Modeling and experimental study of dispersion and deposition of respiratory emissions with implications for disease transmission
2022; Wiley; Volume: 32; Issue: 2 Linguagem: Inglês
10.1111/ina.13000
ISSN1600-0668
AutoresSimon Coldrick, Adrian Kelsey, M.J. Ivings, Timothy G. Foat, Simon T. Parker, Catherine J. Noakes, Allan Bennett, Helen Rickard, Ginny Moore,
Tópico(s)Aerodynamics and Acoustics in Jet Flows
ResumoIndoor AirVolume 32, Issue 2 e13000 ORIGINAL ARTICLEOpen Access Modeling and experimental study of dispersion and deposition of respiratory emissions with implications for disease transmission Simon Coldrick, Corresponding Author Simon Coldrick simon.coldrick@hse.gov.uk Health and Safety Executive, Buxton, Derbyshire, UK Correspondence Simon Coldrick, Health and Safety Executive, Harpur Hill, Buxton, Derbyshire, SK17 9JN, UK. Email: simon.coldrick@hse.gov.ukSearch for more papers by this authorAdrian Kelsey, Adrian Kelsey Health and Safety Executive, Buxton, Derbyshire, UKSearch for more papers by this authorMatthew J. Ivings, Matthew J. Ivings Health and Safety Executive, Buxton, Derbyshire, UKSearch for more papers by this authorTimothy G. Foat, Timothy G. Foat Defence Science and Technology Laboratory, Salisbury, UKSearch for more papers by this authorSimon T. Parker, Simon T. Parker Defence Science and Technology Laboratory, Salisbury, UKSearch for more papers by this authorCatherine J. Noakes, Catherine J. Noakes Leeds Institute for Fluid Dynamics, School of Civil Engineering, University of Leeds, Leeds, UKSearch for more papers by this authorAllan Bennett, Allan Bennett National Infection Service, UKHSA, Salisbury, UKSearch for more papers by this authorHelen Rickard, Helen Rickard National Infection Service, UKHSA, Salisbury, UKSearch for more papers by this authorGinny Moore, Ginny Moore National Infection Service, UKHSA, Salisbury, UKSearch for more papers by this author Simon Coldrick, Corresponding Author Simon Coldrick simon.coldrick@hse.gov.uk Health and Safety Executive, Buxton, Derbyshire, UK Correspondence Simon Coldrick, Health and Safety Executive, Harpur Hill, Buxton, Derbyshire, SK17 9JN, UK. Email: simon.coldrick@hse.gov.ukSearch for more papers by this authorAdrian Kelsey, Adrian Kelsey Health and Safety Executive, Buxton, Derbyshire, UKSearch for more papers by this authorMatthew J. Ivings, Matthew J. Ivings Health and Safety Executive, Buxton, Derbyshire, UKSearch for more papers by this authorTimothy G. Foat, Timothy G. Foat Defence Science and Technology Laboratory, Salisbury, UKSearch for more papers by this authorSimon T. Parker, Simon T. Parker Defence Science and Technology Laboratory, Salisbury, UKSearch for more papers by this authorCatherine J. Noakes, Catherine J. Noakes Leeds Institute for Fluid Dynamics, School of Civil Engineering, University of Leeds, Leeds, UKSearch for more papers by this authorAllan Bennett, Allan Bennett National Infection Service, UKHSA, Salisbury, UKSearch for more papers by this authorHelen Rickard, Helen Rickard National Infection Service, UKHSA, Salisbury, UKSearch for more papers by this authorGinny Moore, Ginny Moore National Infection Service, UKHSA, Salisbury, UKSearch for more papers by this author First published: 21 February 2022 https://doi.org/10.1111/ina.13000 © Crown copyright (2021), Dstl, HSE, UKHSA. Funding information: PROTECT, the National Core Study on Transmission and the Environment. AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract The ability to model the dispersion of pathogens in exhaled breath is important for characterizing transmission of the SARS-CoV-2 virus and other respiratory pathogens. A Computational Fluid Dynamics (CFD) model of droplet and aerosol emission during exhalations has been developed and for the first time compared directly with experimental data for the dispersion of respiratory and oral bacteria from ten subjects coughing, speaking, and singing in a small unventilated room. The modeled exhalations consist of a warm, humid, gaseous carrier flow and droplets represented by a discrete Lagrangian particle phase which incorporates saliva composition. The simulations and experiments both showed greater deposition of bacteria within 1 m of the subject, and the potential for a substantial number of bacteria to remain airborne, with no clear difference in airborne concentration of small bioaerosols (<10 μm diameter) between 1 and 2 m. The agreement between the model and the experimental data for bacterial deposition directly in front of the subjects was encouraging given the uncertainties in model input parameters and the inherent variability within and between subjects. The ability to predict airborne microbial dispersion and deposition gives confidence in the ability to model the consequences of an exhalation and hence the airborne transmission of respiratory pathogens such as SARS-CoV-2. 