key: cord-0827457-o25bexue authors: Shang, Yidan; Dong, Jingliang; Tian, Lin; He, Fajiang; Tu, Jiyuan title: An improved numerical model for epidemic transmission and infection risks assessment in indoor environment date: 2022-01-11 journal: J Aerosol Sci DOI: 10.1016/j.jaerosci.2021.105943 sha: db6af1ff1eb3a5512f2dfebb1ae7a20db93cd056 doc_id: 827457 cord_uid: o25bexue Social distance will remain the key measure to contain COVID-19 before the global widespread vaccination coverage expected in 2024. Containing the virus outbreak in the office is prioritised to relieve socio-economic burdens caused by COVID-19 and potential pandemics in the future. However, “what is the transmissible distance of SARS-CoV-2” and “what are the appropriate ventilation rates in the office” have been under debate. Without quantitative evaluation of the infection risk, some studies challenged the current social distance policies of 1–2 m adopted by most countries and suggested that longer social distance rule is required as the maximum transmission distance of cough ejected droplets could reach 3–10 m. With the emergence of virus variants such as the Delta variant, the applicability of previous social distance rules are also in doubt. To address the above problem, this study conducted transient Computational Fluid Dynamics (CFD) simulations to evaluate the infection risks under calm and wind scenarios. The calculated Social Distance Index (SDI) indicates that lower humidity leads to a higher infection risk due to weaker evaporation. The infection risk in office was found more sensitive to social distance than ventilation rate. In standard ventilation conditions, social distance of 1.7 m–1.8 m is sufficient distances to reach low probability of infection (PI) target in a calm scenario when coughing is the dominant transmission route. However in the wind scenario (0.25 m/s indoor wind), distance of 2.8 m is required to contain the wild virus type and 3 m is insufficient to contain the spread of the Delta variant. The numerical methods developed in this study provide a framework to evaluate the COVID-19 infection risk in indoor environment. The predicted PI will be beneficial for governments and regulators to make appropriate social-distance and ventilation rules in the office. Latest statistics show the COVID-19 pandemic has infected more than 256 million people and claimed over 5.14 million deaths [1] . Novel factors such as high contagiousness, multiple transmission routes and long incubation period have contributed to wide range transmission of COVID-19 around the world. 5 Although the rapid design of new vaccines and theuraputics bring the hope to end the pandemic, due to the emerging virus variants, bottlenecks in vaccine mass production and distribution logistics especially in low-income countries, the epidemiological end of the pandemic might not be reached until 2024 [2] . In fact, the Delta variant has been dominating the global pandemic since the middle 10 of 2021 and has posed challenges to the efficacy of current vaccines. It is expected that social distance rules are necessary for years even though widespread vaccination is reached [3] . In addition, the highly interconnected globalised economy, the biodiversity loss and climate change may increase pandemics in frequency. Considering the emergence of SARS-CoV-1, MERS, H1N1(Swine 15 Flu) and SARS-CoV-2, it is expected to encontour new pandemics caused by respiratory epidemics in the near future [4] [5] [6] . The social distance rules, maskwearing mandate, work-from-home orders and large scales of temporary furlough/unemployed workers are applied to reduce virus spread at office, which also impose significant socio-economic burdens on individuals and businesses. 20 As droplets and aerosols have been widely recognised as the major transmission routes of respiratory epidemics [7, 8] , social distancing by avoiding close contact with other people have been adopted as the major measure to effectively reduce the spread of the virus. Various levels of social distancing measures have been implemented in each country according to their different conditions regard- 25 ing economic scale and medical system capacity as well as the period and scale of COVID-19 spread. For example, the World Health Organisation (WHO) recommends that a distance of 1m (3.3 ft) or more is safe. Australia, Belgium, Germany, Greece, Italy, Netherlands, Portugal and Spain have adopted 1.5m. The United States has adopted 1.8m (6 ft) distancing, and Canada has adopted 30 a policy of 2m (6.6 ft) [9] [10] [11] [12] . However, recent studies suggested that virusladen aerosol transmission distance could reach as far as 3-10m [13] [14] [15] [16] [17] [18] . The increased transmissibility of Delta variant also made the previously proposed rules in debate. According to these experimental and numerical results, current social distance policies by most countries over the World will need to be up- 35 dated and this is expected to bring significant challenges for offices to re-open. In addition, social distancing measures were found to be only moderately effective and a one-size-fits-all social distancing rule is often inconsistent with the underlying science of indoor airborne transmission of virus [19] . To mitigate the impact of preventive measures on workplace productivity, there is a pressing 40 need for goverments and relevent regulatory authorities to quantitatively evaluate the virus infection risk at a certain distance and