Development of a Dispersion Model for Liquid and Gaseous Chemical Agents: Application to Four Types of Street Canyons

Abstract

This study presents a computational fluid dynamics (CFD) modeling framework to simulate two-phase (liquid and gas) chemical agent dispersion in urban canyons. The model was validated against wind tunnel experiments, meeting statistical criteria. To assess geometric impacts on flow and dispersion, the model was applied to four idealized canyon types—Cube (CB), Short (SH), Medium (MD), and Long (LN). Results revealed that increasing building length reduced the horizontal extent but enhanced the vertical extent of wake zones, weakened roof-level wind speeds, and shifted the reattachment point farther downstream. For liquid-phase sulfur mustard (HD), CB showed active canyon exchange and rapid penetration to pedestrian level. SH and MD exhibited more gradual infiltration with weaker variability due to fewer streamwise streets. LN had no streamwise street; transport was primarily driven by canyon vortices and showed slower penetration. Gaseous HD exhibited similar patterns to liquid HD but attained higher in-canyon concentrations due to differences in evaporation and dry deposition effects, indicating prolonged persistence. Overall, canyon geometry strongly influenced pollutant retention and variability. These findings suggest that the model can support chemical hazard assessment and early response planning that considers building geometry.

1. Introduction

With the acceleration of global urbanization, both population and infrastructure are becoming increasingly concentrated in cities [1]. Due to the high density and interdependence of urban infrastructure, cities are particularly vulnerable to security threats and have emerged as major targets for terrorist attacks [1,2]. As urban areas expand, urban warfare has become a prominent aspect of modern conflicts, raising serious safety concerns in densely built environments. Compared to conventional weapons, even small quantities of modern chemical and biological agents can result in mass casualties and are thus classified as weapons of mass destruction (WMD) [3]. Consequently, chemical and biological agents have been employed in both warfare and terrorist activities for decades [4,5,6]. Since their mass use during World War I, increasingly efficient and deadly chemical agents have been developed, and their use in terrorist attacks has grown significantly since the 1990s. Currently, more than 20 countries and terrorist organizations are reported to possess or seek to acquire chemical weapons [7].

Chemical agents are typically released in liquid droplet or gaseous forms and exhibit a wide range of dispersion behaviors depending on particle size [8]. These behaviors include surface deposition, airborne suspension, and re-evaporation from contaminated ground surfaces, resulting in both primary and secondary plumes. The transport and transformation of these agents involve complex microphysical processes and interactions with local microclimatic conditions, making the overall dispersion highly complex [9]. To quantify such behaviors, advanced chemical, biological, radiological, and nuclear (CBRN)dispersion modeling is essential. In the United States, models such as HPAC (Hazard Prediction and Assessment Capability) and CATS (Consequence Assessment Tool Set), developed by the Defense Threat Reduction Agency (DTRA), are widely used [10,11]. In Korea, the NBC-RAMS (Nuclear, Biological, and Chemical Reporting and Modeling Software System), developed by the Agency for Defense Development (ADD), is currently in use [12]. However, most of these models operate at coarse spatial resolutions and fail to capture urban-scale morphological details such as buildings. Moreover, very few models adequately represent phase-specific dispersion mechanisms or deposition processes.

In this context, computational fluid dynamics (CFD) models have emerged as powerful alternatives for simulating chemical agent dispersion in complex urban environments, owing to their high spatial resolution and ability to explicitly resolve detailed urban morphology [13,14,15]. Nevertheless, previous CFD studies have primarily focused on single-phase conditions, such as the transport of gaseous scalars [16,17,18]. These studies have demonstrated the potential of CFD models to capture flow and dispersion characteristics, but dispersion under two-phase (liquid and gas) conditions has rarely been considered. In contrast, this study explicitly incorporates two-phase (liquid and gas) conditions into high-resolution CFD modeling. Through this approach, the model advances beyond conventional single-phase dispersion approaches and offers a more realistic representation of chemical agent behavior in urban environments. Also, urban geometry plays a crucial role in shaping flow fields and ventilation performance [19,20,21,22], and urban street canyons—defined as narrow spaces between buildings—serve as fundamental units for analyzing such environments [23,24,25]. Street canyons generally exhibit reduced natural ventilation compared to open areas [26], and their height-to-width (H/W) and length-to-height (L/H) ratios can significantly influence the retention, circulation, and vertical escape of pollutants [27]. Therefore, understanding flow and dispersion dynamics within street canyons under different geometrical configurations is essential for accurately assessing chemical agent risks in urban warfare or terrorism scenarios.

