# Influence of Various Urban Morphological Parameters on Urban Canopy Ventilation: A Parametric Numerical Study

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## Abstract

**:**

_{d}) is a crucial aerodynamic parameter in this approach. This study examines how C

_{d}varies with urban design parameters such as plan area density (λ

_{p}), average building height (H), frontal area density (λ

_{f}), floor aspect ratio (AR), and sky view factor (SVF). Employing extensive numerical simulations conducted under neutral atmospheric conditions, we explore ranges of λ

_{p}= 0.04–0.07 and λ

_{f}= 0.1–1.2. The numerical model has been validated against existing wind tunnel data. The results show that C

_{d}is insensitive to the model scale and background wind speed. We discover a nonlinear relationship between C

_{d}and the parameters λ

_{p}, λ

_{f}, and SVF. For urban layouts with cubic-shaped buildings, C

_{d}peaks at different λ

_{p}within the range of 0.2~0.8. When λ

_{p}and H are constant, C

_{d}has a linear relationship with AR and λ

_{f}. It is recommended to use λ

_{p}, SVF, and AR as predictors for C

_{d}across various urban configurations.

## 1. Introduction

_{d}and the frontal area density λ

_{f}(hereafter referred to as the C

_{d}·λ

_{f}method). C

_{d}can be calculated using the total force acting on the surface and the mean velocity in a control volume. Another method is based on the classical porous media approach, where the source terms consist of the Forchheimer and Darcy terms, which are determined by porosity (the total volume of air in the given volume) and permeability [16]. In both methods, the drag force coefficient C

_{d}is a key parameter describing the influence of obstacles on the flow in the canopy.

_{d}, such as the plan area density (λ

_{p}, the percentage of building floor area to the plan area), the frontal area density (λ

_{f}, the percentage of the frontal area of buildings to the plan area) [17,18,19,20], the average height of the buildings [21,22,23,24], etc. Current knowledge of the relationships between urban morphology and C

_{d}is primarily developed from idealized urban canopy models, in which buildings are simplified as arrays of cubes. These studies have revealed that how spatial parameters affect C

_{d}varies with array configurations [25,26,27,28]. For instance, Kanda et al. [25] investigated cube arrays with a plan area density of 0–40% using large eddy simulation (LES) and found that C

_{d}was sensitive to λ

_{p}for staggered arrays but not for square arrays. Hagishima et al. [26] expanded on this by conducting wind tunnel experiments on 63 block arrays with different layouts, wind directions, block heights, and plan area densities. They found that C

_{d}was more sensitive to λ

_{p}and λ

_{f}for staggered arrays than for square arrays. Ahmad Zaki et al. [27] also used wind tunnel tests to introduce variability in building orientation and height for building blocks and found that for arrays with a plan area density of 7.7~48.1%, vertical random arrays showed a consistent increase in C

_{d}with λ

_{f}. However, for horizontally random arrays, the estimated C

_{d}peaked at a certain point. Li et al. [24] further investigated the effects of building shape on C

_{d}peaked by wind tunnel experiments on non-uniform building arrays with different shapes (rectangular and H-shaped), wind directions, plan area densities, and frontal area indices. They found that C

_{d}changed significantly when the building floor shape changed from a rectangle to an H shape.

_{d}and spatial parameters. For example, the relationship between C

_{d}and λ

_{p}or λ

_{f}is not simply linear. C

_{d}typically increases λ

_{p}until reaching a plateau at about λ

_{p}= 0.3 [26,28]. Santiago and Martilli [28] have developed a more complex empirical equation, which relates C

_{d}to λ

_{p}(i.e., C

_{d}= 3.32 λ

_{p}when λ

_{p}≤ 0.29; and C

_{d}= 1.85 when λ

_{p}> 0.29). This relationship has been used in later studies [29] to perform mesoscale simulations of local wind circulation. However, these correlations have been obtained from small samples, and the relationships between C

_{d}and different spatial parameters (e.g., λ

_{p}and λ

_{f}) are often studied separately. Moreover, it is also necessary to extend the range of λ

_{p}and λ

_{f}values to cover real cities.

_{d}of idealized urban canopies behaves in a variety of morphological conditions. A parametric analysis is employed focusing on morphological parameters including SVF, λ

_{p}, and λ

_{f}. We conduct an extensive series of three-dimensional Reynolds-averaged Navier–Stokes (RANS) numerical simulations on both cubic and rectangular block arrays with λ

_{p}= 0.04~0.7 and λ

_{f}= 0.1~1.2. The findings have the potential to refine the application of the drag force approach in real-world wind environment assessments.

