CFD Analysis of the Impact of Building Layout and Morphology on Pedestrian-Level Airflow and Pollutant Stagnation in Urban Areas with Well-Developed Surface Boundary Layers

Abstract

This study focuses on the features of wind flow and pollutant diffusion of continuous urban street canyons with distinct surface boundary layers through computational fluid dynamics (CFD) analysis. The CFD analysis is set as cyclic boundary conditions to represent the continuous canyons. This study establishes four cases with different building heights and arrangements, and three cases with different atmospheric stability conditions to evaluate the effects of building types and atmospheric stability on wind flow and ventilation characteristics. Pollutants were emitted in a section below the height of 7.5 m from the ground to figure out the ventilation performance of spaces where pedestrians move within urban street canyons. Ventilation rate and purging flow rate (PFR) were calculated to confirm the results. Furthermore, this study analyzed the effects of the ventilation efficiency of canyons on ventilation performance depending on canyon patterns and diverse conditions of atmospheric stability.

1. Introduction

Population concentration and the continuous development of cities have resulted in the Manhattanization of urban spaces. PM 10 issues have become serious concerns in the Republic of Korea. Urban spaces have seen low ventilation efficiency, and urban residential environments have become worse as pollutants generated inside the city stay within the space. Several cities have established air pollution prevention plans to prevent environmental pollution in urban spaces, and studies on higher ventilation in cities have increased.

The impact of urban buildings on air pollution concentration levels has been examined in various studies. The urban block form can affect the air quality inside buildings, and dense buildings can potentially lead to air stagnation [1]. It has also been shown that optimizing the layout of residential buildings and rationalizing transportation networks can reduce concentrations of fine particulate matter (PM 2.5), thereby lowering pollution levels in urban residential areas [2,3]. There have been many experimental and numerical studies of airflow and air pollution in urban areas [4]. There have been diverse studies based on urban space models that simulate cities, examining the impacts of urban space patterns on wind flow and pollutant diffusion through a wind tunnel test, field measurements, and CFD analysis techniques.

To evaluate urban airflow, wind conditions, pollutant distribution, and ventilation efficiency indexes were used. It was concluded that building orientation affects pollutant dispersion and ventilation in city blocks [5] and that factors such as building density, street frontage, and orientation play an important role in mitigating heat stress [6,7]. This emphasizes the need to consider spatial organization and building appearance to create a comfortable urban environment.

CFD of urban spaces can be utilized for analytical studies that are not feasible in real-world experiments or wind tunnels. Numerical simulation methods based on fluid dynamics are broadly categorized into three types: direct numerical simulation (DNS), Reynolds-averaged Navier–Stokes (RANS) simulation, and large eddy simulation (LES). Recent studies have conducted with the standard k–ε model, and LES or DNS due to the development of high-speed computers, allowing for comparisons with field measurements or wind tunnel test results from previous studies. Previous studies have indicated that LES and DNS require a high computational load compared to the standard k–ε model based on RANS; however, they have higher accuracy in interpretation [8,9]. For instance, Letzel et al. [8] employed an LES analysis technique and revealed that circulation in urban canopies is predominantly vertical. This vertical circulation is effective in removing pollutants from pedestrian spaces and can be more accurately evaluated using LES rather than RANS. Coceal et al. [9] analyzed urban space forms using DNS and compared the results with those from a wind tunnel test. They found that turbulence energy exhibited different features depending on the shapes of the target area, particularly when complex patterns of turbulence energy appeared on irregular arrangements of buildings. They further found that taller buildings caused atmospheric instability, which in turn affected building surface drag. Steady-state LES of convective and stable urban boundary layers has been extensively studied to establish best practices for modeling non-neutral conditions. Grylls et al. [10] investigated the requirements for accurate simulations under convective conditions, emphasizing the significance of domain heights and boundary-layer capping strategies. Tomas et al. [11] focused on stable stratification effects, highlighting variations in the internal boundary layer and pollutant dispersion patterns in comparison to neutral conditions. They emphasized reduced vertical mixing and higher pollutant concentrations within the urban canopy. Boppana et al. [12] created building models with regular and irregular heights, placed them in a zigzag configuration among other buildings, analyzed ventilation patterns in the canopy using LES, and compared the findings with those from a wind tunnel experiment. As a result, LES showed a higher analysis accuracy compared to the standard k–ε model for CFD analysis.

