Virus transport and infection evaluation in a passenger elevator with a COVID‐19 patient

Abstract

Contaminant transport and flow distribution are very important during an elevator ride, as the reduced social distancing may increase the infection rate of airborne diseases such as COVID‐19. Studying the airflow and contaminant concentration in an elevator is not straightforward because the flow pattern inside an elevator changes dramatically with passenger movement and frequent door opening. Since very little experimental data were available for elevators, this investigation validated the use of computational fluid dynamics (CFD) based on the RNG k–$\in$ turbulence model to predict airflow and contaminant transport in a scaled, empty airliner cabin with a moving passenger. The movement of the passenger in the cabin created a dynamic airflow and transient contaminant dispersion that were similar to those in an elevator. The computed results agreed reasonably well with the experimental data for the cabin. The validated CFD program was then used to calculate the distributions of air velocity, air temperature, and particle concentration during an elevator ride with an index patient. The CFD results showed that the airflow pattern in the elevator was very complex due to the downward air supply from the ceiling and upward thermal plumes generated by passengers. This investigation studied different respiratory activities of the index patient, that is, breathing only, breathing, and coughing with and without a mask, and talking. The results indicated that the risk of infection was generally low because of the short duration of the elevator ride. If the index patient talked in the elevator, two passengers in the closest proximity to distance would be infected.

Practical implications

• This study simulates the SARS‐CoV‐2 transmission via four respiratory activities during a complete elevator ride, which have implications for both understanding indoor particle transmission and identifying the most useful measures to reduce the infection risk.

• This study reveals that riding elevators can be safe because of the short duration and high ventilation rate.

• Respiratory activities of the index person have significant impacts on the fellow passengers' health.

• Measures such as covering face and maintaining social distancing can significantly reduce the infection risks.

1. INTRODUCTION

As a result of the COVID‐19 pandemic, more than six million deaths have occurred throughout the world as of May 2022. ¹ One of the main transmission routes of SARS‐CoV‐2 has been by airborne particles generated by SARS‐CoV‐2 carriers, according to the Centers for Disease Control and Prevention (CDC) of the United States. ² Virus transmission during elevator rides has been very concerning, as many people use elevators nearly every day. The high passenger density and closed environment that characterize an elevator ride have facilitated the spread of SARS‐CoV‐2. Cases of possible COVID‐19 transmission in enclosed environments ³ , ⁴ such as elevator cabins ⁵ have been reported. However, although clinical reports have provided evidence of airborne transmission of SARS‐CoV‐2, very few studies are available for quantitative assessment of infection risk during elevator rides. To evaluate this risk, it is necessary to understand the transmission of virus‐laden particles on elevators.

Virus‐laden particles can become suspended in the air and can be inhaled by susceptible people. ⁶ As particle movement is affected by the particle properties and the local airflow, the investigation of particle transport requires detailed information about the thermo‐fluid boundary conditions for the nose and mouth, ⁷ , ⁸ , ⁹ , ¹⁰ , ¹¹ the size distribution ¹² , ¹³ , ¹⁴ , ¹⁵ , ¹⁶ , ¹⁷ of particles generated by different activities, and the viral concentration of the virus‐laden particles. ¹⁸ , ¹⁹ On one hand, small particles tend to remain suspended in the air for a longer time than large particles. ²⁰ The mixing ventilation system commonly used in elevator cabins would mix the particles with the air to form aerosols that continuously expose passengers to infection risks due to long suspension. On the other hand, although large particles tend to fall to the ground within seconds ²¹ and the traveling distance is short, they can be dangerous in elevator cabins, as they contain many virus copies. ²² Therefore, understanding disease transmission in elevator cabins requires that both small and large particles be studied.

Few studies are available for the transmission of virus‐laden particles during elevator rides. Dbouk et al. ²³ examined the airflow pattern and airborne transmission in elevators, but they only explored the particle dispersion caused by a stationary index person, and no fellow passengers or body movement was considered. Shao et al. ²⁴ conducted an in‐situ measurements for respiratory behaviors and implemented the measured results into a CFD model to investigate the particle transmission in an elevator scenario. However, they did not consider the effects of the wake generated by passengers while entering or exiting the elevator cabin. Also, the infection risk in their study was evaluated in terms of the number of particles passing through a specified location. Liu et al ²⁵ considered the impact of wake on particle transmission, but they investigated the transmission of airborne particles with breathing activity only.

Therefore, the objectives of this study were (1) to investigate virus‐laden particle transmission during an elevator ride and assess the virus exposure of susceptible passengers, and (2) to compare the effects of different respiratory activities on the infection risk for fellow passengers.