## 2. Methodology

#### 2.1. RANS Canopy Model with Drag Force Approach

_{p}is the total floor area, A

_{f}is the frontal area of all buildings, H is the average height of the blocks, B is the width of block floor facing the wind, L is the length of block floor along the wind direction, and W is the street width. A

_{B}is the area of each floor, i.e., A

_{B}= B × L. The plan area density λ

_{p}can be calculated using Equation (1):

_{f}can be calculated with the following equation:

_{i}, i.e., projected area normal to the ith direction per unit volume of the control volume can be calculated with the following equation:

_{i}in the ith direction can be calculated using Equation (5) [12,14]:

_{i}is the velocity component in the ith direction. C

_{d}is the drag force coefficient. A

_{i}is not dimensionless, and its value changes with the scale of the model: the models with smaller dimensions have larger A

_{i}. In contrast, for studies using the distributed drag force approach, A

_{i}often refers to the total projected surface area of all buildings facing the wind within the control volume [41]. In this study, the definition of A

_{i}follows the latter definition. The definitions of λ

_{f}vary across studies with different grid sizes. For example, in [18,19], the total projected frontal areas of the first-row buildings within a 100 m by 100 m area have been considered as λ

_{f}.

_{d}if it is required. S

_{k}and S

_{ε}are source terms added to RANS k-ε equations. They represent the production and destruction of turbulence resulting from building obstruction.

_{f}is the total volumetric frontal area of all the blocks within the control volume. Β

_{p}is the fraction of mean airflow kinetic energy lost by drag that is converted into turbulent kinetic energy. Β

_{d}is the dimensionless coefficient for the short-circulating turbulence cascade [42]. C

_{ε}

_{4}and C

_{ε}

_{5}are dimensionless coefficients. In this model, the drag terms play a similar role to the Forchheimer–Darcy terms (see [16] for detailed information), which also represent the turbulent kinetic energy loss due to form drag. The coefficient group (β

_{p}, β

_{d}, C

_{ε}

_{4}, C

_{ε}

_{5}) for the sources in the urban canopy model is still a controversial topic in the published literature. Available values for the coefficient group can be as follows: (β

_{p}, β

_{d}, C

_{ε}

_{4}, C

_{ε}

_{5}) = [(1, 4, 1.5, 1.5), (1, 4, 1.5, 0.6), (1, 5.1, 0.9, 0.9)] [43] for the researchers who are interested in the four coefficients. However, we will not discuss these four coefficients in this paper since this work focuses on how to calculate C

_{d}and how C

_{d}varies with the influence of key factors.

_{d}is obtained at different heights by dividing the whole control volume into various layers of thin slabs [28,44,45]. In this paper, C

_{d}refers to the bulk drag coefficient of the control volume obtained with total drag force and mean flow velocity and can be calculated with Equation (8), where F

_{i}is the total drag force exerted on the building surfaces in the ith direction, $\overline{v}$ is the average velocity magnitude of the bulk control volume on the ith direction, and A

_{i}is the frontal area per unit volume of buildings projecting to the ith direction.

_{d}is traditionally defined in the literature, particularly in experimental studies, as the ratio of the total surface shear stress τ

_{0}to the kinetic energy of the fluid, which is related to the free stream wind velocity U

_{ref}. This is represented mathematically as C

_{d}= τ

_{0}/0.5ρ·U

_{ref}[7,26], where ρ is the fluid density. However, the specific definition of C

_{d}can vary depending on the aims of each study. In our study, we aim to understand how C

_{d}varies in a way that can be applied to the drag force approach in macroscopic CFD simulations; the mean streamwise velocity is therefore used to calculate C

_{d}.

#### 2.2. Idealized Building Array Configurations

_{d}. Two sets of spatial configurations have been investigated and the details are listed in Table 1 and Table 2. The geometric dimensions follow the illustrations in Figure 1.

_{p}, frontal area density λ

_{f}, and sky view factor SVF on C

_{d}. The building floor is considered to be square (B = L). The average building height (H) is in the range of 5–125 m to ensure that λ

_{f}is in the range of 0.05–1.21. The street width is assumed to be fixed at 20 m or 30 m. The largest λ

_{p}is limited to no more than 0.7, allowing for a minimum green coverage ratio (GCR) of 30%.

_{d}to changing floor aspect ratio AR = B/L. This is necessary because real urban environments often feature buildings with rectangular floors. In this case, λ

_{f}can be changed due to the stretch of the projected frontal plane in both the vertical and the horizontal direction. To reduce sample size and simulation time, 7 combinations of λ

_{p}and building heights are designed.

#### 2.3. Numerical Settings

_{H}is 3.0 m/s, ${u}_{\ast}$ = 0.24 m/s, k

_{v}is von Karman’s constant, and the value is 0.41 in this work.

