Transfer and escape characteristics of outdoor pollutants into an indoor space sheltered by urban-like block arrays using large-eddy simulations

. We conducted isothermal large-eddy simulations to generate the velocity and concentration distributions to investigate the air pollution transport from outside to inside of a space surrounded by urban-like block arrays. Contrary to previous study, we assumed that the pollution in the form of scalars are generated outdoors and not indoors which we placed at: 1) middle of window, 2) near window wall, 3) middle of street canyon at ground level, and 4) middle of street canyon at window level. Results showed that regardless of scalar source location, the scalars accumulated inside the indoor space which can be explained by the downdraft effect that are typically found in urban environments. The downdraft effect produced vortices outside and inside the indoor space. For scalars near window, indoor vortex drove the concentration to indoors. On the other hand, outdoor vortex transported the scalars located at street canyon to reach the window where they were eventually transported to indoors also due to indoor vortex. The average normalized indoor concentrations found in this study are 1.25 – 1.50, 1.00 – 1.75, 0.25 – 0.50, and 0.0 – 0.25 for scalars (cid:2) (cid:3) , (cid:2) (cid:4) , (cid:2) (cid:5) , and (cid:2) (cid:6) , respectively. Our study suggests that for natural ventilation studies of urban environments where air pollution is significant, outdoor effects should also be carefully considered.


Introduction
Natural ventilation's (NV) cost effectiveness drove different establishments to introduce outdoor air to indoors to dilute and displace indoor contaminants and prevent airborne disease transmission. With the assumption of fresh and clean outdoor air, previous studies, both experimental and numerical, demonstrated the NV in urban spaces, particularly the resulting indoor ventilation that considers the "sheltering effect"changes in the ventilation due to the surrounding buildings [1]. Factors such as incoming wind directions [2], window position, building arrangements [3], [4], were varied considering sheltering effect to compute the resulting boundary-based ventilation of indoor spaces. In addition, the local ventilations in different sections of an indoor space were also explored [5]. Further, as most of the buildings that experiences the sheltering effect are in urban spaces, such assumptions will not be realistic due to the air pollution brought by factories, cars, and other contaminant sources. Leung et al. [6] summarized that in addition to indoor pollutants, large chunk of indoor air quality is affected by outdoor air. For example, Xie et al. [7] showed 68% -95% outdoor air contribution to the total indoor fine particulate matter (PM ଶ.ହ ) inside a university -even contributing around 89% inhaled PM ଶ.ହ dose of students at hazy days. When such outdoor air quality was introduced to indoors, it defeats the purpose of ventilation which may potentially harm the indoor occupants. Therefore, this study aimed to * Corresponding author: fernandez.ken.bryan.487@s.kyushu-u.ac.jp investigate the transport mechanism of outdoor pollutants to indoor space -utilizing the previous case that considers the outdoor air as fresh and clean [4], [5]. We clarified how the introduction of flow because of surrounding buildings affects the resulting pollutant concentration coming from outdoors. This study may potentially help in considering the use of natural ventilation in urban spaces.

Computational Domain
As this study aims to investigate the previous study that assumes the outdoor air is clean, we utilized the previous model used in the ventilation study of Adachi et al. [4], Hirose et al. [8], and Fernandez et al. [5]. We conducted an incompressible isothermal coupled indoor-outdoor large-eddy simulation in an indoor space surrounded by generic block arrays. Depicted in Fig. 1a is the computational domain with four blocks arranged in staggered manner having three generic blocks with one ventilation building model with windows positioned facing the x-direction. We set the dimensions similar to the mentioned studies with building length of H = 100mm and window area 10% of the side area. We employed cyclic boundary condition such that the 4-E3S Web of Conferences 396, 02004 (2023) https://doi.org/10.1051/e3sconf/202339602004 IAQVEC2023 building domain is replicated both at the spanwise and streamwise directions as shown in Fig. 1b. A constant streamwise pressure gradient was set such that the reference wind speed become approximately 3.40 m/s, which is consistent with the previous wind-tunnel experiments of Ikegaya et al. [3]. To represent the contaminants originating from outdoors, four scalar sources were independently introduced located at the window inlet: 1) middle, 2) side, and at the street canyon located at H/2 upstream of the window inlet: 3) same level with the window, 4) ground, as show in Fig. 2.