2. METHOD

For consideration of the complex flow pattern resulting from thermal plumes, the ventilation system, and wake by movement, a reliable analyzer of the fluid field is required. Recent research on predicting the indoor environment has mainly used experimental measurements and numerical simulations. One can obtain realistic and reliable data from experimental measurements, ²⁶ , ²⁷ , ²⁸ , ²⁹ but full‐scale experimental models can be expensive and time consuming. Researchers can also employ small‐scale experimental models if flow similarity is achieved. However, these experimental measurements are not free from errors. Compared with experimental measurements, the CFD models are much more economical, although they have some uncertainties. Numerous studies ³⁰ , ³¹ , ³² , ³³ , ³⁴ have addressed the prediction of air velocity, air temperature, and contaminant distributions by means of CFD models. The results have exhibited good agreement with experimental data for mixing ventilation in an indoor environment. A trend ³⁵ in many recent studies has been the use of experimental models to obtain data for validating computational models, such as CFD models. The validated CFD model can then be used for further analysis. The experimental data obtained by Mazumdar et al ³⁶ , ³⁷ for passenger movement in a scale model of an air cabin was used in the present study, since that scenario was the most relevant to airflow and contaminant dispersion in an elevator.

Next, the validated model was used for investigating the transmission of SARS‐COV‐2 virus‐laden particles. This study employed the Euler–Lagrange approach to calculate particle dispersion. The fluid phase was treated as a continuum and was solved by the Navier–Stokes equations, whereas the virus‐laden particles were tracked as a discrete phase separated through the flow domain. One‐way coupling was used because the volume fraction of the particle phase is relatively low. Only the fluid phase has momentum and energy impact on the particle phase.

2.1. CFD model

To obtain the flow distribution, this study numerically solved unsteady‐state Reynolds‐averaged Navier–Stokes (RANS) equations with the re‐normalization group (RNG) k‐ϵ turbulence model. ³⁸ The RNG k‐ϵ turbulence model was proved to be the most feasible model among all RANS models tested in, ³⁹ , ⁴⁰ , ⁴¹ , ⁴² , ⁴³ ensuring both accuracy and stability. The governing equations of this turbulence model can be written in a general form as:

$$\frac{\partial \left(\rho \overline{\mathrm{\Phi }}\right)}{\partial t}+\rho {\overline{u}}_i\frac{\partial \overline{\mathrm{\Phi }}}{\partial x_i}-{\mathrm{\Gamma }}_{\phi ,\mathrm{eff}}\frac{\partial \overline{\mathrm{\Phi }}}{\partial x_i}=S_{\mathrm{\Phi }}$$ (1)

where $\mathrm{\Phi }$ represents the thermo‐fluid variables, that is, velocity, enthalpy, and turbulence parameters such as turbulent kinetic energy and the dissipation rate of the turbulent kinetic energy; ${\mathrm{\Gamma }}_{\phi ,\mathrm{eff}}$ and $S_{\mathrm{\Phi }}$ are the effective diffusion coefficient and the source term for the specific equation, respectively; and $u_i$ and $x_i$ represent the directional components for velocity and space coordinates, respectively. ⁴⁴ , ⁴⁵

In addition, this study employed the Boussinesq approximation to account for thermal buoyancy. The numerical algorithm used to couple the pressure and velocity equations was the semi‐implicit method for pressure‐linked equations (SIMPLE), and second‐order discretization schemes were employed to numerically solve the flow and energy equations.

The Lagrangian method describes the particle trajectory by integrating the force balance on the particle, which is set in a Lagrangian reference frame. As described by Newton's law:

$$\begin{array}{c}\frac{{\mathit{du}}_{\mathrm{p}}}{\mathit{dt}}=F_{\mathrm{D}}\left(u-u_{\mathrm{p}}\right)+\frac{g\left({\rho }_{\mathrm{p}}-\rho \right)}{{\rho }_{\mathrm{p}}}\end{array}$$ (2)

where $F_{\mathrm{D}}\left(u-u_{\mathrm{p}}\right)$ is the drag force per unit mass, and is defined as:

$$\begin{array}{c}{F}_{\mathrm{D}}=\frac{18\mu }{{\rho }_{\mathrm{p}}{d}_{\mathrm{p}}^2}\frac{C_{\mathrm{D}}\mathrm{Re}}{24}\end{array}$$ (3)

Here, $\mathrm{Re}$ denotes the relative Reynolds number of particles and is calculated by:

$$\begin{array}{c}\mathrm{Re}=\frac{\rho d_{\mathrm{p}}\left|u_{\mathrm{p}}-u\right|}{\mu }\end{array}$$ (4)

In these equations, $u$ is the air velocity, $u_{\mathrm{p}}$ is the particle velocity, $\rho$ is the air density, ${\rho }_{\mathrm{p}}$ is the particle density, $\mu$ is the molecular viscosity of air, $d_{\mathrm{p}}$ is the particle diameter, and $g$ is gravitational acceleration.