Otherwise, there are reports that RANS’s analysis accuracy is low, and several studies continue to examine the usefulness of analysis through RANS-based models. For example, Santiago et al. employed LES and RANS models, performed a numerical analysis of container arrangement patterns and wind direction [13,14], and compared the results with measurement data of mock urban setting text [15]. As a result, LES and RANS showed similar outcomes in terms of spatially averaged vertical wind velocity. Additionally, Santiago et al. [13] examined drag coefficients and modified drag coefficients by the estimated area of urban canopies in RANS. Hence, it is reported that interpretation via RANS is valid for building coverage ratio within a target range, and the RANS-based interpretation for urban canopy spaces is considered useful. Therefore, RANS methods are one of the most commonly used techniques in unsteady simulation of turbulent flows (USTE) studies. The simulation theory based on the RANS method is also known as turbulence modeling theory. The Navier–Stokes (NS) equations in the RANS model are the governing equations for the mean variables in the flow field. The RANS method provides only average information about turbulence, and turbulence problems involving unsteady flows can be analyzed by converting them into steady problems. Additionally, Sheikh et al. reported on the impact of atmospheric flow and pollutant dispersion in a model street canyon intersection, emphasizing the role of building configurations in pollutant concentration levels [16]. Furthermore, the effects of street canyons on pollutant dispersion in urban areas were explored, emphasizing the importance of understanding pollutant behavior within confined urban environments to enhance urban air quality [17]. These findings provide valuable insights for urban planners and policymakers to mitigate exposure to traffic-exhaust pollutants in cities.

As mentioned earlier, the removal of pollutants residing in urban street canyons has become a crucial issue in urban administration for the sake of the protection of pedestrians’ and residents’ health. Therefore, methods to improve ventilation efficiency in urban spaces and diverse indicators of ventilation efficiency have been examined [18]. CFD analysis and confirmed ventilation efficiency that was practically examined through purging flow rate (PFR; local ventilation volume) [19] by targeting areas around expressways within a city. Yunlong et al. investigated the correlation between urban form parameters and ventilation efficiency index using PFR. Using the PFR index with the urban morphology parameter floor area ratio, they reported that the rational arrangement of buildings can improve ventilation [20].

Meanwhile, studies are focusing on the effects of urban atmospheric stability on pollutant diffusion. Several studies have figured out the diffusion features of pollutants in the atmospheric boundary layer in consideration of thermal stratification. Offerle et al. [21] conducted field measurements to identify the relationship between the surface temperature and wind field found in certain canyons. As a result, they confirmed that the buoyancy effect caused by temperature differences affected the wind field in the canyon spaces.

The previous studies reviewed can be summarized as follows: studies on improving the accuracy of analytical models, research on patterns of weather physical parameters in urban spaces, and research on the development patterns of boundary layers due to urban patterns. Additionally, even within the same city, the presence of a wind field with buildings lined up in a row and a distinct surface boundary layer can lead to changes in the shape of the boundary layer. This can occur due to high-rise buildings affecting the incoming air currents or sudden alterations in the shape and layout of buildings. These factors contribute to a more defined surface boundary layer. As it is challenging to elucidate general concepts regarding environmental assessment factors of outdoor spaces (e.g., wind patterns and dispersion of pollutants) in urban areas, there have been limited studies taking into account these characteristics.

In this study, we consider a scenario where the winds entering the city are weakening because of a fully developed ground boundary layer. This implies that pollutants produced in urban areas can easily accumulate and result in high levels of air pollution. This study focuses on a fundamental investigation of how altering building height and placement within the horizontal canyon space affects pollutant diffusion. We organized and categorized urban spaces into simple cases, and assumed street canyons with distinct boundary layers due to a continuous arrangement of uniform households in the leeward direction in terms of windward. Such an assumption indicates that a space with a distinct surface boundary layer has little influence on inflowing winds, and, consequently, air pollution can be expected to be severe; hence, it is crucial to examine the wind flow and ventilation efficiency for pollutants in such urban spaces.

2. CFD Analysis Overview

2.1. Analysis of Cases and Targets

Regarding the review conditions, we designed a building space with an average floor area ratio and kept the building coverage ratio constant to analyze the wind flow based on the shape of the urban spaces. Building arrangements were grid-patterned and staggered. The buildings were categorized into low-rise, mid-rise, and high-rise buildings based on their heights. A CFD analysis was conducted for four household scenarios, including both regular and irregular cases. Based on the analysis results, we considered the impacts of different building layouts and heights on the wind flow and pollutant concentration within street canyon areas. We analyzed the airflow characteristics and ventilation efficiency of each scenario by averaging the spatial data. We examined four cases of atmospheric stability (i.e., neutral, slightly stable, weakly unstable, and unstable) to confirm the impact of gravity ventilation driven by temperature differences on ventilation in the respective spaces. Figure 1 indicates a conceptual diagram of sequentially-arranged street canyon space.

Figure 2 and

Table 1. Analysis domains.

