key: cord-0970361-10nigbly
authors: Faleiros, David Engler; van den Bos, Wouter; Botto, Lorenzo; Scarano, Fulvio
title: TU Delft COVID-app: A tool to democratize CFD simulations for SARS-CoV-2 infection risk analysis
date: 2022-02-25
journal: Sci Total Environ
DOI: 10.1016/j.scitotenv.2022.154143
sha: 10870316846cf5c30861c745b6e818a6d6460638
doc_id: 970361
cord_uid: 10nigbly

This work describes a modelling approach to SARS-CoV-2 dispersion based on experiments. The main goal is the development of an application integrated in Ansys Fluent to enable computational fluid dynamics (CFD) users to set up, in a relatively short time, complex simulations of virion-laden droplet dispersion for calculating the probability of SARS-CoV-2 infection in real life scenarios. The software application, referred to as TU Delft COVID-app, includes the modelling of human expiratory activities, unsteady and turbulent convection, droplet evaporation and thermal coupling. Data describing human expiratory activities have been obtained from selected studies involving measurements of the expelled droplets and the air flow during coughing, sneezing and breathing. Particle Image Velocimetry (PIV) measurements of the transient air flow expelled by a person while reciting a speech have been conducted with and without a surgical mask. The instantaneous velocity fields from PIV are used to determine the velocity flow rates used in the numerical simulations, while the average velocity fields are used for validation. Furthermore, the effect of surgical masks and N95 respirators on particle filtration and the probability of SARS-CoV-2 infection from a dose-response model have also been implemented in the application. Finally, the work includes a case-study of SARS-CoV-2 infection risk analysis during a conversation across a dining/meeting table that demonstrates the capability of the newly developed application.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which causes the coronavirus disease 2019 , is present in all sorts of bodily fluids (Wölfel et al. 2020) . One of the main routes of human-to-human transmission of COVID-19 is through virion-laden droplets and aerosols of sputum or saliva of an infected person (Asadi et al. 2020 ), expelled either orally or nasally through breathing, speaking, singing, coughing or sneezing (Borouiba et al. 2014 , Mittal et al. 2020 , Gregson et al. 2020 , Bahl et al. 2021 . Virion-laden droplets can enter the body of a susceptible person through the mouth and nose (Mittal et al. 2020 ) (and possibly through the eyes, Kitazawa at al. 2021 ) via inhalation of aerosols, deposition of large droplets or contact with viruscontaminated objects (Goldman 2020) .

The physical process governing the transport of expelled droplets of sputum and saliva are mainly inertia, gravity, air resistance, and evaporation (Xie et al. 2007) . Evaporation continuously reduces the droplets mass until they are reduced to their non-volatile fraction (droplet nuclei) (Liu et al.2017) . Large droplets are greatly influenced by gravity, following semi-ballistic trajectories (Borouiba et al. 2014) . Small droplets (aerosols) instead, are trapped within a hot and moist gas cloud generated by the expiratory activity, reaching significantly larger distances (7-8 m during a sneeze, Borouiba 2020) and remaining airborne for longer periods (minutes to hours). Wells (1934) defined large droplets as those reaching the ground prior to becoming droplet nuclei, while aerosols fully evaporate and become airborne. This threshold, reportedly within 60-100 µm (droplet diameter, Xie et al. 2007 ), depends on the person's height and mouth opening, the exhaled flow velocity, the ambient temperature and the relative humidity.

procedures are described. In addition, Particle image velocimetry (PIV) measurements are performed of unsteady speaking without protection and wearing surgical masks to address the gaps in the reviewed data. Furthermore, a dose-response model (Watanabe et al. 2010) for estimation of the probability of infection and the filtration effect of surgical masks and N95 respirators are made available in the application. A case-study concludes this paper, where a dialogue across a dining/meeting table is simulated through the application, yielding the probability of infection among the attendees.

The purpose of the TU Delft COVID-app is to facilitate the setup of simulations dealing with human-to-human SARS-CoV-2 infection in the widely-used CFD software Ansys Fluent. The application supports the CFD user stepby-step from the geometry design to the generation of user-defined functions (UDFs) that correctly emulate human expiratory activities.

