domain has a size of 3.5m × 3.5m × 6m, as shown in Figure 3Error ! 17 Reference source not found., representing a room without ventilation. Droplets with different 18 diameters from 0.1μm to 700μm, caused by the exhalation, were released from a circular area 19 with a diameter of 1.2 cm located at the center of a 3.5m × 3.5m wall (30). It is worth noting that 20 the mouth diameter (1.2 cm) has been chosen slightly smaller than the value of 1.5 cm that was 21 used by Chao et al. (44) for the average mouth diameter of eight university students (under 30 22 years old). While these two values are in the same range, the smaller mouth diameter in the 23 present research assumes the respiratory event might be released by patients of younger ages 24 or smaller body sizes. 25

The dimensions of this domain have been selected after a series of preliminary simulations, 1 ensuring the adequacy of the room dimensions for analysis of airborne behavior of the droplets 2 where the exhalation jet reaches a velocity value in the order of 2cm/s (less than 1% of the jet 3 velocity) before it reaches the wall in the front of the side of the mouth (located at x=6m) (41). The 4 results implied that after simulating an adequate physical time, droplets with the diameter of 10μm 5 or below linger in a range up to 6m from the releasing surface with a velocity below 2cm/s while 6 droplets with the diameter of 100μm are deposited in smaller distances of about 1m from the jet 7 inlet. 8 9

To ensure the final size of the utilized mesh in a reasonable time frame, different grid 10 resolutions with hexahedral cells were tested, ranging from 189k cells to 4.5M cells. The optimal 11 mesh was identified as the 189k-HYB case, which has minimum and maximum cell sizes of 0.06m 12 and 0.2m, respectively, with a surface growth rate of 2.0. It should be noted that a conic volume 13 with a length of 1 m dense cells was generated around the mouth of the bio-source, as seen in 14

Error! Reference source not found.. All surfaces were considered as solid walls with no-slip 15 boundary conditions (see Table 2 ). Wall treatment is based on an adaptive approach. The other 16 boundary conditions of the model are presented in Error! Reference source not found.. 17

Proper simulation of exhalation activity requires reliable data on the size distribution of 1 droplets and transient exhaled airflow profile. Error! Reference source not found. presents air 2 velocity profiles and droplet size distributions of sneeze and cough, resulting from massive 3 measurements on people of different ages and gender. 4 (43) and droplet size histogram of (c) cough (44), and (d) sneeze (45) 1

In the present transient CFD simulations, the background air was simulated as a non-reactive 3 ideal gas composed of standard air and some amount of water vapor, depending on the relative 4 humidity of each case (see Table 2 ). The results of the simulations, conducted within 60 seconds, 5 implied that the droplets with a diameter of 10 μm or below had become airborne, traveling not 6 more than 5 m from the mouth, while droplets with a diameter of 100 μm fell at short distances of 7 about 1 m from the jet inlet. 8

The droplets were simulated as discrete phases using the Lagrangian model and were 9 assumed to have spherical shapes. To mimic realistic pathogenic droplets, they were assumed 10 to be initially composed of 3% non-evaporative and 97% evaporative mass fractions. The density 11 of the non-volatile fraction was 1280.8 kg.m −3 with a specific heat transfer of 2404.6 J.Kg −1 .K −1 at 12 the standard state temperature of 298.15 K. On the contrary, the evaporative portion was 13 assumed as water with a density of 997.6 kg.m −3 and a specific heat transfer of 4181.7 J.Kg −1 .K −1 14 at the same standard state temperature. In addition, the saturation pressure of this evaporative 15 fraction (water) was set to 3170.3 Pa. The mass-weighted mixture was used for the calculation of 16 the density and specific heat of each droplet. For each droplet's outer surface, it was assumed 17 that the droplets would stick to any wall surface of the room as they reached them. As an averaged 18 value, periodicity of cough and sneeze were considered 0.6 second. At each simulation, cough 19 or sneeze were modelled by a normal breathing velocity of about 1 m/s and intermittence of 5 1 times a minute. 2

Similar to the Lagrangian model, the weighted mixture method for the Eulerian model was 3 employed for the calculation of the air-water mixture in the background air. Finally, the 4 aerodynamic interaction between the particles and the air has been simulated using drag force 5 calculated by Schiller-Naumann's drag force coefficients and the pressure gradient force. 6