Case	Size of Buildings (X × Y × Z) (m)	Mesh Split of Analysis Domains (X × Y × Z) (m)	Floor Area Ratio (%)	Building Coverage Ratio (%)
Case 1	Middle-rise buildings (1.0 H × 1.0 H × 1.0 H)	32 × 32 × 45	125	25
Case 2	Middle-rise buildings (1.0 H × 1.0 H × 1.0 H)	44 × 44 × 45
Case 3	High-rise buildings (1.0 H × 1.0 H × 1.5 H)	62 × 62 × 45
	Low-rise buildings (1.0 H × 1.0 H × 0.5 H)
Case 4	High-rise buildings (0.816 H × 0.816 H × 1.5 H)	34 × 34 × 45		16.64
Case 5, 6, 7	Middle-rise buildings (1.0 H × 1.0 H × 1.0 H)	32 × 32 × 45		25

present target areas per case for the CFD analysis and their details. In all cases, we set the maximum height of the upper layer from the ground to about 6.67 H (1.0 H = 15 m), and 1.0 H was set as the basis for one side of a building. Case 1 is the reference case with an arrangement of middle-rise buildings (X(1.0 H) × Y(1.0 H) × Z(1.0 H)) in a normal grid pattern. Case 2 has middle-rise buildings in a staggered pattern. Case 3 has low-rise buildings (1.0 H × 1.0 H × 0.5 H) and high-rise buildings (1.0 H × 1.0 H × 1.5 H) in a normal grid pattern. Case 4 has the same target areas and building arrangement as Case 1. However, the building coverage ratio was adjusted to a smaller scale to give the same floor area ratio as other cases (Table 1). Only Case 1 was considered for the atmospheric stability analysis, and Case 1 was considered neutral, Case 5 slightly stable, Case 6 weakly unstable, and Case 7 unstable. The mesh split of the analysis model can be found in Table 1. Figure 3 shows the conditions and characteristics of canyon space contaminants.

2.2. Analysis Conditions and Boundary Conditions

To utilize the cyclic boundary condition, the sky plane of the analysis space was set to a free slip condition for all physical quantities except air temperature, and the air temperature was fixed at 30 °C to account for the temperature stratification. The initial temperature condition of the space was set to 30 °C for the entire region. Symmetry condition was set for the side of the analysis space. For the inlet and outlet, a cyclic boundary condition was imposed, and the pressure gradient (Δp/Δx) was given a constant value of 0.008/30 (Pa/m) for the energy and pressure losses occurring between the boundaries of the inlet and outlet sides. The difference scheme used a first-order upwind difference scheme for the advective term and a second-order central difference scheme for the spatial difference. This study utilized the standard k–ε model(Appendix A) as it is most frequently utilized as a turbulence model in CFD analyses. The Prandtl number (Pr) for turbulence was set to 1.0 and the Viollet type was utilized for the ε equation.

The details of the boundary conditions can be found in

Table 2. CFD analysis and boundary conditions.

Items	Wind Velocity	k	ε	Concentration	Temperature
Sky	Free slip
	$\frac{\partial U_1}{\partial X_3}=0$$, \frac{\partial U_2}{\partial X_3}=0$, U3 = 0	$\frac{\partial k}{\partial X_3}=0$	$\frac{\partial \epsilon }{\partial X_3}=0$	C = 0	T = 30 (°C)
Side	Symmetry
	$\frac{\partial U_1}{\partial X_2}=0$$, {\mathrm{U}}_2=0, \frac{\partial U_3}{\partial X_3}=0$	$\frac{\partial k}{\partial X_2}=0$	$\frac{\partial \epsilon }{\partial X_2}=0$	$\frac{\partial C}{\partial X_2}=0$	$\frac{\partial T}{\partial X_2}=0$
Inlet	Cyclic ((Δp/Δx) 0.008/30 (Pa/m))	Cyclic
Outlet
Ground surface	Z0 Log low (Z0 = 0.01 (m))	$\frac{\partial k}{\partial X_3}=0$	$\frac{\partial \epsilon }{\partial X_3}=0$	$\frac{\partial C}{\partial X_3}=0$	(stable) (weakly unstable) (unstable)	T = 29 (°C) T = 35 (°C) T = 40 (°C)
Build. Surface		$\frac{\partial k}{\partial X_n}=0$	$\frac{\partial \epsilon }{\partial X_n}=0$	$\frac{\partial C}{\partial X_n}=0$

. The mean diffusion field was analyzed by assuming the gravitational settling velocity of pollutant transport to be “0”, that is, by uniformly generating pollutants assumed as passive contaminants with no inertia within the area. Since the building coverage ratio is the same in Cases 1 to 3, a constant value of 1.0 μg/m³ sec per unit volume was given to the concentration development rate in the space from the ground to a height of 0.5 H as a condition for pollutant generation. However, since Case 4 has a lower building coverage ratio than the other cases, the condition for concentration development of 0.899 μg/m³ sec per unit volume was given, and conditions for pollutant generation per household area were set identical to those in the other cases. Furthermore, the details of the boundary conditions for temperature can be found in Table 2 and the surface temperature and bulk Richardson number (Rb) for each case regarding atmospheric stability can be found in

Table 3. Atmospheric stability case and bulk Richardson number (R_b).