tailor these rules to the J o u r n a l P r e -p r o o f Journal Pre-proof local context, which relies greatly on an in-depth knowledge of the mechanisms underlying the indoor airborne transmission of virus-laden droplets. Coughing droplets and aerosol characteristics have been experimentally mea- 45 sured [14, [20] [21] [22] . In general, during the droplet transmission process, large droplets rapidly fall to the ground and only small droplets can remain suspend in the air and be transmitted over meters. Real-world situations are often associated with coughing and sneezing, where expelled droplets are composed of different sizes. However, most of these previous experiments focused only on the 50 maximum travel distance of the small size expelled coughing droplets. Despite of their large travel distances (3-10m) , the amount of virus carried by the small droplets is small, and therefore the associated infection risk is expected to be low. Without quantitatively linking the infection probability with the social distance, it is difficult to determine the optimal social distance. Numerical studies have also been performed to investigate coughing travel distance in both outdoor and indoor environments [15, 23, 24] . Compared to experiments, numerical studies can gain insights of the detailed airflow patterns and aerosol movement, and therefore can be used to quantitatively relate the social distance to the probability of infection (PI). Recently, many studies have 60 identified the key environmental parameters such as the wind speed/direction, whether or not wearing a mask and the exposure durations [15, 25, 26] . However, offices are characterized as confined spaces with high personnel densities, long contact hours and frequent communications. Therefore the investigation focus needs to be shifted from the outdoor wind scheme and face covering to 65 temperature, humidity, indoor wind scheme and the selection of the infection risk modelling. To investigate the virus transmission in indoor environment, Sun et al. [16] proposed a novel infection risk model, which was developed by modifying the classical perfect-mixing-based Wells- Riley model [27] . A target probability of infection value, 2%, was set to evaluate the appropriate social 70 distances in different scenarios. The authors also proposed a critical parameter named social distance index (abbreviated as P d in their study). However, in this work, the travel distance of the expelled droplet was calculated under over-simplified assumptions. The inclusion of more office related parameters, such as horizontal drag force, air humidity, thermal plume and droplet-airflow 75 interactions, are expected to improve the infection risk model and hence derive a more accurate estimation of reliable social distances for an office environement. In this study, we developed a new CFD based numerical model to predict realistic transmission of COVID-19 droplets in an office environment. This model includes the office relevant parameters such as horizontal drag force, air humid-80 ity, thermal plume and droplet-airflow interactions, and using this model we were able to deduce the relationship between the infection risk and the social distance. The coughing flow profile and droplets movement after expelled from a sitting person with natural thermal plumes were simulated under different humidity levels. The droplets' evaporation process was validated and included 85 in the analysis of droplet sedimentation and travelling distance to reflect a comprehensive evaluation of the typical office social distancing requirements. The improved Wells-Riley model was calibrated by real cases to predict the PI un-entering into a respiratory zone, where droplets are considered respirable only when entering it. Our results quantified the virus infection risk in the office by estimating PI over different social distance, humidity and ventilation rate. The calm and wind scenarios are simulated to investigate the effect of typical indoor wind on the transport of cough expelled droplets. The infection risk of 95 the Delta variant is also taken into consideration and compared with the SARS-CoV-2 wild type. This study is expected to provide supporting information for policy makers to determine the required distancing policies and required ventilation rate for densely populated offices before reaching widespread vaccination coverage for COVID-19. It will also provide a numerical framework to evaluate 100 infection risks for future epidemic outbreaks. The computational domain is a representative domain for a typical office scenario which consists of a confined space with dimensions of 3.7m×2.0m×2.6m 105 and a sitting manikin on a chair, as shown in Figure 1 . The manikin and the chair models were reproduced from Yan et al. [28] . The manikin's mouth is at a height of 1.2m, with a distance of 3m to the domain boundary in front and 1.4m to the ceiling. A coughing jet is expelled from the mouth opening with an area of 2.8cm 2 . Surrounding the manikin is polyhedral mesh with size 0.5mm at the mouth opening, 1mm on the face and 4mm on the body surface. Five fine prism layers were created around the body to accurately capture the thermal plume and nearwall flow characteristics. The first layer thickness was set 0.2mm and the growth rate was set 1.2 to make sure y + < 1, as suggested by the requirements of the 115 Transition SST turbulence model [15, 29] . The surface of the manikin is covered with polyhedral mesh and it is