Effect of natural ventilation on aerosol transmission and infection risk in a minibus

ACH

Air change rate per hour

C

Concentration

CFD

Computational fluid dynamics

COVID-19

Coronavirus disease 2019

C_c

Cunningham slip correction factor

C_i,s

Vapor concentration at droplet surface

C_i,∞

Vapor concentration of bulk air

DPM

Discrete phase modeling

D_i,m

Diffusion coefficient of vapor in bulk

D_t

Viral dose threshold

d_p

Initial droplet diameter

FB

Fraction bias

FW

Front windows

FW1

Front window on driver's side

FW2

Front window on infector's side

F_a,i

Additional forces

F_drag,i

Drag force

F_g,i

Gravity

f_D

Stoke's drag modification function

g_i

Gravitational acceleration

H

Height of minibus

IF

Intake fraction

IR

Infection risk

IF_d

Intake fraction of droplets

IF_g

Intake fraction of tracer gas

IF_t

Specific threshold for 10-min intake fraction

k

Turbulence kinetic energy

k_c

Mass transfer coefficient

NMSE

Normalized mean square error

N_i

Molar flux of vapor

N_p

Droplet number inhaled by passenger

N_t

Total released droplet number

PLD

Pathogen-laden droplets

Q

Ventilation rate

Q_p

Tracer gas flow rate in passenger's nose

Q_t

Tracer gas flow rate in infector's mouth

Q_v

Volumetric flow rate

R

Correlation coefficient

Re_p

Reynolds number

RH

Relative humidity

RNG

Renormalization group

RW

Rear windows

RW1

Rear window on driver's side

RW2

Rear window on infector's side

Sc

Schmidt number

t

Time

U_p,i

Velocity of droplet

u_i

Velocity of air

Vol

Volume

w

Window opening size

ε

Turbulent kinetic energy dissipation rate

κ

Von Karman's constant

λ

Molecular mean free path of air

μ_t

Turbulent viscosity

ρ

Density of air

ρ_p

Density of droplets

τ_p

Aerosol characteristic response time

Proper ventilation is crucial for reducing infection risks by removing or diluting pathogen-laden droplets (PLD), especially with diseases like Coronavirus disease 2019 (COVID-19).^1–3 While many studies have explored the effect of ventilation on airborne transmission in indoor environments, such as classrooms,^4–6 hospital wards,^7–9 and cars,^10–12 only limited studies explore the ventilation in small, enclosed public transport vehicles like minibuses.

Small public transport vehicles like minibuses are vital for inter- and intra-city transportation. For instance, about 82.6% of commuters rely on minibuses for transportation in Kampala.¹³ However, their enclosed spaces and high passenger density pose significant risks for airborne disease transmission. Moreover, Andrews et al. conducted carbon dioxide measurements and confirmed the highest risk of tuberculosis infection appeared in minibuses compared to buses and trains.¹⁴ The COVID-19 pandemic has highlighted this risk with specific outbreaks linked to minibus travel. For instance, a 17-seat minibus became the site of a COVID-19 outbreak in 2020 when a 24-year-old infected passenger traveled for 60 min and infected two passengers in Hunan, China.¹⁵ The epidemiological analysis and experimental tracer gas measurements conducted in this minibus by Ou et al.¹⁵ revealed that insufficient ventilation led to airborne transmission during the outbreak.

Turbulent ventilation enhances air mixing and transfer efficiency through turbulent motion, and is a highly efficient method of ventilation for a variety of scenarios that require rapid ventilation.^16,17 Increasing ventilation in enclosed public transport is a widely recommended measure for reducing infection risks.¹¹ Tracer gas decay tests in a minibus have revealed that opening windows can significantly increase natural ventilation.¹⁸ However, minibuses in various cities still use traditional designs without air conditioning or use air conditioning systems in recirculating mode, which poses a significant risk during a pandemic.¹⁹ The central air conditioners with indoor recirculation mode will contribute to the dispersion of PLD in the cabin, thereby increasing the risk of passenger infection.²⁰ In such circumstances, opening windows for natural ventilation becomes especially crucial.

Studies have revealed that the position of window openings has a great impact on the airflow organization and droplet dispersion in cabins.^18,21 Additionally, the size of the window openings also influences natural ventilation.²² The impact of window size can vary depending on the specific location of the opening window, yet there is currently a lack of research examining how window opening size affect ventilation under different window opening locations in vehicles. Despite its importance, limited research has investigated the effect of different configurations of window opening on droplet dispersion and thereby infection risk in minibuses. Therefore, a comprehensive quantitative study is needed to investigate the effect of the window opening on droplet spread and infection risk in minibuses.