The turbulence is modelled using Realizable k-epsilon model with "All y+ wall treatment" 7 option in STARCCM, making the model suitable for the coarse and fine meshes. In should be 8 noted that the Realizable k-epsilon is classified under High Reynolds Number turbulence models, 9 and its Y+ can be 100 or even higher. In the present simulations, the Y+ was about 10, which is 10 out of the critical range [11.04~30]. In addition, the "two-layer, all Y+ wall treatment" option in 11 STARCCM adjusts the wall functions for any Y+ in areas near the mouth with smaller Y+ [40] . It 12 is also worth mentioning that since the present does not work with any flow details near the walls 13 and flow velocity near the walls was almost zero, we believe that the expansion ratio equal to 2 14 would be a good choice and does not affect the accuracy of problem for the still flow as the air 15 velocity is zero. 16

The discretization scheme is a second-order one for momentum equations. includes multiple steps to count the number of droplets with different droplet sizes from sub-14 micron to hundreds-micron released from respiratory jet and passing through a specific location 15 of an enclosed space. Therefore, this leads to a 3D temporal profile, which shows a temporal risk 16 cloud being expanded around a bio-source. Details of RAM developed by authors and applied 1 algorithm can be found in (34). 2

A deep ANN with feed-forward multi-layer perceptron architecture has been used in this study 4 (46). A back-propagation learning paradigm was employed to build the surrogate model. The 5 continuous nonlinear sigmoid function with smooth gradient was employed in the model due to its 6 proven capability in making clear distinctions on predictions. A comparison was conducted among 7 five different architecture of ANN in terms of hidden layers and number of neurons to find the best 8 architecture that delivers the best predictive results. The analysis was performed under the 9 circumstances that the ANN was fully unsighted on all 60 values (secondly-basis CFD data for 10 one minute) within each two test cases. As shown in Table 3 , the 10×10 ANN was eventually 11 selected due to showing the least averaged testing error among other architectures. More hidden 12 layers can potentially result in overfitting due to the nature and size of the data. 13 burden related to the number of needed simulations is substantially reduced. For this purpose, 12 20 parameters (e.g., droplet size, number of droplets, the temporal, and spatial profile of cough) are 21 initially identified as the effective parameters (see Table 1 ). After scrutinizing a comprehensive 22 literature review and implementing further assumptions when data does not exist, three 23 parameters, including droplet release velocity from bio-sources, room temperature, and room's 24 relative humidity, are utilized as the effective parameters while considering a minimum of three 25 levels for each parameter. Each parameter is then varied with three increments to initially populate 26 27 cases, as presented in Table 4 . After analyzing the data as presented in the results section, 1 eight additional cases were added to improve the training of the ANN model. As mentioned in 2 Section 2.6, each case has an array of 60 values on a secondly-basis that shows the evolution of 3 vertical spread over 60 s. Furthermore, two cases were used only to validate the model and were 4 not included in the training steps. Although considering 35 cases is not ideal for three main 5 identified parameters, the ANN results shown in the following sections reveal the capability of the 6 model to capture a relatively correct vertical and horizontal spread, which satisfies the main aim 7 of this study to develop a simplified model in recognizing such distances. 8 Since the most crucial parameter for particle dispersion is air velocity, before the main 3 simulations, a mesh sensitivity analysis has been performed to ensure that the final mesh and the 4 velocity field are independent of the element size. For this part, the flow velocity in the far-field 5 zone (i.e., the distance where y/d0 > 20 from the mouth) was investigated, and the results were 6 later validated against the experimental by [39]. The inlet velocity had spanwise (along with 7 discharge hole radii) as well as streamwise (centreline) velocity profiles with the maximum value 8 of 20 m/s. For this purpose, four meshes with different resolutions with hexahedral cells were 9 generated, containing a total mesh number of 189k, 627k, 3.7M, and 4.5M. 10

After this preliminary study, it was observed that a minimum number of 3.7M cells was 11 required for an independent mesh resolution. However, since this research needed a large 12 number of simulations and this could result in an unaffordable computational cost, and also 13 aligned with the aim of this study to develop a simplified model, the viable solution was to generate 14 a mesh, which is relatively fast and also provides results with a fair level of accuracy. 15

