How Outdoor Trees Affect Indoor Particulate Matter Dispersion: CFD Simulations in a Naturally Ventilated Auditorium

This study used computational fluid dynamics (CFD) models, coupling with a standard k-ε model based on the Reynolds-averaged Navier-Stokes (RANS) approach and a revised generalized drift flux model, to investigate effects of outdoor trees on indoor PM1.0, PM2.5, and PM10 dispersion in a naturally ventilated auditorium. Crown volume coverage (CVC) was introduced to quantify outdoor trees. Simulations were performed on various CVCs, oncoming wind velocities and window opening sizes (wall porosities were 3.5 and 7.0%, respectively, for half and fully opened windows). The results were as follows: (1) A vortex formed inside the auditorium in the baseline scenario, and the airflow recirculation created a well-mixed zone with little variation in particle concentrations. There was a noticeable decrease in indoor PM10 with the increasing distance from the inlet boundary due to turbulent diffusion. (2) Assuming that pollution sources were diluted through the inlet, average indoor particle concentrations rose exponentially with increasing oncoming wind speed. PM10 changed most significantly due to turbulent diffusion and surface deposition reduction intensified by the increased wind velocity. (3) Increasing the window opening improved indoor cross-ventilation, thus reducing indoor particle concentrations. (4) When 2.87 m3/m2 ≤ CVC ≤ 4.73 m3/m2, indoor PM2.5 could meet requirements of the World Health Organization’s air quality guidelines (IT-3) for 24-hour mean concentrations; and (5) average indoor particle concentrations had positive correlations with natural ventilation rates (R2 = 0.9085, 0.961, 0.9683 for PM1.0, PM2.5, and PM10, respectively, when the wall porosity was 3.5%; R2 = 0.9158, 0.9734, 0.976 for PM1.0, PM2.5, and PM10, respectively, when the wall porosity was 7.0%).


Introduction
Rapid urbanization, urban transportation, factory production and domestic biomass combustion have caused a dramatic decline in the quality of urban environments [1,2]. Atmospheric particles such as PM 1.0 , PM 2.5 and PM 10 have turned into the most intractable problems of urban air pollution. Epidemiological studies have demonstrated that atmospheric particles are associated with malignancies, respiratory and cardiovascular diseases [3][4][5][6]. As most residents spend 85-90% of their time indoors, indoor air quality is closely related to human health. Therefore, understanding relationships between indoor and outdoor air pollution is critical to better characterize ambient particulate matter exposure and health effects [7,8].
It is well known that vegetation, especially trees, decreases atmospheric particles by capture, filtering, precipitation and turbulent diffusivity [9]. Tree species, canopy porosity, and leaf area operate solutions.
In the airflow model, vegetation is parameterized as a porous medium. For calculation efficiency, tree branches and trunks are approximated as foliage and crowns, so that tree canopies (including branches and trunks) are modeled as a whole [63]. From the perspective of aerodynamics, trees reduce air velocity by applying resistance and pressure. Therefore, the resistance was taken into account based on momentum equations to simulate the effects of trees on turbulent flow fields. For extra sources of turbulent flow, the turbulent flow formation on tree canopies and its dissipation were also accounted for. Model equations are as: Continuity equation: where u i is spatial mean velocity (m/s), and x i is spatial coordinate. Momentum equation: where P is pressure (Pa); ρ is air density (kg/m 3 ); F d is an extra source of resistance on tree canopies; v eff is effective viscosity (Ns/m 2 ), which is calculated as: where k is turbulent kinetic energy (Nm); ε is dissipation rate (m/s); v t is turbulent viscosity (Ns/m 2 ); and c µ is an empirical coefficient (set to 0.09) [64]. Based on conventional parameterization of plant-airflow interactions, F d is expressed as: S = ∑ u i 2 0.5 (5) where S is mean wind velocity (m/s); C d is a drag coefficient for tree canopies. The drag coefficient for trees is estimated as 0.1 ≤ C d ≤ 0.3 [65]. In this study, C d is set to 0.2; α is leaf area density (m 2 /m 3 ), and ηα is the projected area of foliage on the plane perpendicular to the prevailing wind direction (m 2 ).
To model turbulence interactions between tree canopies and fluid (air), the kinetic turbulence equation is expressed as: P k and L k are extra source terms of the equation, and expressed as: L k = −2C d ηaSk (8) Likewise, while considering impacts of tree canopies, the dissipation rate of kinetic energy is calculated as: P ε and L ε are extra source terms of the above equation, and determined as follows: L ε = −4C pε2 C d ηaSε (11) where σ k , σ ε , C ε1 and C ε2 are empirical constants, equal to 1.0, 1.3, 1.44, and 1.92, respectively. The comparisons between field data and simulation results suggest that C pε1 and C pε2 are 1.8 and 0.6, respectively [66]. Foliage reduces atmospheric particles largely by deposition [67]. In Eulerian models, particles are deemed continuums in solving conservation equations between mass and molar concentration. These models are widely used for their accuracy and efficiency. The revised generalized drift flux model, which is a type of revised Eulerian model, takes into account the slippage between particles and the fluid (air). In the model, plants intensify particle deposition via turbulent diffusion. Plants also absorb particles, some of which may re-suspend over foliage [11]. To accommodate these, the deposition and resuspended effects of plants on particulate matter are conveyed through extra terms S sink and S resuspension . In this way, the revised generalized drift flux model can simulate an actual built environment comprehensively and accurately [68,69]. It is expressed as: The slippage velocity of particles (V slip ) is defined by gravity, thermal force by the thermophoresis effect, particle fluctuation due to turbulence and particle acceleration [68], and is calculated as: τ p = The effect of tree canopies on absorbing atmospheric particles is dependent upon their leaf area densities (LADs), deposition velocities and particulate matter concentrations, conveyed as follows: The resuspension of particulate matter, as a term of volume source, is described as: Since grass is depicted as a plane in this model, the leaf area density of grass is expressed as [40]: where V j and V slip,j are the respective mean fluid (air) velocity and gravitational settling velocity of particles in direction j (m/s). C is particle concentration at the inlet (µg/m 3 ); ε p is turbulent diffusivity (m 2 /s), and can be simplified to 1 [68]. S c is the formation rate of particle sources (kg/m 3 s). S sink is the mass of particle absorbed by vegetation per cubic meter within a unit of time (µg/m 3 ); S resuspension is the secondary pollutant generated by foliage per cubic meter within a unit of time [70]; V d is particle deposition velocity on foliage (m/s); P resuspension is the percentage of resuspended particles; v is the magnitude of air velocity (m/s), and α is LAD (m 2 /m 3 ). V pj and V pi are velocities of particles in directions j and i (m/s), respectively. τ p is the relaxation time of a particle; g j is the gravitational acceleration in direction j (m/s 2 ); ΣF j is the resultant force exerted upon the particle (m/s 2 ); S mj is the momentum source of particle in direction j (kg/(m 2 s 2 ); µ is the molecular kinematic viscosity of air(Ns/m 2 ); ρ p is the density of atmospheric particles (kg/m 3 ); and d p is the particle diameter (m); C c is the Cunningham factor induced by slippage. S is the grass surface area (m 2 ), V is grass volume within the computational domain (m 3 ), and LAI grass is the leaf area index of grass (m 3 /m 3 ).