Computational fluid dynamics (CFD) simulations can quantitatively analyze airflow and droplet distribution under various conditions, helping to identify optimized strategies for improving indoor ventilation and reducing airborne transmission.^23–25 There are two methods to simulate indoor natural ventilation with CFD: the coupled approach and the decoupled approach.²⁶ The coupled approach simulates both outdoor and indoor environments in a single computational domain.²⁷ The decoupled approach involves a two-step calculation procedure where the outdoor flow simulation is first conducted for the enclosure as a sealed body to determine the pressure on the boundary, followed by an indoor ventilation simulation using this pressure data.²⁸ While the decoupled approach is simpler to model and grid, it may sacrifice accuracy, leading to significant errors.²⁹ In CFD simulations, initial droplet diameter (d_p) is also an important factor influencing the diffusion process of droplets, with large droplets evaporating slowly and dropping near the infector quickly due to gravity.³⁰ 

To address the gaps in quantitative research on natural ventilation airflow and interpersonal infection risks within minibuses, we conduct a detailed numerical simulation study on airflow patterns, ventilation rates, and interpersonal infection risks under various window-opening scenarios. Using experimental data from a real minibus COVID-19 outbreak,¹⁵ we investigate the impact of five window opening locations and three window opening sizes on airflow organization and droplet dispersion. Moreover, we adopted tracer gas and liquid–solid mixture droplets with initial diameters of 5 and 50 μm to simulate the dispersion of exhaled droplets. This study uniquely employs a coupled approach for simulating the impact of window configurations on natural ventilation and airflow patterns in the minibus, and quantitatively evaluates potential infection risks, providing epidemic prevention suggestions based on the results.

We build a minibus model using the measured dimension information from a real minibus COVID-19 outbreak detailed by Ou et al.¹⁵ [Fig. 1(a)]. As displayed in Fig. 1(b), the dimension of the minibus is 5.60 × 2.10 × 2.00 m³ (length × width × height). The minibus is full and the infector is located at 5C (in scarlet). There are two ring-shaped skylights on the roof and they remain open in all cases. Two pairs of windows exist in the front and rear lateral walls, which can open with a size of 0.10 × 0.55 m², 0.30 × 0.55 m², and 0.50 × 0.55 m² [Fig. 1(b)]. In this study, we used the coupled CFD approach, where indoor and outdoor flow fields are simulated simultaneously, and the size of the entire computational domain is 65.50 × 42.10 × 12.00 m³ (length × width × height), which is 32H × 21H × 6H (H is the height of minibus) [Fig. 1(c)]. The blockage ratio is <1.40% to avoid blockage effects.³¹ 

The grid arrangements of the computational domain are shown in Fig. 1(c). The unstructured grid is applied to the area around the minibus, and the structured grid is applied to the outdoor flow field. The grid configuration on the surface of manikins has a minimum cell size of 0.005 m near mouths and noses and 0.03 m on the bodies. Moreover, the grid sizes on the skylights are 0.01 m, and the sizes for the minibus surface and seats are 0.05 m. The number of total grid elements is 2 509 055, and the grid sensitivity analysis has been estimated.^15,32

We simulate the COVID-19 transmission using Ansys FLUENT 19.2. The renormalization group (RNG) k–ε model is selected to solve the steady airflow field. The RNG k–ε turbulence model is one of the most widely adopted models and extensive studies have confirmed that it can mimic airflow field with significant precision and computational efficiency.^23,33,34 The finite volume method employing a second-order upwind scheme is utilized to discretize governing equations of mass, momentum, energy, turbulent kinetic energy (k), and turbulent kinetic energy dissipation rate (ε). The Boussinesq hypothesis is applied to account for the impact of thermal buoyancy. Simulations are considered converged when the residuals for the continuity equation, velocity components, energy, turbulence kinetic energy, and turbulent kinetic energy dissipation rate are below 10⁻⁴, 10⁻⁶, 10⁻⁹, 10⁻⁵, and 10⁻⁴, respectively.