transitioned to hexhedral(cut-cell) mesh to fill the volume of the computational domain. As shown in Figure 1b , the volume mesh is refined in front of the face and above the head to capture detailed cough jet and thermal plume airflow characteristics. Three volume meshes with cell 120 numbers of 1.23 million, 1.67 million and 2.01 million were created to perform mesh independency test. The velocity data along a 40 cm vertical line 0.5 m in front of the mouth at time=0.5s were extracted and found the increase of cell number from 1.67 million to 2.01 million only produced a negligible change (< 2%) on the velocity profile. The final mesh for the simulation consists of 1.67 125 million polyhedral-hexahedral mixed cells, 6.55 million faces and 3.38 million nodes, with the maximum skewness of 0.87. The floor, the ceiling and the chair were set no-slip walls at room temperature of 25 • C. The surface temperature of the manikin body was set to 32 • C. With J o u r n a l P r e -p r o o f Journal Pre-proof the constant temperature between the manikin body and the room temperature, natural convection occurs and thermal plume rises along the body surface. The humidity was modelled by activating species transport model. For saturated humidity conditions, the mass fraction of water in the air are 1.9% and 3.3% for temperature 25 • C and 32 • C, respectively. The initial cough airflow was set 135 to 32 • C at saturated humidity. Calm and wind scenarios were investigated in this study. For the calm scenario, the indoor airflow is dominated by the thermal plume generated by the manikin. Four side walls (left, right, front and back) of the confined box were set pressure outlet with static pressure of 0 Pa. For the wind scenario, typi-140 cal indoor wind is applied with the direction from the back to the front of the manikin to address the maximum effect of the air current on droplet transmission. The back and front walls were set velocity inlet and outlet, respectively, with a constant wind speed. Wind speed in indoor office environment is 0.05-0.25m/s [30-32]. The maximum wind speed 0.25m/s was used as the worst 145 case scenario to illustrate the cough expelled droplets transmission in a typical indoor environment with wind. The cough jet direction was set horizontal and the coughing flow rate at the manikin's mouth openning was extracted from the measured data of Gupta et al. [33] , in which the fitted equation was described in detail. According to Prior to the cough process, the steady simulation was conducted to form the air velocity/temperature distribution and to establish the thermal plume. Transition SST model was used to simulate the turbulent effect as it is more consistent with the natural convection scenario [15] . The SIMPLE scheme was 160 selected for the pressure-velocity coupling and Second Order Upwind scheme was selected for momentum spatial discretization. A transient simulation was conducted starting from the converged steady results. Adaptive time steps were used to maintain the courant number below 1. The minimum time step was 0.002s when the cough flow rate reached its peak at 0.083s. 10,000 droplets 165 were released 2mm in front of the mouth opening and they were released at the time of 0.05s to mimic the travelling time of cough droplets from throat to the mouth. The initial velocity of droplets released is consistent with the cough jet flow velocity at 0.05s. The size of cough expelled droplets ranges from submicron to hundreds of microns. Zayas et al. [22] measured droplet size distribution from 0.12µm to 858µm and found 97% of droplets are smaller than 1µm. Specifically, most droplets are concentrated at size around 0.3µm. However, as viral load is proportional to the droplet volume and considering the volume of a 0.3µm droplet 175 J o u r n a l P r e -p r o o f Journal Pre-proof is merely 1 × 10 −5 of a 10µm droplet, this study focuses on droplets larger than 1µm. Asadi et al. [34] measured droplet size distribution under different speech voice loudness, a scenario that is slightly different with this study. Morawska et al. [35] measured droplet size distributions generated by cough. However, the size range was truncated at < 20µm. For detailed size distributions covering 180 a wide range of micron particles, Chao et al. [21] experimentally measured the sizes of droplets expelled from coughs and derived a size distribution by curve fitting ranging from 1µm to 1, 000µm. The original unit of the number fraction was "number of particles per unit ln(µm)". In this study, the droplet number fraction is converted to a more convenient unit "num of particles per unit µm" 185 as shown in Figure 2b . Accordingly, the fitting equation is converted to, Where d is the droplet size in µm and fitted parameters are a = 0.43, σ = 0.54 and µ = 13.5, as calculated in Shang et al. [36] . WHO previously suggested that the droplets larger than 5-10µm would quickly drop to the ground within 1m [37] . However, recent studies updated 190 this criteria and suggested a cut-off size of 100µm [7] . On the other hand, the number fraction distribution peaks at 2.87µm and then sharply decreases. When the droplet size reaches 100µm, the number fraction drops to 8.73 × 10 −4 /µm, merely 1.7% of its peak value. Therefore in this study, 100µm is considered as a cut-off size and only 1 − 100µm droplets were taken into consideration. Un-195 steady Lagrangian method is used to track droplets' trajectories. The tracking scheme is set trapezoidal with a step length factor of 5. The evaporation and temperature dependent latent heat model were activated during the simulation. The number of droplets was analysed by checking the vapor concentration field. When the number reached 10,000, the predicted vapor concentration field was 200 found to be free from the droplet number. 