A CFD-based framework to assess airborne infection risk in buildings

Abstract

The COVID-19 pandemic has prompted huge efforts to further the scientific knowledge of indoor ventilation and its relationship to airborne infection risk. Exhaled infectious aerosols are spread and inhaled as a result of room airflow characteristics. Many calculation methods and assertions on risk assume ‘well-mixed’ flow conditions. However, ventilation in buildings is complex and often not showing well-mixed conditions.

Ventilation guidance is typically based on the provision of generic minimum ventilation flow rates for a given space, irrespective of the effectiveness in the delivery of the supply air. Furthermore, the airflow might be heavily affected by the season, the HVAC ventilation, or the opening of windows, which would potentially generate draughts and non-uniform conditions. As a result, fresh air concentration would be variable depending upon a susceptible receptor's position in a room and, therefore, associated airborne infection risk.

A computational fluid dynamics (CFD) and dynamic thermal modelling (DTM) framework is proposed to assess the influence of internal airflow characteristics on airborne infection risk. A simple metric is proposed, the hourly airborne infection rate (HAI) which can easily help designers to stress-test the ventilation within a building under several conditions. A case study is presented, and the results clearly demonstrate the importance of understanding detailed indoor airflow characteristics and associated concentration patterns in order to provide detailed design guidance, e.g. occupancy, supply air diffusers and furniture layouts, to reduce airborne infection risk.

1. Introduction

Research and innovation on ventilation design in buildings has seen significant recent advances [1] in part due to a major scientific effort to identify the way SARS-CoV-2 is transported, causing the COVID-19 pandemic [2,3]. Three routes for transmission have been identified, namely through [4].

• -fomites;
• -ballistic drops (or large droplets);
• -aerosol (or airborne) particles (or droplets).

In literature, the less significant or even ‘minor’ role that fomites have in the spread of the disease has been widely reported. In addition, large droplets are thought to contain far less viral material than airborne particles [[4], [5], [14]], with ongoing discussions on the significance of available results (both for SARS-CoV-2 and other respiratory viruses). However, it seems clear that the third transmission route, involving particles travelling through air dominated by advection over gravitational effects, is the main vector for virus transport and transmission in the near as well as the far field [6]. This is often referred to as the airborne infection route. Notably, terminology differences still exist between the medical and aerosol scientific communities that are also being understood and discussed [4,7].

The main source of uncertainty lies where the behaviour of ballistic drops and aerosol particles is affected by environmental constraints in which tests are conducted. Another source of uncertainty is the measure of the RNA-copies contained in virions found in drops and droplets [8,9]. This mainly depends on the evaporation rate, the sensitivity of sensors, as well as the availability of swab tests in the respiratory tract, which for example are very limited in asymptomatic individuals [10].

While it is quite complicated for building designers and ventilation specialists to navigate the immense amount of literature on airborne infection, over the past years some excellent review papers (among which Nazaroff, 2021) have helped to define terminology for non-specialists whose expertise is recognised to assist furthering the knowledge on airborne transmissible diseases [2].

Amongst those experts, one group is represented by building physicists who are experienced in selecting, using or developing the multitude of simple tools through to more complex models that are available to design ventilation systems. In the UK context, the Chartered Institution of Building Services Engineers (CIBSE) provides technical guidance for the application of both analytical and simulation methods to assess energy and thermal comfort supporting the design of mechanical and natural ventilation systems [12,13]. Dynamic Thermal Modelling (DTM) and Computational Fluid Dynamics (CFD) are two methodologies widely used in industry, with their validity to model the indoor ventilation behaviour of buildings broadly accepted in the practitioners’ community. In particular, the CIBSE AM11 Building Performance Modelling guidance provides extensive indications to practitioners as to how to setup and run DTM and CFD simulations in support of the design of mechanical and natural ventilation systems, in addition to other more commonly used techniques [14]. The key simplification operated in DTM is the use of a single-point-by-zone networked approach for estimating heat and air exchanges between zones and through surfaces. A key limitation of DTM is that zones are effectively well-mixed zones, i.e. with constant flow characteristics throughout the zone volume. CFD overcomes this key limitation by calculating the flow properties locally, and the two approaches have been applied in conjunction to overcome their limitations [15]. While the use of DTM and CFD is widespread in the industry and the validity of models well documented, the assessment of airborne infection risk is still largely limited to academic research, with most recent works using complex methods not practically applicable in the industrial context [16].

Airborne respiratory diseases (such as COVID-19) are transmitted through aerosolised respiratory fluid conveyed by air movement [17]. A significant effort has been dedicated to understanding whether airborne infection risk can be modelled as a gaseous pollutant using the definition of a tracer gas (in the case of diseases, the exhaled breath of infected people) [18]. While the validity of this assumption is debated [[18], [19], [20]], the definition of airborne infection risk through tracer gas models would adapt very well to industrial standard CFD modelling, largely applied in its steady Reynolds Averaged Navier-Stokes (RANS) formulation [[21], [22], [23], [24]].

While many CFD studies focussing on COVID-19 model the airborne aerosol directly within the CFD model [25], significant limitations are posed to the use of this technique. In particular, two concerns are highlighted.

• -an aerosol particle model can only be used in steady RANS with limitations;
• -a transient CFD model cannot be practically used in industry for real buildings.

There is a significant body of evidence, being generated as part of the pandemic response influencing future policy and/or guidance for ventilation design, e.g. along the lines of the new UK Approved Documents F and O [26,27], that room ventilation and layout play an important role in transmission [28]. This, in turn, means that the localised flow patterns significantly affect the airborne infection risk in a building [29,30]. This in turn means that traditional methods not modelling said localised flow patterns are not suitable to optimise design, and a performance-based design strategy (i.e. including a virtual model of the building) would be preferrable to obtain better performing buildings, including against airborne infection risk.

In this paper, the mature industrial knowledge on the use and combination of both DTM and CFD to model indoor ventilation in buildings is used to define a simple methodology framework to assess airborne infection risk. The airborne infection risk is calculated following well-established intake fraction methods that are adapted to post-process steady RANS CFD results. A case study is presented, involving a typical large scale office space and a sensitivity study is performed to stress test the ventilation system against airborne infection risk under different seasons, viral parameters, and opened windows. The focus of the framework is to promote discussion on process more than improving the understanding of airborne infection transmission routes. The presented case study constitutes an excerpt of an actual piece of work performed for a major office building in London, UK. It is therefore the intention of the authors, CFD practitioners in the building industry, to use the present research as a statement on the state-of-the-art in modelling flow patterns in buildings using CFD for performance-based design. In this case, performance entails to establish a relative airborne infection risk narrative, useful to drive design and management of real buildings, building on the currently available knowledge on airborne infection risk and ventilation, highlighted by the COVID-19 pandemic.

Section 1.1 provides a detailed background to this study. In Section 2 the methodology framework is described in detail. Section 3 shows a selection of relevant results, which are then discussed in Section 4, where conclusions are also given. It is important to stress that this study should be considered a work in progress in supporting the direction of travel for these types of assessments and that more research is needed on the application of CFD simulations in the assessment of airborne infection risk.

2. Methodology framework

Fig. 1 shows the methodology framework implemented in this study which includes the following steps.