In the process of geometry definition (figure 1), room size, temperature and relative humidity are specified, along with the size and coordinates of doors and windows. Additional parameters account for the number of people, their location, posture (sitting or standing) and orientation, gender, height, weight and clothing. Each person may be coughing, sneezing, speaking or breathing through the nose. Surgical masks and N95 respirators can be chosen during speaking. Following the user selection, the app detects the important boundaries (mouth, nostrils, eyes, body surface, windows, doors and walls) and defines the mouth opening, temperature of body parts and temperature and relative humidity of the exhaled air (section 3.1). The transient air volume flow rate and flow direction at the mouth, during coughing and sneezing, or through the nose, while breathing, are defined (based on literature data) through the use of UDFs (sections 3.2 and 3.3). The flow velocity components during unsteady speaking either unprotected or wearing a surgical mask are defined based on data obtained from the current PIV experiments (section 6). The droplet size distribution for each expiratory activity is defined based on regression of experimental data reported in the literature (section 3.4). The mass flow rate is defined based on the air flow rate and the mass concentration of saliva/sputum droplets (section 3.4). The penetration of surgical masks or N95 respirators are defined by the app considering both penetration through the mask and through leakages (section 4). Furthermore, the app calculates the probability of the exposed subject to become infected by the coronavirus based on a dose-response model (section 5). An overview of the application capabilities is given on table 1.

It is worth noting that the application is built in a flexible platform, where the equations used to define air flows, droplet distribution, mask penetration and the probability of infection can be easily updated as more accurate data become available from ongoing and future studies. The app can be downloaded on the SDC Verifier's website (TU Delft COVID-app, 2021) Table 2 . Surface area of mouth and nostril during coughing (Gupta et al. 2009 ), speaking and breathing (Gupta et al. 2010 ) and sneezing (Busco et al. 2020 ).

The body temperature varies depending on the body part and the clothing. A recent study (Metzmacher et al. 2018) on skin surface temperature is used here as reference. The mean temperature and relative humidity of the exhaled breath, measured by Mansour et al. (2020) , is about 33°C and 72%, respectively.

The air flow rates during coughing (Gupta et al. 2009 ), sneezing (Busco et al. 2020 ) and breathing (Gupta et al. 2010 ) used in the COVID-app are reported concisely below in the notation of this paper. Only average flow rate for speaking (Gupta et al. 2010) or as a quasi-steady jet approximation from the constant repetition of strong syllables J o u r n a l P r e -p r o o f Journal Pre-proof (Abkarian et al. 2020 ) has been reported in detail for use in simulations and is not reviewed here. The boundary conditions for unsteady speaking used in the COVID-app are based on experimental data reported on section 6.

Coughing flow rate 3.2.1.

The expelled air flow rate from 25 people (12 females and 13 males), while coughing, has been measured with a spirometer by Gupta et al. (2009) . The authors characterized the volume flow rate of air ( ) with a 2-gamma distribution, as follows:

where * = / and = / . , the cough peak flow rate, is reached at = (figure 2). The first term on the right-hand-side of eq. (1) depends on the constants 1 , 1 and 1 (table 4). The second term depends on the functions 2 ( * ), 2 ( * ) and 2 ( * ), where * = ℎ /( ) is the dimensionless cough expired volume. The total air volume expired during one cough is given as:

where ℎ~0 .6 s is the cough duration. 

The authors only measured the sneeze of a single person and did not provide therefore any correlations with gender, height and weight. The constants are given on table 6. The velocity magnitude is calculated as:

where is the air density. The air velocity during sneeze (figure 3, right) for = 1.136 (T = 33.25 °C, p = 1 atm, relative humidity RH = 71.6%) is one order of magnitude larger than that during coughing, reaching a peak velocity of 120 m/s at the mouth, which is about one third of the sound speed in air at normal temperature and pressure. Table 6 . Constants for calculating sneezing volume flow rate from Busco et al. (2020) . and exhalation [l/s] are given as: 

The direction of the exhaled air can be defined based on the two angles and between the symmetry axis of the expelled jet or puff and the horizontal lines on the side and front planes (figure 5), respectively. These angles have been estimated (table 8) from the inspection of photographs of cigarette smoke exhaled by humans during coughing (Gupta et al. 2009 ) and breathing (Gupta et al. 2010 ). Coughing

Exhaled breath (mouth) 4° 90°

Exhaled breath (nose) 60° 69º

Sneezing Eq. (7) 90° Table 8 . Flow direction during coughing (Gupta et al. 2009 ), breathing (Gupta et al. 2010) and Sneezing (Busco et al. 2020 ).