20 representative initial droplet sizes: 1µm, 2µm, 3µm, 4µm, 5µm, 10µm, 13µm, 16µm, 20µm, 25µm, 30µm, 35µm, 40µm, 45µm, 50µm, 60µm, 70µm, 85µm and 100µm were selected to mimic the 1-100µm size range and 500 droplets were released for each size to statistically calculate their movements and size changing due to evaporation. 205 The airflow is solved by the Navier-Stokes governing equations in Eulerian method. The mass and momentum conservation equations are, Where the v is the air velocity vector, p is the static air pressure, g is the gravity, ρ is the air density and µ is the air viscosity. The shear stress transport 210 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 (SST) transition model is used to predict the laminar-to-turbulent cough jet airflow. This turbulence model has been extensively validated with a good balance of computational cost and accuracy compared to LES simulations [15, 29] . The droplet evaporation process requires the air and water species to be 215 calculated separately. The species transport model is used to simulate the air water-vapor mixture airflow. The evaporation process is simulated by a multicomponent Eulerian-Lagrangian model. The humid air is depicted as a mixture of dry air and water vapour and is treated in the Eulerian framework, Where φ is a physical material property such as density and thermal capacity, 220 f is the mass fraction of a specie. The continuity equation is solved separately for air and water species, with shared density ρ mix and shared velocity U mix , Where D k and S vapour are the kinematic diffusivity of water vapour and mass source of water vapour caused by evaporation process. Momentum and 225 energy equations were solved under shared velocity, temperature and pressure for air and water species, Where F md is the interfacial forces acting on the droplet surfaces and S b is the momentum source caused by buoyancy. H mix , T mix and Q md are enthalpy, temperature and interphase heat transfer rate, respectively. The evaporation 230 process is controlled by the equilibrium vapour pressure relative tothe ambient pressure at the surface of droplets. The mass transfer rate and the droplet temperature were calculated by, 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 J o u r n a l P r e -p r o o f Journal Pre-proof Where D dyn is the dynamic diffusivity of water vapour and Sh is the Sherwood number. M vapour and M mix are molecular weights of vapour and the 235 mixture. P (vapour,surf ace) and P (vapour,mix) are partial vapour pressures on the droplet surface and in the humid air. C pd and h l are heat capacity of the droplet and latent heat of water. The droplets were treated as a discrete phase and the their aerodynamic motion ia modelled in a Lagrangian framework. The drag force and the gravity 240 (buoyancy) force are the dominant factors for aerodynamics of micron sized droplets, Where m d , ρ d and U d are droplet's mass, density and velocity, respectively, and the drag coefficient C D is estimated as, Where a 1 , a 2 and a 3 are empirical constants defined by Morsi and Alexan-245 der [38] . In order to accurately model the droplet dispersion with the turbulent airflow, the Discrete Random Walk Model was activated with the time scale constant 0.15. The expelled droplets are composed of water and non-volatile solid compo-250 nents, known as nuclei. The detailed properties of non-volatile solutes can be referred to mucus composition, which are dominated by Na+, K+, Cl-, lactate and glycoprotein. Nicas et al. [39] suggested the mass fraction of the non-volatile components could be as low as 0.88% and Li et al. [23] estimated a 1.8% mass fraction. In this study, when expelled from mouth, the evaporation of water 255 and the shrinkage of particles are expected. In this study we adopt the nuclei density 1, 000kg/m 3 as estimated by Nicas et al. [39] and assume the evaporable water takes 98.2% of the total mass. Assume the droplet nuclei has the same density with water, the nucleus size is estimated by, This leads to the fully evaporated size d f = 0.262d o . In moderately humid 260 and dry environments, the size of a free-falling droplet could decrease 73.8% and thus shrink into a airborne droplet through evaporation process, especially when the thermal plume generated by the human body heat is present [7] . The J o u r n a l P r e -p r o o f Journal Pre-proof parameters of temperature (T), relative humidity (RH) and droplet sizes were considered to affect evaporation of droplet particles. The droplet evaporation modelling is validated with measured evaporation data from Wei et al. [40] for 10µm droplets and 100µm droplets at RH=0% and RH=90% (Figure 3 ). Droplets evaporate faster for larger-sized droplets and in low-humidity environments. For a 10µm droplet, the evaporation process terminates within 1s whereas a 100µm droplet takes much longer time (60s) to fully 270 evaporate when the environment is humid (RH=90%). The simulation-predicted droplet size variation due to evaporation over time showed good agreement with the experimentally measured data. The Wells-Riley model has been widely used to estimate the epidemic in-275 fection