Since the indoor air flow is highly turbulent, and the dispersion of small particles can be easily affected by local eddies, this study used the discrete random walk (DRW) model to account for the effects of instantaneous turbulent velocity fluctuations on the particle trajectories. A study by Chen et al ⁴⁶ has shown that the evaporation rate of particles generated by human respiratory activities is very high. The trajectories of a small droplet and its droplet nucleus due to evaporation are almost overlapping. The present study used an inert spherical particle model to simulate the virus‐laden particles generated by a person's breathing, coughing, and speaking. This study implemented the model by using a commercial CFD software package, ANSYS Fluent version 2020R1.

2.2. Particles from respiratory activities

The size distribution of particles generated by respiratory activities such as breathing, coughing, and speaking varies within a wide range, as shown in Table 1. For breathing, Fabian et al. ¹⁶ recommended three sizes, 0.4, 0.75, and 2.5 μm. For speaking and coughing, a study conducted by Chao et al. ¹⁵ used the size classes from 3 to 750 μm for both activities. Note that in the study by Chao et al., the particle sizes were provided in reference to wet droplets, which were subject to evaporation. The present study used wet particles to calculate the virus concentration and then converted the size distribution into dry particles. Dry particles were preferred because of the short evaporation time. ⁴⁷ Another study, by Yang et al, ¹⁷ revealed that coughing could generate particles that are finer than 3 μm. Since Yang et al ¹⁷ provided the concentration per particle size, the number of particles could be derived by multiplying it by the coughing flow rate. Therefore, the present study combined the data from Yang et al ¹⁷ and Chao et al ¹⁵ for the size distribution of particles generated by coughing.

TABLE 1.

Size distribution of particles generated by different activities

Diameter (μm)	Number of particles
	Breathing 3 (per breath)	Speaking 4 (per second)	Coughing 4 , 17 (per cough)
0.4	612	N/A	N/A
0.75	156	N/A	140 000
1.32	N/A	4	71
2.5	107	N/A	N/A
2.64	N/A	57	974
5.28	N/A	20	362
8.8	N/A	10	119
12.32	N/A	7	44
15.84	N/A	3	42
19.8	N/A	4	36
27.5	N/A	4	36
38.5	N/A	3	25
49.5	N/A	4	30
60.5	N/A	3	28
77	N/A	4	78
99	N/A	3	44
165	N/A	3	37
330	N/A	1	25

Acknowledging that the SARS‐CoV‐2 virus concentration varies among different body fluids, this study considered saliva and sputum, which are two common virus‐laden media released by infected people's noses and mouths. According to an investigation by Pan et al, ¹⁸ the SARS‐CoV‐2 virus concentration in infected people's sputum can be as high as 1.34 × 10¹¹ copies/ml. Meanwhile, To et al. ¹⁹ showed that the SARS‐CoV‐2 virus concentration was 1.2 × 10⁸ copies/ml. To determine the portion of particles made of saliva, this study used a threshold of 20 μm, as Johnson et al ⁴⁸ reported that particles with a diameter greater than 20 μm came from people's mouths, while those with a diameter less than 20 μm were from respiratory tracts. A reasonable assumption was introduced, that is, that all particles released from the mouth are made of saliva and all particles from the nose are made of sputum secreted in the respiratory tract. Under the further assumption of spherical particles, the SARS‐CoV‐2 viral load (copies per particle) can be calculated by:

$$\begin{array}{c}{N}_d=C_d\times \frac{\pi d^3}{6}\end{array}$$ (5)

where $d$ is the diameter of the wet particle and $C_d$ the virus concentration for the specific particle diameter.

It is common knowledge that the transmission of finer particles is more likely to be affected by the airflow. As Equation (5) shows, viral load is proportional to the third power of diameter; the virus concentration for small particles might be underestimated. To obtain a more accurate evaluation of the virus dose for susceptible passengers, the virus concentration for smaller particles needed further calibration. However, few data sets provide supplementary information about the SARS‐CoV‐2 viral load in relation to the size distribution of particles. As the variation in pathogen concentration is similar among respiratory diseases, this study employed data from Lindsley et al ⁴⁹ on influenza RNA detection for particles smaller than 20 μm. Their investigation determined that 35% of the influenza RNA was contained in particles <4 μm in aerodynamic diameter, 23% was in particles from 1 to 4 μm, and 42% was in particles <1 μm. This calibration process was conducted by ensuring the same amount of total viral load for particles smaller than 20 μm. The calculated concentration results also aligned with previous research ⁵⁰ in an airliner cabin.