The angle during a sneeze (Busco et al. 2020) , measured based on the light scattering from laser-illuminated droplets, also accounted for the head movement and is given as a function of time:

= { 40.7 sin(4.71 + 1.77) + 15.5 sin(13.5 + 2.19), 0 ≤ ≤ 0.24 13.7 log( ) + 17.9, 0.24 < ≤ 0.54

The flow angle during speaking depends upon the pronounced syllable as described by Abkarian et al. (2020) . To the authors' knowledge there is not yet sufficient data available to cover each syllable individually. Instead, in this paper the horizontal and vertical components of velocity while reading a passage are given as a function of time (section 6.4).

Sputum and saliva are simulated as water liquid with 98.2% volatile content (Liu et al. 2017) . This means that the droplet nuclei (droplets after complete evaporation) reduce to 1.8% of their initial volume (the diameter reduces to about one quarter of its initial value). The droplets initial velocities are set equal to that of the flow by the application J o u r n a l P r e -p r o o f through an UDF. The most important experimental data used as inputs for the simulations concerns the droplet size distribution and the mass flow rate.

Mass flow rate 3.4.1.

The mass flow rate is usually measured indirectly through measurements of the total mass expelled during one event or of the droplet mass concentration [kg/m 3 ]: 

where ̅ is the ensemble averaged concentration obtained from experiments. Direct measurements of mass concentrations are used to obtain the mass flow rate during breathing (Gregson et al. 2021) .

Techniques that physically capture the total expelled mass are also suited for obtaining the average mass concentration when the total air volume is known. This method is used here for obtaining the mass concentration during coughing, sneezing and speaking.

The total mass during coughing has been measured by weighing a respiratory mask ( The presence of either leakage (mostly mask) or water vapour condensation (plastic bag) affects the results.

The exhaled air volume during a single cough or sneeze is obtained by integrating the volume flow rate during the event duration. For speaking, the average volume rate during counting from 1 to 10 is used (Gupta et al. 2010) :

J o u r n a l P r e -p r o o f which is integrated in time to yield the total expired volume 1−100 while counting from 1 to 100.

To obtain the mass concentration, the expired volume is estimated based on the participants of the saliva mass measurements of Xie et al. 2009 . Considering three Chinese males (1.75 m, 73.5 kg, ̅ = 1.9 m 2 ) and four females (1.63 m, 62.2 kg, ̅ = 1.69 m 2 ) (Rodriguez-Martinez et al. 2020), the weighted average of the expired volume is ̅ 1−100 = 59.9 l.

Based on the above, the average mass concentration for coughing, sneezing, speaking and breathing, used to calculate the mass flow rate from eq. (9), are given on Table 9 . Average mass concentration ̅ (mg/l) for coughing, sneezing, speaking, breathing in and out through the nose (n/n), and breathing in through nose and out through mouth (n/m). a Zhu et al. 2006 : average of three male subjects (ℎ ̅ = 1.72 m, ̅ = 68 kg). b Gupta et al. 2009: eq. (2) (male, h = 1.72 m, m = 68 kg). c Duguid (1946) : one sneeze. d Busco et al. 2020: eq. (3) and (4). e Xie et al. (2009) , average of both weighing methods (18.7 mg for mask and 79.4 mg for plastic bag). f Gupta et al. 2010, eq. (10) . g Gregson et al. (2021) .

Droplet size distribution 3.4.2. The Rosin-Rammler particle size distribution (Vesilind 1980) , also known as Weibull distribution, was first applied by Rosin and Rammler in 1933 while studying the fineness of powdered coal. Currently, it is used in spray technology, meteorology, aerosol science, among others (Alderliesten 2013) . Its cumulative distribution function used for fitting measurements of the cumulative mass fraction of particles smaller than , is given as:

where is the uniformity constant and 0 is the characteristic particle size. The definition of 0 follows from eq.