^{−4}for continuity, momentum, and turbulent equations. The geometry of the computational domain is extended to 8H in height, 8H in the windward direction, and 20H in the leeward direction.

#### 2.4. Validation Study

_{p}= 0.25. There are 7 rows of buildings, and the dimension of each cubic block is H = W = B = 0.15 m. The computational domain is 8H high in the vertical direction (z), 6.6H long in the streamwise direction (x), and 1H wide in the lateral direction (y) in the 3D model. The vertical profiles of streamwise velocity obtained from numerical simulations at the midpoints of 4 canyons (Figure 2b) on the leeward side of the 1st, 3rd, 6th, and 7th obstacles are compared to wind tunnel experiment results. The computation employs a structured grid, and to test the sensitivity of the numerical results to mesh size, we have compared 2 mesh sizes: a fine grid contains 962,444 cells (total grid numbers in x-, y-, and z-directions are 449, 28, and 81, respectively), while a coarse grid contains 684,860 cells (total grid numbers in x-, y-, and z-directions are 446, 22, and 73, respectively).

^{2}). The definitions of RMSE and R

^{2}are shown as Equations (12) and (13), where n is the number of data points; e

_{i}= S

_{i}− O

_{i}; and S

_{i}and O

_{i}are simulated and observed values. The results show that the streamwise velocity (U) is nearly consistent across both grid sizes, indicating low grid sensitivity for the two sets of grids tested. However, some discrepancies occur in the wake region (C7) and just above the roof level. Despite these minor variations, the model well estimates velocities below the rooftop and is suitable for our parametric study.

#### 2.5. Effect of Model Scale and Background Wind Condition

_{d}) varies with the model scale is the precondition of utilizing the drag force approach in wind assessment. Existing parameterization studies on C

_{d}for building arrays tend to use reduced scale models in scales of centimeters and millimeters in wind tunnel and numerical studies. This study examines C

_{d}across different scales (centimeters, decimeters, and meters) for three urban canopy types: low-rise low-density (H = 10 m, λ

_{p}= 0.25), mid-rise high-density (H = 28 m, λ

_{p}= 0.44), and high-rise high-density (H = 63 m, λ

_{p}= 0.44). Figure 4a shows the C

_{d}values for these scenarios, demonstrating that the scale of the model does not significantly affect C

_{d}when morphological parameters are constant. This finding suggests that models with different reduced scales or full scales can use the same C

_{d}value without introducing substantial errors. Subsequent sections of this paper will discuss parametric analyses conducted using full-scale numerical models.

_{d}has also been compared across varying background wind speeds (1–5 m/s at 15 m height), as depicted in Figure 4b–d. The results show that the changes in C

_{d}across different background wind speeds are small for cases with H = 10 m, λ

_{p}= 0.25 and H = 63 m, λ

_{p}= 0.44. For the mid-rise, high-density case (H = 28 m, λ

_{p}= 0.44), where the value of C

_{d}is comparably higher than the other two cases, there is a marginal increase in C

_{d}with higher wind velocities, though the overall variation remains below 0.3. Therefore, we assume that C

_{d}is insensitive to background wind velocity magnitude, and the values of C

_{d}can thus be conveniently applied in practical wind assessment. On the other hand, though with the same λ

_{p}, the value of C

_{d}for the mid-rise canopy (H = 28 m, λ

_{p}= 0.44) is almost double that of the high-rise canopy (H = 63 m, λ

_{p}= 0.44), indicating that the momentum loss of wind speed per unit volume of the mid-rise dense canopy is larger. This contradicts the intuition that a high-rise cluster would result in greater momentum loss of wind.

## 3. Results and Discussion

#### 3.1. Influence of Urban Morphology on Urban Ventilation in Rectangular Building Blocks

#### 3.1.1. Influence of Urban Morphology on Surface Drag Force and Streamwise Velocity

_{d}, a key non-dimensional parameter that influences the total surface shear stress and reference flow speed in the urban canopy, as described in the previous section. Figure 5a shows a positive linear relationship between the total drag per unit plan area and the frontal area density (λ

_{f}), with a consistent rate of increase across different plan area densities (λ

_{p}). This is in line with previous studies that reported an increase in C

_{d}with the increase in λ

_{f}[24,26]. However, it may appear counterintuitive that canopies with λ

_{p}≤ 0.35 experience a higher total drag per unit plan area than those with increased λ

_{p}.