Case	Atmospheric Stability	Air Temperature T (°C)	Surface Temperature Ts (°C)	Rb
Case 1	Neutral	30	30	0.0000
Case 5	Stable	30	29	0.0444
Case 6	Weakly unstable	30	35	−0.3171
Case 7	Unstable	30	40	−0.6511

Bulk Richardson number: R_b = gH(T_H − T_S)/{T + 273)(U_H)²}.

.

The number of volumes for CFD analysis is 90,000 for Case 1, Case 5, Case 6, and Case 7, 179,945.64 for Case 2, 360,000 for Case 3, and 90,000 for Case 4. The mesh type used is a hexahedral mesh. Cyclic boundary conditions were set to simulate the development of the ground boundary layer because this study focuses on urban areas where the ground boundary layer is well developed. In such urban spaces, we expected the airflow to be stable. If pollutants were to occur, they would not easily spread due to the stable airflow. Therefore, this study examined how to arrange and design buildings to enhance airflow at the pedestrian level and facilitate the dispersion of pollutants in these areas.

3. Estimation of Ventilation Volumes and PFR Based on Wind Flow and Interfaces

This study examines the wind flow features and ventilation efficiency within the street canyon space. It is difficult to provide a clear definition of wind flow; however, in this study, we utilized the absolute value of the wind velocity at the pedestrian level (height of 1.5 m: 0.1 H) within the street canyon space as an indicator. The ventilation volume based on the interface was calculated by considering the height of 0.5 H (=7.5 m) of each analysis case area as the interface height to assess ventilation efficiency. Furthermore, the ventilation efficiency indicator, PFR, was used to compare the ventilation volumes. PFR is a local exhaust ventilation and a ventilation metric that utilizes actual ventilation air volume for a localized area. Ventilation volume and PFR can be defined by the following formulas:

$$\mathrm{Q} [{\mathrm{m}}^3/\mathrm{s}] = {\int }_{\mathrm{v}}\mathrm{q}\mathrm{d}\mathrm{v} / \frac{1}{\mathrm{S}} {\int }_{\mathrm{v}}\mathrm{C}\mathrm{d}\mathrm{s} = {\mathrm{q}}_{\mathrm{p}} / \mathrm{C}\mathrm{s}$$

(1)

$$\mathrm{P}\mathrm{F}\mathrm{R} [{\mathrm{m}}^3/\mathrm{s}] = {\int }_{\mathrm{v}}\mathrm{q}\mathrm{d}\mathrm{v} / \frac{1}{\mathrm{V}} {\int }_{\mathrm{v}}\mathrm{C}\mathrm{d}\mathrm{v} = {\mathrm{q}}_{\mathrm{p}} / \mathrm{C}\mathrm{p}$$

(2)

where, in Equation (1), the numerator of the right side refers to the rate of pollutant generation and the denominator indicates the area-averaged concentration of the interface in the target area, q is the rate of pollutant generation per unit volume (μg/m³ s), C is the pollutant concentration (μg/m³), qp refers to the rate of pollutant generation within the target area per unit time (μg/s), and CP is the spatial average concentration of the target area p (μg/m³).

As shown in the definitions of Equations (1) and (2), the interface-based ventilation volume applied here is based on the area-averaged concentration of the interface at the height of the target area, and the interface-based PFR refers to the ventilation volume based on the average concentration of the volume based on the interface within the target area.