Numerical setup
We utilized finite volume method for the following LES incompressible continuity, Navier Stokes, and scalar transport equations: where ‫ݑ‬ is the velocity component in i-th direction in m/s, ρ is the air density in kg/m 3 , P is the pressure in pascals, ߥ is the kinematic viscosity in m 2 /s, and ‫ܥ‬ represents the i-th scalar quantity from i=1 to 4. We simultaneously solved four scalar quantities as shown in Fig. 2. To model the sub-grid scale term, we used a standard Smagorinsky model where ߥ ௦௦ = ‫ܥ(‬ ௦ ߂) ଶ ܵ , and ‫ܥ‬ ௦ = 0.12 is the Smagorinsky constant, ܵ ଶ = ‫ݑ߲(5.0‬ ‫ݔ߲‬ ⁄ + ‫ݑ߲‬ ‫ݔ߲‬ ⁄ ) ଶ is the velocity strain, and ߂ = ‫)ݖ݀ݕ݀ݔ݀(‬ ଵ ଷ ⁄ . Lastly, we utilized passive scalar quantities where ܵܿ = 1 and ܵܿ ௦௦ = 1. We used the OpenFOAM software to solve the equations with temporal and spatial terms as the secondorder backward and central schemes, respectively. The velocity and pressure coupling was solved by the pressure-implicit split-order (PISO) method. Fig. 3 is the mean indoor velocity component comparison of the current study with the previous wind-tunnel experiment using particle image velocimetry by Ikegaya et al. [3]. The LES showed a E3S Web of Conferences 396, 02004 (2023) https://doi.org/10.1051/e3sconf/202339602004 IAQVEC2023 good agreement with the WTE. In addition, the outdoor flow field basically followed the numerical condition in the previous study by Adachi et al [4], where the indoor velocity components were carefully validated using WTE data by Ikegaya et al. [3].  Fig. 7 depict the instantaneous concentration distributions of scalars ‫ܥ‬ ଵ -‫ܥ‬ ସ superimposed on the velocity vector field. The concentrations were normalized by perfect mixing concentration, ‫ܥ‬ , or the average concentration at the inlet boundary, while the velocity vectors were normalized by the reference streamwise velocity component at ‫ݖ‬ = ‫.ܪ2‬ The distributions were taken at the x-z plane in the middle of the ventilation domain (y = 0.15). In general, the four scalars have observed higher concentrations inside the indoor space compared to outdoors, with scalars positioned near window ( Fig. 4 and Fig. 5) have relatively higher concentrations compared to scalars positioned at street canyon ( Fig. 6 and Fig. 7). This implies that outdoor air pollution, in the form of scalar, was able to transfer and accumulate inside regardless of scalar source location being studied in this work.    Looking at the velocity vectors near the inlet of indoor space, a strong downward flow owing to the downdraft effect that is typically formed in urban environments can be observed. This downward flow pushes the scalars ‫ܥ‬ 1 and ‫ܥ‬ 2 , that were positioned near window, to accumulate inside effectively. In addition, as the downdraft effect were split into two flows due to the indoor space opening, with some flow going outdoors and some going indoors, some concentration of ‫ܥ‬ 1 and ‫ܥ‬ 2 also spread outdoors. For scalar ‫ܥ‬ 3 that was positioned at window level at the middle of street canyon (Fig. 6), more concentration can be observed to circulate in the outside vortex structure that was formed by the downdraft effect. Some concentration can accumulate inside but at a lower amount compared to window scalars. Scalar ‫ܥ‬ 4 (Fig. 7), even though located on the ground of the street canyon, can still accumulate inside the indoor space. The vortex outside pushes the scalar upwards and when it reaches the window level, the downward flow eventually pushes the concentration indoors. With this, the four scalars, regardless of its source location, were transferred to indoor space mainly due to the downdraft effect. It is also important to note that there were concentration transfers from indoor to outdoors at the outlet of indoor space for most of the scalars. This is due to the flow coming from outside also formed a big vortex structure inside following counter clockwise direction. Therefore, the concentration can leak from inside to outside at the indoor outlet following the upward flow direction. Fig. 8 -Fig. 11 are the average indoor concentration distributions of scalars ‫ܥ‬ 1 -‫ܥ‬ 4 superimposed on the velocity vector field. The concentrations were normalized by perfect mixing concentration, ‫ܥ‬ , or the average concentration at the inlet boundary, while the velocity vectors were normalized by the reference streamwise velocity component at ‫ݖ‬ = ‫.ܪ2‬ The distributions were taken at the x-y plane in the middle of the ventilation domain (z = 0.05). It can be observed that the scalars positioned near the window have high concentration values compared to the scalars positioned outdoors. In particular, the scalar ‫ܥ‬ 1 (Fig. 8) has 1.25 to 1.50 averaged normalized concentration. Scalar ‫ܥ‬ 2 (Fig. 9) on the other hand, has 1.50 -1.75 averaged normalized concentration at y > 0.17, then 1.25 to 1.50 at 0.17 > y > 0.13, and 1.00 -1.25 at y < 0.13. This is due to the source location is skewed to the left of the domain making the concentration to accumulate more to the left. As previously stated, the downdraft effect that pushes scalars ‫ܥ‬ 1 and ‫ܥ‬ 2 indoors has governed compared to the downdraft effect that pushes outdoors -making their concentration to accumulate more indoors. On the other hand, scalar ‫ܥ‬ 3 (Fig. 10) has 0.25 to 0.50, while scalar ‫ܥ‬ 4 (Fig. 11) has 0.00 to 0.25 average concentration. In their case, most of the generated scalars followed the downdraft effect outdoors than the downdraft effect indoors -making the concentration indoors minimal compared to window scalars. Comparing instantaneous values with averaged values, it is important to note that the instantaneous concentration can become higher than the averaged values. For instance, in Fig. 5, the concentration value at the top of the indoor space can reach up to 2.25 and above -that was higher than the highest value on its time-averaged concentration in Fig. 9 which was 1.75. Take note that this still hold true even the plane shown in this paper for average and instantaneous distributions are different (x-y and x-z). In maximizing the natural ventilation through positioning of occupants inside the indoor space, such surge in concentration due to outdoor air pollution should be considered.