(11): it represents the diameter threshold that separates the particles in two size groups, where the smaller particles ( ≤ 0 ) amount to 63.2% (1 − 1/ ) of the total mass. Measurement data of the particle size distribution during speaking (Chao et al. 2009 and Duguid 1946) , fitted with eq. (11), is shown in figure 6 . Notice that two curve fits are used: one for ≤ 50 μm, prioritizing the data from J o u r n a l P r e -p r o o f Chao et al. 2009 , and another for > 50 μm using both data combined. Dividing the data in two size ranges significantly improves the curve fits, even when a single dataset is used (see figure 7 for sneezing). The fitting parameters and datasets used for all expiratory activities are listed on table 10. The Rosin-Rammler distribution is the standard option available in Ansys Fluent, requiring the user to provide only 0 and , however, the particle diameters are automatically selected within the selected range: [min , max ] . In the COVID-app the user has more control and may select as many diameter ranges [ , , , +1 ] as deemed necessary, where each range is represented by its mean diameter and its mass fraction is given as,

, is the mass of all droplets within the range [ , , , +1 ] and is the mass of all expelled droplets. Thus, only the part of the particle distribution of interest is simulated (e.g. up to 100 µm diameter for airborne transmission) and

represented by the mean diameters of the chosen diameter intervals. The diameter selection process is described in In addition, the use of two Rosin-Rammler distributions to fit the data (table 10) improves the accuracy of the estimated mass fraction of each range with respect to the standard option in Fluent. The mass flow rate per particle diameter range becomes:

Mask penetration is a measure of mask efficiency, based on the droplet concentration upstream and downstream of the mask. Many studies only considered droplet penetration through the mask (Qian et al. 1998 , Lee et al. 2005 Ardon-Dryer et a. 2021), neglecting droplets escaping through leakages between the mask and the subject's face. The penetration of surgical mask and N95 respirator has been measured by Grinshpun et al. (2010) and Cho et al. (2010) using mannequins that simulated real human breathing patterns, with and without leakage (the latter was achieved by gluing the mask to the face of mannequin). These studies have shown that the penetration of droplets due to leakage is the most significant. The total penetration through the mask and leakage is shown in figure 9 . The following empirical fits for surgical masks and N95 respirators, respectively, are suggested: 

Eq. (14) is used in the COVID-app for correcting the mass flow rate of droplets. Unfortunately, Grinshpun et al. (2010) only measured penetration of sub-micrometre droplets, while Cho et al. (2010) limited their measurements to the penetration of N95 respirators for particles of up 4 µm diameter. Therefore, the maximum droplet diameter that may be found downstream of the mask/N95 is found through extrapolation of the dataset from Cho et al. (2010) for the N95 respirator and assumed to be the same for the surgical mask. Figure 9 . Surgical mask and N95 penetration (including leakage). Data used for the curve fits: Grinshpun et al. (2010) and Cho et al. (2010) , obtained from a person breathing at rest.

The probability of infection is calculated based on the dose-response model (Watanabe et al. 2010) :

where is the viral dose given in plaque forming units ( In Ansys Fluent, the number of RNA copies crossing through a surface (e.g. mouth, nostrils and eyes) may be monitored, yielding a direct measure of the probability of infection. In addition, ( ) may be estimated on the entire domain at all times, by assuming the presence of a breathing person at all points in space. In this case, eq. (16) becomes:

where ̅ is the average breathing volume flow rate during inhalation, ( ⃗, ) is the droplet concentration as a function of time and space ⃗, and is the time a subject has been exposed to the infected droplets. Based on eq. . Therefore, for short simulations lasting for less than one minute, the decay of SARS-CoV-2 within airborne aerosols is less than 1% and can be neglected.

In this section, Particle image velocimetry (PIV) experiments are performed to obtain the unsteady flow velocity and direction during speaking, with and without a surgical mask. The main reason for performing these experiments is to be able to reproduce similar flow patterns of unsteady speaking in numerical simulations, where saliva droplets can be accurately modelled and observed. Therefore, the velocity measurements are used to estimate the air velocity at the mouth exit, required while defining the simulation boundary conditions. The image resolution was 0.14 mm/px. Images were acquired in frame-straddling mode (double frame, single exposure) at 10 Hz, with a time interval of 500 µs between frames.

