Airflows inside passenger cars and implications for airborne disease transmission
Varghese Mathai, Asimanshu Das, Jeffrey A. Bailey, Kenneth Breuer
AAirflows inside passenger cars and implications forairborne disease transmission
Varghese Mathai a,1,2 , Asimanshu Das a,1 , Jeffrey A. Bailey b , and Kenneth Breuer a,2 a Center for Fluid Mechanics. School of Engineering, Brown University, Providence, RI 02912, USA; b Department of Pathology and Laboratory Medicine, Warren Alpert MedicalSchool, Brown University, Providence, RI 02912, USAThis manuscript was compiled on July 8, 2020
Transmission of highly infectious respiratory diseases, includingSARS-CoV-2 are facilitated by the transport of tiny droplets andaerosols (harboring viruses, bacteria, etc.) that are breathed out byindividuals and can remain suspended in air for extended periods oftime in confined environments. A passenger car cabin representsone such situation in which there exists an elevated risk of pathogentransmission. Here we present results from numerical simulationsof the potential routes of airborne transmission within a model cargeometry, for a variety of ventilation configurations representing dif-ferent combinations of open and closed windows. We estimate rel-ative concentrations and residence times of a non-interacting, pas-sive scalar – a proxy for infectious pathogenic particles – that areadvected and diffused by the turbulent airflows inside the cabin. Ourfindings reveal that creating an airflow pattern that travels across thecabin, entering and existing farthest from the occupants can poten-tially reduce the transmission.
Airborne transmission | Ventilation | Aerodynamics | COVID-19 | The COVID-19 pandemic is redefining a myriad of social andphysical interactions as we seek to control the predominantlyairborne transmission of the causative severe acute respiratorysyndrome coronovirus 2 (SARS-CoV-2) (1–3). One commonand critical social interaction that must be reconsidered is howpeople travel in passenger automobiles. For maximum socialisolation, driving alone is clearly ideal but this is not widelypractical or environmentally sustainable, and there are manysituations in which two or more people need to drive together.Wearing face masks and using of barrier shields to separateoccupants do offer an effective first step towards reducinginfection rates (4–9). However, aerosols can pass through allbut the most high-performance filters (10) and virus emissionsvia micron-sized aerosols associated with breathing and talking,let alone coughing and sneezing, are practically unavoidable(11–15). Preliminary models indicate a build-up of the viralload inside a car cabin for drives as short as 15 minutes (16, 17),with evidence of virus viability within aerosols of up to 3 hours(18, 19).To assess these risks, it is critical to understand the complexairflow patterns that exist inside the passenger cabin of anautomobile, and furthermore, to quantify the air that mightbe exchanged between a driver and a passenger . Althoughthe danger of transmission while traveling in a car has beenrecognized (20), published investigations of the detailed airflow inside the passenger cabin of an automobile are surpris-ingly sparse. Several works have addressed the flow patternsinside automobile cabins, but only in the all-windows-closedconfiguration (21–23) – most commonly employed so as toreduce noise in the cabin. At the same time, an intuitivemeans to minimize infection pathways is to drive with someor all of the windows open, presumably enhancing the fresh air circulating through the cabin.Motivated by the influence of pollutants on the passengers,a few studies have evaluated the concentration of contami-nants entering from outside the cabin (24) and the persistenceof cigarette smoke inside the cabin subject to different ven-tilation scenarios (25, 26). However, none of these studieshave addressed the micro-climate of the passenger enclosure,and the transport of a contaminant from a specific person inthe cabin (e.g. the driver) to another specific person (e.g. apassenger). In addition to this being an important problemapplicable to airborne pathogens in general, given that theCOVID-19 pandemic is likely to present a public health riskfor several months or years to come, the need for a quantitativeassessment of such airflow patterns inside the passenger cabinof an automobile seems urgent.The current work presents a quantitative approach to thisproblem. While the range of car geometries and driving con-ditions is vast, we restrict our attention to that of two peopledriving in a car, which is close to the average occupancy inpassenger cars in the United States (27). We ask the question:what is the transport of air and potentially infectious aerosoldroplets between the driver and the passenger , and how doesthat air exchange change for various combinations of open-and closed windows.To address this question, we conducted a series of represen-tative Computational Fluid Dynamics (CFD) simulations for
Significance Statement
Outbreaks of respiratory diseases, such as influenza, SARS,MERS and now the novel coronavirus (SARS-CoV-2), havetaken a significant toll on human populations worldwide. Withever-increasing commutes performed by urban populations,driving in an enclosed car cabin with passengers presents arisk of airborne disease transmission. Here we used numericalsimulations to quantify the air flow patterns inside a model cargeometry, for a variety of ventilation configurations. In particular,we identify how the micro-climate of the car interior affects thetransport of a contaminant between occupants in different seatsof the car cabin. Our findings reveal the complex fluid dynamicsat play during everyday commutes in cars, and non-intuitiveways in which open windows can enhance or suppress airbornetransmission pathways.