Aerodynamic and Deposition Effects of Trees around Buildings
Ji et al. studied the impact of trees on PM 2.5 distribution around buildings using wind tunnel experiments [71]. In their tests, buildings and trees were arranged perpendicularly to the oncoming wind at a scale of 1:20 with dimensions of 18L × 12W × 3.5H. The dimension of a single building is 1.5 mL × 0.75 mW × 0.85 mH. To test the impact of trees on airflow and PM 2.5 distribution more accurately, fresh cypress branches and leaves were used. Cypress was fully leached to remove dust. The crown diameter and tree height were 0.23 and 0.35 m, respectively. A "line source" of particles was released from the inlet with an oncoming wind velocity of 4.5 m/s in the wind tunnel. The airflow field and PM 2.5 concentration distributions around buildings at the pedestrian height (85 mm), mid-canopy height (325 mm), mid-building height (425 mm), three-quarters of the building height (637.5 mm), and the top of the building (850 mm) in the vertical plane were investigated.
The simulation model was built based on the size of buildings and trees ( Figure 1). Following research guidelines [62,72], the distance between the windward side of front-row buildings and the inflow boundary was set to 5H, while the distance between the leeward side of back-row buildings and the outflow boundary was 15H. The distance between the left/right symmetric boundary and the target area was 5H, and the distance from the ground to the top boundary was 11H. The oncoming wind at the inlet is gradient wind and is conveyed by the equation: where u(z) is horizontal velocity at height z, and u 0 is the horizontal velocity at height z 0 . In this model, u o = 4.5 m/s, z o = 3.5H m, and α = 0.25 [73]. The turbulent kinetic energy, k (m 2 /s 2 ), and its dissipation rate, ε (m 2 /s 3 ), are set as: where u * is friction velocity, δ is depth of boundary layer, k is von Kàrmàn constant. In this model, u * = 0.52 m/s, k = 0.4, and C µ = 0.09 [74].
In the computational domain, we set the outflow boundary conditions with fixed pressure and zero gradients. Rough wall functions were used for the ground-level boundary. Corresponding constant horizontal velocity and turbulent kinetic energy of the inflow profile were fixed at the top boundary, while the left and right symmetric boundary was modeled as a slippage wall without gradient. To better replicate conditions during the wind tunnel experiment, pollution sources were added to the inlet boundary in simulations.
Three types of structural hexahedral meshes with varying sizes (coarse mesh: X min = Y min = Z min = 0.10H', fine mesh: X min = Y min = Z min = 0.02H', and finest mesh: X min = Y min = Z min = 0.01H') were set in the target area. Calculations were performed using equations (23) to (25) with the grid convergence index (GCI) to test grid independence [75]. The GCI of coarse and fine meshes was 3.47%, while the GCI of fine and finest meshes was 2.97%. Both GCIs were below 5%, which suggested that fine meshes were adequate for calculations [76].
where F and P are empirical constants set to 3 and 2, respectively. r is the ratio between fine and coarse meshes, and u is the velocity (m/s). We compared normalized wind velocity and PM 2.5 concentration at different heights at points A, B and C in the simulation and wind tunnel experiment. Mean errors between the simulated and wind tunnel experimental wind velocities were 8.0, 7.4, and 10.3% at points A, B and C, respectively ( Figure 2). Mean errors in PM 2.5 between the simulation and the wind tunnel experiment were 9.1, 8.8, and 9.6% at points A, B and C, respectively ( Figure 3). Given that real plant branches and foliage were used in the wind tunnel test, but branch and foliage gaps were ignored in the model (i.e., the crown is a whole), the resistance to wind increased and the deposition velocity increased accordingly in the simulation. As a result, the simulated values were generally low. Thus, all data fit very well within permissible errors regardless of wind velocity or PM 2.5 concentration, demonstrating that the model can accurately simulate the impact of trees around buildings on particulate matter dispersion. 8.8, and 9.6% at points A, B and C, respectively ( Figure 3). Given that real plant branches and foliage were used in the wind tunnel test, but branch and foliage gaps were ignored in the model (i.e., the crown is a whole), the resistance to wind increased and the deposition velocity increased accordingly in the simulation. As a result, the simulated values were generally low. Thus, all data fit very well within permissible errors regardless of wind velocity or PM2.5 concentration, demonstrating that the model can accurately simulate the impact of trees around buildings on particulate matter dispersion. foliage were used in the wind tunnel test, but branch and foliage gaps were ignored in the model (i.e., the crown is a whole), the resistance to wind increased and the deposition velocity increased accordingly in the simulation. As a result, the simulated values were generally low. Thus, all data fit very well within permissible errors regardless of wind velocity or PM2.5 concentration, demonstrating that the model can accurately simulate the impact of trees around buildings on particulate matter dispersion.