The subject (male, 32 years old, 1.84 cm, 80 kg) was protected against the laser light by safety goggles and a black screen positioned in front of him (not shown), with a 5 cm diameter opening for the mouth exhaled air. A threecentimetre long circular cylinder of the same diameter was positioned at the opening to help positioning the head and to block the laser light from below. The head positioning was done with the subject's nose slightly touching the upper surface of the cylinder. Therefore, inhalation and exhalation through the nose did not influence the measured flow velocities. The entire setup, including the subject, was encompassed by a black tent (about 15 m 3 ), whose main J o u r n a l P r e -p r o o f objective was to contain the smoke. The entire tent was filled with smoke by turning the smoke generator for about 2 seconds, with the tent closed, and waiting for about 10 minutes for the smoke to become homogeneously spread. Three different expiratory activities were measured: breathing in through nose and out through mouth, breathing in and out through mouth, and speaking. Each activity was recorded for the duration of 50 s (500 images), which comprised about 5 respiratory cycles. The speaking activity consisted of reciting an excerpt of the rainbow passage (Fairbanks, 1960) , a speech often used for the study of voice and articulation and representative of the multiple sounds of the English language:

"When the sunlight strikes raindrops in the air, they act as a prism and form a rainbow. The rainbow is a division of white light into many beautiful colours. These take the shape of a long round arch, with its path high above, and its two ends apparently beyond the horizon. There is, according to legend, a boiling pot of gold at one end. People look, but no one ever finds it. When a man looks for something beyond his reach, his friends say he is looking for the pot of gold at the end of the rainbow."

An example of raw image from the PIV measurements is shown in figure 11 . The images were processed via crosscorrelation analysis, using the software DaVis 8.4 from LaVision. The final interrogation window was 48 x 48 pixels (7 x 7 mm2) with 75% overlap, yielding about 160 x 200 vectors per image. Typical uncertainty of a PIV J o u r n a l P r e -p r o o f displacement measurement is 0.1 px (Raffel et al. 2018) . The velocity magnitude close to the mouth varied in the range of 1-5 m/s (3-18 px). Thus, the uncertainty of the instantaneous velocity is estimated to be within 0.5-3%. Figure 11 . Raw image from PIV measurements.

The mean horizontal 

The TU Delft COVID-app is demonstrated through a case study of two people having a conversation without any protective mask across a small table (mouth-to-mouth distance of one metre), representing the situation of two friends in a restaurant or two colleagues during a meeting. Although, only a short simulation of one minute is performed, in which the infected person speaks for a quarter of the time, the results are extrapolated in time, assuming a reoccurring pattern, to give the probability of infection after a few hours.

The transient simulations were set up in Ansys Fluent using the TU Delft COVID-app. The two subjects, one male 1.80 m and 80 kg and one female 1.65 m and 70 kg (standard app CAD models at sitting position are scaled according to their height) ( figure 15 ). The male is infected with SARS-CoV-2 and releases saliva droplets (modelled as water droplets) containing SARS-CoV-2 virions (7×10 9 RNA copies per litre, Wölfel et a. 2020) while speaking.

The male speaks for the first 15 seconds, followed by 45 seconds of normal breathing (simulation ends at 60 s).

Particles are only released during speaking. The female breathes at regular pace while being exposed to the infected droplets expelled by the male. The breathing patterns are shown in figure 4 . The flow velocity during speaking follows the experimental data ( figure 14, left) . Five different droplet diameters have been chosen for this simulation:

1, 3, 10, 30 and 50 µm, representing mainly aerosol transmission. Each particle diameter is injected with a mass-flow rate obtained from eq. (13).

The simulated volume of 1 × 1 × 1.5 m 3 (height × width × length) was gridded using tetrahedral elements of 10 cm far from the bodies and table, using ANSYS Fluent advanced size functions on proximity and curvature (normal angle of 15°). In addition, the mesh is further refined near the eyes, mouth and nose to 2.5 mm and on the nostril surface to 1.5 mm ( figure 1, right) . From a grid convergence analysis, where two grid refinements (factors of 2 and 4) are used to perform the Richardson extrapolation (Roche 1998), the error in the estimation of second-order statistics of velocity due to discretization is calculated to be less than 1% (appendix 2).