risk. The Probability of Infection (PI), which is defined as the ratio of infected people and susceptable people in a confined space, can be estimated by a classic equation [27] , Where I is the number of infectors, q is the quantum generation rate from one infector that is determined by reverse calculations from actual events, p is the 280 pulmonary ventilation rate, t is the exposure time and Q is the room ventilation rate. For a sitting person, the pulmonary ventilation rate p is estimated as 0.3m 3 /h [16] . The classical equation does not involve room ventilation modes and social distance among people. To address this problem, Sun et al. [16] improved the 285 evaluation equation by introducing a social distance index SDI, air distribution effectiveness E Z and initial infection rate B, The SDI determines the cumulative fraction of cough-expelled droplets that reaches the respirable region at distance d that are potentially inhaled by the susceptible people. However, Sun et al. [16] calculated the distribution of SDI using a oversimplified "distance reaching method", in which the travelling time was calculated by assuming droplets constantly reached their terminal velocity to satisfy the balancing of drag force, gravity and buoyancy. In addition, the height of a droplet when reaching a certain travel distance was not considered in the pre-295 vious calculation as shown in blue plane in Figure 4 . However, this assumption was not reasonable for realistic case as the probability of inhaling micron-sized particles away from the breathing zone is extremely low. Shang et al. [41] investigated the influence of airflow on the micron particles inhalation close to the nostrils and found that only the breathing zone with a radius< 3cm significantly 300 affected the particle respirability. WHO [42] and Safe Work Australia [43] both J o u r n a l P r e -p r o o f Journal Pre-proof suggested that 30cm is a proper range for the breathing zone. In this study, transient CFD simulations were conducted to calculate the SDI with improved accuracy. The "spherical zone method", in which virus-laden droplets reaching 30cm from the centre of the susceptible person's mouth were considered as res-305 pirable droplets, as shown in the red circle in Figure 4 . Therefore, the equation to calculate the social distance index is modified to, Where N vr (d) is the cumulative number of virus reached the respirable region at the distance d, N vt is the total number of virus expelled. C is the virus concentration in the droplet when expelled (before evaporation) and d i is the 310 original diameter of the ith expelled droplet. The airflow field characteristics, such as the cough jet flow and the thermal plume, have a strong impact on the travel distance of expelled virus-laden 315 droplets. Velocity contours on the middle plane at different time points are presented in Figure 5 to provide insights of the cough jet flow travelling in the air. In general, the cough jet exhibits a fast decay after being expelled into the air, and a maximum travel distance of 1.7m is observed at t = 10.0s. Prior to the start of a cough (t = 0s), due to the natural convection effect driven by the 320 temperature difference between the manikin body and the room environment, a relatively stable rising plume with upward thermal buoyancy flow is established near the body, especially for the upper part of the body (head, arms, chest, and the thighs). During coughing, an elongated flow jet with high velocity magnitudes is formed, which quickly reaches to a length of 1m by the end of the 325 coughing (t = 0.5s). At t = 1.0s when the cough ends, a wake region detached from the thermal plume is created and the horizontal travelling distance of this wake remains relatively unchanged. At a later time t = 5.0s, the wake region travels further downstream and reaches to a horizontal distance of nearly 1.7m without significant vertical drop. By the end of the simulation at t = 10.0s, a 330 slight drop of 0.3m is observed for the wake region. Despite this vertical change, the wake region remains suspended in the air with no apparent horizontal motion. Therefore, it is expected that virus-laden droplets can travel at least 1.7m after being released from an infected person due to the entrainment effect of coughing. To manifest how cough expelled droplets evaporate as travelling in the air, the variation of droplet size distributions at different time events (t = 0.05s, 0.1s, 1.0s and 10.0s) under the relative humidity (RH) of 50% are presented in Figure 6 to reflect the droplets shrinkage due to the evaporation. At the beginning of the cough (t = 0.05s), the droplet size distribution remains almost 340 identical to its initial condition (Figure 2b) , which generally has larger but fewer 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 J o u r n a l P r e -p r o o f Journal Pre-proof droplets. Over the course of time, expelled droplets experienced dramatic number and size changes as travelling in the air. The evaporation process of small droplets occurs at a faster rate than that of large droplets. Our results indicate that the evaporation can be divided into two stages: Firstly, fast evaporation oc-345 curs among small droplets ranging from 1µm-4µm, which forms the ub-micron part of the droplets at t = 0.1s. Secondly, the evaporation of larger droplets is concluded, which forms additional droplets with medium size (ranging between 1µm to 8µm) at t = 1.0s. Consequently, the terminal size