4. Model Validation

Validation of the Flow Field in Urban Street Canyon

The wind tunnel experiment is primarily utilized to measure and analyze the flow field and diffusion field within the street canyon space. By comparing the wind tunnel experiment with CFD analysis to validate the prediction accuracy of CFD analysis, it is deemed suitable to utilize CFD analysis for a detailed analysis of the ventilation throughout the entire space. In this wind tunnel experiment, several buildings were positioned in the main direction to facilitate the development of the urban boundary layer within the measurement area. Figure 4 shows the wind tunnel experiment conditions and characteristics of canyon space contaminants. The experiment was conducted in the boundary layer wind tunnel at the Institute of Industrial Science, University of Tokyo. The test section measured 1.8 m in height, 2.2 m in width, and 16.47 m in length. The anemometer used an X-shaped probe (Model 55P61) and an SFP probe (Model 55R55) anemometer (DANTEC, Skovlunde, Denmark). The data were averaged over 60 s then analyzed. In the case of the X-type anemometer, reliability issues may arise if it fails to measure the prevailing wind accurately, leading to errors in the measurements. The SFP probe, on the other hand, was utilized to measure the backdrafts occurring in the canyon space. Wind tunnel experiments were carried out for Case 1, Case 2, and Case 3, as depicted in Figure 2, featuring different building model configurations. The wind speed the inlet was measured 5.5 H upstream from the far end of the measurement area, with y = 0 (center), y = −180 mm (side), and y = 180 mm (side). HR represents the reference height (R = 900 mm), and the wind speed at the location corresponding to the reference height is the reference wind speed (uR). Measured wind speed was uR = 1.87 m/s. The RMSE analysis method was used to assess the reliability of the measured and simulated data. The formula used to calculate the root mean square error (RMSE) between measured and calculated data is shown in Equation (3).

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E} =\sqrt{\frac{1}{N}\sum _{i=1}^N{(U_i^{measure}-U_i^{calcualte})}^2}$$

(3)

where N represents the number of the measured points. $U_i^{measure}$ and $U_i^{calculate}$ represent the measured and estimated air velocity at point i.

Figure 5 shows the results of the measured air velocity and the simulated air velocity points P1, P3, and P5. We found a strong correlation between the experimental and simulated calculated values.

The RMSE analysis shows that Case 1 is highly correlated with 0.31 at point P1, 0.25 at point P3, and 0.21% at point P5. Case 2 was analyzed as 0.21 at P1, 0.23 at P3, and 0.24 at P5, and Case 3 was analyzed as 0.35 at P1, 0.25 at P3, and 0.22 at P5, indicating a high correlation. Additional information on simulation analysis can be found in the work of the authors [22].

5. CFD Analysis Results

5.1. Wind Velocity Distribution of Target Areas

Figure 6 shows the results of the average wind velocity vector in the horizontal plane under isothermal calculation conditions at the pedestrian level (heigh 0.1 H) within the target area. Figure 7 indicates a vertical cross-section of the target area plane based on the center line of the plane (CL; Figure 2). Figure 8 and Figure 9 indicate the mean vertical profile of the horizontal plane regarding the mean wind velocity U₁ and the absolute value of the mean wind velocity (Equation (3)) for isothermal and nonisothermal cases.

$$|\mathrm{U} |=\sqrt{\mathrm{U} \stackrel{2}{\underset{1}{ }}+\mathrm{U} \stackrel{2}{\underset{2}{ }}+\mathrm{U} \stackrel{2}{\underset{3}{ }}}$$

(4)

Figure 6 presents the vectors of wind velocity on a horizontal plane at the pedestrian level (height 0.1 H) in the canyon space of Cases 1–4. Figure 7 indicates a vertical cross-section of the mean wind velocity vector created based on CL (center line; Figure 2) for the results of Cases 1–4.

The wind velocity vector figures in Figure 6a and Figure 7a of Case 1 confirm a clear circulation and flow of the air current within the canyon space. Figure 6b and Figure 7b of Case 2 demonstrate that the circulation flow between the buildings in the mainstream direction splits into two sections and the sizes become smaller. This can be explained by the fact that the wind velocity between the buildings is increased by the building arrangement (Figure 6b), resulting in a stronger flow of suction between the buildings in the traverse direction. Figure 6c and Figure 7c of Case 3 show different circulation patterns before and after the high-rise buildings.