After solving the steady airflow field, we simulate the tracer gas dispersion (C₂H₆) and droplet tracking separately. Tracer gas dispersion can represent the transport behavior of exhaled fine droplet nuclei (<1 μm), which has been confirmed in many studies.^35–37 We adopt C₂H₆ as the tracer gas and the mass fraction of C₂H₆ in the exhalation flow of the infector is 0.32.^15,32

Table I lists boundary condition setups for CFD simulations in this paper. For the domain inlet, velocity and temperature are 16.67 m/s (which means the minibus driving speed is 60 km/h) and 27 °C, respectively. We set up a minibus travel speed of 60 km/h because this is a common travel speed in urban areas. Additionally, the temperature of 27 °C is selected as it is a comfortable weather condition and passengers are more willing to open windows. At the domain outlet, an outflow boundary condition is used.^21,39,40 When the window is open, the interior is chosen as the boundary condition. Conversely, when the window is closed, the wall is employed as the boundary condition. We assume all passengers are sedentary adult, so a heat flux of 58 W/m² is assigned to each passenger to account for the human thermal plume.⁴¹ The infector is assumed to consistently exhale from the mouth, while the other passengers inhale through their noses.

Once the steady airflow field with water vapor is resolved, a set of single-diameter droplets are uniformly emitted from the infector's mouth. The release rate is 80 droplets per time step with a time step of 0.1 s and the process spans 10 min (6000 iterations in total). The initial velocity of the exhaled droplets is 1.5 m/s and the initial temperature is 32 °C. The boundary conditions for droplets are established based on our previous study.^33,38 The trap condition is applied to human body surfaces, seats, and the floor, which indicates that droplets are captured upon contact with these surfaces. On the other hand, the reflect condition is implemented for the bus roof, luggage racks, and vertical walls, accounting for the effect of gravity. As for the domain inlet, domain outlet, and the noses of passengers (excluding the infector), the escape condition is employed. We considered five window opening configurations, three window opening sizes and two initial droplet diameters in this study. In total, 27 cases are simulated as shown in Table II.

Although the passenger intake fraction is obtained, a specific threshold of infection risk requires calculating for passengers. According to the viral dose threshold (D_t = 300 copies),⁴² we calculate the specific threshold for 10-min intake fraction (IF_t) to be 593 ppm.^42–46 Thus, we adopt a threshold of 593 ppm of the IF, indicative of the minimum dose for COVID-19 infection. More details can be found in the  Appendix.

The evaluation of tracer gas spread using field experimental data can be found in Ref. 15. Furthermore, the validation of simulating indoor airflow, temperature, and particle dispersion has been conducted in our previous study.³⁸ In this study, we utilize the wind tunnel experiment data to validate the coupled indoor–outdoor model.⁴⁷ Two grid arrangements are employed for the building model, namely, the fine grid (0.05 m) and the coarse grid (0.1 m). The numerical simulation is conducted using two turbulence models: RNG k–ε model and Standard k–ε model. More validation details can be found in the  Appendix. All the correlation coefficients exceed 0.9 (Table IV), which indicates that the CFD simulations perform well in predicting the coupled indoor–outdoor ventilation airflow. Moreover, the fine grid coupled with RNG k–ε model successfully meets all validation metrics with remarkably high R values (>0.97), suitable fraction bias (FB values) (> −0.15), and low normalized mean square error (NMSE) values (<0.05).⁴⁸ Consequently, RNG k–ε model and fine grid configuration have been selected in our study.

As the minibus is in motion, outdoor airflow results in lower pressure at the front of the external sidewalls compared to the rear [Fig. 2(a)]. The external sidewalls at the front of the minibus are lower than the atmospheric pressure, while the external sidewalls near the rear of the minibus are higher than the atmospheric pressure, which is consistent with other studies.^16,49 Such pressure distribution leads to a unique airflow pattern within the cabin: outdoor air enters the cabin through the rear openings and exits through the front openings, establishing the rear-to-front indoor airflow [Fig. 2(b)]. The unique rear-to-front airflow pattern causes exhaled PLD to spread throughout the minibus when the infector is seated at the rear, leading to widespread aerosol transmission within the minibus.