Conclusion
In this work, we studied the effect of outdoor pollutants in the form of scalar using previous cross-ventilation case that assumed outdoor air as fresh and clean. We conducted isothermal large-eddy simulations to generate the concentration distributions of four scalars positioned at the window ‫ܥ(‬ ଵ and ‫ܥ‬ ଶ ) and street canyon ( ‫ܥ‬ ଷ and ‫ܥ‬ ସ ) to determine how outdoor pollution transport to indoors.
All the scalars produced indoor concentration accumulations with scalars positioned at the window generated higher mean concentration values. Scalar ‫ܥ‬ ଵ and ‫ܥ‬ ଶ had normalized mean concentration distributions of 1.25 -1.50 and 1.00 -1.75, respectively. On the other hand, scalar ‫ܥ‬ ଷ and ‫ܥ‬ ସ had normalized concentration distributions of 0.25 -0.50 and 0.00 -0.25, respectively. These accumulations inside the indoor space can be explained by the downdraft effect that is typically formed in urban environments. The downdraft effect has vortex formations both outside and inside the indoor space. For window scalars, they were pushed by the downdraft effect following the indoor vortex. On the other hand, the street canyon scalars first follow the outdoor vortex and when they reach the window, will then follow the indoor vortex.
Our study demonstrated how the urban outdoor pollution can be an equalizer to the positive effect (costeffectiveness) of natural ventilation. In designing urban dwellings utilizing such mode of ventilation, outdoor conditions should be considered as outdoor air may not typically be fresh and clean. Furthermore, instantaneous results showed that there were instances where the concentrations will be higher than the averaged concentration distributions that should be carefully considered as these "surges" can potentially harm the occupants.