KB and JB conceived the project. VM and KB designed the numerical simulations. AD and VMperformed the numerical simulations. KB conducted the field experiment. All authors discussedthe results and wrote the paper.The authors declare no competing interest. VM and AD contributed equally to this work and are joint first authors. To whom correspondence should be addressed. E-mail: [email protected] or [email protected]
July 8, 2020 | vol. XXX | no. XX | a r X i v : . [ phy s i c s . s o c - ph ] J u l onfig Window Open Window ClosedRLRRFR FL
Fig. 1.
Schematic of the model car geometry, with identifiers the front-left (FL), rear-left (FL), front-right (FL), and rear-right (FL) windows. The two regions colored inblack represent the faces of the driver and the passenger . Table on the rightsummarizes the six configurations simulated, with various combinations of open- andclosed windows. a range of ventilation options in a model four-door passengercar. The exterior geometry was based on a Toyota Prius, andwe simulated the flow patterns associated with the movingcar while having a hollow passenger cabin and six combina-tions of open and closed windows, named as front-left (FL),rear-left (RL), front-right (FR) and rear-right (RR) (Fig. 1).We consider the case of two persons traveling in the car – the driver in the front left-hand seat (assuming a left-hand-drivevehicle) and the passenger sitting in the rear right-hand seat,thereby maximizing the physical distance ( ≈ . k − (cid:15) turbulence model (for details see Methodssection). We simulated a single driving speed of v = 22 m/s(50 mph) and an air density, ρ a = 1.2 kg/m . This trans-lates to a Reynolds number of 2 million (based on the carheight), which is high enough that the results presented hereshould be insensitive to the vehicle speed. The flow patternscalculated for each configuration were used to estimate the air(and potential pathogen) transmission from the driver to the passenger , and conversely from the passenger to the driver .These estimates were achieved by computing the concentrationfield of a passive tracer “released” from each of the occupants,and evaluating the amount of that tracer reaching the otheroccupant (see Methods section).In this paper, we first describe the pressure distributionsestablished by the car motion and the flow induced insidethe passenger compartment. Following that we describe thepassenger-to-driver and driver-to-passenger transmission re-sults for each of the ventilation options, and finally concludewith insights based on the observed concentration fields, andgeneral conclusions and implications of the results. Results and Discussion
Overall air flow patterns.
The external airflow generates a pres-sure distribution over the car (Fig. 2), forming a high-pressurestagnation region over the radiator grille and on the front ofthe windshield. The peak pressure here (301 Pa) is of theorder of the dynamic pressure (0 . ρ a v = 290 Pa at 22 m/s).Conversely, as the airflow wraps over the top of the the car andaround the sides, the high air speed is associated with a lowpressure zone, with the local pressure well below atmospheric(zero gauge pressure in Fig 2). This overall pressure map isconsistent with other computations of flows over automobilebodies (30–32) and gives a physical preview to a key feature –that the areas near the front windows and roof of the car areassociated with lower-than-atmospheric pressures, while theareas towards the rear of the passenger cabin are associatedwith neutral or higher-than-atmospheric pressures.A typical streamline (or pathline) pattern in the car interioris shown in Fig. 3, where the rear-left and front-right windowsare opened (Config. 3 in Fig. 1). The streamlines were initi-ated at the rear-left (RL) window which is the location of astrong inflow (Fig. 3-lower right),due to the high pressure zoneestablished by the car’s motion (Fig 2). A strong air current( ∼
10 m/s) enters the cabin from this region and travels alongthe back seat of the car, before flowing past the passenger sitting on the rear-right side of the cabin. The air currentturns at the closed rear-right window, moves forward and themajority of the air exits the cabin at the open window onthe front-right (FR) side of the vehicle, where the exteriorpressure is lower than atmospheric (Fig 2). There is a muchweaker air current ( ∼ passenger , continues to circulate within the cabin. A smallfraction of this flow is seen to exit through the RL window.The streamline arrows indicate that the predominant di-rection of the recirculation zone inside the cabin is counter-clockwise (viewed from above). These streamlines, of course,represent possible paths of transmission, potentially transport-ing virus-laden droplets or aerosols throughout the cabin and,in particular, from the passenger to the driver .As already indicated, for the particular ventilation optionshown here, the overall air pattern – entering on the rear-leftand leaving on the front-right – is consistent with the externalpressure distributions (Fig 2). The elevated pressure towardsthe rear of the cabin and the suction pressure near the front ofthe cabin drive the cabin flow. This particular airflow patternwas confirmed in a “field test” in which the windows of a (a) (b) Speed, 50 mph P r e ss u r e ( gauge ) Fig. 2.