• 1)Transient DTM calculation to capture the thermal environment throughout the year on an hourly basis. Time-varying DTM results (surface temperatures) are extracted to inform the CFD boundary conditions. A simulation time scenario is defined, which is suitable for CFD modelling. In the context of airborne infection risk a suitable choice criterion might be the day and hour showing a peak CO₂ level in a zone of interest.
• 2)Setup of the CFD model of the building using DTM-computed surface temperatures. The building model geometries in CFD and DTM match in terms of naming conventions and zonal definitions. The boundary conditions include any convective component of the DTM internal heat gains.
• 3)Inclusion of mannequins, in the CFD model, representing all occupants in the building at the simulation time scenario. The mannequins are in fixed positions and are divided into subsets of susceptible receptors and infectious emitters. A suitable boundary condition for the exhaled air is defined, informed by the metabolic activity. The spatially varying concentration of exhaled breath is used as tracer gas defined to represent the infectious aerosol and its concentration throughout the domain.
• 4)Post-processing of CFD results to calculate the intake fraction at each susceptible receptor location, and calculation of a related airborne infection risk metric to stress-test the building performance.
• 5)Performing of sensitivity study by varying viral or ambient parameters to inform the decision-making process on how to improve the ventilation design within given constraints through reducing airborne infection risk.

Fig. 1.

Methodology framework.

2.1. DTM and CFD model overview

The DTM model is setup so that its results can inform boundary conditions used in the CFD model of the building, which is divided into macro-zones. The zones might be defined for a portion of a space or a group of spaces, depending on the different thermal loading throughout the building. It is therefore of importance to model the building geometry following naming conventions which are recognisable between the two models. DTM models are transient, and they usually encompass a full year of typical varying conditions accounting for seasonal, daily and hourly variation in weather conditions for the location of interest.

Hourly changes in solar radiation, humidity and CO₂ levels have been captured which can complement the advanced account of the flow pattern as calculated in CFD. Occupancy profiles with associated heat gains need also to be applied into the occupied zones.

As DTM is a broadly used technique in the industry, the reader is referred to the CIBSE AM11 guidance [14]. The input data into a DTM model can come from information shared by the design team and published guidance on the analytical modelling of the environmental performance of buildings, also available as specific CIBSE guidance [12,31].

The CFD model is also setup following the state-of-the-art guidance on building simulation, which is also detailed in the CIBSE AM11 guidance [14]. The standard industrial practice involves a steady RANS simulation using a suitable turbulence model and computational mesh definition.

The 3D building geometry is analogous to that used in the DTM model, so that all surface temperatures (which in DTM are affected by radiation as well as convection) are used as boundary conditions to the CFD model. Boundary walls, windows, ceilings and flooring are therefore named individually and a surface temperature is applied to the model from the results of the DTM.

The preliminary characteristics of the ventilation system are normally designed before the DTM and CFD analyses are conducted, so all mass flow rates of the supply air diffusers and extract grilles are available from preliminary design documentation. The control system is explicitly modelled in the DTM analysis using occupancy profiles provided by facility managers.

All convective heat sources are included in the CFD model, typically as surface temperatures or heat fluxes, while in DTM heat gains are normally setup as point sources: a conversion might be operated from zonal volume to surface value, so that the CFD and DTM model have the same thermal loading definition.

The results in the DTM solution are finally compared to the CFD results as a verification step to ensure that the different solution methods lead to the same description of the building physics. In this regard, the CO2 levels represent a suitable comparison metric, as in both models occupants are defined explicitly.

It is proposed within this study that it is important to consider how the flow behaves, and this is only possible by simulating or measuring it (noting the significant challenges to assess the aerosol biophysics in the latter).

Of the many studies using CFD to investigate airborne infection risk, many have focussed on healthcare settings [[32], [33], [34], [35], [36]], and other settings [[37], [38], [39], [40]]. Good practice guidance to set up CFD simulations applicable to industrial practices to inform design against airborne infection risk is of utmost importance and currently considered a ‘work in progress’. It is hoped that this paper will support that process.2

Another requirement for the CFD model is a good representation of the thermal boundary conditions, specifically the surface temperatures, as well as the internal heat gains (lights, people and equipment). A typical practice in the industry is for the CFD model to capture the detailed air movement and air temperature distributions at a given point in time, as defined by DTM. Nevertheless, other strategies exist such as using surveying (e.g. infrared imaging) or analytical-based simplified calculations, e.g. via [12,13].

Different approaches might differ in scope of use and in recognition of their strengths and limitations. For example, it would be impractical to use CFD for an annual assessment of ventilation performance on an hourly basis over the course of a year, but this is something that is standard practice and relatively straightforward using DTM. Likewise, DTM calculations have no momentum equations and so assessments of jet performance or localised flow characteristics through an open window would be severely limited, although these limitations would be understood from a CFD study. It is the combined approach of DTM and CFD in recognition of their limitations which has led to the developed modelling approach below.

2.2. Modelling of tracer gas in CFD

In the introduction, reference was made to the different ways that exist to introduce the infectious source into a CFD model. An easy to implement and commonly used way to do this is to physically model each occupant individually with their mouths defined as an inlet into the computational domain, identified as the emission source of infection. A suitable inlet boundary condition is then defined representing the exhaled breath. The implementation of this framework is not dependent on the approach to the modelling of the occupants and other approaches (point sources etc.) could also be used.

Many studies justify the use of the exhaled breath as tracer gas, with its concentration to be monitored throughout the computational domain to calculate the intake fraction of a susceptible receptor. In offices, a suitable position for occupants could be the position they most spend time at, i.e. their workstations. The occupants might represent both susceptible receptors and infectious emitters at the specified occupancy density of a typical working day, with the ability to trace each exhaled breath source individually.

In order to reduce the geometric complexity of the model, human features can be simplified in favour of a simplified body having roughly the same surface area of an average height person, to mimic seated and/or standing positions, as done in numerous studies [22,[41], [42], [43]].

This methodological framework uses the tracer gas formulation in order to predict the intake fraction away from an emission source. This approach is sometimes referred to as Eulerian-Eulerian approach, as opposed to the Eulerian-Lagrangian approach. The exhaled breath containing the aerosolised respiratory fluid is defined as a separate continuous fluid phase whose concentration throughout the domain is calculated using the species scalar transport equation, which yields the concentration of the exhaled breath from the i-th emission source ${\xi }_i$. The 2D formulation of the scalar transport equation reads

$$\frac{\partial }{\partial x}\left(\rho {\xi }_{i}U\right)=\frac{\partial }{\partial x}\left({\mathrm{\Gamma }}_{{\xi }_i}\frac{\partial {\xi }_i}{\partial y}\right)+S_{{\xi }_i}$$ (1)

where x and y are the spatial coordinates, $\rho$ is the air density, U represents the air velocity vector, ${\mathrm{\Gamma }}_{{\xi }_i}$ is the diffusion coefficient and $S_{{\xi }_i}$ the source term of the generated exhaled breath.

This approach entails plume modelling as opposed to cloud modelling. The rationale behind this choice lies in the intrinsic limitations of the RANS technique, which is the tool of choice for the methodology framework. In fact, RANS models the mean statistical properties of the flow, and not the instantaneous flow features an aerosol would interact with.

It is therefore deemed preferable to use the Eulerian-Eulerian approach to model concentration as opposed to the Eulerian-Lagrangian particle tracking approach many academic studies use and recommend, as it could erroneously entail releasing a realistic aerosol into a RANS calculated flow field. While using the Large Eddy Simulation (LES) approach would allow one to model a more realistic aerosol [44], there would be significant limitations to its practical application in industry, which is discussed in ongoing research promoted by the UK government (www.airbods.org.uk - Airborne Infection Reduction through Building Operation and Design for SARS-CoV-2 (AIRBODS), 2022).

Three species are of interest for the CFD model, namely.

• -Fresh air from the ventilation system;
• -Exhaled infectious air from individual or groups of infectious occupants (emitters);
• -Exhaled air from all other occupants (susceptible receptors).