This study proposes a CFD-based modeling framework to simulate passive scalar transport representing chemical agent dispersion under two-phase conditions (liquid and gas). In Section 2, the CFD model setup, validation procedures, and simulation configurations are presented. Section 3 analyzes the spatial distribution and retention characteristics of chemical agents under varying street canyon geometries. Section 4 summarizes the key findings and presents concluding remarks.

2. Materials and Methods

2.1. Model Description

In this study, sulfur mustard (HD) was selected as the target agent. Although the degradation of HD in various matrices, such as concrete, asphalt, and soils, has been investigated, its complete environmental fate—including evaporation, absorption, degradation, and decontamination—remains insufficiently characterized [28]. HD also exhibits a low vapor pressure [29,30] and volatilizes very slowly at ambient temperature [31]. Furthermore, this study focused on the pedestrian level within an urban canyon corresponding to typical building heights. For this reason, the contribution of gas-phase condensation was assumed to be negligible under typical atmospheric conditions.

The CFD model used in this study is the same as that of Kim and Baik [32]. This model is based on the Reynolds-averaged Navier–Stokes (RANS) equations and assumes a three-dimensional, non-rotating, non-hydrostatic, incompressible airflow system. For turbulence parameterization, the RNG k-ε turbulence closure model, based on the renormalization group (RNG) theory proposed by Yakhot et al. [33], is adopted. A staggered grid system is employed, and numerical integration is performed using the finite volume method together with the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. The Reynolds-averaged equations, the mass continuity equation, and the transport equation for passive scalars are formulated as follows.

$${\displaystyle \frac{{\partial U}_{\mathrm{i}}}{\partial t}}+U_{\mathrm{j}}{\displaystyle \frac{{\partial U}_{\mathrm{i}}}{{\partial x}_{\mathrm{j}}}}=-{\displaystyle \frac{1}{{\rho }_0}}{\displaystyle \frac{{\partial P}^{\ast }}{{\partial x}_{\mathrm{i}}}}+\mathrm{v}{\displaystyle \frac{{\partial }^2{U}_{\mathrm{i}}}{{\partial x}_j{\partial x}_{\mathrm{j}}}}-{\displaystyle \frac{\partial }{{\partial x}_{\mathrm{j}}}}\left(\overline{u_{\mathrm{i}}{u}_{\mathrm{j}}}\right),$$

(1)

$${\displaystyle \frac{{\partial U}_j}{\partial t}}=0,$$

(2)

$${\displaystyle \frac{\partial C_l}{\partial t}}+U_{\mathrm{j}}{\displaystyle \frac{\partial C_l}{{\partial x}_{\mathrm{j}}}}=D{\displaystyle \frac{{\partial }^2{C}_l}{{\partial x}_j{\partial x}_{\mathrm{j}}}}-{\displaystyle \frac{\partial }{{\partial x}_{\mathrm{j}}}}\left(\overline{c_l{u}_{\mathrm{j}}}\right)+S_{C_l}-{\displaystyle \frac{V_d}{∆}}{C}_l,$$

(3)

$${\displaystyle \frac{\partial C_g}{\partial t}}+U_{\mathrm{j}}{\displaystyle \frac{\partial C_g}{{\partial x}_{\mathrm{j}}}}=D{\displaystyle \frac{{\partial }^2{C}_g}{{\partial x}_j{\partial x}_{\mathrm{j}}}}-{\displaystyle \frac{\partial }{{\partial x}_{\mathrm{j}}}}\left(\overline{c_g{u}_{\mathrm{j}}}\right)+S_{C_g}-{\displaystyle \frac{V_d}{∆}}{C}_g.$$

(4)

Here, $U_{\mathrm{i}}$ denotes the i-th component of the mean velocity, $P^{\ast }$ represents the pressure fluctuation relative to the mean pressure, $C_l$ is the concentration of the liquid-phase chemical agent [μg m⁻³], and $C_g$ is the concentration of the gas-phase chemical agent [ppm_v]. $u_{\mathrm{i}}$, $c_l$, and $c_g$ denote the sub-grid scale fluctuations of $U_{\mathrm{i}}$, $C_l$, and $C_g$, respectively. The coefficients $\nu$ and $D$ represent the turbulent diffusion coefficients for momentum and chemical agents, respectively. The terms $S_{C_l}$ and $S_{C_g}$ correspond to the source/sink terms for $C_l$ and $C_g$, respectively.