Pressure distributions around the exterior of the car, associated with a vehiclespeed of 22 m/s (50 mph). (a) Surface pressure distribution. (b) Pressure distributionin the air at the mid-plane. The color bar shows the gauge pressure in Pascal, andemphasizes the mid-range of pressures: [ − , Pa; at this speed the full rangeof gauge pressure on the surface is [ − , Pa. et al. R RL Velocity magnitude (m/s)Normal velocity (m/s)
Inflow Outflow
Fig. 3.
Streamlines computed for the case in which the rear-left and front-rightwindows are open. The streamlines were initiated at the rear-left (RL) window opening.The streamline color indicates the flow velocity. Insets show the front-right (FR) andRL windows colored by the normal velocity. The RL window has a strong inflow(positive) of ambient air, concentrated at its rear, whereas the front right windowpredominantly shows an outward flow (negative) to the ambient. test vehicle (2011 Kia Forte hatchback) were arranged as inConfig. 3, i.e. with the RL and FR windows open. Thecar was driven at 30 mph on a length of straight road, anda flow wand (a short stick with a cotton thread attached tothe tip) was used to visualize the direction and approximatestrength of the air flow throughout the cabin. By movingthe wand to different locations within the cabin, the overallflow patterns obtained from the CFD simulations – a strongair stream along the back of the cabin that exits the front-right window, and a very weak flow near the driver – werequalitatively confirmed. Different ventilation configurationsgenerate different streamline patterns (e.g. Supplementarymaterials Figs. S-1 S-2) but can all be linked to the pressuredistributions established over the car body (Fig 2).An important consideration when evaluating different ven-tilation options in the confined cabin of a car is the rate atwhich the cabin air gets replenished with fresh air from theoutside. This was measured by Ott et al. (25) for a vari-ety of cars, traveling at a range of speeds, and for a limitedset of ventilation options. In these measurements, a passivetracer (representing cigarette smoke) was released inside thecabin and the exponential decay of the tracer concentrationmeasured. Assuming the cabin air to be well-mixed (25), theyestimated the air-changes-per-hour (ACH) – a widely usedmetric in indoor ventilation designs.From the simulations, we can precisely compute the totalflow of air entering (and leaving) the cabin and, knowingthe cabin volume, we can compute the air-changes-per-hourdirectly. Such a calculation yields a very high estimate of ACH(of the order of 1000, see Supplemental Fig. S-3), but this ismisleading, since the assumption of well-mixed cabin air is anover-simplification. Instead, a more relevant quantification ofthe ACH was obtained using a residence time analysis (RTA)for a passive scalar released at multiple locations within the passenger cabin. The time taken for the concentration at theoutlets to decay below a threshold (1% of the initial value)was computed, and the inverse of this time yields effectivevalues for ACH (Fig. 4) which compare favorably with thosereported by Ott et al. (25), after correcting for the vehiclespeed (33).As one might expect, configuration 6 – all windows open –has the highest ACH - approximately 250, while among theremaining configurations, Configuration 1 – all windows closed– has the lowest ACH of 62. However, what is somewhatsurprising is that the ACH for Config. 2, in which the thewindows adjacent to the driver and the passenger (FL and RR,respectively) are opened is only 89 - barely higher than theall-windows-closed configuration; the remaining three configu-rations (Configs. 3, 4 & 5) with two or three open windows allshow relatively high efficacy of about 150 ACH. The reason forthese differences can be traced back to the overall streamlinepatterns and the pressure distributions that drive the cabinflow (Fig.2). A well-ventilated space requires the availabilityof an entrance and an exit, and a favorable pressure gradientbetween the two. Once such a cross-ventilation path is estab-lished (as in Config. 3 or Fig. 3), opening a third window haslittle effect on the ACH. However, we will later show that theACH gives only a partial picture and the spreading of a passivescalar can show marked variations between the configurations3–5, despite their nearly constant ACH.
Driver-to-Passenger transmission.
