Numerical Simulations of the Thermal Effect on Flow and Dispersion around an Isolated Building

Xiaohui Huang aCollege of Environmental Science and Engineering, Taiyuan University of Technology, Taiyuan, China

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Hongtao Wang aCollege of Environmental Science and Engineering, Taiyuan University of Technology, Taiyuan, China

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Lizhen Gao aCollege of Environmental Science and Engineering, Taiyuan University of Technology, Taiyuan, China

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Abstract

The effect of temperature on flow and pollutant dispersion around an isolated building was investigated by computational fluid dynamics. First, the accuracy of the standard k–ε turbulence model in simulating the thermal effect on the flow and dispersion was assessed. The results showed that the reattachment of the numerical simulation behind the building was longer than that in the experiment because it could not reproduce the periodic fluctuations in the wake region and that the momentum transfer in the lateral direction was underestimated. Despite this, the temperature and concentration of the numerical simulation were in good agreement with the experimental results. Then, the standard k–ε turbulence model was adopted to investigate the effect of the ground temperature on flow and dispersion. The result indicated that, with the increase in temperature, the reattachment length behind the building significantly decreased and the vertical upward velocity increased, suggesting that rising temperature changed the flow. As the flow changed, the pollutant dispersion also changed. The pollutant plume depth increased while its width decreased with increasing ground temperature. It can be seen from the pollutant flux analysis that both convective transport and turbulent transport play important roles in vertical dispersion. The influence of ground temperature on convective motion was more obvious than that on turbulent motion because of the changed airflow.

Significance Statement

(i) The accuracy of the standard k–ε turbulence model in simulating the thermal effect on the flow and dispersion was assessed. The results showed that the reattachment of the numerical simulation behind the building was longer than that in the experiment because it could not reproduce the periodic fluctuations in the wake region and that the momentum transfer in the lateral direction was underestimated. Despite this, the temperature and concentration of the numerical simulation were in good agreement with the experimental results. (ii) Rising temperature not only increases turbulent motion but also alters airflow and pollutant plume morphology.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Lizhen Gao, lizhengao1965@163.com

Abstract

The effect of temperature on flow and pollutant dispersion around an isolated building was investigated by computational fluid dynamics. First, the accuracy of the standard k–ε turbulence model in simulating the thermal effect on the flow and dispersion was assessed. The results showed that the reattachment of the numerical simulation behind the building was longer than that in the experiment because it could not reproduce the periodic fluctuations in the wake region and that the momentum transfer in the lateral direction was underestimated. Despite this, the temperature and concentration of the numerical simulation were in good agreement with the experimental results. Then, the standard k–ε turbulence model was adopted to investigate the effect of the ground temperature on flow and dispersion. The result indicated that, with the increase in temperature, the reattachment length behind the building significantly decreased and the vertical upward velocity increased, suggesting that rising temperature changed the flow. As the flow changed, the pollutant dispersion also changed. The pollutant plume depth increased while its width decreased with increasing ground temperature. It can be seen from the pollutant flux analysis that both convective transport and turbulent transport play important roles in vertical dispersion. The influence of ground temperature on convective motion was more obvious than that on turbulent motion because of the changed airflow.

Significance Statement

(i) The accuracy of the standard k–ε turbulence model in simulating the thermal effect on the flow and dispersion was assessed. The results showed that the reattachment of the numerical simulation behind the building was longer than that in the experiment because it could not reproduce the periodic fluctuations in the wake region and that the momentum transfer in the lateral direction was underestimated. Despite this, the temperature and concentration of the numerical simulation were in good agreement with the experimental results. (ii) Rising temperature not only increases turbulent motion but also alters airflow and pollutant plume morphology.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Lizhen Gao, lizhengao1965@163.com

1. Introduction

According to the vertical gradient of potential temperature, the atmospheric boundary layer includes an isothermal boundary layer and a nonisothermal layer. In the isothermal boundary layer (i.e., neutral), there exists an approximately adiabatic potential temperature profile in which the vertical motion of fluid particles neither increases nor decreases, and there is no buoyancy effect due to temperature stratification. The nonisothermal boundary layer includes unstable (or convective) and stable boundary layers, and the buoyancy effect is strengthened in the former but suppressed in the later, which cannot be ignored.