The prognostic equations for turbulent kinetic energy (TKE, $k$) and TKE dissipation rate ($\epsilon$) are given as follows.

$${\displaystyle \frac{\partial k}{\partial t}}+U_{\mathrm{j}}{\displaystyle \frac{\partial k}{{\partial x}_{\mathrm{j}}}}=-\overline{u_{\mathrm{i}}{u}_{\mathrm{j}}}{\displaystyle \frac{{\partial U}_{\mathrm{i}}}{{\partial x}_{\mathrm{j}}}}+{\displaystyle \frac{\partial }{{\partial x}_{\mathrm{j}}}}\left({\displaystyle \frac{K_{\mathrm{m}}}{{\sigma }_{\mathrm{k}}}}{\displaystyle \frac{\partial k}{{\partial x}_{\mathrm{j}}}}\right)-\epsilon ,$$

(5)

$${\displaystyle \frac{\partial \epsilon }{\partial t}}+U_{\mathrm{j}}{\displaystyle \frac{\partial \epsilon }{{\partial x}_{\mathrm{j}}}}=-C_{\epsilon 1}{\displaystyle \frac{\epsilon }{k}}\overline{u_{\mathrm{i}}{u}_{\mathrm{j}}}{\displaystyle \frac{{\partial U}_{\mathrm{i}}}{{\partial x}_{\mathrm{j}}}}+{\displaystyle \frac{\partial }{{\partial x}_{\mathrm{j}}}}\left({\displaystyle \frac{K_{\mathrm{m}}}{{\sigma }_{\epsilon }}}{\displaystyle \frac{\partial \epsilon }{{\partial x}_{\mathrm{j}}}}\right)-C_{\epsilon 2}{\displaystyle \frac{{\epsilon }^2}{k}}-R.$$

(6)

The last term on the right-hand side of Equation (6), R, is an additional stress–strain term and is expressed as follows:

$$R={\displaystyle \frac{C_{\mu }{\eta }^3(1-\eta /{\eta }_0){\epsilon }^2}{(1+{{\beta }_0\eta }^3)k}},$$

(7)

$$\eta ={{\displaystyle \frac{k}{\epsilon }}\left[\left({\displaystyle \frac{{\partial U}_{\mathrm{i}}}{{\partial x}_{\mathrm{j}}}}+{\displaystyle \frac{{\partial U}_{\mathrm{j}}}{{\partial x}_{\mathrm{i}}}}\right){\displaystyle \frac{{\partial U}_{\mathrm{i}}}{{\partial x}_{\mathrm{j}}}}\right]}^{1/2}.$$

(8)

In Equations (1), (3) and (4), the Reynolds stresses and turbulent scalar fluxes are parameterized as follows:

$$-\overline{u_{\mathrm{i}}{u}_{\mathrm{j}}}=K_{\mathrm{m}}\left({\displaystyle \frac{{\partial U}_{\mathrm{i}}}{{\partial x}_{\mathrm{j}}}}+{\displaystyle \frac{{\partial U}_{\mathrm{j}}}{{\partial x}_i}}\right)-{\displaystyle \frac{2}{3}}{\delta }_{ij}k,$$

(9)

$$-\overline{c{u}_{\mathrm{j}}}=K_{\mathrm{c}}{\displaystyle \frac{\partial C}{{\partial x}_{\mathrm{j}}}}.$$

(10)

Here, ${ \delta }_{ij}$ is the Kronecker delta. $K_{\mathrm{m}}$ and $K_{\mathrm{c}}$ represent the turbulent diffusivities for momentum and chemical agents, respectively. In the RNG k-ε turbulence closure model used in this study, the turbulent diffusivities are parameterized as follows:

$$K_{\mathrm{m}}=C_{\mu }{\displaystyle \frac{k^2}{\epsilon }},$$

(11)

$$K_{\mathrm{c}}={\displaystyle \frac{K_{\mathrm{m}}}{{Sc}_t}}.$$

(12)

The empirical constants are specified as follows: $C_{\mu }$ = 0.0845, $C_{\epsilon 1}$ = 1.42, $C_{\epsilon 2}$ = 1.68, ${\sigma }_k$ = 0.7179, ${\sigma }_{\epsilon }$ = 0.7179, ${\eta }_0$ = 4.3777, ${\beta }_0$ = 0.012, and ${Sc}_t$ = 0.3.