In addition, thermo‐fluid boundary conditions significantly contribute to particle transmission. Gupta et al. ⁷ , ⁹ studied the flow characteristics of breathing, speaking, and coughing cases. For breathing, a sinusoidal function can be used to mimic the exhaled air velocity variation for a person engaged in stationary activities, as shown in Figure 1A. In the case of speaking, this study assumed that the index person and another person were talking to each other in turns. The speaking of the index person lasted 10 s out of every 20 s. To ensure an air balance in the lungs, the nose has been observed to take in a certain amount of air when a person is speaking. ⁷ Therefore, a breathing‐plus‐speaking case can have the boundary conditions shown in Figure 1B. For uncovered coughing, the flow rate is shown in Figure 1C. As reported by Gupta et al, ⁹ the area and shape of the mouth opening remain nearly unchanged during a cough. Therefore, the flow rate variation can easily be converted to velocity variation. A study by Chen et al ⁸ showed that the velocity of a covered cough can be decomposed into two directions: upward and forward. Under the assumption that the index person was wearing a surgical mask, a filtration efficiency from Pan et al ⁵¹ was applied in the present study. Particles larger than 5.28 μm were all filtered, and the filtration efficiencies for particle sizes of 0.75, 1.32, 2.64, and 5.28 μm were 67.3%, 73.0%, 78.0%, and 93.0%, respectively.

FIGURE 1.

Flow boundary conditions for particle injection: (A) breathing flow velocity, (B) flow velocity of combined speaking and breathing, (C) flow rate of a single uncovered cough

The inhalation of virus‐laden particles by susceptible passengers is calculated by:

${\text{Dose}}_i=\underset{0}{\overset{t}{\int }}\dot{v}\sum _d{N}_d\cdot \frac{n_{i,d}}{V_i}\mathit{dt}$where $n_{i,d}$ is the number of particles with a diameter of $d$ in passenger $i$'s breathing zone, and $V_i$ is the volume of passenger $i$'s breathing zone. The breathing zone is defined as a spherical volume centered at a passenger's nose, with a radius of 0.30 m. Meanwhile, $\dot{v}$ is the average breathing flow rate, as 0.00053 m³/s, which is consistent with the previous study. ⁶² The infection risk for susceptible passengers was determined by a threshold of 2000 accumulative inhaled virus copies. ⁵²

3. RESULTS

3.1. CFD model validation

To validate the accuracy of the CFD model for predicting the airflow pattern and particle transmission in an enclosure with people movement, this study used experimental data from an airliner cabin mockup study. ³⁶ Figure 2 shows an empty small‐scale water model with a moving passenger. In this case, water was used to simulate the air flow in a real airliner cabin. The model was scaled to one‐tenth of the actual size and satisfied the similarity requirements. The cabin was simplified as a half cylinder with a diameter of 0.45 m and a length of 2.24 m. Water was horizontally supplied through the middle of the ceiling with a total flow rate of 2.5 L/s. The outlets were the two long slots along the bottom of the wall on both sides. A block manikin was used to generate the moving body wake. The manikin moved along the z‐direction with a constant speed of 0.175 m/s. All surfaces were modeled as no‐slip walls. Throughout the process, the water temperature was controlled, and iso‐thermal conditions were satisfied.

FIGURE 2.

Schematic of validation case (airliner cabin mockup)

Figure 3A–C compare the simulated and experimental waterflow pattern in the airliner cabin mockup for the ventilated case. Figure 3A,B show two frames of the waterflow pattern where the interaction of the manikin movement is considered. Figure 3B was captured later than Figure 3A at the same location. In both figures, one can observe two large eddies in the wake generated by the manikin movement. The downward evolution of the two eddies was simulated, and the starting points of the eddies, which were located beside the manikin, were captured in the simulation. Figure 3C compares the flow distribution on a horizontal cross‐section. Two major patterns were captured by the simulation, that is, the small eddy behind the manikin head and the 45° downward flow behind the manikin body.

FIGURE 3.

Comparison between experimental data ³⁶ and simulated results: (A) velocity distribution at frame 4 ³⁶ ; (B) velocity distribution at frame 7 ³⁶ ; (C) horizontal velocity distribution

The comparisons above indicate good agreement between the CFD model and the experimental data as shown in Poussou et al. ³⁶ Some of the discrepancies originated from the simplified geometry that significantly reduced the computational load. Overall, the CFD model was found to provide a reasonable simulation of the airflow and contaminant dispersion in an enclosure with a moving object.

3.2. Airflow and particle dispersion in an elevator

3.2.1. Case description

The contaminant transmission and airflow distribution in an elevator cabin are not the same as those in an airliner cabin or small office. ²⁷ , ²⁹ , ³⁴ The occupant density in an elevator is generally higher. The airflow pattern will be markedly complex, as there are three factors interacting with each other: the thermal plume generated by the buoyancy force from the passengers' bodies, the air jets from the elevator's ventilation system, and the wake generated by the movement of passengers as they enter or leave the elevator. Those flow features are similar to those for the air cabin case presented in Section 3.1.