The flows establishedthrough the cabin provide a path for air transmission be-tween the two occupants, and hence a possible infection route.Our focus here is on transmission via aerosols, which are smallenough (and non-inertial) that they can be regarded as faithfultracers of the fluid flow (34, 35).We begin by addressing the problem from the viewpointof an infected driver releasing pathogen-laden aerosols andpotentially infecting the passenger . Fig. 5 shows a comparisonof the spreading patterns of a passive scalar released near the driver and reaching the passenger (for details, see Methodssection). To obtain a volumetric quantification, the averagescalar concentration in a 0.1 m diameter spherical domainsurrounding the passenger’s face is also computed, as shownin Fig. 5(b).The all-windows-closed configuration fares the worst andresults in over 10% of the scalar that leaves the driver reachingthe passenger . In contrast, the all-windows-open setting (Con-fig. 6) appears to be the best case, with almost no injectedscalar reaching the passenger . An overall trend of decreasing
Config A i r c h a n g e r a t e [ h ] - Fig. 4.
Air change rate (or ACH) calculated based on a residence time analysis fordifferent configurations. Here, the air change rate per hour is given by /τ r , where τ r is the residence time in hours.Mathai et al. PNAS |
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Config C on c en t r a t i on % A BD CA BD CA BD C A BD CA BD CA BD C C on c en t r a t i on % c) Config
Fig. 5.
Driver-to-passenger transmission. (a) Schematic of the vehicle with a cut plane passing through the center of the inner compartment on which the subsequentconcentration fields are shown. (b) The bar-graph shows the mass fraction of air reaching the passenger that originates from the driver . (c) shows the concentration field ofthe species originating from the driver for different window cases. The dotted and the solid lines denote the open and closed windows, respectively. Note that the line segmentA-D is at the front of the car cabin, and the flow direction in (c) is from left to right. Here the dotted line represent open window and solid line indicate closed window. transmission is observed when the number of open windowsare increased. However, there is some variability between thedifferent configurations, the reasons for which may not be clearuntil one looks at the overall flow patterns (e.g. Fig. 3).Figure 5(c) shows the concentration field of the scalar ina horizontal plane A-B-C-D within the car cabin roughly athead height of the occupants (Fig. 5(a)). The scalar field con-centration is the highest for Config. 1, where all four windowsare closed. We note that this driving configuration might alsorepresent the most widely preferred one in the United States(with some seasonal variations). Config. 2 represents a two-windows open situation, wherein the driver and the passenger open their respective windows. One might assume that thisis a logical thing to do for avoiding infection from the otheroccupant. Although this configuration does improve over theall-windows closed situation, shown in Fig. 5(b), one can seefrom the concentration field that Config. 2 does not effectivelydilute the tracer particles, and the passenger receives a fairlylarge contaminant load from the driver . To explain this result,we looked more closely at the air flow patterns. In analogywith the streamlines associated with Config 3 (Fig. 3), Config2 establishes a strong air current from the open rear window(RR) towards the open front window (FL), and a clockwiserecirculating flow within the cabin (viewed from above). Al-though this flow pattern is weak, it increases the transport oftracer from the driver to the passenger . Moreover, the incom-ing air stream in Config. 2 enters behind the passenger and isineffective in flushing out potential contaminants emanatingfrom the driver .An improvement to this configuration can be achieved iftwo modifications are possible: i) a change in the directionof the internal circulation, and ii) a modified incoming airflow that impinges the passenger before leaving through theopen window on the front. This has been realized in thetwo-windows-open Config. 3 (Fig. 5(c)), wherein the RL andFR windows are open (same as the configuration shown inFig. 3). Now, the incoming clean air stream from the RLwindow partially impinges on the passenger (seated in the RRseat) as it turns around the corner. This stream of air mightalso act as a “air curtain” (36), and hence the concentration ofpotentially contaminated air reaching the passenger is reduced.The remaining configurations (Configs. 4–6) will be treated as modifications made to Config. 3, by opening more windows.Config. 4 has three windows open (Fig. 5(c)). Since thisrepresents opening an additional window (RR), it may besurprising to find a detrimental effect on the concentration fieldand the ACH (comparing Configs. 3 & 4 in Fig. 5(b),(c)). Theincrease in the concentration can be linked to the modified airflow patterns that result from opening the third (RR) window.Firstly, opening the RR window leads to a reduction in theflow turning at the rear-right end of cabin, since a fractionof the incoming air gets bled out of this window (Fig. S-1).Due to this diversion of the air flow, the region surrounding passenger is less effective as a barrier to the scalar releasedby the driver . Secondly, the modified flow also creates anentrainment current from the driver to the passenger , whichfurther elevates the scalar transport.Config. 5 presents the scenario where the third open win-dow is the FL. This modification leads to an improvement,nearly halving the average concentration when compared tothat in Config. 3. The reason for this is apparent from the con-centration field (Fig. 5(c)). Now that the FL window near the driver is open, the relatively low pressure near the front of thecar creates an outward flow that flushes out much of releasedspecies. With the substantially reduced initial concentrationfield near the driver , the fraction reaching the passenger isproportionately reduced. Thus, among the configurations withthree windows open, Config. 5 might provide the best benefitfrom the viewpoint of driver-to-passenger transmission.Lastly, when all four windows are opened (Config. 6), wecan again use the exterior pressure distribution to predictthe flow directions. The streamlines enter through the rearwindows (RL and RR) and leave via the front windows (FL andFR). However, unlike the configuration with only two windowsopen (Fig. 3), the overall flow pattern is substantially modified(Fig. S-2) and the streamlines obey left-right symmetry and,for the most part, do not cross the vertical mid-plane of thecar. In this configuration, the flow is largely partitioned intotwo zones creating two cross-ventilation paths in which thetotal air flow rate is nearly doubled when compared to thetwo and three window open configurations (Fig. S-3).
