National Academies Press: OpenBook

Air Quality in Transit Buses (2023)

Chapter: Day 2 Session 2

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Suggested Citation:"Day 2 Session 2." National Academies of Sciences, Engineering, and Medicine. 2023. Air Quality in Transit Buses. Washington, DC: The National Academies Press. doi: 10.17226/27033.
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Session 2

Modeling and Simulations for Transmission Risk Decision Making

Nathan Edwards, MITRE (formerly), U.S. Partnership for Assured Electronics (USPAE) (current), Moderator

Presenters

Varghese Mathai, University of Massachusetts, Amherst

Jose-Luis Jimenez, University of Colorado Boulder

Varghese Mathai and Jose-Luis Jimenez covered modeling simulation of transmission risk for decision-making and, broadly, air quality.

Mathai discussed the fluid dynamics of airborne disease transmission. Airborne transmission of respiratory pathogens and latent transmission of droplets deal with particle-laden fluid flows. The principles that guide the research have not changed; these principles can still be applied to many of the aerosols and droplet rate and transmission models. When a person sneezes or coughs, all sizes of droplets are expelled in a ballistic trajectory. Many structures are revealed in simulations of computational fluid dynamics (CFD) associated with a sneeze or a cough. A range of sizes is contained in these droplets, and in simulations it has been shown that these sizes are on a continuum ranging from 1 micron to millimetric. Much of the research is still based on studies from the 1930s by William Wells that say that droplets can come in two sizes—ones that are less than 100 microns and ones that are greater than 100 microns—and that both sizes have their own trajectories. For example, some droplets have a semiballistic kind of motion. Other droplets are rising through the air. In the fluid dynamics research of a particle that is moving through a flow, the droplet experiences a resisting force that would slow it down and then come to a standstill. These tiny droplets never travel beyond 6 feet, which is where the 6-foot rule came from. However, it turns out this is not true, and that the smaller droplets travel farther because the tiny droplets are not traveling across the air; they are being carried with the air. Therefore, the force balance of this simple treatment that William Wells conducted does not work, and researchers have found these droplets can linger.

Mathai noted one simple metric to use to look at a droplet in a flow and tell whether it is going to follow the fluid flow or not: looking at the Navier-Stokes number, which indicates how quickly the tiny droplet can respond to an air current. For example, a given droplet is moving in a particular direction and the air around it is moving in a different direction. Gradually, this droplet is going to try to adapt its speed in the direction of the fluid that is around it. The quicker a droplet adapts to the air flow direction, the more it is following the air particles or aerosols. That is one metric that is

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Suggested Citation:"Day 2 Session 2." National Academies of Sciences, Engineering, and Medicine. 2023. Air Quality in Transit Buses. Washington, DC: The National Academies Press. doi: 10.17226/27033.
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used to tell whether this is an airborne transmission or whether it is a droplet-based transmission, which is covered by other methods.

Mathai further explained that if the droplets are following the fluid, then the Navier–Stokes equations describe the movement of air particles or liquid particles as governed by Newton’s second law. Solving the equations gives the speed of the air particles or the speed of the fluid and the pressure of the fluid in space and time. Most of the flows around us are considered turbulent or composed of many rotating flows and rotating eddies. Within these eddies are small droplets or particles that are advected or carried by these droplets over large distances.

Mathai explained that simulation is computationally intensive using these fluid flow equations. Another approach is to look at larger-scale motions inside the fluid flow, and reduced order modeling can obtain some insightful results. However, the results come at the expense of accuracy, whereas when the fluid flow is fully resolved by means of a direct numerical simulation, the accuracy is very high but comes at computational expense.

Mathai noted there have been several fluid dynamics studies that have shown that it is not just the physical separation but also the duration of exposure that decides potential for infection. To assess the risk of getting an infection, it is necessary to look at the time spent in an interaction. As the air jet that is produced by a person who is talking moves farther away from that person, it is going to spread out and dilute; at the same time, the longer the duration spent breathing in the tiny aerosols, the higher the risk. A speed, space, time diagram can show that, with increasing time and reduced separation, the risk of getting infection increases.

Mathai commented that since the pandemic, there has been a lot of interest in the air flow inside a car. A simulation using a reduced order model of the fluid flow inside a passenger car shows that when the rear left window and the front right window are open, the air enters from behind, circulates some inside the cabin, and then finally exits through the front right window. CFD simulations help predict the approximate flow patterns that exist in many different configurations. CFD can perform many simulations without field tests, and the user can change configurations one by one to see the outcomes. A simulation of a passenger car, driving at 50 miles per hour, looked at the ACH. The ACH numbers were larger than what they effectively should have been because the simulation considers every single fluid flow that comes in and goes out.

Mathai explained, however, that on a relative scale, as the number of open windows increases, the ACH increases. With at least two windows open, opening more windows does not increase the ACH because one window is allowing the air to enter, and one window is allowing the contaminated air to be flushed out. If this is maintained, there is a sufficiently large exchange rate. Aerosol concentrations present inside the car are inversely related to ACH. Looking at the fluid dynamics more closely in a cross section

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Suggested Citation:"Day 2 Session 2." National Academies of Sciences, Engineering, and Medicine. 2023. Air Quality in Transit Buses. Washington, DC: The National Academies Press. doi: 10.17226/27033.
×

of the cabin of the car, contaminants are spreading between the driver, who is sitting in the front seat, and the passenger, who is sitting in the rear right seat. When all the windows are closed, the concentration of aerosols inside this cabin is very high. As windows are opened, the flows are very nonlinear, and doubling the area of opened windows does not necessarily double the change in the flow rate. Also, the single metric of ACH is not sufficient to understand what is going on inside the cabin. There is an assumption that ACH is associated with a well-mixed space. The simulated space is not well mixed, and that is the root cause of the differences in the ACH prediction and what is predicted for aerosol concentration. When the car is driven slower, the natural ventilation is also much weaker and, as a result, there is a greater concentration of aerosols, meaning that the slower the vehicle and the longer the ride duration, the higher the risk exposure.

Mathai commented that the same kind of simulation of air flow patterns can be applied to the inside of a bus or a subway car; the only difference is the kind of boundary conditions or the inflow and the outflow conditions. In a bus simulation, the inflows created vertical air flow patterns, and then the fluid flow was taken out from the bottom of the bus. The vertical lines show that they do not circulate a lot within the cabin. In an experiment, the air inside the bus was being refreshed where 1X = 20 ACH and was compared with 0.25X, 0.5X, and 2X to look at how much of the aerosols released by one occupant inside the cabin spreads to another occupant. The maximum concentration reaching from one person to the other varied, depending on the air flow volume rate, and the patterns were also different, depending on how much air was pumped into the bus. Another experiment using the same ACH looked at the transmission of aerosols being released from a passenger in a different location on the bus. As the ventilation rate increased from 0.25X ACH to 2X ACH, the results showed nonmonotonic trends in how aerosols were transmitted, where increasing the ventilation rate increased transmission. This result is somewhat counterintuitive, but these simulations show the increased turbulence, or fluctuations in velocity, inside the cabin, which leads to more spreading of aerosols locally. When the ACH is increased, a reverse trend produces a reduction in transmission. The spreading of airborne pathogens inside turbulent fluid flows is a competition between the main direction of the motion of the fluid and the level of fluctuation that is present in the flow. The researchers also looked at what happens if the turbulence is increased at the inlet vent. In a laminar case, there was no fluctuation, the particles were flowing in parallel lines, and the transmission was low. The researchers increased the turbulence to around 30% by creating some roughness in the inlet vents, which can lead to increased spread of aerosols from the infectious passenger.

Mathai explained that reduced order modeling simulations can be done in a matter of days; however, there are other settings in which reduced order models cannot be used and require solving the full Navier–Stokes equations. For example, in a public setting when people are waiting in a line, people create a cloud of aerosols around themselves,

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Suggested Citation:"Day 2 Session 2." National Academies of Sciences, Engineering, and Medicine. 2023. Air Quality in Transit Buses. Washington, DC: The National Academies Press. doi: 10.17226/27033.
×

which creates a complex setting. Many factors are involved in the modeling: the speed people walk, the duration of time in line, the physical separation between people, and the surrounding conditions. These conditions include the temperature and humidity in the room or the environment. All of these factors have counteracting effects on how the aerosols spread. The warmer air people are breathing out starts rising, so when people walk in these lines, they create fluid mechanical patterns, which creates a multiscale, multidimensional problem. This scenario required a fully resolved simulation that had both space and time dependence, but the velocity patterns that exist around people walking and stopping can be simplified to the shape of a cylinder. The people, or cylinders, moving create very complex flow structures around them and are not easy to predict. They have upward rising flows and downward settling flows, and these flows also interact with the buoyant plumes because of the temperature differences.

Mathai commented that there is no simple rule for an application because it depends on what questions the researchers are trying to answer and what application is the most practical. Systems such as the waiting-in-line scenario are periodic and time bound, and so need to be solved by using fully resolved simulations. Researchers conducted a set of experiments such as the waiting-in-line scenario. They found that if someone were to breathe out a cloud of droplets that was transferred to the person behind them, there was a settling plume because a current and a rising plume were created because the person was breathing out. There was a competition between the settling plume and the rising plume; therefore, increasing physical separation does not have any noticeable effect on transmission risk. Despite distance, the fluid dynamical pathways of transmission are still there.

Mathai concluded that fluid dynamics, both experimental and computational, can provide several solutions specific to configurations and that the standard approach is to run these simulations on a case-by-case basis and extrapolate. Combining conventional CFD with experimental validation and machine learning techniques can help make headway into the complex problems. Generally, it is good to combine computations and experiments, because, depending on what kind of specific problem is being simulated, the results are often difficult to predict unless there is experimental validation for at least some of the cases studied.

Jimenez talked about simple models that assume the air inside a space is well mixed and that use a simple differential equation—a mass balance model of the virus.

Jimenez explained that if someone is exhaling virus, that virus is going to float around in the air and can be inhaled by someone. Despite continued emission, the virus is going to be in equilibrium or in a steady state due to three processes: first, the virus will lose some infectivity with time through virus decay; second, the aerosols are going to deposit not in seconds, or in minutes, but maybe in an hour; and third, because there is ventilation or filtration, or another technique, the virus will be removed from the air.

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Suggested Citation:"Day 2 Session 2." National Academies of Sciences, Engineering, and Medicine. 2023. Air Quality in Transit Buses. Washington, DC: The National Academies Press. doi: 10.17226/27033.
×

Jimenez noted that in a recent publication, researchers had been able to simplify the risk of infection to study super-spreading events and plot the attack rate to determine the percentage of the people infected. The airborne risk parameter in this case is going to increase when there is less ventilation, longer duration of exposure, no masks, more vocalization, or more intense breathing during exercise. The increase in the risk parameter will increase the number infected. What is new is combining everything into a single risk parameter number, which is done rigorously within the assumptions of the model.

Jimenez stated that, in considering outbreaks from the literature of established airborne diseases, he found, for example, that TB is not very contagious but that in some cases, the bacterial infection does not cause any symptoms (latent TB), or the infection begins to cause symptoms within weeks, months, or even years later (active TB). This is how the disease manages to survive in a population. Therefore, TB needs a very risky situation to infect many people. For example, there were cases in the Navy in which people were sharing a bunk bed for months, and then multiple people got infected. In studying super-spreading events, the conclusion was that the transmission could only be airborne. There is no single super-spreading event that has been established that points to large droplets or to surfaces as the cause of them; they all seem to be airborne.

Jimenez noted that COVID-19 cases follow a pattern, and the model reproduces the data quite well. All the established airborne disease cases, including COVID-19, showed that as the risk parameter increases, the number of cases of infection increases, and vice versa. Though not perfect, the modelled predicted attack rate is about the same as the actual attack rate. Possible reasons for imperfect agreement include assuming the room’s air is well mixed. Sometimes the flow is complex, and that is important if there is significant variability in how much virus is being exhaled by individuals.

Jimenez also stated that the risk parameters are related to how much virus is being released by vocalization, how much virus is being emitted, how much a person is breathing, whether there are people wearing masks, the duration of the event, how many people are present, the volume of the room ventilation, and air cleaning. If these parameters are known for a certain space, then the risk parameter can be calculated. Looking at mitigations in specific cases, if a series of layers of protection is applied, the risk can be reduced, and to quantify how much help each one of the layers of protection gives is one of the ways the model is very useful.

Jimenez explained that in a mock-up subway, running calculations for the different cases will allow for ranking by risk to prioritize the riskiest routes or cars; those are where the best filters can be used, or where more maintenance is necessary. Quantifying the risk, and how much decrease in risk, for each applied layer of protection can be used to continue operations. Vocalization is associated with risk, as people

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Suggested Citation:"Day 2 Session 2." National Academies of Sciences, Engineering, and Medicine. 2023. Air Quality in Transit Buses. Washington, DC: The National Academies Press. doi: 10.17226/27033.
×

produce more aerosols and deposit more virus into the air during greater vocalization. Studies have shown that, as a function of the decibels and the ventilation rate, transmission increases with vocalization. For transportation, requesting no talking on public transportation is about the most effective measure to utilize.

Jimenez noted that with a model that works, other conditions can be extrapolated, for example, how much exhaled air is diluted. For example, a person talking in a room can be modeled and CO2 measured at different distances to measure how much CO2 is exhaled and how much CO2 is reaching a certain distance in front of that person. When cars are closed, they are similar to the close proximity scenario for the dilution factor of exhaled air, meaning they are a relatively risky environment. In an outdoor environment, beyond close proximity, the dilution factor is very large, and transmission is much lower. Because the model works, the conditional probability of infection can be determined for COVID-19. An encounter with someone infectious at an intimate distance will likely cause infection, but at a distance farther than 6 feet, the likelihood may be 20%. If there is infection at a distance and high dilution, there has to be much more infection.

Jimenez discussed the use of the model with CO2 measurements, which can be done quickly and cheaply and serve as an indicator of the presence of exhaled air, which is a surrogate for the presence of a person. When portable meters were set up outside and in a car with the windows closed, the meters quickly went to 4,000, which means the people were rebreathing 10% of the air. That would have been a risky situation if someone had been infected. Once the windows were open, the CO2 level went down. Public spaces should have CO2 level monitors where readings could be taken in real time.

In response to a question on the importance of validating models, Jimenez noted that validation of models is critical and that the many types of models he mentioned have relatively low cost. If a public transportation agency has 200 buses of the same model, doing the detailed modeling using CFD is worth it. Mathai added that CFD and experiments can be used in the initial stages of validation. For example, some of the model predictions might require tweaking to make extended predictions, and then CFD can inform in these situations. It is not practical to have fully resolved CFD solutions in situations in which there is a quick turnaround time, so that is certainly a limitation. At the same time, there should be an awareness of whether the environment is reasonably well mixed or not before a model is used. Again, some of the basic understanding of fluid dynamics can inform making these decisions on what would be reasonable to use.

Jimenez provided via chat during this session the following links with more information:

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Suggested Citation:"Day 2 Session 2." National Academies of Sciences, Engineering, and Medicine. 2023. Air Quality in Transit Buses. Washington, DC: The National Academies Press. doi: 10.17226/27033.
×

Jimenez also added via chat the following:

  • Aerosol Transmission Estimator tool description: Attack Rate vs. Risk Parameter H (hr2 × m−3, vocalization, # people, agent, duration of interaction, good vs. poor ventilation, speaking volume in dB, etc.) in super-spreader events: R2 = 0.90.
  • CO2 used as proxy for exhaled air; meters useful for public awareness in public spaces. Boarding/deboarding is most dangerous on planes.
  • For CO2, such meters are not very expensive. Sensors cost $15, devices for personal use cost $100–$200. But we encounter a lot of reluctance from organizations to deploy them. They often tell us that they fear or know the results will be bad at some locations, which are poorly ventilated. And then that will cause a PR [public relations] problem, so they prefer to keep it quiet.
  • We have been arguing that transparency is critical and have also been encouraging citizen science and activism to bring to light poorly ventilated locations. For some examples, see https://twitter.com/search?q=%23covidCO2.
  • In Madrid, Spain, the public can see live information about the quality of the air in transit vehicles (e.g., in Seville). See https://www.globalvia.com/en/noticia/los-usuarios-de-metro-de-sevilla-ya-pueden-comprobar-la-calidad-del-aire-de-los-trenes/.
  • This is a similar effort from the Boston Public Schools: See https://www.bostonpublicschools.org/Page/8810.

A guest commented via chat that using outdoor air for dilution of contaminants is not a viable solution, as the size of HVAC systems would need to greatly increase to heat or cool outdoor air, not to mention that outdoor air along roadways contains higher levels of pollutants than elsewhere.

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Suggested Citation:"Day 2 Session 2." National Academies of Sciences, Engineering, and Medicine. 2023. Air Quality in Transit Buses. Washington, DC: The National Academies Press. doi: 10.17226/27033.
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Suggested Citation:"Day 2 Session 2." National Academies of Sciences, Engineering, and Medicine. 2023. Air Quality in Transit Buses. Washington, DC: The National Academies Press. doi: 10.17226/27033.
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Suggested Citation:"Day 2 Session 2." National Academies of Sciences, Engineering, and Medicine. 2023. Air Quality in Transit Buses. Washington, DC: The National Academies Press. doi: 10.17226/27033.
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Suggested Citation:"Day 2 Session 2." National Academies of Sciences, Engineering, and Medicine. 2023. Air Quality in Transit Buses. Washington, DC: The National Academies Press. doi: 10.17226/27033.
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Suggested Citation:"Day 2 Session 2." National Academies of Sciences, Engineering, and Medicine. 2023. Air Quality in Transit Buses. Washington, DC: The National Academies Press. doi: 10.17226/27033.
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Suggested Citation:"Day 2 Session 2." National Academies of Sciences, Engineering, and Medicine. 2023. Air Quality in Transit Buses. Washington, DC: The National Academies Press. doi: 10.17226/27033.
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Suggested Citation:"Day 2 Session 2." National Academies of Sciences, Engineering, and Medicine. 2023. Air Quality in Transit Buses. Washington, DC: The National Academies Press. doi: 10.17226/27033.
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Next: Day 2 Session 3 »
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With a major drop in U.S. transit ridership since the start of the COVID-19 pandemic, an increased understanding of infectious disease in confined spaces and the role of droplets and particles in transmission has been increasingly important to the bus industry. A combination of experiments, models, and simulations in fluid dynamics has been employed to understand how aerosols move in spaces containing people.

TRB's Transportation Insights 2: Air Quality in Transit Buses provides a summary of a June 2022 in-person TRB Transit Cooperative Research Program (TCRP) Insight Event.

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