The Navier-Stokes' equations are solved with a pressure-based solver, using the coupled pressure-velocity coupling scheme and a second-order implicit formulation with a Courant Number ( = / ) of 25. An adaptative time stepping scheme is implemented through a user-defined-function, based on the Courant Number, the minimum mesh length (Δ ~ 0.5 mm) and the velocity at the mouth of the infected person, limited to a maximum time step of 25 ms.

The turbulence is modelled using the RANS-based Shear Stress Transport (SST) − model as it ensures a proper selection of the − and − zones without user interaction (Menter et al. 2003 ) and has been chosen as default for the application.

The particle behaviour is simulated from a Lagrangian perspective. The equations of particle motion (Mei, 1996) only consider the inertial term, quasi-steady drag and gravity force. The drag coefficient is calculated from the empirical relations of Morsi and Alexander (1972 For demonstration purposes, the energy equation is not included. This is equivalent to the situation of a hot day (about 33 °C, same temperature of the exhaled breath) in air saturated with water (relative humidity of 100%), where buoyancy effects are negligible, and evaporation does not occur. Droplet evaporation is, however, an important parameter and should be considered for more accurate calculations (this option is also available in the COVID-app, with the only drawback of longer processing times). the mouth is about twofold that obtained from the experimental data ( figure 12, top) . A more quantitative comparison is performed along a vertical profile at 20 cm downstream from the mouth (Figure 17) . The streamwise and transverse components of the average velocity during the simulations are slightly overestimated and underestimated, respectively (peak averages velocities are approximately 20% higher and 30% lower, respectively).

There are a few sources of uncertainty in the measurements that could explain the observed differences. One source is due to flow attachment in the top and bottom of the cylinder attached to the mouth during the experiments ( figure   12 , top-left), resulting in a wider spread of the average "jet" (in fact, it is the average flow of several puffs) and, consequently, a lower average velocity. Another source of uncertainty is the translation of velocity measurements a few centimetres from the mouth to a volume flow rate, and, subsequently, to a velocity inlet based on a mouth opening area. The main issues in this process was the lack of time resolution in the measurements and the necessity of having a protection between the person and the measurements for safety reasons. These two facts combined meant that the velocity measurements was a mixture of several pronounced syllables a few centimetres away from the mouth, which required assuming that the velocity profile was a mixture of distinguishable Gaussians (one for each syllable), yielding the 3D velocity profile through revolution around their axis of symmetry (section 6.4).

Measurements near the mouth (preferably in 3D) with higher temporal resolution would yield better input data for the simulations. Error bars represent one standard deviation, which is considerably higher for this highly unsteady flow than the PIV measurement uncertainty (order of 1% for the instantaneous velocity, Raffel et al. 2018 ).

Additionally, the mouth opening during the experiments was not measured and was assumed to be 120 mm 2 , based on measurements of mouth opening during breathing (Gupta et al. 2010 ) and sneezing (Busco et al. 2020 ). However, during speaking, Gupta et al. 2010 , estimated an average value of 180 mm 2 . Had the latter value been used during the simulations, the mouth velocity would be 2/3 of the simulated value.

Nevertheless, the differences in average velocity between experiments and simulations are most likely within natural biological differences in flow velocity during speaking found across different individuals. Thus, the differences found are deemed acceptable for this study, which did not aim at representing an universal speaking pattern. Higher velocities during the simulation should yield more conservative risks estimates with respect to physical-distancing rules.

The probability of infection is estimated directly from eq. The two methods are observed to yield similar infection risks, however a larger risk is obtained when considering the average inhalation flow rate. For instance, after 60 seconds of simulation, the probability based on inhaled particles is 3.5×10 -8 (figure 18, left) which is slightly larger than that near the mouth shown in ( figure 18, right) , where the probability of infections from 5 cm from the mouth of the exposed subject is within 8×10 -8 -11×10 -8 .