Particle Transportation in a Ventilated Chamber
Chen et al. analyzed the dispersion of particulate matter with a diameter of 10 μm inside a well-ventilated chamber [77].  Figure 3. Comparison of normalized PM 2.5 concentrations in simulations and wind tunnel tests at points A, B and C. C = C x /C in , C x is the concentration at points A, B and C, respectively. C in is the concentration added at the inlet boundary.

Particle Transportation in a Ventilated Chamber
Chen et al. analyzed the dispersion of particulate matter with a diameter of 10 µm inside a well-ventilated chamber [77]. Figure 4a represents the geometry of the chamber, where the air inlet and outlet (0.04 m × 0.04 m) are aligned with the middle plane (y = 0.2 m). In trials, particles were uniformly mixed with supplied air using a separator, and then injected into the chamber with a speed of 0.45 m/s. The model was built in the aforementioned way to calculate the normalized PM 10 concentration along three lines (x = 0.2, 0.4, and 0.6 m) of the central plane and compared with results of an identical chamber of PDA experiments (Figure 4a,c). Mean errors were 8.9, 7.2, and 5.3% on three lines of the central plane, respectively ( Figure 5). To determine computational accuracy and cost, the model was parameterized to accurately forecast particle concentration making it feasible to simulate atmospheric particle transportation for the single-sided ventilation using the revised generalized drift flux model. points A, B and C. C = Cx/Cin, Cx is the concentration at points A, B and C, respectively. Cin is the concentration added at the inlet boundary.

Particle Transportation in a Ventilated Chamber
Chen et al. analyzed the dispersion of particulate matter with a diameter of 10 μm inside a well-ventilated chamber [77]. Figure 4a represents the geometry of the chamber, where the air inlet and outlet (0.04 m × 0.04 m) are aligned with the middle plane (y = 0.2 m). In trials, particles were uniformly mixed with supplied air using a separator, and then injected into the chamber with a speed of 0.45 m/s. The model was built in the aforementioned way to calculate the normalized PM10 concentration along three lines (x = 0.2, 0.4, and 0.6 m) of the central plane and compared with results of an identical chamber of PDA experiments (Figure 4a, c). Mean errors were 8.9, 7.2, and 5.3% on three lines of the central plane, respectively ( Figure 5). To determine computational accuracy and cost, the model was parameterized to accurately forecast particle concentration making it feasible to simulate atmospheric particle transportation for the single-sided ventilation using the revised generalized drift flux model.

Simulation Setup
We built corresponding building and tree models to analyze the impact of outdoor trees on indoor particulate matter dispersion under natural ventilation. The procedures were quantitatively evaluated by simulating a series of test scenarios using different parameters: tree quantity (CVCs = 0.2, 0.8, 1.8, 3.2, and 5.0 m 3 /m 2 ), window opening size (wall porosities = 3.5 and 7.0%), and oncoming wind velocity (u0 = 1.0, 2.0, 3.0, and 4.0 m/s) ( Figure 6).
The building was a typical auditorium surrounded by green space with an area of 8750 m 2 in