_{f}and λ

_{p}. The results reveal a V-shaped curve for the relationship between streamwise wind velocity and λ

_{f}. The lowest streamwise wind velocity appears at an approximate λ

_{f}of 0.3–0.4, being consistent across all the examined λ

_{p}ranges. Furthermore, Figure 6 shows the spatial mean of the intra-canopy streamwise velocity (denoted as <u

_{z}>) at different heights for different λ

_{p}and building heights. The <u

_{z}> at each height is obtained by averaging streamwise velocity at all the air cells in the control volume at the same height. The <u

_{z}> value consistently rises with height until it reaches a threshold for most canopies. However, <u

_{z}> in some canopies with higher heights (H = 75 m, 83 m, 100 m) and smaller λ

_{p}(λ

_{p}= 0.16, 0.35) has a distinctive S-shaped curve, which has two inflection points.

_{f}than to λ

_{p}. Though the drag force per unit area linearly increases with λ

_{f}for any given λ

_{p}, this does not imply a direct negative impact on ventilation performance. From the point of view of the city scale, the intra-canopy wind velocity directly reflects the average ventilation performance of one district, while the total drag force denotes the momentum loss of approaching wind at this control volume and directly affects its leeward control volume. Therefore, a medium λ

_{f}(i.e., λ

_{f}= 0.4 in our study) results in lower drag force, yet it can also lead to reduced wind velocity and poorer ventilation compared to a higher λ

_{f}. Conversely, a high λ

_{f}could cause greater momentum loss and subsequently degrade ventilation in downwind areas. It is the combined effect of both the drag force and the wind velocity in all control volumes of an urban canopy that controls the overall ventilation performance. In other words, the drag force coefficient C

_{d}that developed from both drag force and intra-canopy velocity can be a better choice to denote ventilation performance.

#### 3.1.2. Influence of Urban Morphology on Drag Force Coefficient C_{d}

_{p}= λ

_{f}and B = L = H, i.e., where the building block is cubic with equal dimensions for breadth (B), length (L), and height (H) and where the plan area index (λ

_{p}) equals the frontal area density (λ

_{f}) [7,28].

_{d}is influenced by λ

_{p}, λ

_{f}, and SVF. C

_{d}initially increases with λ

_{p}before reaching a peak at approximately λ

_{p}= 0.35, then undergoes a gradual decline, except when λ

_{p}= 0.65. Notably, the decrease in C

_{d}is more gradual compared to its increase. For a small λ

_{p}(λ

_{p}= 0.16), changes in C

_{d}are minimal. However, for higher λ

_{p}, the obstacles within the control volume increase with the increasing λ

_{p}, and the momentum loss of wind increases. Owing to the wake interference flow or skimming flow regime, the obstruction of downstream buildings is weakened because of sheltering. This suggests a transition in flow characteristics within the canopy—from isolated flow with lower λ

_{p}to wake interference or skimming flow with higher λ

_{p}, where downstream building obstruction is reduced due to sheltering effects [47,48]. Our findings are closely aligned with those of Santiago et al. [28], who performed a parametric analysis on the variation in C

_{d}using a uniform staggered array of cubes (where λ

_{p}= λ

_{f}) and derived an empirical equation (Equation (14)). The trend of C

_{d}for λ

_{f}values below 0.44 reported by Santiago et al. [28] is similar to our results. However, an intriguing behavior is noted where C

_{d}noticeably decreases once λ

_{f}surpasses 0.44.

_{d}·λ

_{f}/H with λ

_{f}; the trend is similar to that of C

_{d}. The maximum value of C

_{d}·λ

_{f}/H appears at approximately λ

_{f}= 0.25–0.4. Similar to C

_{d}, the physical meaning of C

_{d}·λ

_{f}/H is also clear: it represents the obstruction per unit volume of the urban canopy that induces momentum loss in the approaching wind. C

_{d}·λ

_{f}(Figure 7c) represents the obstruction per unit plan area of the urban canopy acting on the approaching wind, and it increases monotonously with the increase in λ

_{p}. The trend is different from what is revealed for C

_{d}and C

_{d}·λ

_{f}/H. For lower λ

_{p}(0–0.51), C

_{d}·λ

_{f}peaks at where λ

_{f}is around 0.35, while for higher λ

_{p}(0.58–0.7), C

_{d}·λ

_{f}peaks at where λ

_{f}is around 0.8.

_{d}, C

_{d}·λ

_{f}/H, and C

_{d}·λ (Figure 7d–f) shares both similarities and differences with the effect of λ

_{f}. Across all cases in this study, we found that C

_{d}is more likely to reach higher values when SVF is between 0.2 and 0.3, not at its lowest when the building clusters show the strongest sheltering effect. This observation diverges from the intuitive expectation that the maximum drag coefficient would coincide with the minimum openness. Particularly, in a densely populated urban area with λ

_{p}of over 0.65, the peak value of C

_{d}and C

_{d}·λ

_{f}/H is observed when SVF is approximately 0.1. Moreover, the relationship between SVF and C

_{d}across varying λ

_{p}values demonstrates a non-linear pattern: as SVF increases, C

_{d}initially rises and then decreases. This trend suggests an SVF range where the drag coefficient is maximized, beyond which further increases in SVF lead to reductions in C

_{d}. Furthermore, the underlying dynamics between SVF and λ

_{f}(Figure 8) can help to understand this relationship. A relatively regular pattern is observed where an increase in λ

_{f}leads to a decrease in SVF. This inverse relationship between SVF and λ

_{f}makes the effect of SVF on parameters C

_{d}, C

_{d}·λ

_{f}/H, and C

_{d}·λ simpler to explain: in general, the smaller the SVF, the larger the parameters related to resistance.

