Numerical investigation on indoor aerosol dispersion due to natural ventilation with single-sided opening

. The purpose of this study is to evaluate the characteristics of ventilation runoff of particles. Using CFD analysis, the indoor space with the single-side opening model is filled with particles and passive scalar to provide differential temperature ventilation. The RANS and the LES analysis methods, as well as the size and the number of particles generated in a room, will be changed to compare the indoor concentration and ventilation rate trends. The particles are assumed to be water particles that do not evaporate. As the result with the turbulence models, the LES analysis tended to be closer to the passive scalar and theoretical behavior characteristics for small particles than the RANS analysis, because the diffusion of particles is also considered. As the result with the number of particles, the behavior characteristics of the LES analysis became closer to that of the passive scalar as the number of particles increased. As the result of the size of particles, in this model particles larger than 10 µm are deposited indoors by gravitational settling, increasing the percentage removed from the indoors. Therefore, it can be concluded that the risk of infection is reduced without ventilation for particles above 10 µm in this model.


Introduction
In December 2019, the first case of coronavirus infection (COVID-19) was reported. In March 2020, WHO considered COVID-19 a global pandemic based on the spread and severity of infection. Infectious diseases such as COVID-19 and severe acute respiratory syndrome (SARS) cause symptoms when microorganisms enter and multiply in the human body. Infectious particles emitted by sneezing, coughing, vomiting from infected person and the particles are dispersed into the air, and transmitted to the uninfected person [1]. The droplets have a wide distribution, roughly ranging in size from 1 to 1000 μm; droplets of above 100 μm fall to the floor in a short time. However, droplets of below 10 μm drift through the air and there are carried by air flow in the space, although not for long periods [2][3]. In addition, there are many droplet nuclei with diameters of 0.5 to 5.0 μm in the respiratory tract of infected persons. It has been confirmed that these droplet nuclei are released into the air in particulate form by sneezing, coughing, etc., and float in the room for a long time, increasing the infection risk of uninfected persons [4]. Therefore, the ventilation rates and airflow patterns are an important role in the airborne transmission of viruses in indoor environments [5][6]. Currently, the Federation of European Heating, Ventilation and Air-conditioning associations (REHVA), the American Society of Heating, Refrigeration and Air-Conditioning Engineers (ASHRAE), and other organizations * Corresponding author: 22w5029k@shinshu-u.ac.jp provide ventilation guidance for COVID-19 [7][8]. These guidelines have a reality but virus removal in indoor spaces requires consideration of many factors. They are such as the ventilation rates by outside air, the filtration effect of air filters, the effect of gravity settling, and virus inactivation. In this regard, a lot of particle analyses are being conducted in the field of indoor environmental studies to elucidate the particle behavior characteristics, and their validity and applicability are being discussed [9]. The purpose of this study is to evaluate the airflow characteristics of fine particulate matter due to natural ventilation of single-sided opening. To achieve this purpose, this study is calculated an indoor space with a single-side opening using Computational Fluid Dynamics (CFD) analysis. The indoor space with a single-side opening is filled with particles and chemical species (passive scalar), and natural ventilation is applied by the temperature difference between the indoor and outdoor space. In CFD analysis, Reynolds-Averaged Navier-Stokes Simulation (RANS) and Large Eddy Simulation (LES) as the turbulence model are adopted, and the analysis conditions for the number and size of particles generated in the indoor space are changed. This study is compared the results of indoor concentration and ventilation rate trends under different conditions. And this study also proposed adequate ventilation conditions under which the behavior characteristics of particulate matter due to natural ventilation.  Figure 1 shows the numerical analysis model in the study. Table 1 shows the numerical analysis conditions. The numerical model consists of an indoor space of 2.5 (x) × 2.5 (y) × 2.5 (z) m with a 2.1 (y) × 0.8 (z) m single-sided opening, and an outdoor space of 10.0 (x) × 10.0 (y) × 10.0 (z) m. Chemical species and particulate matter are generated in the indoor space, and the indoor concentration transition and ventilation rate are calculated by unsteady analysis for 100 seconds. As an initial condition, the indoor concentration of contaminated air and particulate matter (see Table 2) is set to 1. The large eddy simulation (LES) and the low-Re k-ε model (RANS) as the turbulence model is adopted, and indoor concentration and ventilation rate trends with the number and size of generated particles be compared.

Theoretical ventilation rate
The ventilation rates generated by natural convection depends on the difference between indoor and outdoor temperatures, and the height and width of the singlesided opening. The ventilation rates for the single-sided opening can be calculated from the equation (1) proposed by Pham and Oliver [10]. The calculated ventilation rate in this model (ΔT = 20 ºC, Single-sided opening: 2.1(y) × 0.8(z) m) is approximately 0.442 m 3 /s.