Simulation Setup
We built corresponding building and tree models to analyze the impact of outdoor trees on indoor particulate matter dispersion under natural ventilation. The procedures were quantitatively evaluated by simulating a series of test scenarios using different parameters: tree quantity (CVCs = 0.2, 0.8, 1.8, 3.2, and 5.0 m 3 /m 2 ), window opening size (wall porosities = 3.5 and 7.0%), and oncoming wind velocity (u 0 = 1.0, 2.0, 3.0, and 4.0 m/s) ( Figure 6).
The building was a typical auditorium surrounded by green space with an area of 8750 m 2 in total. The green space was divided into 14 equal units (25 m × 25 m), where trees were planted. The crown volume coverage (CVC) was introduced to represent trees planted in the green space and defined as crown volume per area of green space and expressed as [78]:  (Figure 7). After grid independence testing, fine mesh (Xmin = Ymin = Zmin = 0.04H) with a total of 3.1 million cells was selected to ensure a higher resolution in the target region. The boundary setting was similar to that described in Section 2.2.1. The pollution sources were assumed to be transported pollutants diluted through the inlet boundary with no other pollution sources in the domain. In addition, infiltration of building walls was not accounted for in the model because natural ventilation flow rates at window openings were far stronger than those from infiltration. Other boundary conditions settings are shown in Table 1. The computational domain, with a dimension of 385 m × 255 m × 143 m, was divided into three types of structural hexahedral meshes (coarse meshes: X min = Y min = Z min = 0.10H; fine meshes: X min = Y min = Z min = 0.04H; and finest meshes: X min = Y min = Z min = 0.02H) (Figure 7). After grid independence testing, fine mesh (X min = Y min = Z min = 0.04H) with a total of 3.1 million cells was selected to ensure a higher resolution in the target region. The boundary setting was similar to that described in Section 2.2.1. The pollution sources were assumed to be transported pollutants diluted through the inlet boundary with no other pollution sources in the domain. In addition, infiltration of building walls was not accounted for in the model because natural ventilation flow rates at window openings were far stronger than those from infiltration. Other boundary conditions settings are shown in Table 1.
higher resolution in the target region. The boundary setting was similar to that described in Section 2.2.1. The pollution sources were assumed to be transported pollutants diluted through the inlet boundary with no other pollution sources in the domain. In addition, infiltration of building walls was not accounted for in the model because natural ventilation flow rates at window openings were far stronger than those from infiltration. Other boundary conditions settings are shown in Table 1.   To further analyze relationships between natural ventilation potential and indoor particle concentrations, the natural ventilation rate was selected as an evaluation index. According to previous research [81,82], wind pressure is the main driving force of natural ventilation in the study area. Airflow penetrates buildings and trees as a consequence of pressure differences generated on building facades. Affected by wind deflection, the windward wind pressure of a building facade is generally positive, whereas the leeward is negative. Thus, the wind pressure on the facade of the building is expressed as: where P w is wind pressure (Pa), C p is a static pressure coefficient, ρ is air density (kg/m 3 ), and V is wind velocity (m/s). The natural ventilation rate is expressed as follows: where G is the natural ventilation rate (kg/s); F j and F p are the inlet and outlet area (m 2 ), respectively; ζ j and ζ p are coefficients of local resistance at the inlet and outlet, set as 2.59 and 8, respectively [83].
|∆P| is the difference in wind pressure on the facade of windward and leeward sides of the buildings (Pa), and ρ is air density (kg/m 3 ).  (Figure 8a). The windward wind velocity increases progressively with height and rises dramatically when airflows approach the roof (Figure 8c). Similar airflow patterns can be seen in an isolated room with perpendicular wind direction [84]. The windward airflow is separated at the front corner of the building, spreads around the top surface of the building and extends downwind. The wind velocity drops gradually with height and a small clockwise vortex forms near and above the windward wall in the indoor perpendicular direction. Airflows converge near the open windows on the leeward façade where the wind velocity is relatively high. Additionally, a counterclockwise vortex is formed in the turbulent wake area due to the aerodynamic and obstacle effects of trees on airflows.

Baseline Scenario
Trees are effective in reducing atmospheric particles. PM 10 on both sides of the auditorium is higher than indoors with lanceolate distributions (Figure 8b). The indoor concentration is higher in wind corridors, ranging from 70 to 190 µg/m 3 . Re-circulation inside the auditorium creates a well-mixed zone with little variation in particle concentration. PM 10 is lower on windward tree canopies owing to the dust-retention ability of trees (Figure 8d). Due to gravitational deposition effects, the indoor particle concentration on the top of the space is lower than that near the ground, which is in accordance with the results of Jin et al. [84]. Trees are effective in reducing atmospheric particles. PM10 on both sides of the auditorium is higher than indoors with lanceolate distributions (Figure 8b). The indoor concentration is higher in wind corridors, ranging from 70 to 190 μg/m 3 . Re-circulation inside the auditorium creates a well-mixed zone with little variation in particle concentration. PM10 is lower on windward tree canopies owing to the dust-retention ability of trees (Figure 8d). Due to gravitational deposition effects, the indoor particle concentration on the top of the space is lower than that near the ground, which is in accordance with the results of Jin et al. [84]. Particle concentrations differ in windward areas, where the longer the distance, the lower the concentrations (Figure 9). A relatively small concentration peak appears near the windward wall of the auditorium. Because airflows converge by windows, where the particles are blocked by walls, there is a slight increase in particle concentrations. Particle concentrations inside the auditorium decrease further from the windward side. In addition, the indoor concentration is 44 to 60% of that at the inlet values due to dust retention effects of plants and windows hindering particle diffusion Particle concentrations differ in windward areas, where the longer the distance, the lower the concentrations (Figure 9). A relatively small concentration peak appears near the windward wall of the auditorium. Because airflows converge by windows, where the particles are blocked by walls, there is a slight increase in particle concentrations. Particle concentrations inside the auditorium decrease further from the windward side. In addition, the indoor concentration is 44 to 60% of that at the inlet values due to dust retention effects of plants and windows hindering particle diffusion towards the building interior. Due to turbulent diffusion, PM 10 declines most significantly, and the deposition rate is relatively high. However, at leeward sites, concentrations are all below 50 µg/m 3 with smaller differences, regardless of particle size. Concentrations decline faster due to the deposition effect of trees around the leeward sites.