As exhaled air and fresh air chemically represent the same species, no reaction rate needs to be scaled by the volume fraction of the phase in the model, and only turbulent and thermal dispersion drive the concentration. The species equation above is solved for the mass fraction of the species in their gaseous phase.

The exhaled breath concentration is then used to analytically calculate the airborne infection risk, while also allowing an assessment of CO₂ levels within the office.

Although CO₂ concentration within a space has limited validity as a proxy for potential risk of infection (other than poor ventilation in combination with high occupancy at the extreme) [40,46,47], it might represent a useful parameter to gain confidence in the application of the CFD model correlating with DTM results.

2.3. Airborne infection risk calculations

Airborne infection risk is normally calculated following the well-acclaimed analytical methods explained in several major international studies [9,[48], [49], [50], [51]]. However, the COVID-19 pandemic has prompted researchers to improve those methods to apply them to assess infection risk in buildings. In particular, a main source for debate is the use of infectious quanta, which is limited by its assumed well-mixed zone basis, i.e. with physical parameters having a single calculated value within any defined zone. A quantum is defined as the viral load required for a susceptible receptor to become infected according to the definition of probability of infection

$$p=1-e^{-q}\to 1-e^{-1}=0.63$$ (2)

where q=D _v,tot /HID, D is the total inhaled dose (in RNA-copies) and HID is the Human Infectious Dose (HID) parameter. When q = 1 the viral load c _v approaches a limit value for infection, and the probability of infection is 63%. That is the reason for the quantum to be defined sometimes as HID=HID ₆₃. For COVID-19, several papers report HID ₆₃ = 700 RNA-copies [38,52,53]. It should be noted however that the real value is unknown (the dose response curves are extremely difficult to derive with confidence, and will also vary with different variants of the disease). The whole concept of infectious quanta is under review by scientists in the aerosol physics and the virology communities [54].

Respiratory droplets, composed by saliva, mucins and viral material, are of various sizes from 0.5 μm to 1000 μm, depending on the location of where in the respiratory tract they are generated. Although literature describing the exhaled volume of respiratory fluid per respiratory activity is readily available, there might be significant uncertainty regarding the total volume of exhaled fluid, which is essential to calculate the total viral load c _v emitted [55]. The uncertainty depends mainly upon the extremely fast evaporation rate that droplets undergo after leaving the respiratory tract. As viral loads are measured in the respiratory tract, the viral content in droplets is inferred from their dimension. Therefore, a major source of uncertainty is present in assessing the volume of respiratory fluid constituting the droplets, that is emitted, and the viral load therein [17,56,57].

Furthermore, as for the viral load, a major source of uncertainty is its probability distribution as observed in patients [9]. Therefore, in order to estimate airborne infection risk, a chain of hypotheses and assumptions must be undertaken, with calculation uncertainties reduced by moving from the definition of an absolute risk model towards a relative risk model focussing on the subject of the study, e.g. answering questions such as “what happens if the supply air flow rate increases/is reduced by 50%”?

Two alternative well-used methods exist to calculate infection risk.

• -Analytical models of infection risk (e.g. Wells-Riley);
• -Transfer efficiency approaches (e.g. intake fraction);

The most widely used analytical methods are based on the Wells-Riley model [28,52,55], where emissions are parametrised using the definition of quanta and the hypothesis of well-mixed conditions (i.e. constant concentrations for a given zone in the model).

Transfer efficiency approaches are based instead on the calculation of the intake fraction, which is the fraction of the emitted infectious dose that is conveyed to a susceptible receptor [11]. This method is more developed and better suited to deal with a variable concentration of respiratory fluid. Nevertheless, the hypothesis of well-mixed condition is still at the base of the definition of the method. For a detailed explanation of both methodologies the reader is referred to the relevant literature [11].

The importance of the well-mixed condition assumption within the formulation of the calculation is not normally investigated in detail but it is accepted that its adoption helps to reduce the complexity of the calculations.

The airborne transmission risk is driven by aerosol transport through a calculated flow pattern. The main issue is to correctly characterise the aerosol in terms of number of particles and size distribution. In particular, as droplets are formed in different parts of the respiratory tract, the activity performed by the emitter is essential in capturing a representative viral load as emitted by an ‘average’ individual. Fig. 2 shows the aerosol particles' number and size distribution, as reported in literature, per different respiratory activity [58,59]. Results available in literature mainly refer to swab tests and infer the airborne value from the particles shed by a specific physical mechanism, such as friction or bubble bursting, depending on the part of the respiratory tract where they are measured [57]. In order to calculate the intake fraction, a calculation of the respiratory volume at the emission source is needed so that the correct infectious dose emitted, as measured and reported in literature, is calculated [11,60].

Fig. 2.

Droplet number distribution per different activities according to (Morawska et al., 2009).

Notwithstanding the variability of the aerosol composition depending on activity, the viral loads associated to the volume of fluid are extremely uncertain for COVID-19 or other diseases. In particular, the literature reports on a large range of the probability of viral loads in the general population that should be carefully caveated to setup fixed values in post-processing results [9].

The airborne infection risk assessment is performed as an analytical post-processing of the concluded CFD simulation. This approach allows for different aerosol properties to be tested, without the need for a new 3D simulation to be performed with a changed emission source. With the definition of exhaled breath concentration results from the tracer gas CFD model, a subset of results can be post-processed with a fixed flow field without the need for an expensive computation, which is important in the framework of applicability of the method in industry. There is also more flexibility on the aerosol features, as different numbers and sizes of particles can be tested without having to re-run the simulations.

The droplet volume is then calculated from the droplet sizes and distribution for a given activity in terms of ml/l of exhaled air, using indications from literature [57,61].

The aerosol droplets volumes shown in Table 1 are derived from observations of the droplets’ diameter measured at the mouth as in Ref. [59]. It is well-known that these measurements tend to be heavily affected by the shrinkage of droplets occurring due to evaporation [57]. The values in Table 1 are therefore adjusted to correctly calculate the viral load, increasing their diameter by a factor of ∼5 (corresponding to an increase in volume of 125) [55]. This is consistent with findings in literature that point to the fact that sensors need to be improved to correctly measure the evaporation rate of such small particles [56].

Table 1.

Respiratory fluid volume (airborne aerosol droplets) per cubic metre of exhaled air.

Activity	Voiced counting	Whisper counting	vocalisation	whisper	Mouth breathing	coughing
Droplet volume Ev$\left(\frac{m_{fluid}^3}{m_{air}^3}\right)$	1.39×10-12	3.36×10-13	8.89×10-12	2.83×10-13	2.92×10-13	1.23×10-12

The viral load c _v (RNA-copies/ml) is then used to calculate the viral genetic material present in the respiratory fluid. While values reported in literature vary from as little as $1\times {10}^7$ RNA-copies/ml to as large as $1\times {10}^{11}$ RNA-copies/ml, c _v can be useful to stress-test the ventilation system against airborne infection risk, rather than modelling a specific emitter/receptor scenario [10].

The total viral load at the mouth is therefore calculated using the viral parameters, aerosol characteristics, and breath rate BR (m³/s), which is modelled in CFD and depends on the metabolic activity considered as

$$D_v=c_v\bullet E_v\bullet BR(\mathrm{R}\mathrm{N}\mathrm{A}-\mathrm{c}\mathrm{o}\mathrm{p}\mathrm{i}\mathrm{e}\mathrm{s}/\mathrm{s})$$ (3)

To obtain the total number of exhaled RNA copies, the definition of an exposure time t is needed, reflecting conditions at which the simulation is performed. In this study, given the fact that an office has been modelled, a typical working day of 8 h could be considered as a suitable exposure time, assuming primarily sedentary activities and that infectious emitters are continuously present throughout the working day. Another way of plotting results can be assuming a unitary exposure time (t = 1 h) and obtain results per hour, which is also an indicator of how airborne infection risk is affected by local flow features.