Wind Velocity U1 and │U│

Figure 8 indicates the vertical profiles of the mean values on a horizontal plane for Cases 1–4. In the section below the height of 1.0 H, Case 1 has the highest wind velocity, while Case 2 has the lowest, except near the surface. Case 3 has a higher wind velocity than Case 4. In the section above the height of 1.0 H, Case 1 has the highest wind velocity, followed by Case 2. Although this study did not indicate this tendency, it continuously appeared in the analysis domain. In Case 2, the wind velocity is inhibited in the section below a height of approximately 1.0 H due to the staggered building arrangement, and becomes lower; however, the wind velocity reduction effect in the air is found to be huge in Cases 3 and 4. In Case 3, with different building heights, the wind velocity near the ground surface is higher than in Case 1. The reason is that the wind with relatively high velocity passed over low-rise buildings and then hit the high-rise buildings, blowing them downward while simultaneously splitting to the left and right, and sweeping the wind near the ground (Case 3 has a low wind velocity between buildings; however, the wind velocity on the road in the mainstream direction was larger than Case 1. Thus, the scalar wind velocity of the entire horizontal plane is assumed to be high in Case 3 (see Figure A1 in Appendix A)). However, in the section above the height of 1.0 H, Case 3 has a lower wind velocity than Case 2, and the difference in wind velocity becomes smaller among all the cases. As for Case 4, the wind velocity becomes the lowest at a height of approximately 1.5 H or higher. This is due to the large area of high-rise buildings in Case 4, resulting in the larger resistance of the building to the air current flow, leading to lower wind velocity. As a result, from the perspective of wind ventilation at the pedestrian level within a city, it can be assumed that a staggered arrangement of medium-rise buildings or a normal grid arrangement of high-rise buildings is disadvantageous compared to a normal grid arrangement of medium-rise buildings and different building heights if the same group of buildings is a continuous wind field. Figure 9 indicates the wind velocity of Case 1 and Cases 5–7, considering atmospheric stability. There is no significant difference in the section below the height of 1.0 H per case; however, in the section below the height of approximately 0.4 H, Case 7 (unstable) has a slightly higher wind velocity than Case 1, whereas Case 6 (weakly unstable) has a slightly lower wind velocity.

In the section above the height of 1.0 H, Case 1 has a higher wind velocity than Cases 6 and 7, and Case 5 (stable) has the highest wind velocity. This is attributable to the increase in turbulence energy driven by the buoyancy effect in the unstable case (discussed later), and the subsequent increase in turbulence viscosity coefficients. Under the atmosphere stability case, it is assumed that the production of turbulence energy is restrained, and the effect of turbulence viscosity becomes smaller; consequently, the momentum of the average flow is maintained.

5.2. Distribution of Turbulence Energy k

The vertical profile of the average turbulence energy k on a horizontal plane of the isothermal calculations (Cases 1–4) in Figure 10a presents that Cases 1–3 showed slight differences in the section below the height of approximately 0.5 H, and Case 4 had the smallest value. In the section above the height of around 0.5 H, Case 3 had the largest value. Case 2 had a smaller value than Case 1 in the section below the height of 0.5 H, yet a larger value than Case 1 above the height. The results of the calculation, considering atmospheric stability (Case 1, Cases 5–7), in Figure 10b indicate that Cases 1, 5, and 6 had almost identical values, and Case 7 had the larger value in the section below the height of 1.0 H. Cases 6 and 7 had larger values in the section above the height of 1.0 H. Furthermore, as the height increases, the production term Pk (Figure 11a) of k, due to the mean flow, approaches “zero” with a wind field similar to a free shear flow. In the case of atmospheric instability, since there is the production term G_k (Figure 11b) of turbulence energy due to buoyancy, the turbulence energy k of Case 7 became larger. This explains why the coefficient of virtual viscosity ν_t in Figure 12 is larger on the unstable side in Cases 6 and 7. As for atmospheric stability, it is assumed that the turbulence energy k becomes smaller due to the negative G_k, and, consequently, the coefficient of virtual viscosity ν_t becomes smaller. In Section 5.1, atmospheric stability was considered ineffective in wind ventilation at a pedestrian level; however, considering the characteristics of turbulence energy, atmospheric instability is considered to impact the diffusion of pollutants into the air.

5.3. Mean Temperature/Concentration Profiles on a Horizontal Plane

5.3.1. Mean Temperature (T) Profiles on a Horizontal Plane

Figure 13 shows the vertical profile of the horizontal plane mean temperature with respect to CL for the cases considering atmospheric stability. Compared to Case 1 (neutral), Case 5 (stable) shows a positive temperature gradient from the surface to the upper atmosphere, while Case 6 (weakly unstable) and Case 7 (unstable) show a negative temperature gradient between the surface and the upper atmosphere. Case 7 shows a large gradient in the canyon space. This can be thought of as a function of the magnitude of the temperature difference between the surface and the air, depending on the atmospheric stability.