The source/sink terms $S_{C_l}$ and $S_{C_g}$ in Equations (3) and (4) account for the phase change between the liquid and gaseous states of the chemical agent [34], and are defined as follows:

$$S_{C_l}={\displaystyle \frac{C_l{d}_l}{R_l}},$$

(13)

$$S_{C_g}={\displaystyle \frac{C_g{d}_g}{R_g}}-{\displaystyle \frac{C_l{d}_l}{R_l}}.$$

(14)

Here, $d_l$ and $d_g$ represent the evaporation rate of the liquid-phase chemical agent [${\mathrm{s}}^{-1}$] and the condensation rate of the gas-phase chemical agent [${\mathrm{s}}^{-1}$], respectively. In this study, the condensation of the gas-phase chemical agent was not considered, i.e., $d_g=0$. $R_l$ and $R_g$ denote the partitioning coefficients for the liquid and gas phases, respectively, and were both set to 1 in this study ($R_l=1$ and $R_g=1$). The last terms on the right-hand side of Equations (3) and (4) represent the removal of both liquid- and gas-phase contaminants via dry deposition near building walls in the urban canyon [35]. Here, $V_d$ is the dry deposition velocity, and Δ is the distance from the wall surface [36]. According to Montoya et al. [37], the dry deposition velocities of gas-phase chemical agents are relatively low (i.e., $2.6\times {10}^{-4}\pm 1.6\times {10}^{-4}$ m s⁻¹ for trialkyl-phosphono-acetate, a surrogate for the venomous agent X nerve agent). In this study, the dry deposition effect of the liquid-phase chemical agent was considered only, and for simplicity, it was assumed that liquid-phase chemical agents subject to dry deposition would be completely removed without resuspension or re-evaporation.

2.2. Numerical Validation

To validate the CFD model used in this study, the simulation results were compared with the wind tunnel experimental data of Gromke et al. [38] (Figure 1). Figure 1 shows the computational domain and building configuration of the wind tunnel experiment. The building height (H) is 18 m, and following the numerical setup of Gromke et al. [38], the distances from the building to the upwind, downwind, lateral, and top boundaries were set to 8H, 30H, 10H, and 8H, respectively, while the spacing between buildings (W) equals H and the building length (L) is 10H. The computational domain size is 750 m in the x-direction, 540 m in the y-direction, and 150 m in the z-direction, with the number of grid points being 500 (grid size = 1.5 m), 120 (grid size = 4.5 m), and 100 (grid size = 1.5 m), respectively. The simulation was integrated up to 7200 s with a time step of 0.5 s. The chemical agents were continuously emitted at a rate of 10 g s⁻¹ for 7200 s along two line sources located 0.25H away from each building at the ground surface. The inflow boundary conditions for wind speed, TKE, and TKE dissipation rate were prescribed using the vertical profiles adopted by Gromke et al. [38], as follows.

$$u=u_{ref}{\left({\displaystyle \frac{z}{z_{ref}}}\right)}^{0.3},$$

(15)

$$v=0,$$

(16)

$$w=0,$$

(17)

$$k={\displaystyle \frac{{u_{\ast }}^2}{\sqrt{C_{\mu , e}}}}\left(1-{\displaystyle \frac{z}{\delta }}\right),$$

(18)

$$\epsilon ={\displaystyle \frac{{u_{\ast }}^3}{\mathsf{\kappa }\mathrm{z}}}\left(1-{\displaystyle \frac{z}{\delta }}\right).$$

(19)

Here, $u_{ref}$ is the wind speed at the reference height ($z_{ref}$), which is set to 18 m. The friction velocity ($u_{\ast }$) is 0.52 m s⁻¹, $C_{\mu ,e}$ is an empirical constant (0.09), $\kappa$ is the von Kármán constant (0.4), $\delta$ is the boundary layer thickness (75 m), and $z_0$ is the surface roughness length (0.0033 m). The velocity components in the y- and z-directions are set to zero.

Gromke et al. [38] measured the mean concentrations of atmospheric pollutants along the canyon walls (Wall A and Wall B in Figure 1) and used normalized concentrations ($C^{+}$) calculated using the following equation.

$$C^{+}={\displaystyle \frac{CH{U}_H}{Q_l}}.$$

(20)

Here, $C$ is the measured or simulated concentration, H is the building height, $U_H$ is the wind speed at building height, and $Q_l$ is the emission rate per unit length. Figure 2 presents normalized concentration distributions on Wall A and Wall B from wind tunnel experiments and CFD simulations, together with scatter plots illustrating their comparison. The gray area indicates where the difference in $C^{+}$ between the wind tunnel experiment and the CFD model is within a factor of two. In Wall A, the CFD model generally underestimated the concentrations compared to the wind tunnel measurements, whereas in Wall B, it tended to overestimate them. To quantitatively evaluate this, six statistical evaluation metrics—fractional bias (FB), geometric mean bias (MG), normalized mean square error (NMSE), geometric variance (VG), correlation coefficient (R), and the fraction of predictions within a factor of two of the observations (FAC2)—proposed by Chang and Hanna [39] were used (

Table 1. Statistical evaluation metrics (RMSE, FB, MG, NMSE, VG, R and FAC2) for the normalized concentration (C⁺) simulated by the CFD model. Metrics in boldface indicate that the recommended acceptable criteria are met.