distribution (the red curve at t = 10.0s) exhibits a wider diameter range extending from sub-micron 350 to 100µm. Meanwhile, the droplet size with peaking number fraction is reduced from 2.9µm at the beginning of the cough to 0.8µm at 10.0s. These findings are consistent with the literature study conducted by Yan et al. [44] , which indicates the evaporation time for 3.5µm droplets is nearly 0.1s. Predicted trajectories of cough droplets at different sizes are presented in 355 Figure 7 . For small respiratory droplets with an initial size of 10µm, before evaporation occurs, a cone-shaped bundle of trajectories is observed in front of the mouth. However, the 30cm travel distance (red lines) remains relatively short, indicating a quick onset of evaporation. Beyond this distance range, expelled droplets rapidly evaporate into to terminal nuclei with a size of 2.6µm 360 (blue lines). As a result, those droplet nuclei with significantly reduced diameter sizes can travel a relatively long distance along with the coughed airflow. Besides the dominant bundle of trajectories, few droplet nuclei are captured by the body thermal plume, which turns their motion from longitudinal to vertical. Therefore, for smaller sized respiratory droplets, they are expected to remain 365 airborne in the room for a prolonged period over at least 10s. For medium respiratory droplets with a diameter of 60µm, predicted trajectories corresponding to the original droplet size (red lines) are much longer than that of the small-sized droplets (approximately 1m). As evaporation occurs, expelled droplets undergo significant size reduction. Because of the relatively large 370 initial droplet size, the evaporation (with size changing from 60µm to 15.7µm) takes longer period (in seconds). Different from small sized droplets, most terminal nuclei of medium sized droplets are found at the bottom of the descending cloud. Consequently, despite the reduced extent of dispersion process, more terminal nuclei are found in front of the body, which are effectively pulled back 375 and raised upwards by the body thermal plume. For large sized droplets (diameter size of 100µm), a completely different dispersion pattern is observed. At the beginning, the trajectory angle for expelled droplets remains relatively unchanged with no distinct vertical displacement. After all droplets have travelled a projectile length around 1m, they start to 380 descend to the ground due to the combination effect of aerodynamic drag and gravitational force. As the size of droplets is very large, the evaporation is delayed, where the final droplet size (before reaching the ground) is estimated as 50µm, being nearly twice of the corresponding nuclei size (26.2µm). 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 For planes d = 0.1m and 0.2m, most droplets concentrate around the original releasing point, with droplets on the periphery showing reduced size. This indicates that the majority of the expelled droplets are carried forward by the cone-shaped cough jet. In the meantime, evaporation tends to start from the outer side of the droplet cloud due to a better contact between droplets and 395 environment. Besides the dominant droplets cloud, some small-sized droplets are found in a strip-shaped region, which extends from y = -0.7m to upwards, which corresponds to droplet trajectories that are diverted by the body thermal plume as shown in Figure 7 . For plane d = 0.4m, the dominant space of the droplets further expands 400 radially, and large-sized droplets start to descend from the dominant core region due to the gravitational effect. For vertical plane d = 1.0m, the droplets cloud continues to drift downwards. Because most suspending droplets are in the size range of 3 − 10µm, a strong extent of droplet dispersion is observed. For plane d = 1.7m, only few droplets (with the size smaller than 5µm) remain suspended 405 in the air. The study revised the social distance index (SDI) by adding a respirable region for respirable virus-laden aerosols, in which the definition is changed to a spherical shape centered at the mouth opening with a radius of 30cm. The 410 revised SDI stands for the fraction of respirable virus over total expelled virus. The correlation between this SDI and social distance is plotted in Figure 9 , where effects of different relative humidity (RH) are also considered. In general, for the RH=50% case, predicted SDI remains nearly 100% for indoor office with social distance less than 0.6m, which presents strong safety 415 alerts for potential virus spread. As the social distance increases to 0.75m, the SDI rapidly reduces to 50%. It gradually decreases to 10% when the social distance reaches 1.5m and finally, a 2m social distance can ideally prevent the airborne transmission. Results also show that the relative humidity can affect the virus-laden droplet transmission in a certain social distance range, extend-420 ing from 0.75 to 1.75m. Specifically, dryer environment (RH = 10%) slightly increases the SDI, while wetter environment (RH = 90%) tends to lower the SDI. This is because dryer environment enables a higher evaporation rate for expelled droplets, which contributes to a much faster droplets sizes reduction and a longer airborne transmission distance. Consistent findings can be found 425 in Ward et al. [45] , which reports an increase of 6.11% in COVID-19 cases due to a 1% reduction in RH. The "distance reaching method" considerably overestimates the SDI, with the major