Hence, after several attempts, a new mesh arrangement of 189-Hyb with a zonal 16 improvement just before the mouth location was generated that could accurately follow the result 17 of the models with 3.7M and 4.5M cells (Figure 6 ). This optimal mesh, 189k-HYBcase, had 18 minimum and maximum cell sizes of 0.06 and 0.2 m, respectively, while its surface growth rate 19 was 2.0. This resulted in a dense mesh within 0.8 m from the mouth at the central part of the 20 domain. Table 5 summarizes the applied boundary conditions for the validation test. 21 

The first step in the framework of Figure 2 is to validate the CFD model. For this purpose, an 3 experimental study by (39) was used for the validation process due to its resemblance to the CFD 4 model. Due to the lack of reliable experimental data on buoyant air jets in the literature, the 5 validation case used in this research work represents an isothermal non-buoyant jet which helped 6 validating the numerical setup applied to the continuum phase (air). The isothermal free turbulent 7 jet experiment provides the spanwise and streamwise velocity profiles at its inlet location with a 8 maximum value of 8.3 m/s. As expected, the Eulerian CFD model of the background flow is in a 9 fair agreement with the experimental results reported by (39) as demonstrated in Figure 5 while 10 the air velocity at the centerline from the nozzle entrance (y=0) up to the downstream distance of 11 y=50 0 is compared. Since the risk assessment model is more informative in far distances from 1 the bio-source, it can be concluded that for such distances from the jet source ( 0 ⁄ ) > 10, the 2 results are in general in a better agreement when are compared to the experimental data. As 3 mentioned before, poor predictions of 189k and 672k meshes at ( 0 ⁄ ) < 10 regions, was 4 successfully resolved using a coarse mesh, but carefully adjusted size at different regions of the 5 domain (189-HYB). As a result, the maximum error observed at ( 0 ⁄ ) > 10 region increases 6 from 7% to 10% as it is switched from 4.5M cell mesh to 189-HYB. Thus, this mesh size 7 considerably reduces CPU time from order of months to order of weeks where performing 8 numerous numerical simulations were needed. The validation study with more details using 9 multiple metrics can be found in (34). 10

Another similar set of experimental data reported by (47) 

The third step of the proposed framework is investigated in this section. As introduced in Table  17 4, 35 scenarios were simulated in this study, covering wide range of respiratory droplet release 18 events. As explained earlier, the RAM model (34) syntheses the CFD output data to generate an 19 accumulative temporal status of droplets in front of a bio-source. The model counts droplets of 20 any size at any location around the bio-source within the simulation time frame and marks that as 21 a risky location when the number exceeds a defined critical threshold. Here, this value is defined 22 as 100 following a study by (48) . Nonetheless, the model can be promptly adjusted to any other 23 suggested numbers. 24 RAM is an effective tool to monitor the risk cloud expansion through time in a specific 25 environmental and background flow condition. As seen in a base case of Figure 6a , the vertical 26 and horizontal spread of risk cloud are separately illustrated after one minute of droplets' release 27 of cough while the tendency of the risk cloud expansion is toward the ceiling. While the relative 28 humidity of 20% is an extreme condition in a typical room temperature of 22℃, such information 29 is handy to decide on the environmental control, HVAC design, and social distancing standards. 30

This implies any person who stays one minute in the 1.0m vicinity of the bio-source can be subject 31 to the infection. As shown in the following figure, time is a key in the airborne pathogen 1 transmission, and while it is well understood, it is neglected in many risk-assessment studies. When two out of three of the selected parameters are varied, as depicted in Figure 6b to Figure  3 6d, the risk cloud can drastically change. An example is Figure 6b , where a sneeze event is 4 shown in an RH of 80%. Once again, a person should not stay in a 1.9m vicinity of an infected 5 bio-source for one minute and more. As shown in Figure 7c , a sneeze in a hot and dry climate 6 can even cause a stronger risk cloud horizontally and vertically. Inversely, as initially suggested 7 by many studies (49, 50), a humid climate (e.g., RH>60%) can yet be a safer environment in 8 terms of disease transmission via airborne means. This marginal pattern of risk cloud expansion 9 can be seen in Figure 6d , consistent with the former studies. The following sections will present 1 the time evolution of these clouds in more detail. 2