Evaluation Metrics (Best Agreement)	Wall A	Wall B	Acceptable Criteria [39]
$\mathrm{F}\mathrm{B}\left(0\right)$	0.19	−0.11	$-0.3<\mathrm{F}\mathrm{B}<0.3$
$\mathrm{M}\mathrm{G}\left(1\right)$	1.28	0.91	$0.7<\mathrm{M}\mathrm{G}<1.3$
$\mathrm{N}\mathrm{M}\mathrm{S}\mathrm{E}\left(0\right)$	0.08	0.06	$<1.5$
$\mathrm{V}\mathrm{G}\left(1\right)$	1.18	1.05	$<4$
$\mathrm{R}\left(1\right)$	0.92	0.97	$>0.8$
$\mathrm{F}\mathrm{A}\mathrm{C}2\left(1\right)$	0.91	0.99	$>0.5$

). The results showed that the CFD model satisfied all the recommended criteria for statistical evaluation metrics suggested by Chang and Hanna [39], indicating that the model reproduced the wind tunnel concentrations with a reasonable degree of accuracy.

2.3. Computational Configurations and Numerical Setup

In this study, numerical experiments were conducted to analyze the effect of urban street canyon geometry on the concentration distribution of a chemical agent, using four idealized canyon configurations proposed by Li et al. [22]. These canyon types are classified based on the ratio of canyon length (L) to building height (H): Cube (L ≤ H), Short (H < L ≤ 3H), Medium (3H < L ≤ 5H), and Long (L ≥ 7H). Referring to the classification by Li et al. [22], this study specifically defines the configurations as CB for L = H, SH for L = 3H, MD for L = 5H, and LN for L = 11H (Figure 3). Following the recommendations of COST Action 732 [40], the numerical domain was extended to ensure a distance of at least 5${\mathrm{H}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ upwind, laterally, and vertically, and at least 15${\mathrm{H}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ downwind, where ${\mathrm{H}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum building height in the domain. Accordingly, following these recommendations, the domain dimensions were 918 m, 558 m, and 216 m in the x-, y-, and z-directions, respectively, with grid resolutions of 2 m (459 cells), 2 m (279 cells), and 0.8 m (270 cells) in each direction.

The vertical profiles of velocity components (u, v, w), TKE, and TKE dissipation rate at the inflow boundary were given as follows.

$$u=u_{ref}{\left({\displaystyle \frac{z}{z_{ref}}}\right)}^{0.3},$$

(21)

$$v=0,$$

(22)

$$w=0,$$

(23)

$$k={\displaystyle \frac{u_{\ast }^2}{C_{\mu }^{0.5}}}{\left(1-{\displaystyle \frac{z}{\delta }}\right)}^2,$$

(24)

$$\epsilon ={\displaystyle \frac{C_{\mu }^{0.75}{k}^{1.5}}{\mathsf{\kappa }\mathrm{z}}}.$$

(25)

Here, $u_{ref}$ is 4.7 m s⁻¹, $z_{ref}$ is 18 m, $u_{\ast }$ is 0.52 m s⁻¹, $C_{\mu }$ is 0.0845, $\kappa$ is 0.4, and $\delta$ is 1000 m. The liquid-phase chemical agent was released from three square areas, each with sides of length H, located at a distance of 4H upwind of the canyons (red areas in Figure 3). The emission rate for each area was set to 2.02 kg s⁻¹, based on Hanna et al. [41], who modeled chemical dispersion resulting from an actual explosion incident. The chemical agent was released for a duration of 60 s. Additionally, the evaporation rate of the liquid-phase chemical agent was referenced from Jung and Choi [30], who analyzed the evaporation behavior of sulfur mustard (HD) on sand, concrete, and asphalt surfaces under conditions of 25 °C and wind speed of 3.6 m s⁻¹. According to their study, approximately 25% of the total HD applied on a concrete surface evaporated naturally within one hour. Converting this to a per-second evaporation rate corresponds to approximately 8 × 10⁻⁵ s⁻¹, which was used as the evaporation rate for the liquid-phase chemical agent in this study. Based on Giardina and Buffa [42], who investigated the range of deposition velocities according to particle size, the dry deposition effect of the liquid-phase chemical agent was set to 0.3 m s⁻¹. Zero-gradient boundary conditions were applied at the lateral and outflow boundaries, and wall functions of Versteeg and Malalasekera [43] were applied at the solid wall boundaries. Numerical simulations were performed for a total of 3600 s. However, since the chemical agents had sufficiently dispersed out of the urban canyon by 1800 s after its release, the analysis focused on the results up to 1800 s.