Neutral conditions have received the most attention and form the primary basis of research on boundary layer flow response to the presence of a building-like obstacle. However, atmospheric conditions are often nonneutral (Monin and Yaglom 1971; Pasquill and Smith 1983; Stull 1988; Wood et al. 2010; Repetto 2011). According to Mavroidis et al. (1999), unstable conditions were found during the day, whereas stable conditions were found at night. Near-neutral conditions existed around sunset or sunrise, and their occurrence was limited. The influence of temperature stratification on pollutant dispersion has been extensively studied and demonstrated through field measurements by many researchers (Mavroidis et al. 1999, 2003; Higson et al. 1995; Santos et al. 2009a; Biltoft 2001; Yee and Biltoft 2004). Field tests are the most realistic but have high costs and limited measurement points. Therefore, the researchers tried to simulate thermal stratification in wind tunnels, in which unstable (stable) temperature stratification was mainly realized by heating (cooling) the floor or a particular surface and/or by applying a temperature profile at the inflow. For example, Uehara et al. (2000) conducted a stratified wind-tunnel test to investigate the effects of thermal stratification (bulk Richardson number Rib = −0.21, −0.19, −0.12, 0, 0.11, 0.43, and 0.78) on airflow in and above urban street canyons. The vortex that formed in the street canyon became stronger when the atmosphere was unstable and weaker when the atmosphere was stable. The results of these wind-tunnel experiments have been widely used as a standard validation database. Similarly, Yassin (2013a,b) revealed the effects of thermal stability on the dispersion of roof stack emissions around a cubical building. He found that the near-wake concentration was higher under stable conditions than under unstable conditions. In addition, Kanda and Yamao (2016) and Marucci and Carpentieri (2020) investigated the influence of temperature stratification on dispersion in an array of buildings. However, only weak temperature stratification can be simulated in wind tunnels because heat exchange is unavoidable. Similar to wind-tunnel tests but with more arbitrary and controllable temperature setting, temperature stratification in computational fluid dynamics (CFD) is realized by setting the wall temperature and/or inlet boundary (velocity and temperature profiles) in the computational domain. There are many relevant studies in this field (Kim and Baik 2001; Xie et al. 2006, 2007; Santos et al. 2009b; Yoshie et al. 2011; Allegrini et al. 2013, 2014; Li et al. 2016; Tomas et al. 2016; Allegrini 2018; Jiang and Yoshie 2018; Duan and Ngan 2019, 2020; Sessa et al. 2020; Huang et al. 2020; Tsalicoglou et al. 2020; Huang et al. 2021; Masoumi-Verki et al. 2021). These studies revealed that the thermal effect on the flow and dispersion could not be ignored, but it was still unclear.

Research on airflow and pollutant dispersion around isolated buildings was the basis of other related studies and was suitable for a parametric study, and dispersion around a single building was important for both conventional and accidental emissions. Thus, the purpose of this study was to exploit the convenience of CFD in setting temperature to investigate the influence of the thermal effect on dispersion. This paper is organized as follows. The wind-tunnel experiments and validation of the numerical simulation are shown in section 2. Then, section 3 describes the numerical method and simulation setup. The main results and discussion are introduced in section 4. The main conclusions are presented in section 5.

2. Wind-tunnel experiment and validation of the numerical simulation

a. Outline of wind-tunnel experiments

The wind-tunnel experiments were performed in the thermally stratified wind tunnel of Tokyo Polytechnic University with a model building (height H × width W × depth D = 160 mm × 80 mm × 80 mm) (Yoshie et al. 2011). The Reynolds number at the top of the building was approximately 15 000. The temperature of the wind-tunnel floor was 318.8 K. A gas source (C2H4: Cgas = 5% ethylene; diameter: 5 mm; flow rate: QV = 9.17 × 10−6 m3 s−1; exit velocity: UP = 0.47 m s−1) was installed on the floor 40 mm from the leeward side of the building. Figure 1 presents the vertical distributions of the approaching wind velocity u/UH, temperature (TTf)/ΔT, and turbulent kinetic energy (TKE) k/UH2.