1 INTRODUCTION The SARS-CoV-2 pandemic has brought about the need to assess the risks posed by different viral and bacterial transmission routes for hazardous respiratory infections. Knowledge of the relative importance of these different routes is important in understanding the ways in which infection can be transmitted and in determining the best combination of control measures. The two main routes of infectious disease transmission are contact or airborne. Contact transmission may be by direct contact with droplets from a contaminated individual or indirect contact such as touching a contaminated surface (fomite transmission). Airborne transmission arises from pathogen-laden exhaled aerosols which are inhaled.1 Droplets and aerosols exhaled during normal activities (breathing, talking, singing, coughing, and sneezing) have a range of diameters from 100 μm, and this plays an important role in the routes by which infection could occur. Very large droplets (>100 μm), which may be able to carry a larger microbial load, typically follow a ballistic trajectory and are unlikely to fully evaporate before they deposit on surfaces or on a susceptible individual. Those in smaller diameter ranges experience, proportionally, increased evaporation2 with a final diameter depending on their initial size and respiratory fluid composition.3 Studies have suggested4, 5 that the microbial load depends on droplet size and origin, though these relationships remain uncertain and may vary with the type of bacteria or virus. However, the smallest aerosols may be more numerous than large droplets, may remain suspended in the air for relatively long periods, and can be inhaled by a susceptible individual. It is also recognized that dispersion behavior is heavily affected by environmental factors and there is no absolute distinction between the fate of large droplets and aerosols, that is, there is a continuum of behavior across the spectrum of diameters. The mechanism of airborne transmission has long been acknowledged6 and plays an important role in the spread of multiple infectious diseases including bacterial pathogens such as tuberculosis,7 and viral diseases including measles,8 influenza,9 and SARS.10 The World Health Organisation (WHO) recently acknowledged the role of airborne routes in the transmission of SARS-CoV-2.11 Characterization of the range of droplet and aerosol sizes in exhaled breath and their effect on transmission has long been recognized as an important part of understanding the transmission of infection. Early work to characterize the size distribution of exhaled droplets by Duguid12 demonstrated significantly greater numbers of droplets (and correspondingly much greater volumes of fluid) are released during sneezing and coughing compared to talking. More recent investigations (Johnson et al.,13 Gregsonet al.,14), demonstrate a wide variation in the number and size of with different vocal activities and between different people. There have also been a number of studies to characterize exhalation flows,15, 16 which are an important part of defining the initial air movement from the mouth and nose which propel and carry the respiratory droplets and aerosols. Mathematical modeling can help provide insight into the physics of transmission. Droplet evaporation models, (for example Chen et al.,17 de Oliveira et al.,18 Wei and Li,19 Xie et al.,2 Walker et al.,20), can be used to explore the influence of environmental factors such as relative humidity, temperature, and diameter change due to evaporation which can influence how droplets behave. One of the limitations of these models is that they are unable to account for factors such as ventilation flows which can influence the transport and deposition of airborne droplets. Other types of models, such as Noakes and Sleigh,21 Burridge et al.,22 or Jones et al.,23 consider transmission risks as a function of ventilation and pathogen emission rates, but without explicitly modeling the transport and evaporation of droplets. Computational Fluid Dynamics provides a means of modeling both the droplet physics and the effects of ventilation and can model realistic geometries and their effect on the flow. CFD has been used to model the transmission of infectious diseases, particularly in relation to the SARS and current SARS-CoV-2 outbreaks (e.g.24-29). The main benefit of CFD is that it can combine models to describe the interaction of exhaled droplets with environmental flows that influence the behavior of droplets, such as ventilation and thermal effects. CFD modeling can also be used to understand the effects of mitigation methods such as screens, more complex geometries, or the influence of additional people within the environment. There are, however, numerous challenges to modeling these scenarios using CFD. Droplets of a few microns size in exhalations can evaporate in less than a few seconds. Furthermore, room geometries may be of the order of