In order to demonstrate the effects of ambient relative humidity on the variations of the plume and 3 the movement of the droplets, the velocity fields and particle dispersions of cases 4 and 15 are 4 shown in Error! Reference source not found.. Both cases have identical temperature, while the 5 relative humidity and the sneeze velocity are different. As it can be seen, the locations of the fallen 6 heavier droplets depend on the sneeze velocity (the initial velocity of the particles). However, 7 since the locations of the airborne droplets are relatively the same, one can conclude that that the 8 transmission of these droplets is mainly affected by the relative humidity rather than the initial 9

velocity. This finding can be explained by considering the fact that small droplets lose their initial 10 momentum because of the drag force, and then cannot travel much dissimilar from each other as 11 the large droplets can. Since the initial sneeze velocity for these two cases are different, the small 12 airborne droplets will follow different velocity fields created by two sneezes, leading to two 13 different droplet dispersions. 14 As shown in Figure 8 , a cough case study with a typical room temperature of 22℃ and low RH 1 of 20% is again demonstrated for time snapshots of 10s, 20s, 50s, and 60s. While the risk cloud 2 reaches 1.0m only in few seconds, it is mainly vertically expanded from few centimeters to about 3 the ceiling height. For this specific case, and as an example where extractors are ceiling mounted, 4 RAM can help to attain similar environmental conditions in this room. Inversely, Figure 9 shows 5 a sneeze case (Case 27) with a temperature of 29℃ and a low RH of 80%, where the risk cloud 6 is quickly expanded toward the ground and almost remains temporally the same. Therefore, if a 7 room has a ventilation system with a floor-mounted extractor, controlling the environmental 8 condition toward achieving the same risk cloud expansion can be a better solution while enacting 9 a 2.4m distance rule between occupants. 10 t=40 sec. 

The synthesized vertical and horizontal spread of RAM profiles of data cases in Table 4 is 2 depicted in Figure 10 . As stated before, thirty-five training cases are simulated with the CFD 3 model in addition to two testing cases. 4

Regarding the horizontal spread of the exhaled droplets for these 35 different conditions, as 5 depicted in Figure 10a , many of the curves are overlapped and cannot be distinguished from 6 each other. Consequently, until t=30 s, all cases can be classified into six groups in which no 7 horizontal progress can be observed. It should be mentioned that in the horizontal risk 8 measurement, the distance between two successive horizontal planes is 0.1 m. From the 9 beginning of the numerical experiment (t=1s), the horizontal spread of droplets starts at minimum 10 values of 1m for V=18 m/s. As the exhalation velocity increases, the initial horizontal spread also 11 increases such that for V=50 m/s, the horizontal spread at the initial time step reached 1.8 m/s. 12

In most cases, no evolution of the risk cloud on the horizontal spread is detected, mainly because 13 of the particle dynamics due to drag and buoyant forces that progressively become significant in 14 the vertical direction and change droplets to upward direction. 15

Regarding to the vertical expansion as illustrated in Figure 10b , three main regimes can be 16 identified in the data as highlighted in the graph. Regime I is associated with a sudden vertical 17 expansion of the risk cloud (below 30s) when small droplets are affected by the buoyant plume of 18 Nonetheless, it should be mentioned that it is not a straightforward procedure to draw a general 5 conclusion on the expansion pattern of cloud risk. This further justifies the necessity of developing 6 models similar to RAM to predict safe distances in complex environmental conditions. Regime II 7 is a more frequent pattern for the risk cloud movement as droplets tend to gradually elevate toward 8 the ceiling. The pattern is again very complex to be generalized. Eventually, Regime III states 9 those few cases mainly with a temperature of 29℃ and RH of 80% (e.g., 9, 18, 27) . The rate of 10 evaporation in these cases is very low, and the plume is not very strong due to a lower 11 temperature difference between jet and room. Hence, a horizontal spread of the risk cloud can be 12 seen in Figure 10a . 13 Eventually, two samples from Regimes I and II are selected to show the performance of the 1 training process after 1M iterations using the backpropagation method. Regime III was omitted 2 as its behavior is clearer to be predicted without using a complex predictive model. As mentioned 3 before, the ANN inputs are velocity, temperature, humidity, and time where the output of the ANN 4 is spread of droplets in the vertical or horizontal direction. Also, the criteria to stop the training 5 iteration of ANN was the discrepancy of the predicted value with respect to the CFD value to 6 reach below a small value, namely 0.001. Moreover, it should be mentioned that the below-7 chosen test cases are considered extreme prediction cases in which ANN did not priory include 8 any of the temporal vertical spread evolution. 9