We utilize tracer gas and solid–liquid mixed droplets to explore the dispersion process of human exhaled droplets. Tracer gas is adapted to mimic the dispersion of fine droplets (<1 μm).³⁸ This study examines mixed solid–liquid droplets with sizes of 5 and 50 μm. The simulation of 50 μm droplets is specifically conducted when investigating the impact of initial droplet diameter on droplet transport in Sec. III A. The ambient relative humidity is 35% in all cases. The tracer gas concentration in our study has been normalized by the concentration of C₂H₆ in the exhalation flow of the infector. We adopt intake fraction of tracer gas (IF_g) and droplets (IF_d) to measure the potential infection risk of passengers. The exposure time for all cases is 10 min. Based on the viral dose threshold, we calculated a specific threshold for the intake fraction of 593 ppm. When the intake fraction exceeds this value, it means that the passenger will have a high risk of infection.

The droplet diameter is the fundamental property that determines its transport characteristics. The transport behavior of a droplet depends on the force acting on it.⁵⁰ When the droplet diameter increases, its dominant influencing mechanism changes into gravity force from drag force.⁵  Figure 3 indicates the dispersion of droplets with different initial diameters when all windows are closed. When the initial droplet diameter (dp) is 5 μm, the droplets rapidly evaporate into 1.82 μm nuclei within 0.01 s under RH = 35% [Fig. 3(a)], while 50 μm droplets evaporate completely into 18.25 μm droplet nuclei within 1.1 s at RH = 35%. For the droplet with dp = 5 μm, the droplet evaporation time is shorter and droplet nuclei are smaller, so the fine droplets will spread more forward and upward [Fig. 3(b)]. When dp = 50 μm, more droplets will deposit due to gravity, so fewer droplets are suspended in the cabin. Basically, the droplets with the larger initial diameter will deposit quicker, and hence, they accumulate around the infector and the less suspended in the minibus.

Figure 3(c) illustrates the 10-min exposure intake fraction of each passenger under different initial droplet diameters when all windows are closed. Larger droplets (d_p = 50 μm) evaporate slower and the droplet nuclei are bigger, causing them to deposit faster due to gravity. When d_p = 5 μm, all passengers can inhale PLD. However, with d_p = 50 μm, one passenger (6B) does not inhale any PLD, and passengers behind the infector inhale fewer droplets. This indicates that, compared to d_p = 5 μm, the range of droplet dispersion is smaller at d_p = 50 μm, resulting in fewer passengers inhaling less PLD. As larger droplets accumulate in proximity to the infector, IF_d of passenger 5D increases from 831.25 to 1097.92 ppm when d_p increases from 5 to 50 μm. Considering all passengers in the minibus, fine droplets can transmit in the whole cabin and lead to widespread passenger infection. Therefore, we adopt droplets with d_p = 5 μm to explore the exposure infection risk in the following study.

Figure 4 shows the airflow field of cross-sectional planes along the corridor and at the height of the infector's mouth under different window opening locations. In Case [None, 0], Case [FW1, 0.5], and Case [FW1 + FW2, 0.5], the flow field distributions appear similar [Figs. 4(a)–4(c)]. There are two vortexes located at the bus front and bus rear in the profile along the corridor. The areas adjacent to the openings (skylights and windows) display relatively higher airflow velocity, while most other area has low airflow velocity (<0.3 m/s). Table III lists the natural ventilation under different window opening locations. As expected, the case with all windows closed, relying solely on two skylights for ventilation exhibits the poorest ventilation, and the ACH is just 17.55 h⁻¹. With all windows closed, the tracer gas concentration exceeds 1200 ppm in most areas (Fig. 5). Due to the poor natural ventilation with all windows closed, IF_g exceeds 600 ppm for all passengers, as depicted in Fig. 6. The weak airflow causes most droplets to accumulate near the infector (Fig. 5), resulting in IF_d around the infector reaching a peak of 831.25 ppm at 5D (Fig. 6).

Ventilation is slightly improved, from 23.17–24.90 h⁻¹ to 24.18–25.95 h⁻¹, when a pair of front windows is open compared to having only one front window open (Table III). Opening a front window reduces the tracer gas concentration at the bus front to 1000 ppm, but high tracer gas concentration persists adjacent to the infector (Fig. 5). Furthermore, although more droplets can move upward and forward with the airflow, only a small fraction of them can exit the cabin. In Case [FW1 + FW2, 0.3], the tracer gas concentration at the bus front decreases to 600–800 ppm, yet numerous droplets are still suspended within the cabin. Similar to the exposure infection risk, there is a slight reduction in IF_g and IF_d when one or a pair of front windows are opened, but they remain at relatively high levels for all passengers (Fig. 6).