5.3.2. Vertical Cross-Section of Concentrations (C)

Figure 14 shows the contaminant concentrations for Cases 1 through 4 at the CL of the center cross-section of the target area (see Figure 2), and Figure 15 shows the contaminant concentrations for Case 1 and Cases 5 through 6. For each case, the distribution of concentrations in the sections below the height of 1.0 H or 1.5 H was smaller near the front wall facing the wind in the windward direction and was larger near the wall facing the wind in the leeward direction behind the building. This is because the circulation flow within the canyon transports fresh air upward to the windward wall, accumulates the pollutants generated within the canyon, passes near the leeward wall, and is discharged into the air. In Figure 14, as for the cases without considering atmospheric stability, in the section below the height of 1.0 H, the concentrations in the canyon space are high in the order of Cases 4, 2, 1, and 3. Case 2 has a lower wind velocity than Case 1 due to the building arrangement, with smaller turbulence energy in the section below the height of 0.5 H. Thus, it is assumed that the diffusion effect of the concentration is relatively lower. In Case 3, it is assumed that the difference in building heights within the canyon space resulted in circulations formed between the rear of the low-rise buildings and the front of the high-rise buildings, which makes it easier for the pollutants generated within the canyon space to diffuse and dilute into the air. The higher concentrations in Case 4 are attributable to the following factors—although Case 4 has the same gird arrangement as Case 1, the buildings are high and the building area facing the wind direction is large, which impedes the wind velocity. Furthermore, as shown in Section 5.2, the turbulence energy within the canyon space becomes smaller and the diffusion effect becomes relatively lower. Meanwhile, in Figure 15 for cases taking into account atmospheric stability, Case 5 (stable) has the largest concentrations, followed by Case 7 (unstable), Case 6 (slightly unstable), and Case 1 (neutral). This is the same trend as the concentration distribution within the canyon space for the atmospheric stability cases examined in the wind tunnel test by Zaki et al. [17,18]. The reason for this trend, as mentioned in Section 5.2, is that the turbulent diffusion effect is increased by the buoyancy effect during atmospheric instability, while the effect becomes lower during atmospheric stability.

5.3.3. Mean Concentration (C) Profiles on a Horizontal Plane

Figure 16 presents the vertical profile of the mean concentration (C) on a horizontal plane in the isothermal calculation. In the section below the height of 1.0 H, Case 3 shows a low concentration, whereas Case 4 shows the highest concentration. Furthermore, in the section above the height of 1.0 H, Case 3’s concentration becomes the lowest, whereas Cases 1 and 2 have no significant difference. However, the concentration of Case 4 became higher than the other cases. If the result is compared with the results of turbulence energy k in Figure 7a, Case 4 has a smaller turbulence energy k, yet a higher concentration. Meanwhile, in Case 3, the turbulence energy k became larger; however, the concentration became lower. As mentioned earlier, the scale of turbulence energy k has a huge impact on concentration diffusion. Such findings are contradictory when compared to the results of wind velocity (the concentration is low even though the wind velocity in the air becomes lower (Figure 8)). If a constant value is given to the pressure gradient at the inflow–outflow boundary, and the magnitude of this pressure gradient is set to the same value for all cases as in this study, Case 3’s value becomes the smallest in terms of the average wind velocity in the air due to the higher building drag.

However, the distribution of mean concentrations within households became smaller in Case 3, even with a decrease in the mean wind velocity in the air. In the nonisothermal calculation (Figure 17), the concentration of Case 5 (stable) became higher than Case 1 (neutral), and Cases 6 (weakly unstable) and 7 (unstable) became lower than Case 1. Hence, there is a relationship between the fluctuation of the concentration and the magnitude of the turbulence energy k due to atmospheric stability.

5.4. Comparison and Evaluation of Ventilation Efficiency in the Target Area

In this section, the ventilation efficiency of each case is examined based on the interface-based ventilation volume per unit surface area ((m³/s)/m²), which is exchanged between the top interface of the target area and the air, and the practical ventilation volume per unit surface area PFR ((m³/s)/m²). Here, the target area is set as the canyon space up to the height of low-rise buildings (0.5 H). Figure 18 shows the interface-based ventilation volume per unit surface area and PFR per unit surface area for the cases with and without considering atmospheric stability. It indicates that the trends in interface-based ventilation volume and PFR are similar.

Overall, we can see that the trends of the perimeter reference ventilation and PFR are very similar, but the perimeter reference ventilation per unit land area is slightly larger than the PFR per unit land area. This is because the average concentration of interface in the air above the canyon space is smaller than the average concentration in the target space within the canyon (Equations (1) and (2)). In terms of the interface-based ventilation volumes per unit surface area in the isothermal calculation, Case 2 is slightly smaller than Case 1, while Case 3 is the largest, being about 120% that of Case 1.

Additionally, Case 4 shows the smallest value; approximately 70% that of Case 1. As for PFR per unit surface area, Case 2 became slightly smaller than Case 1. However, Cases 3 and 4 showed the same results as the outcomes regarding the interface-based ventilation volume—Case 3 showed the largest value, being approximately 130% of Case 1, and Case 4 became about 70% of Case 1. Based on these results, it can be assumed that Case 3, with uneven building heights, is the canyon pattern that is effective in improving ventilation efficiency, and Case 4, with high-rise buildings in a row, has low ventilation capacity. In other words, from the perspective of ventilation efficiency, Case 3 is the best in terms of urban canyon space.