As seen in Figure 11a , the expected values are plotted against ANN output predicted values in 10 addition to lines of ±10% error. Figure 11b shows the transient evolution of the vertical risk cloud 11 predicted by the ANN model. The averaged relative error of all test cases calculated by averaging 12 60 data samples in each training case is about 9.2% (i.e., 2,100 training data samples), which 13 can be considered a fair relative error over the used datasets. Some cases in regime I 14 demonstrate higher relative errors (e.g., Case 24 with 14.2% error) due to the sudden change in 15 the data pattern as the role of both buoyant and drag forces are simultaneously significant and 16 challenging to be projected. 17 (a) (b) Figure 11 . ( J o u r n a l P r e -p r o o f Figure 12a shows the performance of ANN in the prediction of Case T1 as it adapts itself with 1 the CFD data through the risk cloud spread in the vertical direction within one minute. The ANN 2 model demonstrates a fair prediction up to 50s. In contrast, after this range, even though the CFD 3 data within the time interval between 50s and 60s shows a monotonically increasing behavior, 4 the ANN predicts nearly constant values at this range. The reason lies within several training 5 cases that have these characteristics in which, in a pretty long period of the last seconds, the 6 vertical spread has a constant maximum value. This long period of constant height for the risk 7 cloud can also be seen in the second test case (Case T2). As seen in Figure 12b , the same 8 issue and even more severe remains for the temporal prediction of Case T2. 9

Nonetheless, the ANN model can reasonably predict the final vertical expansion of the risk cloud, 10 as it can be seen in and Figure 12b . In both parts of Figure 13 , ANN not only could follow the 11 trend, but it could precisely predict the exact value. However, where there is a rapid and sharp 12 gradient, ANN shows a less precision. In general, the ANN performance on the prediction of both 13 validation cases can be considered satisfactory as the average error for the vertical spread 14 prediction of risk cloud is about 29.6%. This implies that the developed model can anticipate the 15 temporal variation of risky distances even though the model underperforms for some intervals. 16

This flaw can be mitigated by increasing the dataset size though the main aim of this paper is to 17 conduct a feasibility study to develop an early model to simply estimate the temporal risk cloud The step-by-step growing of the training cases' population and its effect on the averaged ANN 1 training error is depicted in Table 6 . For each step when the number of cases is increased, it is 2 possible to evaluate the ANN training error. As the population of the training cases grows, the 3 overall performance of the employed ANN increases while there is a decrease in the average and 4 maximum values of the relative error for all cases. 5 

Safe distance against airborne pathogen transmission is a parameter of space and the exposure 9 time to various sizes of virus-laden droplets released from a bio-source. This paper proposes a 10 framework to develop a surrogate model to be assigned to bio-sources instead of running 11 intensive CFD simulations, to predict risk clouds released from them. Thus, a CFD model is first 12 developed to simulate a range of parameters, covering many aspects of respiratory events, 13

including clinical factors such as droplet release velocity, number and distribution of droplets, 14 evaporation of droplets, and environmental factors, including room temperature and humidity. 15

Then, 35 case studies have been defined and simulated to generate a comprehensive dataset. 16

The CFD results have been analyzed based on a tempo-spatial-based risk assessment model 17 (35) previously developed by the authors, which determines the vertical and horizontal spread of 18 respiratory droplets. The surrogate model based on an artificial neural network is then fitted to 19 data to successfully predict the size of the risk cloud around a bio-source under different climatic 20 and clinical conditions. 21

According to the simulated cases, the vertical spread of droplets can be divided into three regimes 22 with different trends. Some cases are under strong impact of plume while others are mildly or not 23 influenced. This is beneficial since it is an indication of generalization in the behavior of the 24 exhaled jets. Thus, it is expected that the trained ANN to also reflect such generalization in its 25 predictions. Consequently, as the thermal plumes and ventilation systems are not considered in 26 this study, these parameters are among the limitations of this research. 27 Moreover, thet results suggest that it is possible to apply ANN to a series of simplified CFD cases 1 to generate a simplified calculation model for estimating safe social distances and ventilation 2 designs under different environmental situations, which is more practical for non-experts to use. 3

Although the predicted results calculated by ANN are satisfactory for the test cases, successful 4 J o u r n a l P r e -p r o o f

Virology, transmission, and pathogenesis of SARS-CoV-19 2

Two metres or one: 21 what is the evidence for physical distancing in covid-19?