Conversely, Case [FW2 + RW2, 0.5] and Case [All, 0.5] exhibit significantly stronger airflow, and the velocity in most areas is over 0.4 m/s [Figs. 4(d) and 4(e)]. Moreover, the two vortex structures disappear in the section along the corridor. Effective ventilation occurs when both a front window and a rear window are open, resulting in an ACH of 66.43–209.56 h⁻¹. With enhanced ventilation resulting from a front and rear window opening, the tracer gas concentration within the cabin drops to 200–300 ppm, representing an up to sixfold reduction compared to Case [None, 0] (Fig. 5). Moreover, the droplets in the cabin are substantially diminished, especially near the infector. As for exposure infection risk, IF_g of almost all passengers decreases by more than half compared to Case [FW1 + FW2, 0.3] (Fig. 6). IF_d appears to different variations on different passengers. Six passengers in columns A and B experience an increase in IF_d (Fig. 6). This is because airflow is enhanced in the whole cabin [Fig. 4(d)], making droplets disperse more even throughout the cabin (Fig. 5). However, for other passengers, there is a reduction in IF_g and IF_d to varying degrees.

Optimal ventilation is achieved when all windows are open, providing an ACH ranging from 119.84 to 478.79 h⁻¹. Noteworthy, ACH can vary by as much as 27 times between no windows open and all windows open. When all windows are opened, both the tracer gas concentration and the number of droplets are significantly reduced (Fig. 5). The tracer gas concentration in the cabin is less than 100 ppm. It is evident that the droplets exhibit a large birth time in Case [All, 0.3], indicating droplets can rapidly disperse forward and eventually discharge from the cabin as soon as they are exhaled by the infector. IF_g for all passengers drops significantly, with values falling below 200 ppm (Fig. 6). Likewise, all passengers experience low IF_d, indicating that they inhale very few PLD.

Variations in the window opening size induce changes in the velocity field and natural ventilation, as illustrated in Figs. 7 and 8. In both Case [FW1, w] and Case [All, w], increasing the window size leads to an enhancement of indoor airflow velocity, particularly in the vicinity of the windows (Fig. 7). While in Case [FW1, w], the enhanced airflow is significantly weaker than in Case [All, w]. It is also implied in the natural ventilation (Fig. 8). When all windows are open or one window is open at the front and rear, ACH increases linearly with the increase in opening area. However, in Case [FW1, 0.5] and Case [FW1 + FW2, 0.5], ACH changes slightly with the increase in window opening area. Although the tracer gas concentration in the bus front reduces from 1200 to 800 ppm, the indoor tracer gas concentration remains at 600–1200 ppm when the front window opening size increases from 0.1 × 0.55 m² to 0.5 × 0.55 m² (Fig. 9). Droplets are more concentrated adjacent to the infector in Case [FW1, 0.1], while more droplets will spread to the bus front and fewer droplets are near the infector in Case [FW1, 0.5]. In terms of infection risk, IF_g surpasses 584.36 ppm for all passengers and peaks at 7740.38 ppm for 5D when only a front window measuring 0.10 × 0.55 m² is open (Fig. 10). Expanding the size of the front window to 0.50 × 0.55 m² results in a reduction in IF_g for most passengers.

In Case [All, w], the cross-ventilation is amplified with larger window openings (Fig. 7). When the opening area of all windows is 0.10 × 0.55 m², only small regions near the rear and front windows achieve an airflow velocity of 1 m/s. However, when the opening area of all windows increases to 0.50 × 0.55 m², due to enhanced cross-ventilation, the airflow velocity in most areas of the cabin rises to 1 m/s. When all windows are open or one window is open at the front and rear, ACH increases linearly with the increase in opening area (Fig. 8). The impact of window opening size on exhalation becomes more pronounced (Fig. 9). In Case [All, 0.1], the tracer gas concentration in the bus most area is over 100 ppm and relatively numerous droplets suspended in the cabin. When open window size increases from 0.1 × 0.55 m² to 0.5 × 0.55 m², the tracer gas concentration reduces to 10–100 ppm and suspended droplets decrease considerably. Moreover, from the droplet birth time, we can find that droplets can discharge from the cabin quickly as exhaled in Case [All, 0.5]. Larger window size leads to decreased IF_g for most passengers, while four passengers who are behind the infector experience a slight increase (Fig. 10). Regarding droplets, the impact of larger window sizes varies with IF_d increasing slightly for some passengers and decreasing for others. This phenomenon may be attributed to that enhanced airflow promotes a more even dispersion of droplets within the cabin, consequently reducing the disparities in IF_d among passengers.