_{d}·λ

_{f}/H or C

_{d}·λ

_{f}as the indicator to describe the impact of turbulence on urban wind optimization depends on the optimization methodology employed. For example, for a GIS-based least-cost-path method (similar to that in [49]) that divides the city into a grid of patches, C

_{d}·λ

_{f}could be a more acceptable indicator since it directly implies the total momentum loss of wind on each grid. If only the lower level of the canopy (below the roof of mid-rise building clusters) is the optimized target, C

_{d}·λ

_{f}/H could also be a favorable indicator. Though current evidence is still insufficient to determine which one of the two indicators is superior, both of them are promising alternatives for the commonly used parameter λ

_{f}.

_{d}, C

_{d}·λ

_{f}/H, and C

_{d}·λ

_{f}with 2D contour graphs to further reveal the response of these three indicators under the combined effect of λ

_{p}and λ

_{f}. It can be seen that a local maximum of C

_{d}and C

_{d}·λ

_{f}/H appears near (λ

_{p}, λ

_{f}) = (0.3~0.5, 0.4). A local maximum of C

_{d}·λ

_{f}appears near (λ

_{p}, λ

_{f}) = (0.6, 0.4~0.8). The trend of C

_{d}in our results is almost identical to that of Santiago et al. [28] when λ

_{p}is smaller than 0.44. Interestingly, C

_{d}obviously decreases when λ

_{p}exceeds 0.44. Urban buildings are influenced by their nearest surroundings, but lacking a detailed representation of the area is a huge challenge for accurate ventilation predictions. Figure 9d–f demonstrates how the combination of λ

_{p}and SVF influences these resistance-related parameters (C

_{d}, C

_{d}·λ

_{f}/H, and C

_{d}·λ

_{f}) through interpolation results. Unlike the effect of λ

_{f}, these resistance parameters show an overall decreasing trend with the increase in SVF. The contour plots of C

_{d}in Figure 9 could be used in macroscopic or drag force approach-based numerical simulations that can reduce mesh number and simplify the physical model (refer to [11,15]).

#### 3.2. Effect of Building Floor AR (Aspect Ratio) on Drag Force Coefficient C_{d}

_{f}= λ

_{p}, where λ

_{f}increases with rising building height. However, in real urban areas, λ

_{f}also changes with the aspect ratio (AR) of the building floor. This section investigates the variation in C

_{d}with changing building floor AR. This group of cases is designed with fixed variables (i.e., canopy height H, building plan area density λ

_{p}, and street width W) listed in Table 2. Figure 10 illustrates that C

_{d}increases linearly with AR, and the slope of C

_{d}becomes the largest in canopies with larger λ

_{p}and larger H (i.e., λ

_{p}= 0.44, H = 50 m; and λ

_{p}= 0.58, H = 40 m).

_{d}. Despite having less research interests in GIS-aided urban ventilation studies compared to λ

_{p}and λ

_{f}, the significance of building floor AR requires more attention.

_{f}may increase due to taller buildings or larger building floor AR in urban planning. For a fixed H/W, a linear increase in C

_{d}with rising λ

_{f}is observed when it is related to floor length. However, C

_{d}initially increases and then decreases with increasing λ

_{f}for taller buildings. Therefore, considering the building floor AR reveals that neither λ

_{f}nor λ

_{p}can fully capture the variations in C

_{d}in isolation. As shown in Figure 10, the sky view factor SVF changes little with building floor AR but is influenced by λ

_{p}and H/W distinctly. This recommends a two-step approach to estimating C

_{d}, starting with λ

_{p}and SVF for a rough estimate, then refining it with the floor AR for better precision. Based on the above analysis, it is highly recommended to use three parameters (i.e., λ

_{p}, SVF, and floor AR) to estimate the drag force coefficient C

_{d}for a given urban area. In addition, using λ

_{p}, λ

_{f}, and floor AR for C

_{d}estimation is reasonable too. Although the logic between λ

_{f}and C

_{d}still needs comprehensive exploration, it is possible to develop relationships and is easier to obtain frontal area density for practical design activities with the GIS technique.