Passenger-to-Driver transmission.
In this section, we lookinto the particle (and potential pathogen) transmission from et al. A BCD a)b) c)
Config C on c en t r a t i on % A BD CA BD CA BD C A BD CA BD CA BD C C on c en t r a t i on % Config
Fig. 6.
Passenger-to-driver transmission. (a) Schematic of the vehicle with a cut plane passing through the center of the inner compartment on which the subsequentconcentration fields are shown. (b) The bar-graph shows the mass fraction of air reaching the driver that originates from the passenger . (c) shows the concentration field ofthe species originating from the passenger for different window configuration. Here the dotted line represent open window and solid line indicate closed window. the passenger to the driver . Fig. 6 shows a comparison of thespreading patterns of a passive scalar within the car cabin.The general trend suggests a decreasing level of transmissionas the number of open windows is increased, similar to theresults found for the driver-to-passenger transmission. Config.1 (all windows closed) shows the highest concentration levelat the driver ( ∼ driver tothe passenger (Fig. 5(b)), a difference that can be attributedto the fact that the air-conditioning creates a front-to-backmean flow.As before, the lowest level of scalar transport correspondsto Config. 6 with all windows open, although we note that theconcentration load here (about 2%), is noticeably higher thanthat for the driver-to-passenger transmission (about 0.2%).The streamline patterns for this configuration (SupplementalFig. S-2) show that the air enters through the rear win-dows,(RL and RR) and exits through the respective frontwindows (FL and FR). There is, therefore, an average rear-to-front flow in both the left and right halves of the cabin whichenhances transmission from the passenger to the driver .Among the remaining configurations (Configs. 2–5), Config.3 shows a slightly elevated level of average concentration. Thecounter-clockwise interior circulation pattern is at the heartof this transmission pattern. A substantial reduction in theaverage concentration can be achieved by additionally openingthe rear window adjacent to the passenger (Config. 4). Thisallows for much of the scalar released by the passenger to beimmediately flushed out through the rear window, analogousto the way in which opening the driver-adjacent (FL) windowhelps to flush out the high concentration contaminants fromthe driver before they can circulate to the passenger (Fig. 5(c, Concluding remarks
In summary, the flow patterns and the scalar concentrationfields obtained from the CFD simulations demonstrate thatestablishing a dominant cross-ventilation flow within the carcabin is crucial to the minimization of particle transport be-tween car occupants and to lessening the exchange of po-tentially infectious micro-particles. With this flow patternestablished, the relative positions of the driver and passen-ger determine the quantity of of air transmitted between the occupants.It is, perhaps, not surprising that the most effective wayto minimize cross-contamination between the occupants is tohave all of the windows open (Config. 6). This establishestwo distinct air flow paths within the car cabin which help toisolate the left and right sides, and maximizes the ACH in thepassenger cabin. Nevertheless, driving with all the windowsopen might not always be a viable or desirable option, and inthese situations there are some non-intuitive results that arerevealed by the calculations.The all-windows-closed scenario with air-conditioning on(Config. 1) appears to be the least effective option. Perhapsmost surprising is that an intuitive option – of opening thewindows adjacent to each occupant (Config. 2) is effective,but not always the best amongst the partial ventilation op-tions. Config. 3, in which the two windows farthest from theoccupants (FR and RL, respectively) are open, appears togive better protection to the passenger . The particular airflowpatterns that the pressure distributions establish – channelingfresh air across the rear seat, and out the front-right window –help to minimize the interaction with the driver in the frontleft position.The role of car speed cannot be ignored when addressing thetransport between the vehicle’s occupants. Since the Reynoldsnumber of the flow is high, the air flow patterns will be largelyinsensitive to how fast the car is driven. However, the air-changes-per-hour (ACH) is expected to depend linearly on thecar speed (33) and consequently, the slower the car speed, thelower the ACH, the longer the residence time in the cabin, andhence the higher the opportunity for pathogenic infection.The findings reported here can be easily translated to right-hand-drive vehicles, of relevance to countries like the UK andIndia. In those situations similar, but mirrored, flow patternscan be expected. Furthermore, although the computationswere performed for a particular vehicle design (loosely modeledon a Toyota Prius), the overall results are expected to be validfor many four-windowed passenger vehicles. One should expect,however, that trucks, minivans and cars with an open moon-roof may well exhibit different airflow patterns and hencedifferent scalar transport trends.There are, to be sure, uncertainties with our analyses andwe must be clear that we do not make any definitive assessmentof the health risks associated with riding in an automobile.