3. Results

3.1. Characteristics of the Mean Wind Flow in Canyon Types

This study focused on analyzing the flow characteristics at pedestrian height (z = 2 m) within the urban canyon and examined the flow patterns across different canyon types (Figure 4). Horizontally, as the building length increased, the size of the wake zone outside the building array (dashed line in Figure 4) decreased, while the wind speed outside the building array increased. As the building length increased, the proportion of flow recirculating around the building array increased, while the horizontal outward flow intensity from the spanwise street canyon weakened. Vertically, with increasing building length, the size of the wake zone outside the building array increased, whereas the wind speed above the urban canyon decreased (Figure 5). As a result, the flow reattachment point on the leeward side of the building array (purple dot in Figure 4) shifted farther away from the buildings. The weakened wind speed above the urban canyon reduced the intensity of the in-canyon vortex, thereby weakening the outward flow near the ground surface. Except for the CB case, vortices induced by flow separation were formed outside the 1st spanwise canyon, but from the 2nd spanwise canyon onward, they were located inside the spanwise canyon and gradually decreased in size (Figure 4).

In the CB case, the flow entering along the streamwise street was dispersed multidirectionally within each canyon due to the influence of buildings (Figure 4a). In particular, multiple vortices were formed in the narrow passages between buildings, and the exchange of flow between adjacent urban canyons was relatively active. The velocity of the flow entering the streamwise street increased near the entrance but gradually decreased further inside as it was interfered with by the outward flow from the spanwise street canyon, leading to the development of complex flow patterns [44]. Up to the 2nd spanwise canyon, the near-ground flow pattern resembled that of an isolated street canyon (outward flows directed from the center of the spanwise street canyon toward both ends). However, as the wind speed along the streamwise street weakened, the flow patterns from the 3rd spanwise street canyon onward were increasingly influenced by the outward flow from the spanwise canyon, resulting in the formation of complex flow structures.

Even in the SH case, where the urban canyon length was relatively short, the velocity of the flow entering the streamwise street increased near the entrance but decreased further inside due to the interference of the outward flow from the spanwise canyon. However, since this interference was weaker than in the CB case, the streamwise flow was maintained up to the 4th building row. In the 1st spanwise canyon formed by the lower buildings (S1 and S2) and the upper buildings (S13 and S14), a stronger streamwise flow was maintained compared to outside the building array, and near the ground surface, the internal flow directed outward from the building array was dominant (Figure 4b). However, from the 2nd spanwise canyon onward, the streamwise flow weakened, and the outward flow from the spanwise canyon became dominant. In the 4th spanwise canyon, the near-ground flow directed toward the streamwise street formed an eddy circulation within the streamwise street, which deflected the streamwise flow toward the central building (S11). In the 5th spanwise canyon, the eddy circulation formed within the streamwise street created a blocking pattern at the exit. The flow pattern within the spanwise street canyon formed by the central buildings (S7–S12) exhibited a symmetrical distribution. The flow patterns of MD and LN were similar to that of SH, and as the building length increased, the flow patterns became simplified (Figure 4c,d).

3.2. Dispersion Characteristics of Chemical Agents

Using the dispersion model developed in this study, the diffusion characteristics of liquid- and gaseous-phase HD were analyzed at pedestrian height and in vertical cross-sections for each canyon type. In CB, SH, and MD types, where a streamwise street exists, Liquid HD penetrated into the streamwise street canyon and gradually diffused into the spanwise canyons (Figure 6). The horse-shoe vortex formed at the windward side of the building and the circulation generated by flow separation above the building roof became more pronounced as the building length increased.