When the minibus is moving, the surrounding turbulent flow patterns induce the distribution of higher surface pressure at bus rear than bus front. The outdoor fresh air will enter the bus cabin through rear windows and exhaust from front windows. Therefore, when an infected individual is seated at the rear, the back-to-front airflow will make the droplet spread in the whole cabin, and the infection risk of other passengers is high.^32,51 Increasing ventilation in enclosed public transport is a widely recommended preventive measure.¹¹ Fresh air per capita is a metric used to measure ventilation in many building standards. In China, the minimum ventilation standard set by the Chinese building guide is at least 30 m³/h per person.⁵²  Figure 11 shows the fresh air rate per person under different window opening configurations in the minibus. When there are no windows open, the indoor ventilation rate is a mere 16.90 m³/h per person, falling well below the minimum ventilation standard. This deficient ventilation results in a high potential infection risk for all passengers: IF_g is over 600 ppm for all passengers. The situation slightly improves when one or a pair of front windows are open, yielding a fresh air rate of 22.32–24.99 m³/h per person. However, it still cannot meet the minimum standard. The infection risk of all passengers remains high with all passengers' IF_g more than 600 ppm and IF_d of 5D up to 2960.42 ppm.

Notably, opening both a front and a rear window proves to be an effective means of enhancing natural ventilation, with the fresh air rate reaching 63.98–201.84 m³/h per person. This remarkable increase in natural ventilation can be attributed to the pumping effect, as revealed in Ref. 32. Opening windows at locations with substantial pressure differences creates a “pumping” effect, significantly boosting natural ventilation. Shu et al.¹² also indicated that opening a front and a rear window could remove PLD more effectively than opening a pair of front windows. This remarkable enhanced natural ventilation reduces passengers' infection risks significantly. When all windows are opened, even if they are all sized at 0.10 × 0.55 m², the ventilation rate surpasses the minimum indoor ventilation standard by 3.85 times, amounting to 115.42 m³/h per person. Furthermore, there is a significant reduction in the potential infection risk for all passengers, with the majority of passengers' IF_g and IF_d reducing to below 30 ppm. Therefore, to maximize the benefits of window-based natural ventilation, it is recommended to open both front and rear windows to ensure sufficient ventilation for passengers.

Window opening size is also an important factor affecting the natural ventilation in the bus cabin. Figure 7 depicts that when all windows are open or one window is open at the front and rear, ACH increases linearly with the increase in window opening size. While in Case [FW1, w] and Case [FW1 + RW1, w], ACH does not change significantly with the increase in window opening size. This may be because when only the front windows of the bus are open, the airflow is not smooth and obstructed, resulting in limited improvement in cabin ventilation. On the contrary, when both the front and rear windows are open simultaneously, a more effective ventilation flow path is established, making it easier for air to circulate within the cabin.²⁸ Additionally, the simultaneous opening of front and rear windows may induce a convective effect, encouraging air to flow more effectively throughout the compartment, thereby enhancing ventilation. The findings can also be explained that the opening size of windows effectively influences natural ventilation only when the windows are positioned at locations with a pressure difference.⁴⁹ The outside fresh air can enter through a high surface relative pressure region of an opening (i.e., bus rear) and exit through a low relative pressure region (i.e., bus front).³² Owing to that natural ventilation is driven by wind forces, only when openings have pressure difference, expanding the window opening size will enhance the ventilation.⁵³ Hence, rather than opting for opening a single large window in the vehicle, it is more advisable to open multiple smaller windows at various locations, particularly in the bus front and rear.

It is important to acknowledge several limitations in our current research. Various respiratory activities, such as breathing, speaking, coughing, and sneezing, can significantly impact the generation and dispersion of respiratory droplets. Our study only considered the breath activity of the infector at a specific seat. In future studies, we will investigate more respiratory activities and explore additional influencing parameters, such as infector location and ambient temperature. Moreover, solar radiation has an impact on the thermal environment in bus cabins which we did not consider in this study. During hot summer or cold winter, opening windows will become less feasible. A combination of natural and mechanical ventilation may be more effective and satisfy human thermal comfort, and we will investigate this in future studies. Furthermore, public vehicles are often mandated to operate at less than half of their full occupancy to mitigate infection risk. This policy has led to substantial economic losses for transportation companies and inconvenience for travelers. Hence, it is valuable to conduct further research on infection risk associated with different seating arrangements within the bus. It will enable us to provide more specific recommendations for optimizing occupancy while ensuring safety.