An important caveat arises at this point. This method considers that the whole totality of the viral load is carried by the airborne droplets. The role of ballistic drops is neglected from this analysis, along with the role of post-evaporation from fomites or the deposition of ballistic drops onto surfaces. This is a strong assumption, which should be tested as more data becomes available over time [7,62,63]. Arguably, many swab tests reported in literature show that ballistic drops carry a minimal quantity of the virus as produced in the oral cavity where viral loads are known to be small [64]. It is possible to find references pointing to airborne transmitted doses as high as 90–95% of the total viral load within a breath cycle [65]. From this point onwards the airborne viral load will be referred to as total viral load.

In order to calculate the viral dose at susceptible receptor locations, the total viral load emitted is multiplied by the exhaled breath concentration ξ as computed in CFD

$$D_{v,tot}\left(x,y,z\right)=D_v\bullet t\bullet \xi \left(x,y,z\right)(\mathrm{R}\mathrm{N}\mathrm{A}-\mathrm{c}\mathrm{o}\mathrm{p}\mathrm{i}\mathrm{e}\mathrm{s})$$ (4)

Where $\xi \left(x,y,z\right)$ is the exhaled breath concentration calculated measuring the volume percentage of exhaled breath to the total volume within a cell, and t is the exposure time.

In order to calculate the airborne infection risk, the probability of infection is calculated which depends on the definition of a Human Infectious Dose (HID). Some studies report HID ₆₃ = 700 RNA-copies, which comes from a thermodynamic equilibrium dose-response model [66], while others report lower values HID = 410 RNA-copies, from mice studies on coronaviruses [67]. Consistent with the airborne infection risk methodology of choice, the HID ₆₃ value is used in the present study, although this could be very easily updated at some point in the future when there is increased confidence in the supporting data. It is noted how only in the case of predicting absolute risk, this value assumes a physical importance, whereas in the scope of the present study, a relative risk is acceptable when looking to direct design in a more resilient direction.

The probability of infection is calculated as

$$P_I\left(c_v\right)=1-e^{-D_{v,tot}/{HID}_{63}}(\%)$$ (5)

The individual risk of infection R, i.e. for a susceptible single person to be infected, can be calculated assuming a probability distribution $P_{c_v}$ for the viral load $c_v$, which is integrated along with the probability of infection

$$R={\int }_{c_v}{P}_I\left(c_v\right)P_{c_v}{dc}_v(\%)$$ (6)

The individual risk R is to be interpreted in relative terms, i.e. it not referred to a specific community risk but rather on the variability of the risk throughout the tested building. This is similar to the relative exposure index (REI) as proposed in recent studies [55,68].

As the viral load probability distribution is mostly unknown, a log-normal distribution is used, consistently with literature implementing the intake fraction methods [11].

$$P_{c_v}=\frac{e^{-{\left(\ln c_v-{\mu }_{c_v}\right)}^2/2{\sigma }_{c_v}^2}}{c_v\sqrt{2\pi }{\sigma }_{c_v}}$$ (7)

Where ${\mu }_{c_v}={\log }_{10}5.6$ and ${\sigma }_{c_v}={\log }_{10}1.2$ (RNA-copies/ml) are respectively the average and standard deviation of $c_v$ as measured in recent investigations [17], although other studies propose higher values with an average of 10⁷ RNA copies [48].

Given the uncertainty over the actual probability distribution $P_{c_v}$ of airborne SARS-CoV-2 viral loads, especially regarding ${\mu }_{c_v}$ and ${\sigma }_{c_v}$, it seems sensible to refer to equation (5) to represent results, and relativise them based on the highest and lowest probability of infection that is found in the office which is the object of the present investigation. An easy to interpret parameter is therefore proposed, that is closely related to the probability of infection $P_I\left(c_v\right)$ and that can be defined as hourly airborne infection rate (HAI). It is calculated from equation (4) assuming a unitary exposure time $t=1\left(hr\right)$, and then normalising by HID ₆₃

$$HAI\left(x,y,z\right)=\frac{D_v\bullet \xi \left(x,y,z\right)}{{HID}_{63}}(\%)$$ (8)

The authors believe that the proposed approach within this framework has the potential to efficiently and effectively derive detailed insights in supporting industry when practically deciding how to reduce infection risk, still within its given limitations.

2.4. Sensitivity study

The above modelling process is used to evaluate the effect of ambient and viral parameters on the airborne infection risk using the combined DTM & CFD approach. Some of the effects which might be of interest to drive design.

• -Effect of different period of year (cool and warm natural ventilation modes);
• -Effect of ventilation rate (full and half air flow rates);
• -Effect of viral load parameters;
• -Effect of opened windows (open-office with openable windows).

The idea behind the methodology is that the ventilation system can be stress-tested against multiple variables that might affect its behaviour in order to drive design choices. Further analyses of effects could include a variation in the furniture layout, as well as the inclusion of screens or other obstructions to effectively promote improved natural ventilation and mitigate any identified issue in the local ventilation features. Further effects could include the variation of supply air grilles and extracts location of the mechanical ventilation system, as well as its interaction with the furniture layout.

In setting up the sensitivity study it is important to adequately study the boundary conditions to be applied in order to model various effects. A particular challenge is represented by opening windows, i.e. when the indoor flow interacts directly with the outdoor aerodynamics of the building. This is affected in particular by the type of building that is the object of the study [69]. During the pandemic response, it has been discussed that there is a low ratio of naturally ventilated buildings within the total building stock which could lead to an increase in overall airborne infection risk across the population [70]. Notably, one historic reference often quoted was how Florence Nightingale recognised the need for ‘fresh air’ as far back as the mid-1800s [71]. While the methodology proposed in the present study allows testing of how any specified application of natural ventilation openings compares with alternative designs, the beneficial operation of any single design can also be tested. The opening is modelled in CFD as a flow outlet, having a specified pressure coefficient distribution, c _p, which mainly depends on aerodynamic considerations on the shape of the building and the wind direction. It is normally unlikely to have this information for a real building, and a widespread approach used to estimate the pressure coefficients can be found following indications provided for wind loading, e.g. those available in the Eurocode 1 [72] for a variety of building shapes. The dynamic pressure applicable to the opening is given by:

$$p=\frac{1}{2}{c}_p\rho U^2\left(Pa\right)$$ (9)

Where $\rho =1.25$ kg/m³ is the density of air, and $U$ is a typical wind speed that might be compatible with opening windows on a typical day of the year.

It should be noted that this is a simplified approach and alternative approaches might wish to be considered such as a fully coupled (or integrated) outdoor-indoor modelling of flow conditions.

3. Case study

In order to show how the methodology framework is applied to a standard CFD workflow, a case study is presented, which is an excerpt of a real work conducted for an open-space office situated in London, UK. The methodology framework steps are described in detail in their implementation to set out the work in the following sections.

3.1. The office building

The building comprises of the upper 5 storeys of a 10-storey building, which is a portion of an urban block in central London, in a densely built area. The total floor area is ∼12,000 m², with the largest storey having a floor area of ∼2500 m². Two levels are of particular interest, which are the ones most densely occupied throughout the year. All floor levels feature a largely open-office layout, with a mix of large perimetral offices, single offices, and open-space areas, all connected by corridors. The façade of the building is glazed with non-openable windows. Close to the core of the building, multiple various sized window-less meeting rooms are present, along with storage and utility rooms.