several meters in dimension and have air change intervals spanning many minutes. Combining these variables and scales into single simulations means that computer run times can become prohibitively long. A further challenge is that the input conditions or source terms (e.g., for exhalations) need to be defined from the outset and these can have a large influence on the results. Long simulation times can limit the scope of sensitivity analysis that can be carried out on the inputs, and a heavy reliance is made on the strength of input assumptions. Validation is an important aspect of a modeling study to provide assurance that the assumptions and inputs used in the simulation are appropriate. One of the challenges in validating exhalation models is that the experimental data to cover all aspects from droplet production through transport to deposition, viral load, and infection do not currently exist. For this reason, many previous modeling studies have focussed on validating components of the model as a means of gaining confidence in the overall predictions. A number of studies have compared CFD simulations to exhalation flows from people,29 idealized experiments with manikins in chambers,30 and bioaerosol chamber experiments using artificial generation of microbial aerosols from a nebulizer.31 However, to our knowledge, there are no previous studies that directly compared CFD or droplet model simulation studies with human volunteers exhaling microorganisms. In the current study, a CFD model of exhalations has been developed and compared to experimental data for surface deposition and air sampling of exhaled bacteria carrying droplets from human participants. The experiments were carried out to quantify the airborne dispersion and deposition of exhaled droplets to provide data for SARS-CoV-2 risk assessments, using detection of respiratory and oral bacteria as a surrogate for virus-laden droplets. Component validation studies were also carried out on individual elements of the CFD model, such as an exhalation jet and single droplet evaporation, to give confidence in the overall predictions from the model. 2 INDOOR EXHALATION DISPERSION EXPERIMENTS Experiments were carried out by the United Kingdom Health Security Agency (UKHSA) to investigate the behavior of exhaled aerosol and droplet particles. The study measured respiratory bacteria as a means of assessing the dispersion characteristics of aerosols and droplets in a 4 x 2.3 x 2.3 m (Length × Width × Height) environmental chamber, shown in Figure 1(A). The chamber was unventilated during experiments, with the only flow provided by air samplers operated during the study. FIGURE 1Open in figure viewerPowerPoint (A) Experimental set up in the environmental chamber and modeled geometry (B). The modeled geometry shows the sampler locations with the naming convention used to present the results Ten laboratory workers were recruited to carry out the study, with an age range of 21–59 years and gender balance of 50% female and 50% male. Ethical approval for the study was given by the UKHSA Research Ethics and Governance of Public Health Practice Group (UKHSA REGG). The participants wore hooded Tyvek suits, shoe coverings, and gloves to reduce shedding of non-oral microorganisms and remained seated facing forwards during the study. Participants provided a spit sample into a universal container before each experiment, primarily to assess bacterial load. Participants were seated at one end of the chamber and were required to perform a sequential set of activities as follows: cough three times; read out loud the numbers from 1 to 100; inhale and exhale 3 times; sing happy birthday twice loudly; inhale and snort 3 times; read out loud the numbers from 1 to 100; and cough three times. Samples were collected by air samplers (Andersen 6 stage and Slit samplers) and on 15 Columbia Blood Agar (CBA) settle plates placed at 20 cm intervals directly in front of and to the side of the subject. The Andersen samplers operated at 28.3 L/min and collected particles onto six CBA plates fractionated by particle diameter, though the breakdown by diameter was not included in the results. The slit samplers sampled onto a rotating CBA plate at the same flow rate. Both samplers were operated for a period of 10 min. Sampler positions are described in the CFD modeling section below. Immediately before the start of the experiment, the settle plates had their lids removed, the air samplers were switched on automatically and the ventilation was turned off remotely. At the end of each 10-min period, the samples were collected and incubated for analysis and the room was ventilated with filtered air for at least 10 min at 180 air changes per hour before the next study. The number of colony-forming units (CFUs) collected and cultured on each plate was used to define the bacterial deposition onto the surface or the total sampled from the air over the ten-minute experimental period. The type of bacteria and their origin (e.g., organisms from the respiratory tract) that formed the colonies in these assays have not yet been determined. Consequently, a proportion of the colonies detected may have come from other sources. 