As shown in Figure 4, the elevator cabin was 2.00 m long, 1.65 m wide and 2.50 m high. The elevator lobby was 11.50 m long, 5.00 m wide, and 4.00 m high. The simplified manikin was 0.40 × 0.20 × 1.68 m. The mouth of a manikin was located 223 mm below the head top, with an opening area of 1.2 cm². The temperature setpoint for indoor air was 24°C. According to ASHRAE standards, ⁵³ , ⁵⁴ the ventilation rate of the elevator was 72 ACH (air changes per hour), and the ventilation rate of the lobby was 3 ACH. The inlet of the elevator was a 0.05 m wide slot along the periphery of the elevator ceiling, and the outlet of the elevator was a 0.02 m high slot at the bottom of the walls. Meanwhile, two square ceiling diffusers were used in the lobby. The size of each diffuser was 0.40 × 0.40 × 0.03 m, and the direction of the airflow from the diffusers was 15° downward. Since this study considered a relatively large lobby in order to minimize the impact of lobby shape on particle transmission, the outlets of the lobby were the two boundaries along the Y direction, which were connected to the main lobby on the ground floor.

FIGURE 4.

Geometry and mesh of a typical elevator‐lobby area

Table 2 describes the boundary conditions of the CFD model.

TABLE 2.

Boundary conditions in the CFD model

Boundary	Momentum	Thermal	DPM
Inlet (lobby)	2.07 m/s (15° downward)	22°C	Reflect
Inlet (elevator)	0.47 m/s (normal to boundary)	20°C	Reflect
Nose of the index person	User‐defined functions	34°C	Reflect
Mouth of the index person	User‐defined functions	34°C	Reflect
Outlet (lobby)	Pressure outlet	24°C, backflow	Escape
Outlet (elevator)	Pressure outlet	24°C, backflow	Escape
Susceptible passengers' bodies	No‐slip	31°C	Trap
Lobby walls	No‐slip	Adiabatic	Trap
Elevator walls	No‐slip	Adiabatic	Trap

Many previous studies ⁵⁵ , ⁵⁶ , ⁵⁷ have shown that in indoor air environments, the geometry of the human body has an insignificant impact on the airflow around a person. To reduce the calculation time and to leave some room for dynamic mesh adjustment, this study used six cuboids to mimic the six passengers in the CFD model. The index person with SARS‐CoV‐2 is marked in red in Figure 4. The shortest distance between passengers when they were in the elevator cabin was 600 mm in row and 320 mm in column.

The interactions of the flow forces would significantly affect the transmission of SARS‐CoV‐2 among passengers. To comprehensively compare the infection risks during an elevator ride, this study considered four dynamic scenarios, each divided into three sub‐cases. The four scenarios are distinguished by the different particle‐generation activities of the index passenger: breathing, speaking, uncovered coughing, and covered coughing. All cases included the particles generated by nose breathing. For the sake of simplicity, the cases were named as follows:

• Case 1—breathing case: only breathing activity was considered;

• Case 2—uncovered coughing case: both coughing and breathing activities were considered, and no interference was applied to the coughing jet;

• Case 3—covered coughing case: both coughing and breathing activities were considered, and a surgical mask covered the mouth;

• Case 4—speaking case: coupled speaking and breathing activities were considered, and the index passenger alternately spoke for 10 s and listened for 10 s.

Each case was further divided into three sub‐cases, namely, 13 seconds for entering the elevator ($t\in \left[0s,13s\right]$, sub‐case 1), 120 s for riding the elevator ($t\in \left(13s,133s\right]$, sub‐case 2), and 13 seconds for leaving the elevator ($t\in \left(133s,146s\right]$, sub‐case 3). The passengers changed their facing directions after entering the elevator cabin. While entering the elevator, they faced towards the elevator. While staying in the elevator and leaving the elevator, they faced toward the lobby. The data transfers between the sub‐cases were achieved with an interpolation function. For example, the final condition at $t=133s$ in sub‐case 2 served as the initial condition of sub‐case 3. The airflow information (i.e., velocity distribution, temperature distribution, turbulence kinetic energy, and the dissipation rate of turbulence kinetic energy) and the particle information (i.e., position, momentum, diameter, and temperature) from one sub‐case were inherited by the subsequent sub‐case. As for sub‐case 1, the initial condition for the air flow inside the lobby and the elevator was separately pre‐computed by running steady‐state calculations until convergence.