Thus, even though slightly overestimated, the method based on the average inhalation flow rate gives insightful information on the relation between infection risk and physical-distancing. This is shown in figure 18 (right) after 60 s of exposure. At a distance of 30 cm from the mouth, the risk is approximately 5×10 -7 . Nearer than 30 cm, this risk might increase or decrease depending on the exposed subject's height. At the infected subject's height, the risk increases to about 3×10 -6 (3 persons in every 1 million). Further than 30 cm from the infected person's mouth the risk decreases logarithmic reaching about 1×10 -7 (1 in ten million) at 90 cm distance. However, if only small particles (1 and 3 µm) are considered, the probability for the same exposure times reduce to 2, 5 and 8 persons per 100 million. The latter can be considered to be a conservative estimated of infection risk when using masks (particles larger than 5 µm do not penetrate through the mask nor through leakages, see figure 9 ). The actual risk when using masks is expected to be lower, considering the mask penetration (figure 9).

J o u r n a l P r e -p r o o f 

Droplet evaporation has been neglected in the case-study presented. Had evaporation been considered (option in the app), the particles would gradually reduce in size and eventually reach their droplet nuclei size. For the initial particle diameters selected this would result in droplet nuclei of 0.25, 0.75, 2.5, 7.5 and 12.5 µm. Additionally, if evaporation had been included, the virion content per droplet would remain the same (only water evaporates).

However, as a droplet reduces from 50 µm to its nucleus size of 12.5 µm, its probability of being inhaled increases. This is seen in figure 22 , where the fraction of droplets inhaled to droplets deposited on the table is shown to decrease as the particle diameter increases (7.7%, 0.6% and 0.06% for 10, 30 and 50 µm droplets, respectively).

Therefore, if evaporation is considered, the number of inhaled droplets of 30 and 50 µm initial diameters would most likely increase considerably, yielding a higher risk of aerosol infection.

J o u r n a l P r e -p r o o f 

An application, referred to as TU Delft COVID-app, has been developed for a relatively simple and quick CFD simulation setup of human expiratory activities (sneezing, coughing, breathing and speaking) that yield the risk of COVID-19 transmission. The software incorporates data from several experiments from literature and measurements performed in this study. The software also includes probabilistic models to evaluate infection risk probability. The models and data integrated in the tool have been described in detail, laying the foundations of an application that has the potential to democratize the use of CFD for analysis of indoor SARS-CoV-2 spread and associated prevention strategies.

PIV experiments of a person reciting a speech with and without a surgical mask have been performed to obtain the instantaneous air volume flow rate and flow direction at the mouth, allowing for realistic simulations of unsteady speaking. The average flow fields from PIV are compared to that obtained numerically during the simulations.

Experimental limitations yielded differences in the average peak velocity of about 20-30% at a distance of 20 cm downstream from the mouth. This is regarded insignificant in comparison to natural biological differences between individuals across the world population.

To demonstrate the capabilities of the application, a numerical simulation of a conversation across a dining/meeting table has been setup in Ansys Fluent with the TU Delft COVID-app. The simulation results indicate that one hour of J o u r n a l P r e -p r o o f conversation between two persons sitting one-metre apart, where only the infected person talks for one quarter of the time, yields a risk of aerosol infection (droplets < 50 µm) of 2 persons per million. However, analysis of the fraction of particles being inhaled as a function of their diameter shows that the estimated risk would be higher had evaporation been considered, as the likelihood of a droplet to be inhaled increases as its diameter reduces as a result of evaporation. When considering only particles smaller than 5 µm (mask penetration diameter threshold) the simulated risk reduces to 2 persons in 100 million, suggesting at least a two orders of magnitude reduction of the risk of infection when face masks are used (the actual mask penetration has not been considered).

Furthermore, the simulation results show that particles of 10 µm initial diameter or larger are the most relevant when analysing the risk of infection at a one-metre distance conversation.

The TU Delft COVID-app has been developed based on experimental data and an established commercial CFD software (ANSYS Fluent), which yields reliability and accessibility to the application. However, prior to applying the tool for decision making regarding policy measures it is recommended a follow up study that compares results obtained from this application to that of a real life situation. In addition, the results from the case study presented here are mostly illustrative of the application capabilities. It is clear from this analysis that evaporation must be considered in future simulations (readily available at the software).