difference between the "spherical zone method" and the "distance reaching method" being found among the distance 0.7m-1.8m. Noticably, Com-430 pared to the SDI curve in the study of Sun et al. [16] , the current study predicts a much sharper decrease of SDI for the distances between 0.6m and 1.5m, J o u r n a l P r e -p r o o f Journal Pre-proof which makes the probability of infection rate more sensitive to the social distance around this range. This is mainly due to significantly different social distance index profiles caused by the different calculation methods adopted in 435 two studies. First, Sun et al. [16] used a simplified approximate model to calculate droplets trajectories rather than conducting CFD simulations. The model only calculated the time for a droplet to fall to ground and ignored the horizontal drag force, which significantly overestimated the droplets' travel distance. Second, Sun et al. [16] adopted the assumption that all droplets that reach a 440 certain distance are respirable, whereas in this study, as shown in Figure 4 , the respirable zone is changed to a sphere with radius 30cm. In the modified Wells-Riley model, the parameter of quantum generation rate q has not been determined. It needs to be reversely calculated through actual 445 cases. We collected actual data from 4 published COVID-19 superspreading events including 3 events in confined bus spaces in China and 1 event in a call centre in Korea. The calculated corresponding q values are listed in Table 1 . The calculated q is between 0.142-0.168 quantum/s and the average value 0.158 quantum/s is used for the infection risk evaluation. The estimation of q is considerably stable as the variation among 4 cases is less than 10%. To validate the reliability of the estimated q value, four probability of infection (PI) curves over exposure time curves are plotted along with the reported PI values in the actual cases, as indicated by circles in Figure 10 . In general, the comparison shows that the predictions from the modelling match 455 the actual data very well, with the largest difference of 10.1% found in the Hunan Bus 1 case. However, Sun et al. [16] used the similar method and estimated the infective quantum q to be 0.238 quantum/s, 51% higher than that in the current study. As comparisons, Bounanno et al. [46] estimated the q under different scenarios and found the high quanta emission rate could reach up to Based on the reversed calculated quantum generation rate, the infection risk in a typical workplace is predicted in the contour plots to present the effects of social distance and ventilation rate ( Figure 11) . A 8-h working exposure scenario 465 and a ceiling supply, floor return ventilation form (Ez=1) were selected to represent the typical working environment and low, medium and high (RH=10%, 50% and 90%) humidity conditions were considered. The initial infection rate is assumed 2.8% based on the estimation from existing antibody tests [16, 53] . Three contour lines indicating infections rates of 2%, 10% and 20% were plot-470 ted to classify the contour plots into low, medium, high and ultra high risk categories. In general, the downward inclined contour lines demonstrated that longer social distance and higher ventilation rate effectively lead to lower infection risk. In the medium humidity (RH=50%) case, considering most standards for the 475 workplace ventilation rates are higher than 15m 3 /(h.p), 1.8m could be considered as a safe social distance that effectively controls the PI below 2%. The 2% J o u r n a l P r e -p r o o f Journal Pre-proof the 10% separation contour line, a social distance of 1.5 − 1.6m is required for a typical ventilation rate. The 20% separation contour line is more dependent on the ventilation rate. To maintain this risk level, a ventilation rate of merely 10m 3 /(h.p) is required to a 1.5m social distance arrangement. When the social distance decreased to 1.05m, this risk level could still be achieved if the 485 ventilation rate is adjusted to 50m 3 /(h.p). The low and high humidity cases exhibited the similar trend with the medium humidity case. The major difference is that the lower humidity drives the separation lines upwards (longer social distance required) and the higher humidity drives them downwards (shorter social distance required). When there is indoor ventilation, the air flow is expected to have a significant impact on the transport of the cough expelled droplets. We, therefore, simulated the worst case scenario when there is wind blowing from the manikin's back to the front and compared to the results under the calm scenario. According to the 495 literatures, indoor air flow rate is in the range of 0.1 − 0.25m/s. Here, the air flow rate was chosen to be 0.25m/s in order to simulate the worst scenario. To illustrate the effect of indoor wind on the virus-laden droplet transmission, the airflow field and the droplet transmission with wind under relative humidity of 50% are shown in Figure 12 . Figure 12(a,b) show the airflow and the distribution 500 of the droplets at a representative time t = 10s. The distribution of the droplets that deposit or escape the compulational domain is visualized in Figure 12c . The velocity contour and airflow streamlines in Figure 12a show that a wake region is formed in front of the manikin with relatively low velocity and strong vortices. The wind accelerates upwards above the chair and manikin's head, The dispersion of droplets in Figure 12b shows that large