As this study investigated the particle transmission affected by the wake generated by passenger movement, a dynamic mesh was used for the entering and leaving subcases. To reduce the calculation load, the total mesh was divided into two zones, that is, a static mesh zone and a dynamic mesh zone. The geometries of the two mesh zones were defined as a merged condition, meaning that the cells of the two zones shared the same variables on the interfaces, and physically meaning that the interface did not exist. For the dynamic zone, remeshing took place for every time step, with a maximum cell skewness setting of 0.75. This setting balanced the calculation time and the mesh quality. Mesh of a zone with moving boundaries was subject to deformation when the boundary movement was in progress. Since the whole mesh was set to be tetrahedral, the smoothing method and the remeshing method were employed to improve the quality of the mesh when it was deformed. Further details can be found in the FLUENT theory guide. ⁵⁸

3.2.2. Grid independence check

It is important to check the grid independence for predicting indoor airflow. For the interests of this study, the sub‐case 2 (2 min elevator riding) of Case 4 (speaking case) was chosen to check the grid independence. The original mesh presented in this study has around 3 million tetrahedral elements. Usually, researchers can halve and double the mesh elements to check whether the fineness of a mesh is satisfying. Therefore, one mesh with 1.6 million elements and another mesh with 5.3 million elements are used for comparison. Considering the unsteady‐state calculation and the randomness of the model used for tracking the particles, it is better to compare the airflow distribution at a fixed time. Thus, this section compares the vertical air velocity profiles calculated with these three grid numbers at t = 133 s. Three locations were selected for the comparison, which were located at the centers of the two closest passengers in row. All calculations in this study achieved convergence, with the residuals of the momentum and turbulence terms converged at 10⁻³, and the residual of the energy term converged at 10⁻⁶. The results of vertical air velocity profiles are shown in Figure 5.

FIGURE 5.

Comparison of the vertical air velocity profiles calculated with different grid numbers

Overall, the results of the original mesh (3000 k elements) agree well with the finer mesh (5300 k elements) for all the poles. Among the poles, Pole 1 shows the best alignment and Pole 3 shows the worst alignment. Pole 1 is closest to the elevator door, and furthest from the index passenger, where the elevator outlet and respiratory flow have least impact on the local airflow. The coarser mesh (1600 elements) shows slightly different air flow trends of the lower parts at Pole 2 and Pole 3. Thus, the comparison suggests that the original mesh is sufficient for the cases.

3.2.3. Airflow pattern

Figure 6A–D show the transient results of the airflow velocity distribution during a complete elevator ride. The figures were captured on a cross‐section plane located in the middle of the elevator cabin. Figure 6A depicts a characteristic moment in sub‐case 1, when the passengers were entering the elevator cabin. In Figure 6A, the airflow was affected by the thermal plume generated by the passengers' bodies, the mixing ventilation system in the lobby, and the wake generated by the movement of the passengers. The simulated results from the end of sub‐case 1 served as the initial state of sub‐case 2, which can be observed in Figure 6B, where the inertial movement of air was distinct. The airflow was dynamically steady within the first 60 seconds of an elevator ride, as shown in Figure 6C. Figure 6D depicts a moment in sub‐case 3; again, the wake was obvious but in the opposite direction to that in sub‐case 1.

FIGURE 6.

Transient velocity distribution (unit: m/s)

As an important part of the findings, the temperature distribution inside the elevator cabin was very uniform because of the mixing ventilation and the high air change rate. Thus, the details of temperature distribution were omitted from this part for conciseness.

3.2.4. Particle dispersion

Figure 7A–D show the particle dispersion throughout the process. For each breathing period, a total number of 875 particles ranging from 0.4 to 2.5 μm was exhaled. Since the direction of the breathing jet was 60° downward, the particles would first travel down. Next, the thermal plume generated by the passengers' bodies lifted the particles to a higher level. The wake that followed the passengers' movement entrained some particles and brought them along in the direction of the movement. Meanwhile, the circulations generated by the ventilation system played an important role during the two‐minute elevator ride. The particles were well mixed and were in a dynamic balance in the elevator cabin within the first 60 s. The susceptible passengers in close proximity to the index person faced higher exposure to the particles. The balance was achieved in a short time because of the high air change rate in the elevator cabin.

FIGURE 7.

Transient particle dispersion of Case 1 (unit: m)

In the reference breathing case (case 1), only small particles (with diameters ranging from 0.4 to 2.5 μm) were released. However, in the cases where larger particles were released, the large particles (>77 μm) would fall to the ground very quickly after release. Therefore, susceptible people would be less likely to be exposed to large particles than to small ones.