Fig. 3 shows various 3D views of the two floors that have been modelled for this study. The two floors are adjacent but not air-connected, therefore core services are not modelled in detail, as they are separated from the remainder of the floor by fire doors.

Fig. 3.

Geometry level of detail with main parts included in the model.

The ventilation system was designed by MEP engineers prior to the airborne infection risk study. Fresh air is supplied through 156 floor supply air diffusers, which use a displacement grille from which the supply air direction is tangential to the floor, aiding thermal comfort and air mixing. The grilles supply 100% fresh air without recirculated air, representing a potential operational mode within a pandemic. Two extract grilles of large size ($5\times 2$ m each) are located at two opposite sides of the central services core. An additional roof recirculation unit system is present, composed by fan coil units with a single inlet and multiple outlets (the larger light grey prisms in Fig. 3). This system improves air mixing across the occupied zones of the building. It consists of 69 units, having 69 return air vents and 189 supply air grilles. The ventilation system is shown in light grey in Fig. 3.

In total, there are 340 occupants modelled in each floor. 17 emitters are identified, representing infectious people. They are placed around the building, so they would test the risk within different types of rooms/areas within the office. The positioning of emitters is selected in order to stress-test the performance of all typical rooms and areas within the building. The exhaled air is monitored to understand its spatial concentration and the transport to any potential susceptible person inhaling in the office.

In order to identify different risk scenarios associated to a different type of space within the office, emitters were marked in four groups, so when interrogated these can be assessed as individual transported flows grouped using 5 species in total. This was mainly done for ease of interpretation of the airborne infection risk results. In some ventilation scenarios it may be necessary to separate each emission source rather than group them.

Fig. 4 shows emitters in their modelled locations divided into each relevant group.. Emitters are placed as following.

• Group 1. The four emitters are located in the largest research lab, an open plan desk space to the north-east of the floor, in the open-space office to the north-east, and along the corridor in the south-west of the floor.

• Group 2. The four emitters are located in an 8-person research lab, two open plan desk regions to the north, and in the tea spot in the southeast corner.

• Group 3. The four emitters are located across another research lab, a collaboration space, in the centre of the open-space office and within one of the offices.

• Group 4. The five emitters are located in a 10-person research lab, 4-person meeting room, 6-person meeting room, locker space and near the kitchen to the south of the town hall.

Fig. 4.

Locations of groups of emitters for which a dedicates exhaled air species was setup. The floor plan is coloured with the concentration of exhaled breath (blue to red, 0–0.001% concentration). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

3.2. DTM model overview

Fig. 5 shows the DTM model of the building with the thermal zones applied, which are also split into 3 zones vertically (supply air zone, occupied zone and above). In order to model the thermal mass of adjacent floors, Fig. 5 also shows the full building model, noting that the surrounding buildings within this building block are not shown. A detailed description of the DTM process is not provided here, as a standard approach following published guidance was used to set up the model [14]. Calculations have been performed using the software DesignBuilder [73], and informing the settings of the model from information shared by the design team and from CIBSE guidance [12] (see Fig. 6).

Fig. 5.

Views of the DTM model - internal zoning on assessed floor level and external full building model. On the right the CO₂ concentration across different spaces demonstrates the choice strategy of CFD scenario, which is also used to assess the compatibility of results obtained from both DTM and CFD. The spaces taken as reference are shown in the floor plan on the left.

Fig. 6.

Computational Grid: (top left) view of triangulated surface mesh; (bottom left) hexahedral volume mesh with prismatic wall layers; (right) volume mesh resolution across whole computational domain.

A useful addition to standard DTM practice was the inclusion of CO₂ calculations. Occupancy profiles as shown in Fig. 5 were applied at all zones, with resulting estimates for CO₂ levels shown for 3 locations across the building over two typical weekdays in the winter season (a breakroom, an open-plan office, and a research laboratory). The times showing peak CO₂ values were then used to choose an appropriate CFD scenario of interest for airborne infection risk. In constant supply air flow rate systems, the peak CO₂ levels would often correlate quite well with peak occupancy periods. Given the state-of-the-art design of the ventilation system, peak CO2 concentrations across multiple spaces amounts to ∼800 ppm.

3.3. CFD model overview

The CFD model implements the Reynolds-averaged Navier-Stokes (RANS) technique, which is a well-established CFD method to model indoor ventilation used by many practitioners.

The turbulence model of choice is the k-$\epsilon$ realisable formulation as coded in the Ansys Fluent software, which is a widely used commercial CFD software used for the computations in this study [74].

The CFD model discretises the RANS equations using the finite volume method and implements an appropriate turbulence model combined with a suitable algorithm (SIMPLE in this study). The temperature filed is resolved by adding an additional energy equation to the solution. All CFD computations were performed on the Wirth Research High Performance Computing cluster, parallelising the run over multiple processor cores.

The model setup for this study uses a high-resolution approach, i.e. the computational model is discretised so that a maximum cell size of ∼0.3 m is obtained (Fig. 6). This is higher than standard industrial approaches (as the meshing strategies suggested in the CIBSE AM11 guidance) and allows for a better representation of the turbulent mixing than more traditional approaches using less resolution. The total cell count is ∼250 million cells. The solution has been run over several preparatory meshes (from ∼80 million to ∼300 million cells) and no mesh dependence of the results has been identified, with ∼0.5% maximum variation in the calculated exhaled breath concentration used in this work (comparison not shown for brevity).

The mesh includes hexahedral elements, which are combined with prismatic layers over all solid surfaces. The transition between hexahedra and prisms is operated using pyramidal elements. At least 4 cells are included in the prismatic boundary layer mesh, and the first size of the element is optimised to limit the y ⁺ value to ∼30.

The CFD model (showed in Fig. 3) includes all 340 workstations and occupants modelled individually. The CFD model has been setup from the 3D CAD geometry in a way that findings of the DTM analysis could be incorporated in the CFD setup. Boundary walls, windows, ceilings and flooring are therefore named individually and a surface temperature is applied to the model from the results of the DTM.

Table 2 shows the thermal boundary conditions which are applied to solid surfaces within the model. Values in the table match results of the DTM modelling.

Table 2.

Surface thermal boundary conditions applied to solid elements in the model.

Boundary	Thermal BC		Surface (m2)	Notes
	Summer	Winter
Perimetral walls	T = 24 °C	19 °C		Opaque building envelope
Windows	T = 27 °C	17 °C	436.2 (total)	All glazed surface
Ceiling	T = 24 °C	21 °C
Floor	T = 24 °C	21 °C	1897.0	Core (∼500m2) excluded
HVAC system	φ = 0 W/m2			Ductwork volumes
Desktop	φ = 100 W/m2		1.2 (each)	Top surface of desks
Desks	T = 24 °C	21 °C		Lateral and bottom desk sides
Mannequin body	φ = 24.5 W/m2		1.92 (each)	340 occupants
Mannequin head	φ = 24.5 W/m2		0.14 (each)
Internal Partitions	T = 25 °C	21 °C
Core walls	T = 25 °C	21 °C		All fire doors considered closed

Particular care was taken modelling occupants. The human features were eliminated in favour of a simplified body having roughly the same surface area of an average height person, to mimic seated and standing positions. The positions of workstations had been communicated through the layout of the office contained in the CAD model, while the most likely position of occupants was obtained in specific workshops with the clients and their facility managers. Mannequins represent both susceptible and infectious persons at a specified occupancy density representative of a typical working day. The heat gain from equipment or lighting in this model is applied as a surface temperature on the top surface of every desk. The heat gain from occupants is applied as a constant heat flux applied to the different parts of the mannequin. Fig. 3 shows where heat sources are applied, i.e. on the top surface of all desks and over occupants body parts. Fig. 7 shows the mannequin representation, both in seated and standing positions, as modelled in CFD. Mannequins were detailed further by dividing the surfaces of the head, the body and the mouth respectively, as shown in Fig. 7.