#### 3.3. Limitations and Future Work

_{p}), average building height (H), frontal area density (λ

_{f}), floor aspect ratio (AR), and sky view factor (SVF) on the drag force coefficient (C

_{d}) using numerical simulations under neutral atmospheric conditions. Our research aimed to provide insights into how these parameters influence urban ventilation, leveraging a distributed drag force approach to model buildings as porous volumes. This approach simplifies the complex urban canopy, making it feasible to simulate urban-scale airflow with practical computational demands. The numerical model was validated against existing wind tunnel data, ensuring the reliability of our findings. However, the applicability of the model can be questionable when the airflow is not fully developed.

_{d}, such as building orientation, variability in building height, and the presence of vegetation. However, introducing these parameters as variables would have significantly increased the complexity of the model and the computational demand. Therefore, the question of whether it is appropriate to take urban surfaces as regular geometry is still open, and the effect of spatial inhomogeneity can be a future research direction. Moreover, different validation studies may be required for studies involving these parameters. Future studies can add more parameters, including those mentioned above, to provide a more comprehensive understanding of urban airflow dynamics.

_{d}using either numerical simulations or scaled outdoor measurements [50,51,52,53] that are exposed to varying weather conditions. An observation campaign in the real city is also planned in future work.

## 4. Conclusions

_{p}) and the frontal area density (λ

_{f}), which represent urban density and roughness, respectively. Additionally, the sky view factor (SVF) is calculated for each layout. Three-dimensional RANS simulations with varying λ

_{p}and λ

_{f}were conducted with building blocks explicitly resolved inside the canopy model. The numerical model has been validated against wind tunnel results from the published literature. We compute the drag force coefficient C

_{d}(an aerodynamic parameter derived from the total drag and average wind speed) within the urban canopy in these simulations. This coefficient C

_{d}can simplify urban airflow modeling by implicitly considering building surfaces, thus reducing computational demands.

_{p}, C

_{d}increases linearly with rising λ

_{f}, with a consistent rate across different λ

_{p}values. Conversely, the average wind speed within the canopy firstly decreases and then increases with increasing λ

_{f}, and the minimum appears at around λ

_{f}= 0.3–0.4. Effective city-scale ventilation depends on the combined impact of these parameters. Since C

_{d}incorporates both drag and intra-canopy wind speed, it can be a promising indicator for urban ventilation assessment.

_{d}is obtained. The response to the combined effects of λ

_{p}, λ

_{f}

_{,}and SVF is illustrated with a 2D contour graph. A local maximum of C

_{d}and C

_{d}·λ

_{f}/H will appear when (λ

_{p}, λ

_{f}) = (0.3~0.5, 0.4), and a local maximum of C

_{d}·λ

_{f}/H would appear when (λ

_{p}, λ

_{f}) = (0.6, 0.4~0.8). The variation in C

_{d}with model scale and background wind velocity is insignificant. With the condition of λ

_{p}= λ

_{f}, the estimated C

_{d}peaks at a medium value of λ

_{p}. The changing of C

_{d}with λ

_{f}behaves in different patterns when λ

_{p}varies. When λ

_{p}is small, C

_{d}exhibits little or no sensitivity to changes in λ

_{f}. However, C

_{d}typically peaks around λ

_{f}= 0.3–0.4, except when λ

_{f}is 0.65. Moreover, for a given building height and λ

_{p}, there is a positive linear relationship between C

_{d}and λ

_{f}. It is strongly recommended to use λ

_{p}, SVF, and the building floor AR as key indicators for characterizing the drag force effect of urban areas.

_{d})-related parameters enables assessing of urban scale ventilation with 3D numerical models. Employing C

_{d}-related parameters, as opposed to traditional length scale and displacement height metrics, can improve the assessment of urban-scale ventilation through 3D numerical models with a drag force approach. Utilizing a drag force approach within mesh-reduced numerical methods shows considerable promise for practical evaluations of urban ventilation and air quality. Moreover, the approach and methodology set up in this work have significant implications for the monitoring and modeling research on urban climate, and the application of the method can be extended to the area of human exposure and public health. The application of the methodology and the findings in this work also offer scientific references for sustainable urban planning and strengthen the resilience of urban development.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Geometric dimensions of building obstacles in the control volume. (

**a**) perspective-view model sketch, (

**b**) top view of the control volume.

**Figure 2.**(

**a**) Vertical cross-section in the domain of the canopy model for RANS simulation (14 rows) and wind tunnel experiment (7 rows). (

**b**) The positions of vertical profiles of streamwise velocity in 4 canyons on the leeward side of the 1st, 3rd, 6th, and 7th obstacles. The profiles obtained at the same positions of the wind tunnel experiments are used for validation study.