Transient calculation
The ventilation rate under an unsteady state is calculated by using CFD analysis. To calculate the ventilation rates, this study is used two calculation methods: one is to calculate from indoor concentration decay method as shown in Fig.  2 and Eq. (2), and the other one is to calculate from the airflow rate at the opening as shown in Eq. (3). Each calculation method is compared under unsteady conditions.
where, t [s] is the elapsed time, V [m 3 ] is the indoor volume, Cs [m 3 /m 3 ] is the initial indoor concentration, and Ct [m 3 /m 3 ] is the indoor concentration after t seconds.
where, vx [m/s] is the velocity of x component, Adoor [m 2 ] is the opening area.    Figure 3 shows the particles spacing for initial condition of CFD analysis. Table 3 also shows the quantity of particles with particles spacing. Particles should be dispersed uniformly in the interior space from a point 50 mm away from the interior wall, with a particle spacing of 80-200 mm. For a particle spacing of 200 mm, 2,197 particles are generated in the room as an initial condition; for 80 mm, 29,791 particles are generated. Particle size is assumed to be 10 μm. Figure 4 shows the result of passive scalar and particle behavior at 50 seconds. Because of ensemble averaged air pattern in the RANS turbulence model, airflow pattern suppressed generation of fine eddies at small times. On the other hand, in the LES turbulence model, the eddies larger than the mesh are calculated directly, and the smaller eddies are calculated. Therefore, the LES turbulence model is suitable for the generation of fine eddies. Figure 5 shows the passive scalar and the indoor concentration decay trend of particles at each particle spacing. The RANS analysis shows a tendency to approach the decay of the passive scalar as the number of particles increases. However, after 20 seconds, the particle concentration decay deviates from that of the passive scalar. The errors in the attenuation rate with respect to the passive scalar in 0-100 seconds are as large as approximately 8.6 % for the 80-mm and approximately 12.2 % for the 200-mm. In contrast, the LES analysis showed that the attenuation of particle concentration closely followed the attenuation of the passive scalar. As a result, the errors in attenuation are much smaller, at approximately 1.2 % and 1.6 % for the 80-mm and 200-mm. Figure 6 shows the calculated ventilation rate. For both the RANS and the LES analysis, the airflow rates at the opening follow the theoretical value (approximately 0.442 m 3 /s). The ventilation rate based on the indoor concentration decay method in the passive scalar increases to approximately 0.65 m 3 /s in approximately 15 seconds. It decreases and tends to approach the theoretical value after approximately 20 seconds. The initial increase or decrease in ventilation rate could be due to the large temperature difference between the indoor and outdoor environments, which was the initial condition. The ventilation rate due to particle concentration decay shows a decrease in ventilation rate in the RANS analysis, especially after approximately 20, 40, and 70 seconds. This decrease in the ventilation rate due to particle concentration decay is likely caused by the trapping of some particles in the indoor circulation flow. As a result, these particles circulate and remain in the room, thereby reducing the amount of outflow to the outside. Figure 7 shows the calculated average ventilation rate. Figure 8 shows the error against the theoretical value. For both the RANS and the LES analyses, the error tends to decrease as the number of particles increases. The error rate for this condition is 35-40 % for the RANS analysis, while it is less than 18 % for the LES analysis.

Passive scalar and particle quantity
The particles with a diameter ranging from 0.1 to 100 μm are generated uniformly indoors at intervals of 80 mm spacing. Figures 9-12 show the 1.0, 10, 50, 100 μm particles behavior after 1.0, 20, 50 and 100 seconds in the LES analysis, respectively. The 100 μm particles are greatly affected by gravitational settling, and deposition on the floor surface is observed after 20 seconds. Similarly, the 50 μm particles are affected by gravitational settling, with a decrease in their concentration observed indoors after 50 and 100 seconds. On the other hand, the 1.0 μm and 10 μm particles are still observed suspended in the air after 100 seconds, likely supplemented by the indoor circulation flow. Figure 13 shows the indoor concentration of passive scalar and particle quantity. Particles with large diameters (50, 100 μm) show comparable gradual decay trends in both the RANS and LES analyses. This is attributed to their susceptibility to gravitational settling and subsequent deposition on indoor surfaces, such as the floor. However, the particles with smaller diameters (0.1 to 10 μm) show differences in the concentration decay trends indoors due to the greater influence of the circulating flow generated indoors. Figure 14 shows the ventilation rates for both the RANS and the LES analysis for particle sizes of 1.0, 20, and 50 μm. The ventilation rate for the 1.0 μm particles shows a decrease after approximately 20 and 70 seconds for the RANS analysis. The reason is thought to be that, as in Case 1, the particles are supplemented by the circulating   flow, and the rate at which they exit outdoors decreases. By contrast, the LES analysis tends to be closer to the theoretical value than the RANS analysis because the diffusion of particles is considered. The 20 μm particles can be transported out of an indoor environment through the air current, similarly to those with a diameter of 1.0 μm. However, the impact of gravitational settling results in backflow occurring in the vicinity of the opening, which leads to a lower rate of ventilation flow than the theoretical value. The 50 μm particles are deposited by gravitational settling, resulting in a ventilation rate of almost 0 m 3 /s after 20 seconds. Figure 15 shows the calculated average ventilation rates, assuming the particles were deposited on the floor. The results indicate that particles larger than approximately 10 μm in diameter are removed from indoors by gravitational settling. In other words, this model suggests that reducing ventilation rates does not increase the risk of infection for particles larger than 10 μm in diameter.

Conclusion
In this study, CFD analysis investigated how natural ventilation with a single-sided opening removes airborne particles indoors, verify the accuracy of the analytical conditions. As the result with the turbulence model, the LES analysis tended to be closer to the passive scalar and theoretical behavior for particles with small diameters in both Case 1 and Case 2. As the result of Case 1, the results were closer to the passive scalar decay, when the number of particles was increased. However, the disadvantage is occurred that increasing the number of particles increases the computational load and analysis time. As the results of Case 2, the particles larger than 10 μm are deposited indoors due to gravitational settling, increasing the percentage of the particles removed from the indoors. Therefore, it can be concluded that the risk of infection can be reduced for particles larger than 10 μm without ventilation.