Oncoming Wind Speed and Window Opening Size
Oncoming wind velocities are set to 1.0, 2.0, 3.0, and 4.0 m/s to explore the effects of oncoming wind velocity on indoor particle concentration distributions ( Figure 10). For clarity, only scenarios where CVC = 0.8 m 3 /m 2 are presented. Particle concentrations tend to increase exponentially with the increasing oncoming wind velocity whether windows are half or fully open. This appears to because the increased wind velocity enhances indoor/outdoor cross ventilation and particle diffusion. This result is contrary to research indicating a negative correlation between normalized oncoming wind speed and average indoor particle concentrations [61]. The reason is that polluted sources in their study originated from traffic, while our study assumed that the pollution sources were wind transported and diluted through the inlet. Among wind velocity increments, average indoor concentrations differ more significantly among PM1.0, PM2.5 and PM10.These differences are slight in PM10, PM2.5 and PM1.0 when wind velocity is 1.0 m/s. However, PM10 and PM2.5 differ by 35 μg/m 3 when the wind velocity reaches 4.0 m/s. PM10 varies most significantly with wind velocity, followed by PM2.5 and PM1.0 successively, as increasing wind velocity facilitates turbulent diffusion of larger particles and diminishes surface deposition.

Oncoming Wind Speed and Window Opening Size
Oncoming wind velocities are set to 1.0, 2.0, 3.0, and 4.0 m/s to explore the effects of oncoming wind velocity on indoor particle concentration distributions ( Figure 10). For clarity, only scenarios where CVC = 0.8 m 3 /m 2 are presented. Particle concentrations tend to increase exponentially with the increasing oncoming wind velocity whether windows are half or fully open. This appears to because the increased wind velocity enhances indoor/outdoor cross ventilation and particle diffusion. This result is contrary to research indicating a negative correlation between normalized oncoming wind speed and average indoor particle concentrations [61]. The reason is that polluted sources in their study originated from traffic, while our study assumed that the pollution sources were wind transported and diluted through the inlet. Among wind velocity increments, average indoor concentrations differ more significantly among PM 1.0 , PM 2.5 and PM 10  This section focuses on the effect of window opening size on indoor particle concentrations. For clarity, indoor and outdoor PM 10 is compared when windows are fully open (wall porosity = 7.0%) and half open (wall porosity = 3.5%) in the baseline scenario ( Figure 11). PM 10 is similar on the windward facade of the auditorium when windows are half or fully open. The airflow converges in relatively small areas and the wind velocity increases when the wall porosity is 3.5%, the turbulent diffusion accelerates as a result. Hence, the indoor PM 10 is higher than that when the wall porosity is 7.0%. This result agrees well with the study demonstrating that 9% wall porosity resulted in greater normalized concentrations compared with 18% [61]. The difference reaches its maximum when windows are half and fully open within 70 m ≤ X ≤ 75 m, at approximately 30 µg/m 3 . This means an increment of 20% in PM 10 results by closing the windows by half. Near leeward windows, the concentration drops faster when the wall porosity is 3.5%. At leeward sites, the difference decreases gradually and the concentration is approximately the same when 0 m < X < 12.5 m, whether the wall porosity is 3.5% or 7.0%.
increasing oncoming wind velocity whether windows are half or fully open. This appears to because the increased wind velocity enhances indoor/outdoor cross ventilation and particle diffusion. This result is contrary to research indicating a negative correlation between normalized oncoming wind speed and average indoor particle concentrations [61]. The reason is that polluted sources in their study originated from traffic, while our study assumed that the pollution sources were wind transported and diluted through the inlet. Among wind velocity increments, average indoor concentrations differ more significantly among PM1.0, PM2.5 and PM10.These differences are slight in PM10, PM2.5 and PM1.0 when wind velocity is 1.0 m/s. However, PM10 and PM2.5 differ by 35 μg/m 3 when the wind velocity reaches 4.0 m/s. PM10 varies most significantly with wind velocity, followed by PM2.5 and PM1.0 successively, as increasing wind velocity facilitates turbulent diffusion of larger particles and diminishes surface deposition. relatively small areas and the wind velocity increases when the wall porosity is 3.5%, the turbulent diffusion accelerates as a result. Hence, the indoor PM10 is higher than that when the wall porosity is 7.0%. This result agrees well with the study demonstrating that 9% wall porosity resulted in greater normalized concentrations compared with 18% [61]. The difference reaches its maximum when windows are half and fully open within 70 m ≤ X ≤ 75 m, at approximately 30 μg/m 3 . This means an increment of 20% in PM10 results by closing the windows by half. Near leeward windows, the concentration drops faster when the wall porosity is 3.5%. At leeward sites, the difference decreases gradually and the concentration is approximately the same when 0 m < X < 12.5 m, whether the wall porosity is 3.5% or 7.0%.