Mathai et al.
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July 8, 2020 | vol. XXX | no. XX || vol. XXX | no. XX | he simulations solve for a steady turbulent flow, while thetransmission of scalar particles that might represent pathogenicaerosols will be affected by large scale, unsteady, turbulentfluctuations that are not captured well in the current work.These effects could change the amount of tracer emitted byone occupant that reaches the other occupant (37). AlthoughRANS simulations represent a widely-used model for scientific,industrial and automotive applications (38), there are stillknown limitations to its predictive capabilities, and a moreaccurate assessment of the flow patterns and the turbulentdispersion requires a much more computationally intensive setof simulations, such as Large Eddy simulation (LES) or DirectNumerical Simulations (DNS) – an undertaking far beyondthe aims and scope of this work.Nevertheless, despite these caveats, these results providecritical insight for the hundreds of millions of people whoneed to travel in a car during the COVID-19 pandemic, andestablishes a starting point for an extended analysis of themicro-climate inside vehicle interiors which we hope will yieldsafer and lower-risk approaches to personal transportation. Methods
The car geometry was chosen based on the basic exterior of aToyota Prius. The interior was kept minimal, and comprisedof two cylindrical bodies representing the driver and the pas-senger . The CAD model for the car geometry was preparedusing SolidWorks, and subsequent operations including do-main discretization (meshing) and case setup were carried outusing the ANSYS-Fluent module.The steady Reynolds-averaged Navier-Stokes (RANS) equa-tions with a standard k − (cid:15) turbulence model was solved on anunstructured grid, made up of about 1 million tetrahedral gridcells. The domain size was 6 h × h × h in the streamwise,normal, and spanwise directions, respectively, where h is thecar height. A single vehicle speed of U = 22 m/s (50 mph),which was set as the inflow condition upstream of the frontof the car body. A pressure outlet condition was applied atthe exit. The simulations were iterated until convergence wasachieved for the continuity and momentum equations, andthe turbulence dissipation rate, (cid:15) . Each simulation run tookroughly 1.5 hrs of computational time on a standard work-station. A grid-independence study was performed, whichestablished that the resolution adopted was sufficient for thequantities reported in the present work.The mixing and transport of a passive scalar were modeledby solving species transport equations describing an advection-diffusion equation. Separate simulations were performed forthe scalar released near driver , and then for its release near the passenger’s face. The scalar was set to be a non-interactingmaterial, i.e. with an exceedingly low mass diffusivity, whichmeant that only advection and turbulent diffusion contributedto its transport dynamics. This approach mimics the mixingof a high Schmidt number material, such as dye or smoke,which are commonly used as a tracers in turbulent fluid flows(39). The injection rate of the species was very low in orderthat it did not influence the air flow. This was verified bycomparing the concentration fields for various injection rates,which showed negligible variation. This strategy was followedin order that the effects of turbulent diffusion effects were alsocaptured in the analyses.
1. Lidia Morawska, Julian W. Tang, William Bahnfleth, Philomena M. Bluyssen, Atze Boerstra, and Giorgio Buonanno et al. How can airborne transmission of covid-19 indoors be min-imised?
Environ. Int. , 142:105832, 2020. .2. Renyi Zhang, Yixin Li, Annie L Zhang, Yuan Wang, and Mario J Molina. Identifying airbornetransmission as the dominant route for the spread of covid-19.
Proc. Natl. Acad. Sci. , 2020.3. Chad J Roy and Donald K Milton. Airborne transmission of communicable infection-the elu-sive pathway. Technical report, ARMY MEDICAL RESEARCH INST OF INFECTIOUS DIS-EASES FORT DETRICK MD ..., 2004.4. J.W. Tang, C.J. Noakes, P.V. Nielsen, I. Eames, A. Nicolle, Y. Li, and G.S. Settles. Observingand quantifying airflows in the infection control of aerosol- and airborne-transmitted diseases:an overview of approaches.
J. Hosp. Infec. , 77(3):213 – 222, 2011. .5. A. C. K. Lai, C. K. M. Poon, and A. C. T. Cheung. Effectiveness of facemasks to reduceexposure hazards for airborne infections among general populations.