**Figure 3.**Vertical profiles of streamwise velocity at 4 points from wind-tunnel data and numerical predictions. Subplots (

**a**–

**d**) are the profiles obtained at the location C1, C3, C6, C7, respectively.

**Figure 4.**(

**a**) Drag force coefficient (C

_{d}) values across different model scales, from full size to wind tunnel scale, and variations of C

_{d}under varying background wind speed (1–5 m/s at 15 m height) and building height: (

**b**) H = 10 m, (

**c**) H = 28 m, and (

**d**) H = 63 m.

**Figure 5.**(

**a**) Total drag force per unit plan area with different λ

_{p}, (

**b**) mean streamwise wind velocity per unit plan area with different λ

_{p}.

**Figure 6.**Vertical distribution of streamwise velocity in different canopies with various λ

_{p}: (

**a**) λ

_{p}= 0.16; (

**b**) λ

_{p}= 0.35; (

**c**) λ

_{p}= 0.51; (

**d**) λ

_{p}= 0.70.

**Figure 7.**(

**a**–

**c**) Variation in C

_{d}, C

_{d}·λ

_{f}/H, C

_{d}·λ

_{f}with λ

_{f}(for λ

_{p}= 0.04~0.7); (

**d**–

**f**) Variation in C

_{d}, C

_{d}·λ

_{f}/H, C

_{d}·λ

_{f}with SVF (for λ

_{p}= 0.04~0.7).

**Figure 9.**(

**a**–

**c**) Contours of C

_{d}, C

_{d}·λ

_{f}/H, and C

_{d}·λ

_{f}with varying λ

_{p}and λ

_{f}; (

**d**–

**f**) contours of C

_{d}, C

_{d}·λ

_{f}/H, and C

_{d}·λ

_{f}with varying λ

_{p}and SVF.

**Figure 10.**(

**a**–

**g**) Variation in C

_{d}with AR for cases in Table 2; (

**h**) variation in the increasing slope of C

_{d}with building height.

**Table 1.**Groups of rectangular block arrangements to test the response of C

_{d}to λ

_{p}, λ

_{f}, and SVF.

Set | λ_{p} | B = L (m) | W (m) | H (m) | λ_{f} | SVF | Set | λ_{p} | B = L (m) | W (m) | H (m) | λ_{f} | SVF |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0.04 | 5 | 20 | 5 | 0.05 | 0.70 | 6 | 0.44 | 40 | 20 | 28 | 0.31 | 0.30 |