3.2.5. Size distribution of inhaled virus‐laden particles

As particle size plays an important role in the particle transmission and the number of virus copies carried, information about the size distribution of inhaled particles is helpful in determining potential intervention methods. For example, this information can guide decisions about whether to increase social distancing. Large particles contain many more copies of a virus than small particles but fall to the ground very quickly, whereas small particles can travel further and remain suspended for a longer time. Figure 8 shows the size distribution of particles with respect to the number of inhaled virus copies during the two‐minute elevator ride. The subscript “b,” as in “0.4b” and “0.75b” on the x‐axis, indicates that the particles were generated by breathing (injected from the nose). Those x‐values without a subscript indicate that the particles were from other activities (injected from the mouth). As mentioned previously, the viral concentration in sputum was higher than that in saliva. The results show that the majority of the inhaled virus copies were from particles with a nucleus diameter less than 10 μm, which agrees with the findings of Chen et al. ⁵⁹ No particles with a diameter greater than 77 μm was found in the breathing zones of susceptible passengers. As the traveling ability of larger particles was more limited than that of smaller particles, a larger number of virus copies inhaled were observed from passengers with closer proximity to the index person. A change in orientation also affected the infection risk.

FIGURE 8.

Size distribution of inhaled virus‐laden particles. (A) Size distribution of particles inhaled by susceptible passengers in the breathing case (Case 1) (B) Size distribution of particles inhaled by susceptible passengers in the uncovered coughing case (Case 2) (C) Size distribution of particles inhaled by susceptible passengers in the covered coughing case (Case 3) (D) Size distribution of particles inhaled by susceptible passengers in the speaking case (Case 4)

3.2.6. Virus copies inhaled during different respiratory activities

The infection risk for each susceptible passenger was estimated by counting the number of virus copies inhaled. Figure 9 shows the cumulative number of virus copies inhaled by different passengers in the elevator. One can compare the infection risks for the five susceptible passengers. In the breathing case (Case 1), the number of virus copies inhaled by all susceptible passengers was low and nearly negligible, even though a two‐minute elevator ride plus 26 seconds of walking in close proximity to the infected person would intuitively be considered dangerous. In the uncovered coughing case (Case 2), one‐time coughing occurred at t = 33 s (20 s after entering the cabin). A sharp increase in the virus dose for passenger B was observed immediately after the coughing. The increased virus dose for the other passengers neatly followed the order of their distance from the index person; the observed increase in virus dose occurred later for passengers further from the index person. The covered coughing case (Case 3) exhibited the same trend as Case 2, but the infection risks for all susceptible passengers were significantly lower, as the coughing jet was suppressed, and large particles were filtered out by the mask. In the speaking case (Case 4), the face directions of the index person and passenger D changed, because this study assumed that they were having a face‐to‐face conversation during the elevator ride. In total, the index person spoke for 60 s during the 2‐min ride. The infection risks for all susceptible passengers were relatively high because of the continuous particle injection. However, differently from Case 2, no sudden increase in particle inhalation was observed immediately after the speaking activity began. Overall, the susceptible passengers who were downstream from the index person faced the highest infection risk. Passengers B and D would be infected with COVID‐19.

FIGURE 9.

Assessment of the infection risk during the elevator ride with different respiratory activities. (A) Infection risk for susceptible passengers in the breathing case (Case 1) (B) Infection risk for susceptible passengers in the uncovered coughing case (Case 2) (C) Infection risk for susceptible passengers in the covered coughing case (Case 3) (D) Infection risk for susceptible passengers in the speaking case (Case 4)

4. DISCUSSION

4.1. Effects of different activities

To quantitatively compare the infection risks of different respiratory activities, this study investigated four typical elevator ride scenarios. The number of inhaled virus copies during a complete elevator ride for each passenger is shown in Table 3. If the index person's only respiratory activity during the ride was breathing, the amount of virus intake by other passengers would be very low in comparison with the estimated 2000‐copy threshold for infection risk. The trend that passengers closer to the index person had a higher virus intake suggests the effectiveness of distancing, even for small airborne particles. Distancing also reduces the exposure to larger particles, as they have a shorter transport range. The virus intake by fellow passengers can be reduced to only 7%–15% if the index person covers his/her mouth while coughing. Meanwhile, the results indicate a much higher infection risk in the talking case. The two passengers closest to the index person were at the greatest risk of infection, as the viral dose exceeded the threshold. The talking case demonstrates the importance of orientation, as downstream passengers faced the highest infection risk. Overall, the activity of breathing can be considered insignificant when coughing or speaking activities are present.

TABLE 3.

Summary of inhaled SARS‐COV‐2 virus copies for different respiratory activities by the index person

Passenger	B	C	D	E	F
Breathing	6.0	1.5	3.2	2.2	0.8
Uncovered coughing	1040.3	179.4	234.4	126.4	41.7
Covered coughing	73.6	13.0	17.8	11.4	6.2
Speaking	4011.0	728.2	6848.0	1640.5	521.7

Compared with a related study ⁵⁰ in which infection risks for fellow passengers were high during a long flight, this study found relatively low infection risks during a typical elevator ride. This was mainly because of the short duration of the ride. The intensity of viral exposure for a certain period was still considerable. Furthermore, the high air change rate could alleviate the infection risk. According to ASHRAE standards, ⁵³ , ⁵⁴ an air change rate of only 3 or 4 times per hour is sufficient for offices, and it is about one‐eighteenth of the air change rate in the present study. The risk can be further reduced if susceptible passengers wear masks.