In the case of buildings with uneven heights, the diffusion effect in the vertical direction is improved; however, horizontal advection is suppressed by the resistance of buildings, lowering the diffusion efficiency in the target area. However, this result is only applicable when the pollutant sources are localized. Regarding the households with similar pollution sources, which is the target case in this study, the horizontal advection has little effect on the introduction of fresh air, and ventilation is activated only by diffusion in the vertical direction. Thus, the ventilation efficiency of Case 3 is improved by the variation in building height, which enhances the diffusion effect in the vertical direction. The comparison of interface-based ventilation per unit surface area and PFR per unit surface area for Case 1 (neutral) regarding the nonisothermal calculation results is as follows. First, the interface-based ventilation volume per unit surface area of Case 5 (stable) is around 74% of Case 1. The volumes of Cases 6 (weakly unstable) and 7 (unstable) are around 125% and 160%, respectively, of Case 1. PFR per unit surface area has a slightly smaller value than the interface-based ventilation volume per unit surface area, with almost the same trend. Based on these results, it can be confirmed that the ventilation volume increases in the order of stable, neutral, and unstable atmosphere. This is because the buoyancy effect by atmospheric stability has a strong influence on the mixing between the upper and lower layers due to turbulent diffusion, which promotes the diffusion of the pollutants.

The relationship between the interface-based ventilation volume and Rb in the atmospheric stability case can be found in Figure 19. It is possible to confirm the simple correlation that the more unstable the atmosphere, the greater the ventilation volume and the higher the ventilation efficiency, and vice versa.

6. Conclusions

This study assumed a continuous urban street canyon space and aimed to create a space with the same floor area ratio and building coverage ratio as possible. We created several scenarios by adjusting building arrangements and heights within the space, conducted a CFD analysis, and assessed wind ventilation and ventilation efficiency for each scenario. As a result, this study reached the following conclusions.

• In the calculation without considering atmospheric stability, the mean wind velocity on a horizontal plane within the street canyon space had high values for the grid-pattern arrangement of mid-rise buildings; however, near the ground (the section below the height of around 0.5 H), the case with buildings of varying heights showed the highest value. Additionally, when building heights were set to be high even in the same grid-pattern arrangement, the wind velocity decreased within the canyon space. The wind velocity above the canyon space significantly decreased in the presence of buildings with uneven heights and high-rise buildings.
• In the calculation considering atmospheric stability, cases showed little difference in the mean wind velocity on a horizontal plane in the section below the height of 1.0 H. This indicates that, from the perspective of wind ventilation at the pedestrian level, atmospheric stability has little effect on ventilation improvement.
• In the calculation without considering atmospheric stability, pollutant concentrations were higher in the staggered arrangement of middle-rise buildings (1.0 H) and in the grid-pattern arrangement of high-rise buildings (1.5 H) than in the grid-pattern arrangement of middle-rise buildings (1.0 H). The case with uneven building heights (0.5 H and 1.5 H) showed the lowest concentration. This is due to the higher wind turbulence caused by uneven building heights, which promotes the diffusion of pollutants upwards. However, it is assumed that high-rise buildings (1.5 H), with uniform heights and grid-pattern arrangements, have higher pollutant concentrations than middle-rise buildings (0.5 H). This is because the turbulence energy is smaller in the section below the height of the buildings, leading to less diffusion into the air.
• In calculations involving atmospheric stability, since pollutant concentrations are closely linked to turbulence energy, concentrations tend to be lower in unstable conditions with high turbulence energy and higher in stable conditions. This indicates that atmospheric stability does not have a significant effect within the canyon space in terms of wind ventilation; however, it does impact the diffusion of pollutant concentrations.
• In the calculation without considering atmospheric stability, interface-based ventilation volumes per unit surface area based on interfaces and PFR per unit surface area were found to be the most effective for buildings with irregular heights and the least effective for high-rise buildings in a grid-pattern arrangement.
• In the calculation considering atmospheric stability, the ventilation volumes per unit surface area and PFR per unit surface area were smallest in the case of atmospheric stability and largest in the case of atmospheric instability.

Under conditions with the same floor area ratio or building coverage ratio as a street canyon space, which exists continuously and infinitely, with distinct surface boundary layers, planning buildings with uneven heights and grid-pattern arrangements can effectively enhance wind ventilation and pollutant dispersion efficiency at the pedestrian level within the street canyon space. Furthermore, since the impact of atmospheric stability on ventilation efficiency within urban street canyon spaces has been recognized, it is essential to investigate the ventilation design of urban areas taking this factor into account.