droplets (> 20µm post-evaporation, shown in red) quickly deposit on the floor. However the transports of droplets smaller than 20µm (post-evaporation, shown in blue) are mostly dominated by the airflow field. Interestingly, large amount of droplets 510 are trapped in the airflow wake region and are gradually released forward by the wind, thus forming a continuous droplets band from the breathing zone to the outlet of the computational domain. Consequently, as shown in Figure 12c , large particles (> 20µm post-evaporation, shown in red) tend to deposit on the manikin and on the floor within 1.5m from the manikin. Deposition of droplets 515 with size 15 − 20µm (shown in yellow) scatter 1.5m -3m in distance and almost all droplets < 15µm (shown in blue) suspend in the air, being carried away by the wind and escape the computational domain. This is consistent with literatures that it takes at least 30mins for 1-5µm particles to deposit on the ground [54] . Since the middle of 2021, the Delta variant has been dominating the global pandemic. According to reports about transmissibilities of major SARS-CoV-2 variants, the Delta variant is roughly 200% transmissible compared with the original virus strain (wild type) [55] . Therefore, the q of the Delta variant in this study is estimated as 0.316 quantum/s. The SDI and the PI are estimated in the wind scenario for the wild SARS-CoV-2 strain and the Delta variant (Figure 13 ), and compared with the wild virus type case in the calm scenario (without wind). Similar with the calm scenario, the SDI remains 100% when the distance is within 0.6m from the manikin. When the distance is larger than 0.6m, the SDI for the wind scenario 530 decreases at a slower rate than that for the calm scenario. When the distance reaches 1.8m, the SDI for the wind scenario remains at 18%, while the SDI for the calm scenario reaches 0. The SDI for the wind scenario drops to 2% at a distance of 3m. In order to keep the infection under control, social distance rule needs to be 535 designed to control the reproduction number R not higher than 1. Considering a typical office with 10 people, adopting an PI value of 10% would result in R ≤ 1. We further considered the impact of two virus types (the wild type vs the Delta variant) and plotted the constant PI=10% lines after typical 8h-working time for both calm and wind senarios (Figure 13b ). 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 To safely reopen the office before reaching the comprehensive COVID-19 vaccination , the social distance rule applied in the indoor environment needs to be carefully evaluated. This study used Computational Fluid Dynamics(CFD) 555 techniques and investigated how probability of infection (PI) of COVID-19 changes with different social distance. The study was carried out by simulating a typical office enviroment under varient humidity levels, wind scenarios and virus types. Several conclusions can be addressed from the CFD results: 1) Most of the cough expelled droplets evaporate to nuclei within 1s at the 560 room temperature and a relative humidity (RH) of 50%. It is essential to include the evaporation process into the virus-laden droplets transmission simulations; 2) In the calm environment, 2-meter social distance is a sufficient measure to maintain a low risk of infection in present office environment. PI is 565 slightly higher in a dryer environment due to the stronger evaporation effect, which leads to longer suspension time for cough expelled droplets. On the contrary, a wet environment reduces the droplet evaporation and decreases PI. In general, a social distance of 1.8m is recommended to maintain a low infection risk target when the ventilation rate meets the 570 standards 15m 3 /(h.p). At a higher ventilation rate, the required social distance can be slighted decreased; 3) The presence of indoor wind and the Delta variant of SARS-CoV-2 significantly affects the existing social distance rule. With a wind speed of 0.25m/s, social distance of 2.8m is recommended for the wild virus type 575 and 3m is insufficient to contain the transmission of the Delta variant. The results from this study can offer practical references to adjust social distance rules and ventilation rates under different PI risk targets and actual humidity levels. Future works will focus on conducting CFD simulations to finetune the parameters in the modified Wells-Riley model by considering effects of 580 different ventilation schemes and multiple human manikins on airflow patterns . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 Figure 3 : Evaporation validation. The numerical results are compared with measured data from Wei et al. [40] for droplet evaporation process validations. Two humidity levels (RH=0% and RH=90%) are considered for two droplet initial sizes (a) 10µm and (b) 100µm cases. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 J o u r n a l P r e -p r o o f Journal Pre-proof Figure 9 : Social Distance Index (SDI) calculated as the number fraction of virus entering respirable areas. Results are compared with the "distance reaching method" and the simplified analytical solution from Sun et al. [16] 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 Figure 11 : Contour of Probability of Infection (PI) after typical 8h-working time in a ventilated office environment. RH=50%, 10% and 90% conditions are plotted to represent normal, dry and wet environments, respectively. 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