4.2. Limitation and future work

The RANS model with the RNG k‐$\in$ turbulence model was used for numerical simulation. The CFD models were subject to a trade‐off between accuracy and computational load. For the discrete phase model, this study assigned an inert property for the virus‐laden particles because the evaporation time was short for the range of particle size.

For estimating the infection risk, this study assumed a well‐mixed breathing zone. Since the breathing zone was defined as a sphere with a radius of 0.3 m, it was subject to a non‐uniform distribution of particles. Especially for transient cases, clusters of particles can be frequently observed. The use of an averaged particle concentration in a breathing zone can lead to either overestimation or underestimation of the actual risk. However, since the flow field was highly turbulent, this assumption should be appropriate.

Currently, due to the limited availability of information about SARS‐COV‐2 virus‐laden particles that originate from the human respiratory system, a high viral load was chosen from the clinical studies. In addition, what was shown by the clinical studies were the probabilities of virus presence in particles. The present study averaged the viral load for all particles, assuming that the statistical mean was able to represent the infection risk. Moreover, SARS‐COV‐2 has evolved, and many variants have been identified and reported by the CDC. The Omicron variant, as the dominant strain of the virus circulating around the world, is less severe in general than earlier variants such as Alpha, Beta and Delta. ⁶⁰ However, the Omicron variant has also been reported to be more contagious, which is believed to have resulted from immune evasion. ⁶¹ Such facts may lead to a different quantum of infection, and the threshold of 2000 inhaled virus copies from earlier COVID‐19 studies may already be outdated.

Although this study validated the CFD model with experimental data from a dynamic airline cabin mockup, the simulated results may be different from the real flow pattern in an elevator‐lobby space. An experimental validation with a similar space layout is needed.

As shown in the results for sub‐case 1 (entering the elevator cabin) and sub‐case 3 (leaving the elevator cabin), the order in which passengers move and the position of the index person also play important roles. In reality, the particle transmission during different elevator rides can vary considerably. For example, different riding times can lead to different levels of exposure to viruses for susceptible passengers. The passengers or the index person may get on or off the elevator in the middle of a ride. Their face orientations may vary. In addition, combinations of respiratory activities may occur. These variations can greatly affect the particle transmission. However, the qualitative conclusions should still be the same.

One should also consider the impact of the ventilation system on the particle transmission during an elevator ride. This study used a mixing ventilation system with air blown into the cabin from the periphery of the ceiling. The reasonably high ventilation rate caused the particles to be well mixed in the elevator space. If other types of ventilation were employed, such as a displacement ventilation system or personalized ventilation system, then stratification or a non‐uniform distribution of particles could be expected. An appropriate ventilation system design has considerable potential to reduce the infection risk for the non‐index passengers.

5. CONCLUSION

This study used a CFD model with particle dispersion to estimate the infection risks for susceptible passengers in an elevator ride. The study led to the following conclusions:

• Experimental data on fluid flow and contaminant dispersion in a small‐scale airliner cabin mockup was used to validate the CFD model, which was able to simulate the case reasonably well. The model can be used to study airflow and particle dispersion during an elevator ride. The simulation of moving passengers with a dynamic mesh was satisfactory.

• Particle generation and transmission patterns vary considerably among different respiratory activities. The breathing activity of a SARS‐COV‐2 infected person releases the fewest virus‐laden particles, and fellow passengers may not be infected with COVID‐19. When the index person coughs during an elevator ride, covering the cough thoroughly can reduce the virus intake of fellow passengers by 85% to 93%. Among four different scenarios, talking to each other seems the most dangerous in regard to becoming infected with COVID‐19. In the talking scenario, it is highly possible that the passengers who are in close proximity to the index person will be infected.

• An elevator cabin is a crowded and confined space that facilitates the transmission of virus‐laden particles. The infection risk decreases with the distance from the index person. Thus, social distancing is helpful during elevator rides.

AUTHOR CONTRIBUTIONS

Chengbo Du performed writing—original draft, formal analysis, visualization, and software. Qingyan Chen involved in supervision, conceptualization, funding acquisition, reviewing, and editing.

CONFLICT OF INTEREST

No conflict of interest declared.

Du C, Chen Q. Virus transport and infection evaluation in a passenger elevator with a COVID‐19 patient. Indoor Air. 2022;32:e13125. doi: 10.1111/ina.13125

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.