3.3.Crown Volume Coverage
Particle concentrations decline gradually with increasing CVC, and PM10 varies within the widest range (Figure 12). At windward sites, concentrations decline gradually as the distance to the inlet boundary increases. This decrease is most striking when CVCs equal 3.2 and 5.0 m 3 /m 2 . Concentrations increase and reach a peak at about 10 m from windward windows. The higher the CVC, the more evident the peak. Wind velocity and airflow are lower when CVC is higher. Thus, natural ventilation is affected, and cross ventilation becomes weaker, resulting in an increase in particle concentration. Inside the auditorium, the difference of PM10 approaches 50 μg/m 3 when CVCs are 0.2 and 5.0 m 3 /m 2 (Figure 12a). The difference of PM1.0 changes consistently with distance. When CVCs are 1.8, 3.2 and 5.0 m 3 /m 2 , the concentration difference is relatively small along the horizontal plane (Figure 12c). At leeward sites, particle concentrations decline initially and then increase gradually as the distance from the auditorium increases, and concentration changes tend to be consistent irrespective of CVC.

Crown Volume Coverage
Particle concentrations decline gradually with increasing CVC, and PM 10 varies within the widest range (Figure 12). At windward sites, concentrations decline gradually as the distance to the inlet boundary increases. This decrease is most striking when CVCs equal 3.2 and 5.0 m 3 /m 2 . Concentrations increase and reach a peak at about 10 m from windward windows. The higher the CVC, the more evident the peak. Wind velocity and airflow are lower when CVC is higher. Thus, natural ventilation is affected, and cross ventilation becomes weaker, resulting in an increase in particle concentration. Inside the auditorium, the difference of PM 10 approaches 50 µg/m 3 when CVCs are 0.2 and 5.0 m 3 /m 2 (Figure 12a). The difference of PM 1.0 changes consistently with distance. When CVCs are 1.8, 3.2 and 5.0 m 3 /m 2 , the concentration difference is relatively small along the horizontal plane (Figure 12c). At leeward sites, particle concentrations decline initially and then increase gradually as the distance from the auditorium increases, and concentration changes tend to be consistent irrespective of CVC. particle concentration. Inside the auditorium, the difference of PM10 approaches 50 μg/m 3 when CVCs are 0.2 and 5.0 m 3 /m 2 (Figure 12a). The difference of PM1.0 changes consistently with distance. When CVCs are 1.8, 3.2 and 5.0 m 3 /m 2 , the concentration difference is relatively small along the horizontal plane (Figure 12c). At leeward sites, particle concentrations decline initially and then increase gradually as the distance from the auditorium increases, and concentration changes tend to be consistent irrespective of CVC.  Figure 13. Concentration distributions clearly differ between windward and leeward sites. Trees planted in windward and leeward sites intercepted particles and reduced the kinetic energy of airflow resulting from the shelter effect of tree canopies. Hence, particulate dispersion was impeded by trees in windward and leeward sites. The concentrations decrease with the increase of CVCs. At windward sites, concentrations clearly decline with increasing CVCs. The indoor and leeward sites have the smallest particle concentrations when CVC is 1.8 m 3 /m 2 . It is also evident that PM10 differences among various CVCs are larger than those of PM1.0 and PM2.5. Moreover, with CVC increasing, the declining tendency of concentrations became lower when CVCs > 1.8 m 3 /m 2 .  Figure 13. Concentration distributions clearly differ between windward and leeward sites. Trees planted in windward and leeward sites intercepted particles and reduced the kinetic energy of airflow resulting from the shelter effect of tree canopies. Hence, particulate dispersion was impeded by trees in windward and leeward sites. The concentrations decrease with the increase of CVCs. At windward sites, concentrations clearly decline with increasing CVCs. The indoor and leeward sites have the smallest particle concentrations when CVC is 1.8 m 3 /m 2 . It is also evident that PM 10 differences among various CVCs are larger than those of PM 1.0 and PM 2.5 . Moreover, with CVC increasing, the declining tendency of concentrations became lower when CVCs > 1.8 m 3 /m 2 .
Tree planting density imposes relatively significant impacts on particle concentration distributions [85]. These observations show that the oncoming wind velocity is positively correlated with indoor particle concentration, prompting us to examine connections between CVC and indoor concentration in scenarios when the oncoming wind velocity is 4.0 m/s and wall porosity is 3.5% ( Figure 14). Particle concentration and CVC exhibit significant quadratic patterns. Concentrations decline gradually with CVC initially and then increase slowly. This tendency is similar to the results of Yin et al. [78]. PM 10 , PM 2.5 and PM 1.0 reach their minima (52.4 µg/m 3 for PM 10 , 34.5 µg/m 3 for PM 2.5 , and 16.5 µg/m 3 for PM 1.0 ) when CVCs are 4.12, 4.73, and 3.59 m 3 /m 2 , respectively. Average indoor PM 10 concentration fluctuates most significantly with CVC, while PM 2.5 and PM 1.0 change slowly, because larger sized particles are more readily deposited on leaves [86]. kinetic energy of airflow resulting from the shelter effect of tree canopies. Hence, particulate dispersion was impeded by trees in windward and leeward sites. The concentrations decrease with the increase of CVCs. At windward sites, concentrations clearly decline with increasing CVCs. The indoor and leeward sites have the smallest particle concentrations when CVC is 1.8 m 3 /m 2 . It is also evident that PM10 differences among various CVCs are larger than those of PM1.0 and PM2.5. Moreover, with CVC increasing, the declining tendency of concentrations became lower when CVCs > 1.8 m 3 /m 2 . Tree planting density imposes relatively significant impacts on particle concentration distributions [85]. These observations show that the oncoming wind velocity is positively correlated with indoor particle concentration, prompting us to examine connections between CVC and indoor concentration in scenarios when the oncoming wind velocity is 4.0 m/s and wall porosity is 3.5% ( Figure 14). Particle concentration and CVC exhibit significant quadratic patterns. Concentrations