3 COMPUTATIONAL FLUID DYNAMICS MODELING OF EXHALATIONS In line with previous CFD studies,24, 25, 27-29 the approach adopted for modeling exhalations is the Euler-Lagrange approach. The Eulerian fluid is modeled on a fixed computational mesh through which the flow field is calculated. The Lagrangian method involves computationally tracking the trajectories of individual droplets as a discrete phase, throughout the calculated flow field from their point of introduction until they deposit on a surface or escape the domain. One of the main benefits of this method is that a fixed count of particles having specific diameters can be modeled. Model outputs such as deposited mass can therefore be calculated for use in further analysis such as in a Quantitative Microbial Risk Assessment (QMRA).32 While other studies33, 34 have used a purely Eulerian drift-flux framework to study size-resolved particle concentration and deposition, such approaches may not be able to capture trajectories for larger droplets with significant inertia. The simulations in this study were carried out using the commercial software ANSYS Fluent 19.0.35 The mixture of air, water vapor, and exhaled carbon dioxide in the Eulerian phase was modeled using a species transport model. The local mass fraction of each species was solved for with a convection-diffusion equation which included a source term for the transfer of water vapor from the Lagrangian droplets to the Eulerian phase. 3.1 Geometry and meshing The modeled geometry is shown in Figure 1(B). The tables holding the settle plates were 0.5 m high and approximated by cuboidal volumes, with the centerline settle plates labeled PCL1-PCL10 and the right hand side settle plates labeled PR1-PR5, with PCL1 and PR1 being closest to the subject. The centerline plates were set out to a distance of 2 m from the subject's assumed knee position, and the right hand plates were set out to 1 m from the subject's assumed knee position. The air samplers, at 1 m height, were represented by floating cylindrical volumes, labeled Andersen "AS" and slit "SS". AS1 and SS1 were located at 1 m, AS2 and SS2 at 2 and 2.5 m, respectively, and AS3 at 1 m to the left of the participant. The subject was approximated by a simplified geometry,36 having a mouth defined by a circular opening set at a height to match a sitting position. In the experiments, there will have been some variability of the subject's dimensions, along with the distance from the subject's face to the first settle plate. The chamber was meshed using unstructured tetrahedral cells, with prismatic inflation layers adjacent to the solid surfaces. In the region where the thermal plume from the person impinged on the ceiling, wall y+ values were approximately 11.5, with an average of 2.5 on the body surface. Mesh refinement was applied in the region of the mouth and the exhaled jet, based on isolated jet simulations. Cell sizes varied from approximately 3 mm at the mouth, to approximately 75 mm in the room, away from walls or openings. The results reported here were obtained on meshes of approximately 655 000 nodes, which provided reasonable run times. A mesh sensitivity study was carried out, which showed that particle sample results were insensitive to further mesh refinement. An explanation for this behavior is that the sampled results are driven by ballistic deposition or sedimentation, rather than wall-parallel flow, where mesh effects can be important. Increasing the overall mesh density to 2.3 million nodes did not appreciably change the diameter ranges or quantity of particles collected by the settle plates or air samplers. The air samplers mainly collected small particles, which are influenced by the room air flow. 3.2 Boundary conditions The experiments were carried out at an ambient temperature of 22°C and a relative humidity (RH) of between 44% and 50%. All solid walls were set to the ambient temperature value and the solution initialized with a RH of 50%. As the people in the experiments were fully clothed apart from their face, only the convective heat flux from the subject was modeled, which was applied as a surface heat flux of 25 W/m2. This value is similar to that measured by Zhu et al.29 for a resting subject. The inlet of each air sampler was a circular region, set as an outflow through which air was drawn at a constant volume flow rate, equal to the experimental flow rate. The room was specified as being unventilated during the trials, but there was likely to be a small air exchange through the door seal and ventilation system. A pressure boundary matching the position of the ventilation inlet in the