In the CB case, the liquid-phase HD that penetrated into the 2nd~4th streamwise streets was transported along the relatively strong streamwise flow up to the 2nd spanwise canyon, but from the point where the streamwise flow weakened, it dispersed toward the spanwise street canyon (Figure 6a,b). In the upper (1st) and lower (5th) streamwise street canyons, the flow exiting the building array from the spanwise canyon was dominant up to the 3rd spanwise canyon, causing the penetrated liquid chemical agent to be released outward. However, from the 4th spanwise canyon onward, the inward flow into the building array became dominant, leading to dispersion toward the center of the canyon. At the center of the spanwise canyons (y/H = $-$1), the vortex transported the high-concentration liquid HD agent of the upper layer down to the pedestrian height within the urban canyon (Figure 7a–c), and the liquid HD transported to pedestrian height subsequently dispersed into the streamwise street. In the central streamwise street canyon (y/H = 0), Liquid HD was transported along the flow, moved upward due to the updraft formed around x/H = 4.5, and then partially returned near the ground by the downdraft around x/H = 8.

In the SH case at t = 600 s, the internal flow directed outward from the building array near the ground surface was dominant in the 1st spanwise canyon. Consequently, the liquid HD in the urban canyon formed by the lower buildings (S1 and S2) and the upper buildings (S13 and S14) was transported from the streamwise street to the center of the canyon (Figure 6d). However, beginning with the 2nd spanwise canyon, the outward flow toward the streamwise street became dominant, and the inflow into the canyon interior was gradually weakened (Figure 6e). In the spanwise canyon formed by the central buildings (S7–S12), the inflow from both streamwise streets was dominant, allowing the liquid HD to penetrate from the streamwise street into the spanwise canyon. In addition, the vortex inside the canyon transported the liquid HD from the upper layer into the canyon interior, after which it exhibited a tendency to reside within the canyon. At the center of the spanwise canyon (y/H = 0), where the inflows from both streamwise streets converged and collided, the updraft was dominant, preventing the liquid HD in the upper layer from reaching pedestrian height within the canyon (Figure 7d). In addition, once the liquid HD moved toward the center of the spanwise canyon, it was transported out of the canyon through the upward flow. In the central streamwise street canyon (y/H = $-$2), the liquid HD was transported along the gentle updraft that developed from x/H = 0.5, and as the updraft weakened near x/H = 6, horizontal diffusion became dominant at pedestrian height.

In the MD case, as the liquid HD penetrated along the streamwise street, a distribution similar to that of SH was observed, in which relatively high concentrations were maintained along the streamwise street while gradually decreasing toward the spanwise street (although only one streamwise street existed in MD) (Figure 6g–i). In the case of LN, the concentration of Liquid HD at pedestrian level increased sequentially from the 1st spanwise canyon over time and then decreased thereafter (Figure 6j–l). This is because, in the LN case, no streamwise street existed, and thus the liquid HD in the upper layer of the urban canyon was transported down to pedestrian height by the canyon vortex (Figure 7j–l). The liquid HD above the building roofs showed that the high-concentration hot spots gradually shifted toward the leeward region over time. In addition, as the building length increased, the wind speed above the urban canyon decreased, resulting in a reduced migration speed of the average-concentration hot spots (Figure 8).

For gaseous HD generated by evaporation from liquid HD, the concentration patterns were generally similar to those of liquid HD (Figure 9 and Figure 10). These results indicate that the dispersion of gaseous chemical agents is analyzed to be due to the combined influence of two processes: transport by flow patterns determined by canyon type, and the process in which liquid chemical agents are evaporated to be released during their dispersion. The concentration patterns of gaseous chemical agents may vary depending on the evaporation rate of the chemical agents. Therefore, it is found that an analysis of flow patterns together with the spatial dispersion characteristics of liquid chemical agents over time is necessary to understand the dispersion characteristics of gaseous chemical agents. In addition, the concentration of gaseous HD inside the urban canyon was relatively higher than that outside the canyon compared to liquid HD (particularly in the spanwise canyon). This is because, while the concentration of liquid chemical agents gradually decreased within the canyon over time due to continuous evaporation and dispersion, gaseous chemical agents continued to be released inside the canyon through the evaporation of liquid chemical agents. In this study, it was also assumed that liquid chemical agents deposited on building walls or near the ground surface through dry deposition were completely removed without resuspension or re-evaporation into the air. Therefore, while liquid HD was partially removed by buildings or the ground surface due to dry deposition, such a removal process was not considered for gaseous HD because the effect of dry deposition is negligible.