Fig. 7.

Mannequin models to introduce infectious flow in form of exhaled breath.

To the head and body surface a heat flux was applied, resulting in a different temperature of the head and body. The exhaled breath is introduced in the computational domain in CFD through an inlet boundary modelled onto the mannequin's head surface (a mouth). It is modelled as a 1.3 cm high and 7 cm wide rectangle, having an area of 9.1 cm². To achieve a mass flow rate of 0.5 m³/h, which is compatible with a sedentary breathing rate, a volumetric flow rate of BR = 0.139 L/s is applied at the mouth. This value takes into account the alternance between exhalation and inhalation.

The average air speed at the mouth (0.15 m/s) is consistent with the statistical averages of respiratory activity observed in transient experiments and simulations [50]. Table 3 shows the mouth outflow parameters set in the computations.

Table 3.

Air inlet and outlet boundary conditions in summer and winter for the HVAC system and the mannequins. No other openings are modelled in the runs with closed external windows.

Boundary	Air temperature		Mass flow rate/inlet vel.	Surface (m2)	Notes
	Summer	Winter
Air Extract grilles (floor level)			8.51 kg/s	10.2 (total)	2 ($5\times 2$ m) extract vents
Air floor supply grilles (hor.)	24 °C	21 °C	U = 0.11 m/s	0.08 (each)	156 floor grilles
Air floor supply grilles (ver.)	24 °C	21 °C	U = 1.47 m/s	0.05 (each)
Roof recirculation units - returns			0.074 kg/s = 60 L/s	35.8 (total)	69 returns from recirculation units
Roof recirculation units - supply	24 °C	21 °C	0.027 kg/s = 22 L/s (each)	37.0 (total)	189 supply grilles from recirc. units
Mannequin mouths	37 °C	37 °C	0.15 m/s	0.0091 (each)	0.5 m3/h = 0.139 L/s

The HVAC ventilation system had been designed before the DTM analysis was conducted, so all mass flow rates of the supply air diffusers and extract grilles were available from design documentation and set up accordingly in the DTM and CFD calculations, having accounted for the role of the control system modelled in DTM.

Three gaseous species have been set up in the model, having the same physical properties.

• -Fresh air from the ventilation system;
• -Exhaled infectious air from 4 separate group of emitters (17 in total);
• -Exhaled air from susceptible receptors' mouths (340 occupants in total).

As exhaled air and fresh air chemically represent the same species, no reaction rate was scaled by the volume fraction of the phase in the model. The species transport equation above is solved for the mass fraction of the species in their gaseous phase.

The fact that the exhaled breath of all occupants is traced through the definition of a separate flow phase allows comparison between the results of the DTM and the CFD models and perform a simple verification of their validity. It must be noted that this is not normally required in standard CFD practice, if available guidance is followed (CIBSE AM11 guidance, 2020). A way of doing this is to compare the CO₂ concentrations as calculated in CFD and DTM.

The background levels of CO₂ are assumed at 412 ppm. The proportion of CO₂ within exhaled breath per occupant was assumed to be approximately 4.5% or 45000 ppm. This calculation considers the CO₂ emitted by all occupants regardless of infection status, so that the estimated CO₂ is a reflection of the floorspace occupancy profile.

Fig. 5 shows the CO₂ levels varying with occupancy in three different locations within the office. A close match of the predicted values has been observed that reassures on the validity of the computations. The comparison has been omitted from this paper as an ad hoc study is in preparation on the relation between CO₂ levels and airborne infection risk (see www.airbods.org.uk [45]).

3.4. Airborne infection risk assessment

The airborne infection risk assessment is performed following the methodology set out in Section 2.3. The problem is linearised with the concentration of exhaled breath ξ _i as calculated in the CFD model, and a viral load c _v = $3\times {10}^9$ RNA-copies/ml is used as the viral load at the emission source. The same c _v is used for all infected occupants. The total dose D _v emitted is calculated using the breath rate at which exhaled breath is emitted and the volume of respiratory fluid within a cubic metre of air E _v. The volume is quintupled to account for the evaporation at the mouth and the total RNA copies that are exhaled in an hour is calculated.

D_v is multiplied by the exposure time t and the exhaled breath concentration ξ _i to find the exhaled breath concentration at susceptible locations D _v,tot. In this methodological framework, the exposure time is taken as t = 1 h and the inhaled dose is normalised with a human infectious dose HID ₆₃ = 700 RNA-copies to infer the relative indicator of infection risk HAI, as defined in Section 2.3. HAI can have values from 0 to >100% depending on the exhaled breath concentration. The variation of the exposure time t has an appreciable effect on the inhaled dose D _v,tot. However, given the steady simulation setup used, dose fluctuations and the movement of infected emitters is not considered, therefore it is unlikely that D _v,tot would persist for the time in which occupants are within the space. The definition of HAI allows to have a discussion on the likelihood of a space to favour or impede infection, or a more qualitative assessment of risk, which is what this methodology is devised for. An HAI < 5% could be considered a suitable threshold to identify a negligible risk, depending on the average HAI throughout the computational domain (in this case ∼3%).

4. Results and discussion

Table 4 shows the CFD runs solved within the sensitivity study. A baseline run is chosen, representing a typical winter day with the windows closed. A key objective for this project was to understand the effect of opening a window in winter, and so winter with windows closed was chosen as the baseline scenario.

Table 4.

List of runs and variation of ambient and viral parameters.

Run	Season	Viral Load cv (RNA-copies/ml)	Ventilation	Open Windows
0 - Baseline	Winter	$3\times {10}^9$	Full	closed
1 - Season	Summer	$3\times {10}^9$	Full	closed
2 - Viral load	Winter	$\mathbf{1}\times {\mathbf{10}}^{\mathbf{10}}$	Full	closed
3 - Ventilation	Winter	$3\times {10}^9$	Half	closed
4 - Opening	Winter	$\mathbf{1}\times {\mathbf{10}}^{\mathbf{10}}$	Full	cp = 0

The 5 CFD scenarios are a subset of many more DTM scenarios that formed part of space-operational discussions with the design and management team. The discussions were used to ascertain the role of different seasons, operation of the mechanical ventilation system, community infection rate (deriving required resilience to a specified event) and window opening options, for example.

4.1. Flow pattern

A detailed account of the flow pattern observed for the baseline run is given in this section. Fig. 8 shows the air speed at 1.2 m above floor level. Most susceptible occupants are seated throughout the workstations, so this is an important height to assess.

Fig. 8.

Run 0 – Baseline. Winter with closed windows. Viral load of infectious emitters c_v = $3\times {10}^9$ RNA-copies/ml. Air speed (left) and temperature (right) distribution across floor for the run 2 (summer). Analogous to both floors. shows the position of infectious emitters.

The characteristics of the ventilation system are evident from the flow pattern, showing air speeds in the range of 0–0.3 m/s. Floor displacement grilles supply air in a tangential flow pattern with the CFD capturing the local turbulent mixing and air dispersion away from the grilles. The typology of flow displacement shown, i.e. having inlets at the ground with a tangential direction, enhances turbulence mixing throughout the space. Large extract grilles are located around the central core of the building (identifiable with the increased speed close to the cores).

Fig. 8 also shows (on the right) the air temperature distribution. The ventilation system is already optimised for thermal comfort. As a result the air temperature is quite uniform ∼24 °C at this height. ‘Hot spots’ are present which represent the localised heat gains from either occupants or equipment within the office. The colder rooms are meeting rooms with low equipment and occupant heat gains. The open spaces are where most occupants are concentrated showing slightly higher air temperatures.