chamber was defined (shown in blue in Figure 1B) to balance the outflow of air through the samplers. This was specified as a relative pressure of zero and backflow temperature equal to the room temperature. In practice, the leakage flows are unknown. However, the air velocity through this balancing opening was very small and did not influence the flows in the room. 3.3 Turbulence modeling The Reynolds-Averaged Navier-Stokes (RANS) approach was used as it is less computationally intensive than other approaches which aim to directly resolve large-scale turbulent fluctuations. There are numerous RANS turbulence models available which provide good predictions in different types of flows. A challenge is that there is no universally applicable turbulence model which provides optimal predictions in all physical scenarios (e.g., jet flow and near wall flow). Therefore, a level of compromise is often required. Based on initial simulations of buoyancy-driven flow in a room and of an isolated turbulent jet, the k-ω SST model37 was used across all simulations. 3.4 Modeling of dispersed respiratory particles Respiratory particles were modeled using Fluent's multicomponent model. The particles consisted of two components; a solid part (consisting of salts, proteins, and surfactant) specified as non-volatile and a liquid part (water) which could evaporate into the Eulerian phase. All of the solids were grouped into the non-volatile part, with a volume-weighted density calculated from the average of the non-volatile components1 as shown in Table 1. The resultant average solids density was 1830 kg/m3, giving the particles initial mass fractions of 98.75% water and 1.25% solids. This water content was similar to the artificial saliva water content described by Walker et al.20 of 97.9%. TABLE 1. Particle solids composition, taken from Stettler et al1 Concentration (g/L) Density (kg/m3) Salt 9 2160 Protein 3 1362 Surfactant 0.5 1082 3.4.1 Momentum exchange The exchange of momentum between the Eulerian and Lagrangian phases was two-way and accounted for by equating the change of momentum of a particle to the sum of the forces acting on it38: dp p dt = F D + F B + F O (1) The term on the left is the change in particle momentum (kg m/s) and the forces on the right are the drag force (FD), buoyancy force (FB), and other forces (FO), in (N). Virtual mass and pressure gradient forces were not included as the density of the Eulerian phase was much lower than the particle density.38 The effects of Brownian motion were not modeled as it has been suggested39 that the effect is only significant for particles ≤0.03 µm, which is considerably smaller than the particles considered in the current study. 3.4.2 Turbulent dispersion Turbulent dispersion introduces a random pattern to the motion of particles, to reflect the effect of small-scale turbulent fluctuations that have been averaged out in the RANS approach. Turbulent dispersion was modeled using the discrete random walk model, DRW,40 where the drag term in Equation 1 was determined from both the mean flow and a fluctuating component. This fluctuating component was a random proportion of the local RMS value of the velocity fluctuations which were derived from the turbulent kinetic energy of the flow. The default DRW model was implemented so that the same random seed was used for each simulation, such that two simulations run with turbulent dispersion would have identical solutions. The DRW model is known to give poor predictions of wall impaction rates of small particles in wall-parallel flows because of the assumption of isotropic turbulent fluctuations in the two-equation turbulence model RANS approach.41 However, for this scenario, air flows were low and deposition was likely to be dominated by sedimentation for the majority of the particle sizes. Ceiling and wall deposition rates, where sedimentation does not contribute, were expected to be very small in comparison and were not directly compared in this study. 3.4.3 Mass transfer Particle mass transfer was modeled using the diffusion-controlled model,38 which assumes that the rate of vaporization of component i is governed by the concentration gradient between the droplet surface and Eulerian phase: dm i dt = Sh π d p D i M w , i C i , s - C i , ∞ (2)where Sh is the Sherwood number (-), which in turn depends on the Reynolds (-) and Schmidt (-) numbers, Di is the diffusion coefficient (m2/s), dp is the particle diameter (m), Mw,i is the molecular weight of the component (kg/kmol), and Ci,s and Ci,∞ are the concentrations (kmol/m3) at the particle surface and in the Eulerian continuum, respectively. 3.4.4 Heat transfer Heat transfer to the particle was modeled using the multicomponent energy equation, accounting for heat transfer by convection and vaporization38: m p C p dT p dt = hA p T ∞ - T p + ∑ i h f g , i dm i dt (3)where mp is the particle mass (kg), Tp is the particle temperature (K), T∞ is the continuum temperature (K), Cp is the particle heat capacity (J/kg K), h is the heat transfer coefficient (W/m2 K), Ap is the particle surface area (m2), and hfg,i is the latent heat of vaporization of component i (J/kg). 