Relationship Between Indoor Particle Concentrations and Natural Ventilation Rate (G)
The relationship between indoor average particle concentration and natural ventilation rate (G) varied among the simulations (Figure 15). Average indoor concentration and natural ventilation rate show a similar trend and a positive correlation. PM10 changes most significantly with the natural ventilation rate. Indoor particle concentration clearly increases when the wall porosity is 3.5% compared with that when the wall porosity is 7.0%, because the natural ventilation rate is higher when windows are fully open. When the air exchange frequency is constant, airflow discharges rapidly, removing pollutants and reducing indoor particulate matter. Previous studies have demonstrated that absolute or relative difference in wind pressure in buildings is weakly correlated with indoor particle concentrations [58,88]. Our simulation results indicate that the natural ventilation rate is significantly and positively correlated with indoor particle concentration linked to window opening size. Previous research has also shown that indoor and outdoor particulate concentrations are closely correlated (R 2 = 0.9104) when windows are closed and there are no obvious indoor pollution sources. The indoor/outdoor concentrations ratios (I/O ratios) were significantly correlated with outdoor wind velocity and relative humidity [56]. Our results were based on having the windows open (half open), thus expanding the understanding of relationships on indoor/outdoor particulate matter transportation. The World Health Organization air quality guidelines (WHO AQGs) identify PM 2.5 as an indicator for particulate matter evaluation. We selected interim target-3 (IT-3) with a PM 2.5 of 37.5 µg/m 3 as a criterion [87]. When CVC > 2.87 m 3 /m 2 , PM 2.5 concentration is below 37.5 µg/m 3 and achieves the IT-3 of WHO AQG for 24-hour mean concentrations. Above all, the indoor PM 2.5 is in line with WHO AQG specifications when 2.87 m 3 /m 2 ≤ CVC ≤ 4.73 m 3 /m 2 .

Relationship Between Indoor Particle Concentrations and Natural Ventilation Rate (G)
The relationship between indoor average particle concentration and natural ventilation rate (G) varied among the simulations (Figure 15). Average indoor concentration and natural ventilation rate show a similar trend and a positive correlation. PM 10 changes most significantly with the natural ventilation rate. Indoor particle concentration clearly increases when the wall porosity is 3.5% compared with that when the wall porosity is 7.0%, because the natural ventilation rate is higher when windows are fully open. When the air exchange frequency is constant, airflow discharges rapidly, removing pollutants and reducing indoor particulate matter. Previous studies have demonstrated that absolute or relative difference in wind pressure in buildings is weakly correlated with indoor particle concentrations [58,88]. Our simulation results indicate that the natural ventilation rate is significantly and positively correlated with indoor particle concentration linked to window opening size. Previous research has also shown that indoor and outdoor particulate concentrations are closely correlated (R 2 = 0.9104) when windows are closed and there are no obvious indoor pollution sources. The indoor/outdoor concentrations ratios (I/O ratios) were significantly correlated with outdoor wind velocity and relative humidity [56]. In this study, the impact of outdoor trees on PM1.0, PM2.5 and PM10 inside a typical auditorium was analyzed using numerical simulations. Like the I/O ratio, this CFD method may be used as an alternative approach to investigate relationships between indoor and outdoor particle concentration distributions, especially when trees are planted outside. For future consideration, our study points to some simulation improvements. First, green spaces, by definition, have trees, shrubs and/or herbs. Our study only modeled the impact of trees and herbs, leaving open the question of more diverse green space configurations. Further, this study used CVC to quantify the trees outside, which does not reflect the distribution pattern or arrangement of trees. This may exert a different influence on the indoor particulate matter dispersion. Future simulations should take into account the coupling effects of tree distribution patterns on microclimate. Second, airflow is variable and affects particulate diffusion even it is constant, but our simulations set the particles as a steady state without affecting airflow. Hence, our conclusions remain to be validated by more field experiments. Third, the impact of plants on dust retention changes with growth, suggesting that dynamic vegetation growth should be included in future simulations. Fourth, previous research has shown that temperature and solar radiation were weakly correlated with indoor particulate matter (R 2 = 0.32-0.47 for temperature and R 2 = 0.06-0.15 for solar radiation) [55]. However, the effects of solar radiation, and heat transfer between buildings and plants were not taken into account in this simulation. Nevertheless, these factors should be considered in future studies, so that simulation results can better reflect actual conditions. Finally, we did not consider indoor generated particle sources in our simulations. We exclude them because our focus was on the effect of outdoor trees on indoor particle concentration distributions, but in the real built environment, indoor air pollution is affected not only by outdoor pollutants, but also indoor-generated sources, i.e., cooking, smoking, cleaning, and general activity. A comprehensive analysis concerning outdoor/indoor polluted sources, particle penetration and infiltration should be conducted to thoroughly understand outdoor and indoor particle transportation in built environments.