0.04 | 5 | 20 | 10 | 0.10 | 0.70 | 0.44 | 40 | 20 | 30 | 0.33 | 0.28 | ||

0.04 | 5 | 20 | 20 | 0.20 | 0.57 | 0.44 | 40 | 20 | 40 | 0.44 | 0.22 | ||

0.04 | 5 | 20 | 30 | 0.31 | 0.49 | 0.44 | 40 | 20 | 50 | 0.56 | 0.19 | ||

2 | 0.08 | 8 | 20 | 8 | 0.08 | 0.69 | 0.44 | 40 | 20 | 63 | 0.70 | 0.15 | |

0.08 | 8 | 20 | 20 | 0.20 | 0.51 | 0.44 | 40 | 20 | 72 | 0.80 | 0.14 | ||

0.08 | 8 | 20 | 30 | 0.31 | 0.41 | 0.44 | 40 | 20 | 90 | 1.00 | 0.11 | ||

3 | 0.16 | 20 | 30 | 10 | 0.08 | 0.66 | 7 | 0.51 | 50 | 20 | 10 | 0.10 | 0.52 |

0.16 | 20 | 30 | 20 | 0.16 | 0.52 | 0.51 | 50 | 20 | 20 | 0.20 | 0.36 | ||

0.16 | 20 | 30 | 30 | 0.24 | 0.43 | 0.51 | 50 | 20 | 30 | 0.31 | 0.27 | ||

0.16 | 20 | 30 | 40 | 0.32 | 0.37 | 0.51 | 50 | 20 | 40 | 0.41 | 0.21 | ||

0.16 | 20 | 30 | 50 | 0.40 | 0.32 | 0.51 | 50 | 20 | 50 | 0.51 | 0.18 | ||

0.16 | 20 | 30 | 75 | 0.60 | 0.24 | 0.51 | 50 | 20 | 78 | 0.80 | 0.12 | ||

0.16 | 20 | 30 | 100 | 0.80 | 0.19 | 0.51 | 50 | 20 | 98 | 1.00 | 0.10 | ||

0.16 | 20 | 30 | 125 | 1.00 | 0.16 | 8 | 0.58 | 63.8 | 20 | 20 | 0.18 | 0.35 | |

4 | 0.25 | 20 | 20 | 5 | 0.06 | 0.70 | 0.58 | 63.8 | 20 | 40 | 0.36 | 0.21 | |

0.25 | 20 | 20 | 10 | 0.13 | 0.57 | 0.58 | 63.8 | 20 | 64 | 0.58 | 0.14 | ||

0.25 | 20 | 20 | 20 | 0.25 | 0.40 | 0.58 | 63.8 | 20 | 80 | 0.73 | 0.12 | ||

0.25 | 20 | 20 | 30 | 0.38 | 0.31 | 0.58 | 63.8 | 20 | 100 | 0.91 | 0.10 | ||

0.25 | 20 | 20 | 40 | 0.50 | 0.25 | 0.58 | 63.8 | 20 | 120 | 1.09 | 0.08 | ||

0.25 | 20 | 20 | 50 | 0.63 | 0.21 | 9 | 0.65 | 83.2 | 20 | 120 | 0.94 | 0.08 | |

0.25 | 20 | 20 | 64 | 0.80 | 0.17 | 0.65 | 83.2 | 20 | 100 | 0.78 | 0.10 | ||

0.25 | 20 | 20 | 80 | 1.00 | 0.14 | 0.65 | 83.2 | 20 | 83 | 0.65 | 0.11 | ||

0.25 | 20 | 20 | 96 | 1.20 | 0.12 | 0.65 | 83.2 | 20 | 60 | 0.47 | 0.15 | ||

5 | 0.35 | 29 | 20 | 10 | 0.12 | 0.54 | 0.65 | 83.2 | 20 | 40 | 0.31 | 0.21 | |

0.35 | 29 | 20 | 20 | 0.24 | 0.38 | 0.65 | 83.2 | 20 | 30 | 0.23 | 0.27 | ||

0.35 | 29 | 20 | 29 | 0.35 | 0.30 | 10 | 0.7 | 102.4 | 20 | 20 | 0.14 | 0.35 | |

0.35 | 29 | 20 | 40 | 0.48 | 0.24 | 0.7 | 102.4 | 20 | 30 | 0.21 | 0.26 | ||

0.35 | 29 | 20 | 50 | 0.60 | 0.20 | 0.7 | 102.4 | 20 | 40 | 0.27 | 0.21 | ||

0.35 | 29 | 20 | 66 | 0.80 | 0.16 | 0.7 | 102.4 | 20 | 50 | 0.34 | 0.17 | ||

0.35 | 29 | 20 | 83 | 1.00 | 0.13 | 0.7 | 102.4 | 20 | 70 | 0.48 | 0.13 | ||

0.35 | 29 | 20 | 100 | 1.21 | 0.11 | 0.7 | 102.4 | 20 | 102.4 | 0.70 | 0.09 | ||

6 | 0.44 | 40 | 20 | 10 | 0.11 | 0.52 | 0.7 | 102.4 | 20 | 120 | 0.82 | 0.08 | |

0.44 | 40 | 20 | 20 | 0.22 | 0.37 | 0.7 | 102.4 | 20 | 140 | 0.96 | 0.07 |

**Table 2.**Groups of rectangular block arrangements to test the response of C

_{d}to floor aspect ratio (for each group: B/L = 0.25, 0.5, 0.75, 1, 2, 3, 4).

Set | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

λ_{p} | 0.16 | 0.25 | 0.35 | 0.44 | 0.44 | 0.51 | 0.58 |

W (m) | 30 | 20 | 30 | 20 | 20 | 20 | 20 |

H (m) | 10 | 30 | 66 | 28 | 50 | 20 | 40 |

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**MDPI and ACS Style**

Zeng, L.; Zhang, X.; Lu, J.; Li, Y.; Hang, J.; Hua, J.; Zhao, B.; Ling, H.
Influence of Various Urban Morphological Parameters on Urban Canopy Ventilation: A Parametric Numerical Study. *Atmosphere* **2024**, *15*, 352.
https://doi.org/10.3390/atmos15030352

**AMA Style**

Zeng L, Zhang X, Lu J, Li Y, Hang J, Hua J, Zhao B, Ling H.
Influence of Various Urban Morphological Parameters on Urban Canopy Ventilation: A Parametric Numerical Study. *Atmosphere*. 2024; 15(3):352.
https://doi.org/10.3390/atmos15030352

**Chicago/Turabian Style**

Zeng, Liyue, Xuelin Zhang, Jun Lu, Yongcai Li, Jian Hang, Jiajia Hua, Bo Zhao, and Hong Ling.
2024. "Influence of Various Urban Morphological Parameters on Urban Canopy Ventilation: A Parametric Numerical Study" *Atmosphere* 15, no. 3: 352.
https://doi.org/10.3390/atmos15030352