The cumulative number of RNA copies N, infectious dose (d = N/16,000) and the probability of infection given by eq. (15) that have been obtained based on the number of droplets inhaled during the 60 seconds long simulated conversation (section 7) and the average viral load in the sputum from Wölfel et al. 2020 (7 billion RNA copies per litre) are given on 

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Fluid dynamics simulations show that facial masks can suppress the spread of COVID-19 in indoor environments

The Transmission of SARS-CoV-2 Infection on the Ocular Surface and Prevention Strategies

Airborne Transmission of SARS-CoV-2: Theoretical Considerations and Available Evidence

Filtering Efficiency of N95-and R95-Type Facepiece Respirators, Dust-Mist Facepiece Respirators, and Surgical Masks Operating in Unipolarly Ionized Indoor Air Environments

Model Calculations of Aerosol Transmission and Infection Risk of COVID-19 in Indoor Environments

Probable airborne transmission of SARS-CoV-2 in a poorly ventilated restaurant

Evaporation and dispersion of respiratory droplets from coughing

Measurement of temperature and relative humidity in exhaled breath

Velocity fidelity of flow tracer particles

Ten Years of Industrial Experience with the SST Turbulence Model. Turbulence

Transmission of SARS-CoV-2: A Review of Viral, Host, and Environmental Factors

Real-time human skin temperature analysis using thermal image recognition for thermal comfort assessment

The flow physics of COVID-19

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

An Investigation of Particle Trajectories in Two-Phase Flow Systems

Airborne transmission of SARS-CoV-2

Performance of N95 Respirators: Filtration Efficiency for Airborne Microbial and Inert Particles

Particle Image Velocimetry. A Practical Guide

Numerical Study of Three Ventilation Strategies in a prefabricated COVID-19 inpatient ward

Verification and Validation in Computational Science and Engineering

Height and body-mass index trajectories of school-aged children and adolescents from 1985 to 2019 in 200 countries and territories: a pooled analysis of 2181 population-based studies with 65 million participants

The total number and mass of SARS-CoV-2 virions

Community Outbreak Investigation of SARS-CoV-2 Transmission Among Bus Riders in Eastern China

Flow visualization of an N95 respirator with and without an exhalation valve using schlieren imaging and light scattering

How human thermal plume influences near-human transport of respiratory droplets and airborne particles: a review

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

Aerosol and Surface Stability of SARS-CoV-2 as Compared with SARS-CoV-1

The Rosin-Rammler particle size distribution

Visualizing the effectiveness of face masks in obstructing respiratory jets

Development of a Dose-Response Model for SARS Coronavirus: Dose-Response Model for SARS-CoV

On air-borne infection. Study II. Droplets and droplet nuclei

Virological assessment of hospitalized patients with COVID-2019

Infection Prevention and Control of Epidemic-and Pandemic-Prone Acute Respiratory Infections in Health Care. WHO Guidelines. World Health Organization

How far droplets can move in indoor environments -revisiting the Wells evaporation-falling curve

Exhaled droplets due to talking and coughing

Identifying airborne transmission as the dominant route for the spread of COVID-19

Study on transport characteristics of saliva droplets produced by coughing in a calm indoor environment

The grid discretization error is estimated by calculating changes in the turbulence kinetic energy k in a cross plane, 10 cm downstream from the mouth of the infected person (figure A2.1). This process is performed three times, once for the grid used during the simulations of reference size h, followed by two grid refinements by a factor of 2, i.e. for cell sizes of h/2 and h/4 (the grid itself is non-uniform, but all the cells are scaled accordingly). The simulations are then performed for 1.2 s, where the person starts to speak at 1 s from the start of the simulation. The turbulence kinetic energy is then averaged both in space (along the plane) and time (t = [1, 1.2] s) and compared for different grid sizes (figure A2.2).

The turbulence kinetic energy seems to be converging to a value within [6.85, 6.86]×10 -3 m 2 /s 2 . An estimate of k for an infinitesimally small grid cell (k = 0) is obtained by using the Richardson extrapolation (Roache 1998) :where = 2 is the grid refinement ratio and is the order of the grid convergence:The estimated value of ℎ=0 = 6.8536×10 -3 m 2 /s 2 (also plotted in figure A2 .2) is then used as a reference to estimate an error of 0.7% due to grid discretization, in comparison to the value obtained from the grid used during the simulations ( = 6.8082×10 -3 m 2 /s 2 ).J o u r n a l P r e -p r o o f