J. R. Soc. Interface , 9(70):938–948, 2012. .6. Trisha Greenhalgh, Manuel B Schmid, Thomas Czypionka, Dirk Bassler, and Laurence Gruer.Face masks for the public during the covid-19 crisis.
BMJ , 369, 2020. .7. Nancy H. L. Leung, Daniel K. W. Chu, Eunice Y. C. Shiu, Kwok-Hung Chan, James J. McDe-vitt, Benien J. P. Hau, Hui-Ling Yen, Yuguo Li, Dennis K. M. Ip, J. S. Malik Peiris, Wing-HongSeto, Gabriel M. Leung, Donald K. Milton, and Benjamin J. Cowling. Respiratory virus shed-ding in exhaled breath and efficacy of face masks.
Nat. Med. , 26(5):676–680, 2020. .8. Shu-An Lee, Sergey A Grinshpun, and Tiina Reponen. Respiratory performance offered byn95 respirators and surgical masks: human subject evaluation with nacl aerosol representingbacterial and viral particle size range.
Ann. Occup. Hyg. , 52(3):177–185, 2008.9. Roshun Povaiah. Social distancing in cabs: Why plastic panels won’t be effective.
The Quint ,2020.10. Nancy HL Leung, Daniel KW Chu, Eunice YC Shiu, Kwok-Hung Chan, James J McDevitt,Benien JP Hau, Hui-Ling Yen, Yuguo Li, Dennis KM Ip, JS Malik Peiris, et al. Respiratoryvirus shedding in exhaled breath and efficacy of face masks.
Nat. Med. , 26(5):676–680,2020.11. Jitendra K. Gupta, Chao-Hsin Lin, and Qingyan Chen. Characterizing exhaled airflow frombreathing and talking.
Indoor Air , 20(1):31–39, 2010. .12. Matthew Meselson. Droplets and aerosols in the transmission of sars-cov-2.
N. Engl. J. Med ,2020.13. Jing Yan, Michael Grantham, Jovan Pantelic, P Jacob Bueno De Mesquita, Barbara Albert,Fengjie Liu, Sheryl Ehrman, Donald K Milton, EMIT Consortium, et al. Infectious virus inexhaled breath of symptomatic seasonal influenza cases from a college community.
Proc.Natl. Acad. Sci. , 115(5):1081–1086, 2018.14. Roman Wölfel, Victor M Corman, Wolfgang Guggemos, Michael Seilmaier, Sabine Zange,Marcel A Müller, Daniela Niemeyer, Terry C Jones, Patrick Vollmar, Camilla Rothe, et al.Virological assessment of hospitalized patients with covid-2019.
Nature , 581(7809):465–469,2020.15. Wan Yang, Subbiah Elankumaran, and Linsey C Marr. Concentrations and size distributionsof airborne influenza a viruses measured indoors at a health centre, a day-care centre andon aeroplanes.
J. R. Soc. Interface , 8(61):1176–1184, 2011.16. G Aernout Somsen, Cees van Rijn, Stefan Kooij, Reinout A Bem, and Daniel Bonn. Smalldroplet aerosols in poorly ventilated spaces and sars-cov-2 transmission.
Lancet Respir.Med. , 2020.17. Joseph Allen, Jack Spengler, and Richard Corsi. Is there coronavirus in your car? here’s howyou can protect yourself.
USA Today , 2020.18. Neeltje Van Doremalen, Trenton Bushmaker, Dylan H Morris, Myndi G Holbrook, AmandineGamble, Brandi N Williamson, Azaibi Tamin, Jennifer L Harcourt, Natalie J Thornburg, Su-san I Gerber, et al. Aerosol and surface stability of sars-cov-2 as compared with sars-cov-1.
N. Engl. J. Med , 382(16):1564–1567, 2020.19. Valentyn Stadnytskyi, Christina E Bax, Adriaan Bax, and Philip Anfinrud. The airborne lifetimeof small speech droplets and their potential importance in sars-cov-2 transmission.
Proc. Natl.Acad. Sci. , 117(22):11875–11877, 2020.20. L. D. Knibbs, L. Morawska, and S. C. Bell. The risk of airborne influenza transmission inpassenger cars.
Epidemiol. Infect. , 140(3):474–478, 2012. .21. Alex Alexandrov, Vladimir Kudriavtsev, and Marcelo Reggio. Analysis of flow patterns andheat transfer in generic passenger car mini-environment. In , pages 27–29. Citeseer, 2001.22. Jin Pyung Lee, Hak Lim Kim, and Sang Joon Lee. Large-scale piv measurements of ven-tilation flow inside the passenger compartment of a real car.