The flow physics of COVID-19

A Cough Aerosol Simulator for the 24 Study of Disease Transmission by Human Cough-Generated Aerosols

Modelling aerosol 27 transport and virus exposure with numerical simulations in relation to SARS-CoV-2 transmission by 28 inhalation indoors

CFD Simulation of Human Coughs and Sneezes: A 30 Study in Droplet Dispersion, Heat, and Mass Transfer2010

A simplified benchmark of ultrafine particle 32 dispersion in idealized urban street canyons: A wind tunnel study

Distribution of droplet aerosols generated by mouth 35 coughing and nose breathing in an air-conditioned room

Temporal size distribution and concentration of particles near a 37 major highway

Numerical Analysis of Airway Mucus Clearance 1 Effectiveness Using Assisted Coughing Techniques

A schlieren optical study of the human cough with and 3 without wearing masks for aerosol infection control

Study on the initial velocity distribution of 6 exhaled air from coughing and speaking

CFD analysis of the human 8 exhalation flow using different boundary conditions and ventilation strategies

Cough Expired Volume and Cough Peak Flow Rate 11 Estimation Based on GA-BP Method

Cough aerosol in 13 healthy participants: fundamental knowledge to optimize droplet-spread infectious respiratory disease 14 management

Does COVID-19 Spread Through Droplets Alone? 16 Frontiers in Public Health

Enhanced spread of expiratory droplets by turbulence in a cough jet. Building and 18 Environment

Size distribution of virus laden droplets from expiratory ejecta of infected 20 subjects

Coupling Computational Fluid Dynamics Simulations and Statistical Moments 22 for Designing Healthy Indoor Spaces

The airborne lifetime of small speech droplets and their 26 potential importance in SARS-CoV-2 transmission

Visualizing the effectiveness of face masks in obstructing 29 respiratory jets

Influence of the geometry of 31 the airways on the characterization of exhalation flows. Comparison between two different airway 32 complexity levels performing two different breathing functions

Dynamic airflow simulation within an isolation room

Numerical investigation of influence of human walking on dispersion and 37 deposition of expiratory droplets in airborne infection isolation room. Building and Environment

Transient CFD simulation of the respiration process and inter-person exposure 40 assessment. Building and environment

Feng Z-g. Modeling the evaporation and dispersion of airborne 42 sputum droplets expelled from a human cough

Numerical study of the effects of human body heat on particle 44 transport and inhalation in indoor environment

Violent expiratory events: on coughing and 46 sneezing

Influence of human breathing modes on airborne cross 1 infection risk

Experimental and numerical study on the transport of droplet aerosols generated by 3 occupants in a fever clinic

Trajectories of large respiratory droplets in indoor environment: 5 A simplified approach

Evaluation of cough-jet effects on the transport characteristics of 7 respiratory-induced contaminants in airline passengers' local environments. Building and Environment

Issues Affecting Respirator Selection for Workers Exposed to Infectious Aerosols: Emphasis on 14 Healthcare Settings

Modelling of evaporation of cough droplets in inhomogeneous 16 humidity fields using the multi-component Eulerian-Lagrangian approach

Thermal effect of human body on cough droplets evaporation and dispersion in 19 an enclosed space

Numerical and experimental verification of initial, transitional and 21 turbulent regions of free turbulent round jet

Two-equation eddy-viscosity turbulence models for engineering applications

The role of computational fluid dynamics tools on investigation of pathogen 25 transmission: Prevention and control

Relative humidity in droplet and airborne transmission of disease

Sneezing and asymptomatic virus transmission

Characterization 31 of expiration air jets and droplet size distributions immediately at the mouth opening

Characterizations of particle size distribution of the droplets 34 exhaled by sneeze

Deep learning in neural networks: An overview

Velocity measurements in a high-Reynolds-number, 38 momentum-conserving, axisymmetric, turbulent jet

Review of infective dose, routes of transmission and 40 outcome of COVID-19 caused by the SARS-COV-2: comparison with other respiratory viruses

Mechanistic theory 43 predicts the effects of temperature and humidity on inactivation of SARS-CoV-2 and other enveloped 44 viruses

An Overview on the Role of Relative Humidity in Airborne 46 Transmission of SARS-CoV-2 in Indoor Environments

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: