Numerical Investigation on the Droplet Dispersion inside a Bus and the Infection Risk Prediction

Abstract

COVID-19 can be easily transmitted to passengers by inhaling exhaled droplets from the infected person in a bus. Therefore, studying droplet dispersion would provide further insight into the mechanism of virus transmission and predict the risk of infection among passengers on a bus. In this research, a bus equipped with air-conditioning was employed as the research object. To determine the dispersion path, concentration distribution, and escape time of the droplets, computational fluid dynamic (CFD) was applied to simulate the flow field and the droplets’ dispersion. The effect of the air supply rate, the location of vents, and the location of infected persons on the dispersion were discussed. Based on the distribution of droplets in the cabin calculated by CFD, a superposition method was used to determine the number of virus particles inhaled by every individual passenger over a four-hour journey. Then, infection risk was assessed by the Wells-Riley equation for all the passengers in the cabin after the whole journey. The results show that the distribution of droplets in the cabin is greatly influenced by the location of the infected person, and the airflow pattern is highly associated with the air supply rate and the location of vents. The infection risk of passengers located at the droplet dispersion path and the distance from the infected persons less than 2.2 m is over 10%. The increase in the air supply rate could speed up the spread of the droplets but at the same time, it could reduce the infection risk.

1. Introduction

There have been significant economic losses and severe public health crises as the result of the COVID-19 epidemic [1]. The ongoing COVID-19 pandemic motivates scholars to understand the mechanism of airborne transmission. As the name indicates, airborne transmission is defined as the spread of respiratory droplets released by an infected person and inhaled by a susceptible person [2]. A systematic review reported that the risk of airborne transmission indoor is much higher compared with outdoors [3,4,5]. Among the indoor environments, the infection risk in buses may be the highest due to high occupant density, poor ventilation configuration and long exposure time.

It has been proved that there is a potential for airborne transmission in bus microenvironments [6,7]. During the COVID-19, 24 of 68 people became infected after traveling long distances by bus according to the study by Shen et al. [8]. In another study, 12 passengers were infected by the same person with the COVID-19 virus in two buses in one day [9]. Similarly, two potential airborne transmission of infection from infected drivers were reported by Infection Control Department [10]. Therefore, studying the dispersion and transport of droplets and predicting the infection risk of passengers in the bus have positive guiding significance for the prevention and control of the epidemic.

As early as 2012, a study by Zhu et al. [11] showed that the probability of infection of passengers close to an infected person and in the airflow path was up to 27.2%. Since the outbreak of the COVID-19, several studies have been conducted studies on the dispersion of droplets in the bus. The role of air supply directions and relative humidity was studied by Yang et al. [12]. The results showed that the droplet dispersion was mainly influenced by gravity, airflow field, and upward thermal body plume. Zhang et al. [13] tested four cases with different boundary conditions to investigate the coughed droplets’ transport characteristic from an infected person in a rail cabin. Their results showed that the droplets remove more efficiently and spread much farther with the flow from the front to back. Zhang et al. [14] studied the effects of ventilation systems, opening windows, and wearing masks, and proposed strategies to reduce the infection risk. They found that opening windows could help lower the droplets concentration by almost 50%, and wearing a mask can significantly minimize the infection risk. Ahmadzadeh et al. [15] studied the effects of the window, contaminant source, and output flow location on the dispersion of droplets in the train cabin. Their study showed that opening a window reduces the duration of particles remaining in the cabin, and the best position for the infected person was near the exit. However, the effect of operation and structural parameters of the bus on droplet spread, such as air supply rate and location of vents, have not been revealed yet. Thereby, it’s of great necessity to conduct further research.

Generally, virus particles are always released with the droplets exhaled by the infected person when they are coughing or sneezing [16,17,18]. Thus, an appropriate risk assessment model may be established based on the number of inhaled droplets to estimate the risk of infection [19,20]. Therefore, it is important to obtain accurate distribution of droplet. Computational fluid dynamic (CFD) is an effective and economical approach to modeling the transport of droplets in enclosed setting [21]. Hence, the transport and distribution of droplets from the coughing of an infected person in a bus were investigated using CFD method in this paper. It was possible to determine how many droplets passengers inhaled. Finally, the infection risk of passengers was estimated with the Wells-Riley equation after a four-hour journey. The effects of three different air supply rates and four different locations of vents were discussed separately. The results can serve as a theoretical foundation for designing ventilation system of public transportation

2. Methodology

As noted above, the distribution of exhaled droplets in a bus is crucial for determining a passenger’s infection risk. Zhang et al. [22] has compared the performance of Reynolds averaged Navier-Stokes (RANS) turbulence model, detached-eddy simulation [DES], and large-eddy simulation (LES) on predicting indoor airflow. The RANS turbulence model includes a zero-equation model, three two-equation models (the RNG k-ε, low Reynolds number k-ε, and SST k-ω models), a three-equation model ($\overline{v^2}-f$ model), and the Reynolds-stress model. Studies have shown that the LES model can better capture fluid characteristics, but it takes more computational time. While the RNG k-ε model has good comprehensive performance and requires less computation time. In addition, the RNG k-ε model was used to predict the flow field in the aircraft cabin and passenger car cabin in previous studies [12,23], which was in good agreement with the experimental data. Therefore, RNG k-ε model was applied in this study. Then, the Lagrangian approach was used to track the droplets, combining Wells-Riley equations to evaluate the infection risk for passengers [24].

Model for Predicting Infection Risk

For estimating infection risks due to indoor airborne transmission, the Wells-Riley equation which takes the inhaled dose of an infectious agent into account in terms of the quanta was proposed [25,26]. Quanta was defined by Wells. It indicates that the chances of becoming infected is 1 − 1/e if a person inhales one. From infection cases of the specific disease, Quanta can be estimated epidemiologically. The number of quanta generated per cough is 20 (geometric mean), and 15 coughs per hour were considered in the current study. However, there is no uniform distribution of virus particles inside the bus, and it changes over time. In order to determine the number of quanta inhaled by a person during the exposure time interval, the following equation is proposed [19]:

$$N\left(x,t_0\right)=cp{{\displaystyle \int }}_0^{t_0}v\left(x,t\right)f\left(t\right)dt$$

(1)

Here, v(x, t) represents the number density of droplets in a passenger’s breathing area, f(t) is the viability of the virus, usually taken as 1, c is the quanta number density in droplets, p is the breathing rate. Furthermore, bus trips can take several hours. It takes a long time to simulate every cough during the exposure interval in order to obtain N(x, t₀). Therefore, in order to determine the cumulative number of virus particles inhaled by passengers, the superposition method was introduced [24,27].

3. Geometry and Case Setups

3.1. Geometric Model of Bus

This study investigated the droplet dispersion in a real bus with dimensions of 11.5 m × 2.5 m × 2 m (L × W × H). Figure 1 shows the arrangement of the seats on the bus. The driver’s seat and 12 rows of passenger seats were on the left, and the other 11 rows of passenger seats were on the right. A diagram of the air supply diffusers was illustrated in Figure 2. Air was delivered through two round diffusers with a diameter of 0.05 m along the air duct, 16 air supply diffusers with a diameter of 0.05 m at the front and rear of the cabin, over each luggage carrier, 7 rectangular air supply diffusers with a dimension of 0.13 m × 0.037 m (L × W) were evenly distributed on both sides of the cabin. The air supply vents cover an area of 0.22 m². The ceiling vents have dimensions of 0.65 m × 0.44 m (L × W). The passenger height is 1.7 m, which was composed of five parts: feet, legs, arms, and torso. Since the passengers may move around their heads, a breathing area of 0.027 m³ around each passenger’s nose was constructed, as shown in Figure 3.

3.2. Case Setups

To investigate the influence of the operation parameters and structural parameters on the droplet dispersion characteristics, 15 cases were discussed with different air supply rates, location of vents and location of an infected person (listed in

Table 1. Case description.

Case Number	Case Description
Case 1.1	Vents 1, Air supply velocity 3 m/s, index infected person is passenger 2B
Case 1.2	Vents 1, Air supply velocity 3 m/s, index infected person is passenger 6C
Case 1.3	Vents 1, Air supply velocity 3 m/s, index infected person is passenger 12C
Case 2.1	Vents 2, Air supply velocity 3 m/s, index infected person is passenger 2B
Case 2.2	Vents 2, Air supply velocity 3 m/s, index infected person is passenger 6C
Case 2.3	Vents 2, Air supply velocity 3 m/s, index infected person is passenger 12C
Case 3.1	Vents 3, Air supply velocity 3 m/s, index infected person is passenger 2B
Case 3.2	Vents 3, Air supply velocity 3 m/s, index infected person is passenger 6C
Case 3.3	Vents 3, Air supply velocity 3 m/s, index infected person is passenger 12C
Case 4.1	Vents 4, Air supply velocity 3 m/s, index infected person is passenger 2B
Case 4.2	Vents 4, Air supply velocity 3 m/s, index infected person is passenger 6C
Case 4.3	Vents 4, Air supply velocity 3 m/s, index infected person is passenger 12C
Case 5	Vents 3, Air supply velocity 2 m/s, index infected person is passenger 2B
Case 6	Vents 3, Air supply velocity 3 m/s, index infected person is passenger 2B
Case 7	Vents 3, Air supply velocity 4 m/s, index infected person is passenger 2B

). Although the air return vent is often located in the middle of the bus, some studies have shown that it may be locate at different positions. For example, the return air vent was located at the front of the bus in the studies by Ou et al. [28], Luo et al. [9], Yang et al. [12] Therefore, the effects of the location of the vent were considered in this study. The dispersion of coughed droplets in the cabin was studied when the infected passenger was located at Seat 2B, 6D, and 12C, respectively. Time steps was used to model the transient transport of droplets was 0.05 s. Moreover, Exhaled airflow from the mouth when the patient coughing was developed with user define functions (UDF). As shown in Figure 4, a cough lasts around 0.5 s, with a maximum velocity of approximately 9 m/s [29,30]. What’s more, there was a 30 degrees angle between the exhaled airflow and the horizontal plane. During a single cough, one hundred thousand 5 μm-diameter droplets with a density of 980 kg/m³ were released to ensure a stable distribution of droplets. Mouths and noses of other passengers were set as wall. As demonstrated in Chen and Zhao’s study [31], when the ambient humidity is less than 80%, the effect of evaporation on dispersion can be ignored for 5 μm droplets. Hence, the evaporation of the droplets was neglected in this study. In addition, discrete random walk model was used to model turbulent dispersion of droplets.

Boundary Conditions

The boundary conditions and solver settings are listed in

Table 2. Boundary conditions settings.

Boundary Name	Boundary Conditions
air supply diffusers	velocity inlet, perpendicular to the diffuser, temperature is 290 K, turbulent intensity is 10%, escape
air return vents	Pressure outlet, 0 Pa, escape.
body surfaces	no slip wall, heat flux is 20 w/m2 for passengers, trap.
Ceiling, floor, side wall	heat transfer coefficient is 3 w/(m2·K), reflect, normal restitution coefficient is 0.1, tangential restitution coefficient is 0.01.
windows	heat transfer coefficient is 5 w/(m2·K), reflect, Normal restitution coefficient is 0.1, tangential restitution coefficient is 0.01.
Seats and others	adiabatic conditions, trap.

and

Table 3. Solver settings.

Setting Items	Setting
Turbulence model	RNG k-ε
Wall function	standard
Discretization scheme	second-order upwind
Couple method	SIMPLE

, respectively.

In order to determine the appropriate grid strategy, two grid configurations (7.1 million and 12 million) of Case 5 were used to assess the grid independence. The evaluation index was based on the average flow velocity in the three cross-sections. There was a relatively small difference between the 7.1 million and 12 million grids, as shown in

Table 4. The verification of grid independence.

X-Directional Cross Section	Velocity (m/s)
	7.1 Million	12 Million
1.5 m	0.187	0.192
4.5 m	0.185	0.176
8.5 m	0.220	0.212

. In addition, the simulation of the dispersion of the droplets generated by the patient’s cough in the bus cabin was carried out. Passenger P7 was selected as the infected person, and the detailed simulation settings could be found in previous studies [24]. The fraction of droplets settled on the passenger surface was also used to verify the grid independence. There was not much difference in the fraction of droplets settled on passengers in the two grids configuration, as depicted in Figure 5. Therefore, all analyses below were based on the 7.1 million grids. Fluent meshing19.2 was used to create unstructured meshes for all simulations. In this grid, there were 2 mm for the mouth, nose, and face of passengers; 20 mm for the rest of the passengers’ bodies and seats, 3 mm for the air supply diffusers and 40 mm for the others. Almost all cells had a skewness value of is less than 0.88.

4. Results and Discussion

4.1. Validation

Experimental data from Zhang et al. [32] were used to validate the present numerical model. It can be seen in Figure 6 that the size of the chamber with an inlet and an outlet is 4 m × 2.4 m × 2.1 m. Figure 7 shows the trend of particle-number density at point 1 obtained by the present numerical model. Comparing with the experimental data, the simulation results could capture those transient features of the experiment data. However, there was a certain difference between the experimental results and the numerical simulation values. It might be caused by the following reasons. First, the parameters in the simulation are difficult to match exactly with the experiments, Secondly, the average particle number concentration of the cells near point 1 is obtained in the simulation. In addition, the concept of parcel is used to represent the released particles in Fluent’s DPM model. There can be multiple particles in a parcel. Therefore, the particle concentration of the simulation might be overestimated. Considering the passenger infection risk studied in this paper for the purpose of indicating high-risk regions, it is reasonable to use this model to predict the spread of droplets.

4.2. Flow Field inside Bus

The internal flow field of the bus is the basis to model the transport characteristics of droplets due to an infected person coughing. The locations of these sections are shown in Figure 8. Figure 9a–c show the air velocity in the cross section at x = 1.2 m, x = 4 m, x = 8.9 m, respectively. Figure 9d,e show the velocity at y = 0.46 m, y = 0 m, respectively.

The air entered the cabin from the air supply diffusers, and returned to the vents at the rear. As shown in Figure 9a–c, the flow field structure was different in the three cross sections, as a result of the asymmetric arrangement of the air supply diffusers, in cross section at x = 1.2 m and x = 8.9, there was more air flowed to the right from the left side air supply diffusers than in the cross section at x = 1.2 m. In addition, two large-scale vortices were visible in the upper part of the cross section, indicating that the flow is mixed convection.

Figure 9d,e show that the cabin had a dominant longitudinal airflow, with air flowing upwards along with human bodies and reaching the upper part of the cabin as a result of blocking by seats, then quickly flowed to the vent. It could be seen that the location of the vent directly affects the flow direction, and the direction of the longitudinal airflow in most regions is toward the vent.

4.3. Spreading of Droplets inside Cabin

Due to the space limitations, the following sections focus on Case 4. Figure 10a–c show the dispersion of the droplets in Case 4.1, 4.2, and 4.3, respectively. Droplets emitted by passenger 2B were propelled forward by 4.5 m due to the air jet generated by coughing. Then the droplet was driven by the airflow, and moved rapidly upward because of the upward airflow between the seats. At the same time, the droplet moved to the other side of the cabin, and then diffused to most areas of the cabin. The exhaled droplets from the coughing of the infected person 6D spread mainly within the right side of rows 6–11. The infected person 12C was in the last row of the cabin, and behind the vent. The droplets quickly escaped from the vent after coughing, and didn’t spread to the area in front of the vent. The droplet was mainly concentrated in 10–12 rows.

The airflow pattern is mainly influenced by the location of the vent. The droplets produced by the infected person spread toward the vent due to airflow. Actually, Case 5, Case 6, and Case 7 had the same airflow pattern basically, the droplets spread to the vent more quickly and then escaped from the cabin due to the large air flowrate.

4.4. Passenger Infection Probability Prediction

The superposition method was used to obtain the number of virus particles inhaled by the passenger after the journey based on the previous simulation of cough droplet dispersion. Then, risk of airborne infection was estimated by the Wells-Riley equation. The infection risk of every individual passenger after a 4-h trip is shown in Figure 11.

Figure 11 show the infection probability of passengers in Case 1, Case 2, Case 3, Case 4, respectively. As described in Section 4.3, the relative location of the infected person and the vent significantly influenced the dispersion of the droplets. Passengers at the pathway of droplet dispersion had a probability of infection of more than 3%, while the risk of infection for other passengers was less than 1%. Accordingly, the distribution of airborne infection risk in a cabin was determined by the relative position of an infected person and the vent. Furthermore, the infection risk for the passenger closest to the infected person is the highest, up to 20%. It could be found that the risk of infection of passengers is affected by their distance from the infected person.

The distance between the infected person and the vent directly determines the time for the droplets to escape. Droplets exhaled by the infected person would escape slowly when they are far from the vent. Therefore, the infected person located far from the vent might increase the airborne infection risk for passengers, as shown in Figure 11d,i. While the coughed droplets produced by the infected person close to the vent would quickly escape from the cabin, as shown in Figure 11a,f, the other passengers’ infection risk was relatively small. The chances of passengers becoming infected can be effectively reduced when placing the infected person near the vent.

Figure 12a–c show the infection probability of passengers in Case 5, Case 6 and Case 7, respectively. It was found that passengers in rows 2–7 were at high risk of infection, and passengers near the infected person had the highest infection risk. Basically, passengers who were closer to the infected person had a higher risk of infection. In other words, the risk of infection for passengers decreased from the second to the seventh row. In addition, the risk of passenger infection was significantly reduced as the air supply rate increased. The average infection probability of passenger in Case 7 was half 50% lower than that of Case 5.

In Case 6, the infection risk of passengers for 2D and 2E was higher than that in Case 5 and Case 7, which seems counterintuitive. It might be that the lateral airflow was stronger in Case 6 so that more droplets spread to the right side of the second row. In Case 7, the longitudinal airflow with a relatively high velocity in the aisle might carry the droplets rapidly to the rear of the cabin when the droplets were moving from the left side to the right side, and only a small proportion of droplets spread to the right side of the second row. The droplets’ residence time in the breathing area was short due to the relatively high longitudinal airflow. Therefore, the risk of infection for the passenger on the right side of the second row in Case 6 may be higher.

It should be noted that passengers on a different side of the infected person had a relatively low risk of infection, it could be explained that only a few droplets can cross the aisle and diffuse from one side to the other side in the bus. In addition, it may be due to a large amount of air supply diffusers on the left side, The left side air-condition diffuser delivers more air in the front region of the cabin, so there might be more air flow from the left side to the right side. Passengers on the other side are at less risk of infection than those on the same side as the patient. For example, the infected person 2B is located on the left side of the bus, and the left-side passengers are at a higher risk of infection. The infected person 6D was seated on the right side of the bus, so the right-side passengers are at greater risk of infection. In contrast, the infected person 12C was seated in the middle of the cabin, with little difference in infection risk between those passengers on both sides. It can be explained as follows. The flow field was asymmetrical as the air supply diffusers were essentially in a symmetrical arrangement in this region. The flow field structure therefore became unstable due to the turbulent fluctuation. The airflow could move to the left or to the right. Therefore, the infection risk of passengers due to coughing was affected by the lateral airflow in the local area. In other words, the lateral airflow directly determined whether the infected person brought risk to passengers on different sides.

5. Conclusions

In this paper, the CFD with the Lagrangian approach was used to study the dispersion of droplets generated by the cough of infected persons, and gain the information about the dispersion path and the concentration distribution of droplets. Then, the virus dose inhaled by the passengers in the cabin was obtained for a 4 h bus ride. The infection risk of each passenger was predicted combining with Wells-Riley equations.

The air supply strategy of “multi-row air supply and centralized air return” intensifies the droplet dispersion along the longitudinal, while the asymmetric arrangement of the air supply diffusers causes the droplet to spread laterally in the cabin. Therefore, the droplet distribution in the cabin is fairly uneven, and its distribution is closely related to the location of the infected person and the vent. The direction of the longitudinal airflow in the cabin is determined by the location of the vent, which can affect the distributions of airborne infection risk.

The time for droplets escaping the cabin is affected by the air supply rate. The larger the air supply rate, the greater the speed of droplet escape, the smaller the infection risk of passengers. When the air supply velocity increased from 2 m/s to 4 m/s, the average infection risk of passengers is decreased by nearly 50%, and the maximum infection risk is decreased from 65% to 30%.

In general, compared to the passengers located on the same side of the infected person, passengers located at the different sides have a lower infection risk, the average infection risk of the different-side’s passenger is 50–80% lower than the same side.

Admittedly, some factors were not taken into account. For instance, the effect of racial and personal on emitted droplets during the cough was ignored, which might consequently influence the infection risk of passengers. We only investigated the dispersion of 5 μm droplets in this study. As we know, the diameter of coughed droplets range 0.4–200 μm. It indicates that the infection risk of passengers may be underestimated. What’s more. We assume that droplet was delete from the computation domain once it collides with the wall. Which might overestimate the removal efficiency.