J. Vis. , 14(4):321–329, 2011..23. S. Ullrich, R. Buder, N. Boughanmi, C. Friebe, and C. Wagner. Numerical study of the airflowdistribution in a passenger car cabin validated with PIV. In A. Dillmann, G. Heller, E. Krämer,C. Wagner, C. and. Tropea, and S. Jakirli´c, editors,
New Results in Numerical and Experimen-tal Fluid Mechanics XII. , volume 142 of
Notes Numer. Fluid Mech. Multidiscip. Des.
Springer,2018.24. Daniel Müller, Doris Klingelhöfer, Stefanie Uibel, and David A. Groneberg. Car indoor airpollution - analysis of potential sources.
J. Occup. Med. Toxicol. , 6(1):33, 2011. .25. Wayne Ott, Neil Klepeis, and Paul Switzer. Air change rates of motor vehicles and in-vehiclepollutant concentrations from secondhand smoke.
J Expo Sci Environ Epidemiol. , 18(3):312–325, 2008.26. E. M. Saber and M. Bazargan. Dynamic behavior modeling of cigarette smoke particles insidethe car cabin with different ventilation scenarios.
Int. J. Environ. Sci. Technol. , 8(4):747–764,2011. .27. Federal Highway Administration (FHWA). Average vehicle occupancy factors for computingtravel time reliability measures and total peak hour excessive delay metrics.
Federal HighwayAdministration (FHWA) , 2019.28. Saboora Khatoon and Man-Hoe Kim. Thermal comfort in the passenger compartment usinga 3-d numerical analysis and comparison with fanger’s comfort models.
Energies , 13(3):690,2020.29. Miloš Fojtlín, Michal Planka, Jan Fišer, Jan Pokorn`y, and Miroslav Jícha. Airflow measure-ment of the car hvac unit using hot-wire anemometry. In
EPJ web of conferences , volume | 10.1007/BF03326259 Mathai et al.
14, page 02023. EDP Sciences, 2016.30. Andreas Kleber. Simulation of airflow around an opel astra vehicle with fluent.
Journal Article,International Technical Development Center Adam Opel AG , 2001.31. Akshay Parab, Ammar Sakarwala, Vaibhav Patil, and Amol Mangrulkar. Aerodynamic anal-ysis of a car model using fluent-ansys 14.5.
Int. J. Rec. Technol. Mech. Electric. Eng. , 1(4):07–13, 2014.32. Exa Corporation Ross, Michelle Murray. Jaguar land rover achieves goal of sophisticatedengineering with exa powerflow 4.1.
PRweb , 2009.33. B Fletcher and CJ Saunders. Air change rates in stationary and moving motor vehicles.
J.Hazard. Mater. , 38(2):243–256, 1994.34. Varghese Mathai, Enrico Calzavarini, Jon Brons, Chao Sun, and Detlef Lohse. Microbubblesand microparticles are not faithful tracers of turbulent acceleration.
Phys. Rev. Lett. , 117(2):024501, 2016.35. Zellman Warhaft. Passive scalars in turbulent flows.
Annu. Rev. Fluid Mech. , 32(1):203–240,2000.36. AM Foster, MJ Swain, R Barrett, P D’Agaro, LP Ketteringham, and SJ James. Three-dimensional effects of an air curtain used to restrict cold room infiltration.
Appl. Math. Model. ,31(6):1109–1123, 2007.37. Paul E Dimotakis. Turbulent mixing.
Annu. Rev. Fluid Mech. , 37:329–356, 2005.38. Jorge E Bardina, Peter G Huang, and Thomas J Coakley. Turbulence modeling validation,testing, and development, 1997. NASA-TM-110446.39. Elise Alméras, Varghese Mathai, Chao Sun, and Detlef Lohse. Mixing induced by a bubbleswarm rising through incident turbulence.
Int. J. Multiph. Flow , 114:316–322, 2019.
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July 8, 2020 | vol. XXX | no. XX || vol. XXX | no. XX | upplementary Material Fig. S-1.
Streamlines colored by velocity magnitude for Config. 4 with three windows(FL, RL and RR) open. The opening of the third RR window adjacent to the passengercauses a portion of the incoming air stream to be bled out.
Fig. S-2.
Streamlines colored by velocity magnitude for Config. 6 with all four windowsopen. The flow gets compartmentalized into a left and right zone. In each of thesezones the streamlines are directed from the rear window (with higher pressure) towardthe front window (with lower pressure). V o l u m e i n f l o w Config C ab i n v o l u m e [ h ] - Fig. S-3.
Volume of air entering the windows per unit time, compared to the overallcabin volume. The all-windows-open case draws in a significantly more amount of air,whereas the other cases do not exhibit much difference.Mathai et al.
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