To comprehensively analyze the dispersion characteristics of chemical agents according to urban canyon type, the average concentrations of liquid and gaseous HD at each time were compared for the building arrays of the urban canyons (Figure 11). During 0 $<$ t $\le$ 600 s, the average concentrations of Liquid and Gaseous HD within the building arrays were in the order of CB, SH, MD, and LN (i.e., the longer the building length, the slower the infiltration rate into the urban canyon). During 600 $<$ t $\le$ 1200 s, the average concentration of Liquid HD decreased for all canyon types except LN, which showed a slight increase (i.e., in the absence of a streamwise street, the penetration of Liquid HD from the upper layer of the canyon continues). In contrast, the concentration of Gaseous HD increased for all types except CB (i.e., in CB, the escape of Gaseous HD from the urban canyon becomes more pronounced). During 1200 $<$ t $\le$ 1800 s, the average concentration of Gaseous HD appeared in the reverse order of 0 $<$ t $\le$ 600 s, namely LN, MD, SH, and CB (i.e., the wider the spacing between buildings, the easier the escape of Gaseous HD from the urban canyon).

4. Summary and Conclusions

In this study, a modeling methodology was presented to analyze the dispersion characteristics of two-phase chemical agents by incorporating the dry deposition effect into the computational fluid dynamics (CFD) model and adding a transport equation for a non-reactive scalar. To validate the performance of the CFD model, the simulation results were compared with wind tunnel measurements, and the scalar pollutant concentrations predicted by the CFD model satisfied all the recommended criteria of statistical evaluation metrics, demonstrating its reliability in reproducing pollutant dispersion. Using the developed CFD dispersion model, the effects of geometrical configurations on flow and chemical agent dispersion characteristics were investigated for four types of urban canyons (Cube, Short, Medium, and Long).

As the building length increased, the horizontal size of the wake zone outside the building array decreased, while its vertical size increased; the wind speed above the urban canyon decreased, and the location of the flow reattachment point shifted farther leeward of the buildings. In addition, the wind speed above the building array increased toward the leeward region. Sulfur mustard (HD) released outside the building array entered through the streamwise street and then dispersed into the spanwise canyons, exhibiting a tendency to remain in regions where the wind speed was reduced. In the CB case, where the building length was short and the number of canyons was large, flow interactions between canyons were active inside the building array, resulting in relatively active dispersion of chemical agents between canyons at pedestrian height. In addition, the vortex formed at the center of the spanwise canyon transported HD from the upper layer down to pedestrian height within the urban canyon, after which it was transported into the streamwise streets. In the SH case, HD penetrated into the spanwise canyons formed by the upper and lower rows of buildings from the streamwise street, but the inflow intensity into the spanwise canyons decreased as it moved further inside through the streamwise street. In the spanwise canyon formed by the centrally located buildings, the inflow from both streamwise streets was dominant, and the HD that penetrated through the streamwise street was dispersed into the spanwise canyon. In the MD case, the flow and dispersion patterns of HD were relatively simple but similar to those of SH. In the LN case, where no streamwise street existed inside the urban canyon, HD in the upper layer was mainly transported down to pedestrian height within the canyon by the vortex of the spanwise canyon. The dispersion characteristics of gaseous HD were generally similar to those of liquid HD. However, due to the differences in evaporation and deposition effects, the concentrations inside the urban canyon were higher for gaseous HD than for liquid HD. This implies that gaseous chemical agents can persist within the canyon without rapidly decreasing in concentration over time, suggesting the possibility of prolonged impacts. However, due to the differences in evaporation and deposition effects, the concentrations inside the urban canyon were higher for gaseous HD than for liquid HD. This implies that gaseous chemical agents can persist within the canyon without rapidly decreasing in concentration over time, suggesting the possibility that the harm caused by this may persist for a long time.

As a result of comparing the time-averaged concentrations of the chemical agent by urban canyon type, the overall average concentration inside the building arrays was higher for shorter building lengths in the initial stage, whereas after a certain time it became higher in the reverse order. In other words, the shorter the building length, the faster the initial infiltration rate, but the shorter the residence time within the urban canyon as time progressed. Consequently, the variability remained highest in the order of CB, SH, MD, and LN throughout the 30 min period.

Our study focused on passive scalar transport under two-phase (liquid–gas) conditions and therefore did not consider factors such as chemical transformations, vegetation effects, or complex meteorological conditions. Incorporating these aspects is essential for more realistic scenarios, and we plan to address them in future work. Nevertheless, the dispersion model developed in this study serves as a foundational tool for chemical hazard assessment and the establishment of initial response strategies that account for urban morphology. Furthermore, by analyzing canyon types, the evaluation of geometrical effects on flow and dispersion provides fundamental information for preparing initial response strategies that consider building geometry in actual chemical and biological release scenarios.