Fig. 9 shows the exhaled air concentration for all susceptible occupants (on the left) and infectious occupants (right). The high concentrations on the right are purely driven by the position of infectious emitters. Higher concentrations in the emitter plots are likely to indicate poorer performance of the ventilation system, with reduced fresh air concentration in these areas with concentrations closer to the source value of 1.0. This is mainly observed in the small rooms (meeting rooms or single offices) containing an infected person. Original small room ventilation system design – the supply air grilles - may have been based on occupancy level, e.g. specifying a l/s per person, rather than other factors such as floor surface area or volume of the room. This is shown to have an impact on the ability of the ventilation system to dilute infected air. In open space areas, there is more efficient dispersion of the exhaled breath and lower concentrations are observed.

Fig. 9.

Run 0 – Baseline. Winter with closed windows. Viral load of infectious emitters c_v = $3\times {10}^9$ RNA-copies/ml. Exhaled breath concentration from all susceptible occupants (left) and exhaled breath concentration from infectious emitters (right) across the floorplan. shows the position of infectious emitters.

As a comparison, Fig. 9 on the left shows the exhaled air concentration, which is characterised by an alternance of high concentration spots (the susceptible people) with low concentration ones (the plumes of heated fresh air from the floor supply grilles).

4.2. Stress-testing the space: the hourly airborne infection rate

The HAI, calculated as per the procedure in Section 2.3, effectively shows concentration of diluted airborne viral material relative to the human infectious dose, set at the HID ₆₃. HAI is used here to stress-test the ventilation system and assess its airborne infection resilience. Fig. 10 shows both investigated floors of the building object of the investigation. All emitters are setup with the same respiratory properties. At first glance it is evident that in both floors there is a wide range in ventilation performance depending upon location.

Fig. 10.

Run 0 – Baseline. Winter with closed windows. Viral load of infectious emitters c_v = $3\times {10}^9$ RNA-copies/ml. Hourly airborne infection rate at both tested floors. The red zone in the legend indicates any HAI>20%. shows the position of infectious emitters. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

On the lower floor, the most significant area of risk was observed in the small, isolated meeting room. The office space in the south-west corner of the lower floor (bottom left of image) also shows HAI∼17% or above. Both of these areas show local areas with HAI>20%. In conversation with the design team, it emerged that the isolated meeting room was considered an area with higher infection risk, while the corner office was not (compared to the surrounding areas). This interpretation is based on the occupancy density of the two rooms, which indicated the need to ground the estimations and interpretations with feedback on space usage.

The open plan office areas show a larger dispersion of viral material with an evident tendency to transport from the emitter. This is due to the combined effect of the many floor supply diffusers mixing infected air locally together with its subsequent transport across the floor plan.

On the upper floor, areas with HAI greater than 5% were observed in both open spaces and the medium to small offices having emitters. The transport of airborne infection risk as a function of the room airflow characteristics is evident by the shape of the localised higher HAI values and there is even evidence of transport of this risk through open doorways (small office to the north of the floor (central top of image). Local HAI therefore depends upon the nature of the space and its ventilation features.

The two floors tested have a similar performance. This can be attributed to the ventilation strategy of the HVAC system as well as the similar layout and floor plan.

There is only a small variability of HAI with height above the floor. This is attributed to the characteristics of the studied ventilation system, although this might not be the case with other types of system. Only the height of 1.2 m above floor level is therefore considered in further results.

4.3. Sensitivity analysis

4.3.1. Effect of season

Fig. 11 shows the effect of changing the ventilation system mode from warming into cooling (i.e. summer season).

Fig. 11.

Run 1 – Season. Summer with closed windows. Viral load of infectious emitters c_v = $3\times {10}^9$ RNA-copies/ml. Hourly Airborne Infection rate in the summer season for both tested floors. shows the position of infectious emitters.

HAI tends to be lower in summer than in the winter season, at the height shown in the plots. Air and surface winter temperatures are likely to be slightly cooler than in summer leading to a change in airflow characteristics and how exhaled breath is transported. The detail provided by the HAI distributions captures the change in ventilation performance and airborne infection risk via the change in room airflow characteristics which are a function of (amongst other things).

• -fresh air flow rates into a space
• -local air temperature variations
• -and surface-to-air temperature variations.

4.3.2. Effect of respiratory activity and viral load

Fig. 12 shows the lower floor of the building in winter, with an increased viral load. The HAI distributions show how the local risk of airborne infection transmission changes locally when the viral load is increased by a factor of ∼3. Some increase in airborne infection risk is indicated under increased viral load. The following should be noted, though.

• -Further work is needed to determine scalability of viral parameters to different infection risk scenarios.
• -HAI sensitivity varies depending on the ventilation rate of a local area. Highly-ventilated areas show that HAI is less sensitive to variations in viral load, while less-ventilated areas are extremely sensitive to the viral load. This sensitivity could provide insights into design responses to improve airborne infection resilience.

Fig. 12.

Run 2 – Viral Load. Winter with closed windows. Viral load of infectious emitters c_v = $1\times {10}^{10}$ RNA-copies/ml. Effect of viral load (increased from $3\times {10}^9$ RNA-copies/ml) with fixed respiratory activity (mouth breathing). shows the position of infectious emitters.

While the variability of results is an issue in the context of absolute risk, varying the viral parameters can be very useful to stress-test the ventilation system and assess its resilience, even if comparatively, against near-field and far-field airborne infection risk.

4.3.3. Effect of ventilation rate

Fig. 13 shows the effect of halving the supply air diffuser ventilation flow rate at the lower floor level. While this is a rather unlikely scenario, as the system is sized to meet thermal comfort requirements, this test is useful to understand the sensitivity of HAI estimates under a lower ventilation rate. The open space office to the east (right side of each image) shows a mild increase in HAI, but overall the difference with the full ventilation rate is minimal in this location. The smaller open space offices, though, show a rather marked increase in HAI from about 7.5% to 12%.

Fig. 13.

Run 3 – Ventilation. Winter with closed windows. Viral load of infectious emitters c_v = $3\times {10}^9$ RNA-copies/ml. Lower floor level modelled with half ventilation rate. shows the position of infectious emitters.

Fig. 13 therefore seems to confirm the importance of tuning the ventilation rate locally to control the spread of the virus. However, in already well ventilated areas a reduction or increase in ventilation rate may not significantly reduce risk. A balanced approach is needed in consideration of practical constraints as well as potential adverse impacts, e.g. on energy usage.

4.3.4. Effect of openings

In order to test whether opening a window would improve risk or otherwise, the effect of openings is simulated by substituting a portion of the glazed area of the perimetral wall of the office with a pressure outlet. A constant notional pressure is applied to the opening boundary, c _p = 0 in the present sensitivity study. The internal pressure acting on the opening is directly calculated in CFD having setup the HVAC system properties.

The external pressure coefficient should be informed by a full aerodynamic study assessing the wind interaction with the building, which would also consider the effective area of the opening and any local shape effects. The approach to assess wind effects does not form part of the framework, and the present section only provides an example on how it might be used.

Fig. 14 shows the effect of opening windows (indicated as red dashed lines) in winter, with an outdoor temperature of 5 °C.

Fig. 14.

Run 4 – Openings. Winter with opened windows. Viral load of infectious emitters c_v = $1\times {10}^{10}$ RNA-copies/ml. Flow pattern in the presence of openings, air speed (left) and temperature (right) distributions. shows the position of infectious emitters.