To address the lack of quantitative research on natural ventilation airflow and the associated interpersonal infection risks in minibuses, we conducted a detailed quantitative investigation into airflow patterns, ventilation rates, and interpersonal infection risks across different window-opening scenarios. By conducting CFD simulations, we have explored the impact of different locations and sizes of open windows on the natural ventilation in a minibus. In addition, we have quantified the potential infection risk of each passenger by employing tracer gas and droplets (with initial diameters of 5 and 50 μm). The key findings are as follows:

1. When only two skylights are available for ventilation, ACH is merely 17.55 h⁻¹. It results in a high potential infection risk for passengers with IF_g and IF_d reaching as high as 2566.41 and 831.25 ppm when the window opening size is 0.30 × 0.55 m². When opening a pair of front and rear windows measuring 0.30 × 0.55 m², ACH increases to 289.93 h⁻¹ and IF_g substantially lowers to 8.92–188.16 ppm, which is 7–137 times less than when no windows are open.

2. When only the front windows are open, the opening size has a modest impact on natural ventilation. In contrast, for situations with both front and rear windows open, natural ventilation exhibits a linear relationship with the window opening size. Therefore, enhancing natural ventilation by expanding the window opening size is effective only when there is a pressure difference.

3. Droplets with an initial diameter of 5 μm can disperse throughout the entire cabin, causing every passenger to potentially inhale PLD. When the initial droplet diameter increases to 50 μm, droplets accumulate near the infector due to the gravity and appearing passenger inhales no PLD. Nonetheless, IF_d of the passenger seated near the infector increases.

In practical implications, it is recommended to enhance natural ventilation for passengers in a minibus by opening the front and rear windows. Rather than opening a single large window, a better approach is to open multiple smaller windows at various locations, particularly at the front and rear.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 42175095, 41875015, and 42005069) and a grant from the Special Projects of the Strategic Science and Technology Innovation Foundation of Guangdong Province (No. pdjh2022a0005). The support from Guangdong Major Project of Basic and Applied Basic Research (2020B0301030004 and 2021B0301030007), the UK GCRF Rapid Response Grant on “Transmission of SARS-CoV-2 virus in crowded indoor environment,” the Innovation Group Project of the Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai) (No. 311020001), the Basic and Applied Basic Research Foundation of Guangdong Province (No. 2024A1515010736), and Fundamental Research Funds for the Central Universities, Sun Yat-sen University (Project No. 24xkjc004), are also gratefully acknowledge.

The authors have no conflicts to disclose.

Qiqi Luo: Formal analysis (equal); Methodology (equal); Software (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Jiaying Pan: Formal analysis (equal); Software (equal); Visualization (equal); Writing – review & editing (equal). Jian Hang: Conceptualization (equal); Funding acquisition (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). Qihan Ma: Software (equal); Writing – review & editing (equal). Cuiyun Ou: Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal). Zhiwen Luo: Conceptualization (equal); Funding acquisition (equal). Liyue Zeng: Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Figure 12(a) illustrates a cubic building model with a height of 2.50 m (H_v = 2.50 m). The scale ratio between the building model and the wind tunnel model is 10:1. The domain dimensions match the simulation conducted by Jiang et al.⁴⁷ There is an opening located in the middle of the windward wall with a size of 0.84 × 1.25 m² [Fig. 12(b)]. Two grid arrangements are employed for the building model, namely, the fine grid (0.05 m) and the coarse grid (0.1 m). The numerical simulation is conducted using two turbulence models: RNG k–ε model and Standard k–ε model.

We select three lines to compare the normalized velocity profiles (U_ref = 10 m/s) between the simulation results and the wind tunnel data [Fig. 1(b)]. As shown in Fig. 1(c), the velocity profiles obtained from the simulation results exhibit a high level of agreement with the experimental data. It is further confirmed by the correlation coefficients, all of which exceed 0.9 (Table IV), which indicates that the CFD simulations perform well in predicting the coupled indoor–outdoor ventilation airflow.

We adopt a threshold of 300 copies of the viral dose, indicative of the minimum dose for COVID-19 infection.⁴²