Conclusions
We adapted computational fluid dynamics (CFD) models, considering the aerodynamic and deposition effect of trees, to investigate the impact of outdoor trees on indoor PM1.0, PM2.5 and PM10  Figure 15. Relationships between G and average indoor particle concentrations when wall porosities are 3.5% (a) and 7.0% (b), respectively.
In this study, the impact of outdoor trees on PM 1.0 , PM 2.5 and PM 10 inside a typical auditorium was analyzed using numerical simulations. Like the I/O ratio, this CFD method may be used as an alternative approach to investigate relationships between indoor and outdoor particle concentration distributions, especially when trees are planted outside. For future consideration, our study points to some simulation improvements. First, green spaces, by definition, have trees, shrubs and/or herbs. Our study only modeled the impact of trees and herbs, leaving open the question of more diverse green space configurations. Further, this study used CVC to quantify the trees outside, which does not reflect the distribution pattern or arrangement of trees. This may exert a different influence on the indoor particulate matter dispersion. Future simulations should take into account the coupling effects of tree distribution patterns on microclimate. Second, airflow is variable and affects particulate diffusion even it is constant, but our simulations set the particles as a steady state without affecting airflow. Hence, our conclusions remain to be validated by more field experiments. Third, the impact of plants on dust retention changes with growth, suggesting that dynamic vegetation growth should be included in future simulations. Fourth, previous research has shown that temperature and solar radiation were weakly correlated with indoor particulate matter (R 2 = 0.32-0.47 for temperature and R 2 = 0.06-0.15 for solar radiation) [55]. However, the effects of solar radiation, and heat transfer between buildings and plants were not taken into account in this simulation. Nevertheless, these factors should be considered in future studies, so that simulation results can better reflect actual conditions. Finally, we did not consider indoor generated particle sources in our simulations. We exclude them because our focus was on the effect of outdoor trees on indoor particle concentration distributions, but in the real built environment, indoor air pollution is affected not only by outdoor pollutants, but also indoor-generated sources, i.e., cooking, smoking, cleaning, and general activity. A comprehensive analysis concerning outdoor/indoor polluted sources, particle penetration and infiltration should be conducted to thoroughly understand outdoor and indoor particle transportation in built environments.

Conclusions
We adapted computational fluid dynamics (CFD) models, considering the aerodynamic and deposition effect of trees, to investigate the impact of outdoor trees on indoor PM 1.0 , PM 2.5 and PM 10 concentration distributions. Using CVC as an evaluation index for outdoor tree planting, our study thoroughly compared indoor particle concentration distributions with different CVCs, oncoming wind velocities, window opening sizes, and the capacity of natural ventilation potential. The following conclusions can be drawn: (1) The building envelope restricts airflow and particle dispersion and dilution. In our baseline scenario, a relatively large vortex formed inside the auditorium. As a consequence, the inside air re-circulated and created a well-mixed zone with little variation in particle concentration. Inside the auditorium, the concentration declined with increased distance from the windward side. In addition, the concentration inside was 44 to 60% of that at the inlet boundary, because the dust-retaining ability of trees and window area obstructed diffusion of particles to indoors. Indoor PM 10 fluctuated most significantly with increasing distance from the inlet boundary. PM 2.5 and PM 1.0 changes were not clear because the deposition was more effective among larger particles due to turbulent diffusion. (2) Under the assumption that pollution sources were diluted through the inlet, the average indoor particle concentration rose exponentially with increasing oncoming wind speed. The difference among PM 1.0 , PM 2.5 and PM 10 was relatively small when wind velocity was 1.0 m/s, but the concentration changed significantly as the wind velocity increased to 2.0 m/s. As increased wind velocity intensified turbulent diffusion of larger particles and reduced surface deposition, PM 10 changed most significantly, followed by PM 2.5 and PM 1.0 . (3) Indoor cross-ventilation was improved when the wall porosity was 7.0%. Thus a 20% increment in PM 10 was achieved by closing windows by half. Near the leeward windows, the concentration declined much more quickly when the wall porosity was 3.5% than that when the wall porosity was 7.0%. The difference gradually narrowed as the distance to the leeward wall increased and the concentration was very similar under the condition when 0 m < X < 12.5 m. (4) The average indoor particle concentration declined initially and then increased with a higher CVC. When the CVC ranged between 2.87 and 4.73 m 2 /m 3 , the indoor PM 2.5 concentration could meet the requirement of IT-3 of the WHO AQGs for 24-hour mean concentrations. (5) Average indoor concentrations were positively correlated with natural ventilation rates and increased more quickly when the wall porosity was 3.5%. Airflow removed more pollutants and shortened longevity of particles indoors when the wall porosity was 7.0%. Thus, the indoor particle concentration was lower than that when the wall porosity was 3.5%.
Our findings indicate that trees planted around buildings, window opening size, and predominate wind velocity all have significant impacts on indoor atmospheric particle concentrations. To plan new buildings, it will be necessary to deliberately evaluate tree planting designs and ambient wind conditions around buildings at early design stages. Such planning will maximize the natural ventilation potential while decreasing the indoor particle concentration. Further, ventilation strategies (changing window opening size), outdoor movable tree planting pools, and layout of interior space may be adapted for existing buildings, so as to lower the indoor particle concentrations. Our conclusions could be used as guidelines for assisting building architects, urban planners and landscape architects to evaluate natural ventilation strategies with enhanced consideration for improving indoor air quality in public buildings.