The effect of opened windows on internal conditions is quite evident both considering the air speed and temperature distribution. Close to the window, air speeds increase due to incoming air. This significantly modifies the flow pattern compared to the closed window case shown in Fig. 8.

Thermal comfort is also impacted by a reduction in air temperature from about 23 °C to less than 20 °C. This could be an issue, especially if windows are manually operated, as their control and the resulting airborne infection risk would be heavily dependent on occupant behaviour.

Fig. 14 shows the thermal leaks from spaces to the adjacent ones. Partitions were modelled with mostly closed doors, with door cracks were suitable to account for the fact that sealed doors are unlikely in the context of an office. Results show that risk in a space might be not limited to the conditions solely within that space.

This implementation has obviously some limitations as to how in reality such a condition would occur (i.e. it is unlikely that occupants would fully open windows in winter), however it serves well to verify the suggestion of policy makers that opening windows improves risk, and during the pandemic some public buildings could be accessed under the conditions that windows would stay open, even in winter.

Fig. 15 shows the HAI distribution with closed and open windows. At a first glance, the effect of increased ventilation from opening the windows is evident, with much lower HAI values being observed in the spaces where windows have been opened. However, it should be noted.

• -There is a very large reduction in HAI within single and small offices (see hashed areas to the left and top of Fig. 15);
• -The change in local ventilation performance results in a variation of local risk, even greater in some instances with the windows open, with increased transport of viral material at a distance;
• -Although open spaces tend to show a reduction in HAI values close to the open windows (large hashed area), the ventilation performance in adjacent rooms connected via open doorways may be adversely impacted showing increased airborne infection risk (circular hashed area);

Fig. 15.

Run 4 – Openings. Winter with opened windows. Viral load of infectious emitters c_v = $1\times {10}^{10}$ RNA-copies/ml. Hourly airborne infection rate calculated for closed (left) and open (right) windows. shows the position of infectious emitters.

Results of the sensitivity study were useful in the context of the project this study is based upon in support of recommending design mitigations to reduce infection risk It is evident that the effect of openings on airborne infection risk is complex considering the geometry of the space, and how adjacent spaces are connected. Opening windows to reduce airborne infection risk is sensible for small offices with a sub-optimal ventilation system. However, for larger densely occupied spaces, the effect of openings is not so easily understood. The present results indicate that the risk can increase locally within the space, while in adjacent spaces with closed windows it seems that risk tends to increase substantially as a result of the internal crossflows that occur from the interaction of natural and forced ventilation.

5. Summary and Conclusion

In this paper a methodological framework is proposed that is based on the current state-of-the-art of industrial application of performance-based design of building ventilation using advanced simulation tools, such as CFD and DTM, combining their outputs to overcome some of their inherent individual limitations. The framework could help designers to investigate the performance of natural and/or mechanical ventilation systems with respect to associated airborne infection risk in buildings. An easy to interpret parameter is proposed, the hourly airborne infection rate (HAI). This captures the airborne concentration of viral material and normalises it to a human infectious dose value of interest, such as HID ₆₃.

Assumptions to set up the methodology for SARS-CoV-2 emissions, its airborne transport and, ultimately, COVID-19 transmission risk are dependent upon many uncertainties, not least a broad scientific debate surrounding airborne infection. A key strength of the methodology is that the results from within the framework can be easily modified when more specific infection transmission data becomes available or to test how different risk levels might influence ventilation designs. This would also allow building designers and ventilation specialists to fine tune system and space operations during or planning for a pandemic response.

Within the extremely versatile framework, industrial state-of-the-art CFD results can produce outputs to provide a detailed visual guidance on the airborne infection resilience of a building, so that its layout and ventilation can be stress-tested in detail beyond standard well-mixed zone approaches.

A case-study is presented to show how to apply the methodology framework to a real large-scale office building, based on a real project undertaken by the authors. The main conclusions from the work can be summarised as follows.

• -There is a marked difference in resilience between zones depending on ventilation characteristics. In particular, the risk depends on the ability of the system to disperse and dilute the emission (exhaled air from an infected emitter).
• -Increasing ventilation rate does not significantly influence the airborne infection risk in already well-ventilated areas, i.e. there may be other measures that warrant consideration such as the optimisation of the layout of workstations.
• -Increasing the ventilation rate is of extreme importance in poorly-ventilated spaces. Designs for occupancy alone might not be sufficient to guarantee that a space is with ‘acceptable’ risk, noting that the associated metric is not yet well defined in absolute terms.
• -In general, single offices with small occupancy and small offices with medium occupancy are the most critical locations in a building if designed with same ventilation flow rate per person as other areas. There is a case of discussing the ‘blunt’ way that ventilation flow rates are typically applied to a space without understanding ventilation effectiveness when airborne infection resilience is a consideration.
• -Viral parameters can affect the airborne infection resilience, although to a lesser extent in well-ventilated open spaces.
• -Although opening windows, within the context of this study, tends to reduce airborne infection risk overall and especially in small offices, some areas may experience increased risk. This might be in the immediate vicinity of an infected person or even in adjacent rooms, depending upon the airflow characteristics within and between rooms.
• -Many multi-objective considerations are possible with the use of this framework. One might be the airborne infection resilience as a function of thermal comfort and/or energy usage.
• -The ‘well-mixed’ hypothesis in many assessment methods, including Wells-Riley based approaches, could lead to different interpretations and decision-making with respect to the ventilation performance and associated airborne infection resilience highlighted within this detailed CFD-based approach guided by DTM results. This CFD approach includes consideration of a large variability and variety of physical parameters involved in the phenomenon of aerosol transport, such as air velocity, turbulence and exhaled breath concentrations.

This preliminary work shows the need for more research towards the formulation of guidance to design ventilation systems capable of reducing airborne infection risk. However, the framework discussed here can already provide valuable insights supporting building designs and how they are operated. Facility managers would benefit from how the size of the rooms, the season, the configuration of window openings and many other aspects can be used effectively to make spaces safer with a current or planning for a future epidemic event.

The limitations of the current study, which may be investigated at some point in the future, can be briefly summarised as follows, although the framework is unlikely to be significantly impacted by this work.

• -Modelling of an opening considering actual wind conditions and external aerodynamics, as well as shape and type of opening.
• -Use of a community infection rate, which was not used in this paper.
• -Identification of probability distribution of viral parameters to calculate airborne infection risk and individual risk of infection.
• -Identification of occupancy patterns with appropriate metric to include those within risk assessment.

Although there is good confidence that decisions can be made to reduce airborne infection risk when scenarios are tested in a comparative, qualitative way within this proposed framework, any quantitative assessment at this moment in time is unlikely to derive additional benefit as accepted metrics do not yet exist for appropriate targeting. In addition, there are significant uncertainties in the field of airborne infection risk, rendering any quantitative assessment within any methodology having inherent limitations.

It is possible that, at some point in the future, airborne infection risk metrics might be included alongside additional metrics such as those associated with indoor air quality. That said, if appropriate caveats are presented along with the results in this framework, then an ‘acceptable absolute risk’ could form part of the client conversation when mitigation solutions are explored. The term relative risk may then be used to compare different scenarios from within an original design instead of against benchmark scenarios.

In practical terms, this proposed framework could then possibly become an integral part of standard design development practices.

CRediT authorship contribution statement

Giulio Vita: Writing – review & editing, Writing – original draft, Methodology, Formal analysis, Data curation, Conceptualization. Darren Woolf: Supervision, Methodology, Writing - review & editing. Thomas Avery-Hickmott: Visualization, Validation, Software, Data curation. Rob Rowsell: Supervision, Resources, Project administration, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

The data that has been used is confidential.