3.4.5 Particle material model The surface concentration of a solution particle is affected by its composition and the departure from an ideal solution becomes important, especially at high solute fractions. Drying of respiratory droplets has been extensively studied, and there are numerous approaches that can be taken.18, 20 In the current work, the model of Walker et al.20 was implemented to define the particle surface vapor concentration. For a multicomponent particle, the surface concentration can be given by38: C i , s = γ i x i φ i P sat , i Z V RT p (4)where γi is the activity coefficient (-), χi is the component mole fraction (-), φi is the fugacity coefficient (-), Psat,i is the saturation vapor pressure (Pa) at temperature Tp (K), and ZV is the vapor compressibility (-). For an ideal gas at low pressure, the fugacity coefficient and compressibility are assumed to be equal to 1. Non-ideal solution effects are accounted for through the activity, αi (-), which is the product of the activity coefficient and component mole fraction42: α i = γ i x i = P i P sat , i (5)where Pi is the modified vapor pressure. Walker et al.20 parameterized the solute mass fraction, Ys, (-) in terms of water activity, αw, for deep lung fluid and artificial saliva. The parameterization for artificial saliva was implemented in Fluent as a lookup table that returned the water activity from the solute mass fraction in the particles. Assuming the solute to be non-volatile, with water being the only vaporizing component, the surface concentration was calculated by C w , s = α w P sat , w RT p , α w = f Y s (6) To check that the modifications to the material model were correctly implemented, it was compared against data from Hamey43 using pure water droplets. The model of Walker et al.20 neglects the effects of surface curvature. The effect was not implemented in the Fluent model as it has been shown to be small for particles greater than 100 nm,42, 44 which represents the majority of particles considered in this study. An additional simplifying assumption was made, based on data in Walker et al.20, that the models for artificial saliva and deep lung fluid were sufficiently similar that the same material model could be used for all the particles in the simulations. 3.5 Specification of the exhalation carrier flow The geometry of the mouth during coughing, talking, and singing is variable and highly uncertain. Rather than attempt to capture these intricacies, exhalations were assumed to originate only from the mouth region which was defined as a circular orifice with a fixed diameter, depending on the activity. A source term was applied over this opening and consisted of a gaseous "carrier" flow with a specified temperature, RH, and transient velocity profile at a particular angle (Figure 2), along with a simultaneous injection of particles. It is known that jet dispersion results are sensitive to the inlet turbulence intensity. There is little available information on this quantity for this specific application, so the intensity and length scale were set as 10% and 0.01 m, respectively. FIGURE 2Open in figure viewerPowerPoint Initial jet expansion angles viewed from the side and front. The front projection is the same for both speaking and coughing The details of the modeled carrier flow are given in Table 2. Five different carrier flows were simulated in total. Of the activities listed in the experiments, only the speaking, singing, and coughing activities were modeled. These activities account for the majority of the total exhalation time and have relatively well-defined sources. The carrier flow source terms for talking and singing were implemented as finite duration square waves which did not fully account for the cyclic nature of speech or breathing patterns. To examine the effect of exhalation occurring for only part of the total duration while speaking and singing, modified flows were defined which aimed to capture the maximum velocity projecting the particles, rather than an average. For modified speaking (Source 2), the duration of exhalation was halved and the average flow rate doubled. For modified singing (Source 4), the duration was halved, the average flow rate doubled and then scaled as described in the following section. Coughs are exhalations for their full duration which were approximated as a triangular wave having a duration of 0.4 s and a peak velocity at 0.08 s.15, 16 The carrier flow velocity was spatially varied over the mouth opening within the initial expansion angle, or half cone angle, of the jet, shown in Figure 2. These values were taken from
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