Fig. 1.
Fig. 1.

Approaching flow for the wind-tunnel experiment.

Citation: Journal of Applied Meteorology and Climatology 61, 12; 10.1175/JAMC-D-21-0233.1

b. Validation of the numerical simulation

1) Computational domain and grid setup

Figure 2 shows the domain and grid. The building and gas source were parallel to the wind tunnel. The calculation domain was 12.5H × 7.5H × 6.25H (length × width × height). The upstream and downstream domain lengths were 2H and 10H, respectively. The height and width of the domain were consistent with the measured section of the experiments. The blockage ratio was 1.0%, which was well below the recommended value (Tominaga et al. 2008; Franke et al. 2007). The grid was structured, with the building discretized as 25(x) × 26(y) × 40(z). The stretching ratio was under 1.2. The height of the first layer adjacent to the ground was 0.002 m, with a dimensionless wall distance y+ of 10–22. There were 0.8 × 106 grids in total.

Fig. 2.
Fig. 2.

Computational (a) domain and (b) grid.

Citation: Journal of Applied Meteorology and Climatology 61, 12; 10.1175/JAMC-D-21-0233.1

2) Numerical model

The standard k–ε turbulence model (SKE; Launder and Spalding 1972) with scalable wall functions (scalable wall functions avoid the deterioration of standard wall functions under grid refinement below dimensionless wall distance < 11) of Ansys Fluent was adopted. The turbulence kinetic energy k and its rate of dissipation ε are obtained from the following transport equations:
t(ρk)+xi(ρkui)=xj[(μ+μtσk)kxj]+Gk+Gbρε+Sk,
t(ρε)+xi(ρεui)=xj[(μ+μtσε)εxj]+C1εεk(Gk+C3εGb)C2ερε2k+Sε,
μt=ρCμk2ε,
Gk=ρujui¯ujxi,
Gb=βgiμtPrtTxi=giμtρPrtρxi, and
β=1ρ(ρT)p,
where ρ is the air density; ui is the mean velocity component in the xi direction (in this study, i.e., u, υ, and w in the x, y, and z directions); μ is the molecular viscosity; μt is the turbulent viscosity computed by combining k and ε as in Eq. (3), where Cμ is a constant (=0.09); Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients; Gb is the generation of turbulence kinetic energy due to buoyancy; C1ε, C2ε, and C3ε are constants; σk and σε are the turbulent Prandtl numbers for k and ε, equal to 1.0 and 1.3, respectively; Sk and Sε are user-defined source terms; Prt is the turbulent Prandtl number for energy (=0.85); gi is the component of the gravitational vector in the xi direction; and β is the coefficient of thermal expansion.

3) Boundary conditions and solution method

The inflow surface was set as a velocity inlet condition, and the inflow profiles (u, T, k, and ε) were consistent with the wind-tunnel test (Yoshie et al. 2011). The inflow value of ε was calculated according to
ε=Pk+Gk,
where
Pk=uwdudzand
Gk=gβwT.
In Eqs. (7)(9), Pk and Gk are the turbulence kinetic energy production and buoyancy production terms, respectively; u′, w′, and T′ are the velocity fluctuations and temperature fluctuations, respectively. The source was set as the mass-flow inlet and the emission parameters were consistent with those in the experiments. The ground and building walls were set as no-slip wall boundary conditions with the temperature in line with the wind-tunnel experiments. The two sides of the domain (parallel to the x axis) and the top surface were set as symmetric boundary conditions. The outlet was a pressure outlet. The turbulent Schmidt number Sct (a dimensionless scalar, defined as the ratio of the dynamic viscosity coefficient to the dispersion coefficient, which is used to describe the fluid with momentum dispersion and mass dispersion at the same time) was set to 0.7. In the calculation, the semi-implicit method for pressure linked equations-consistent (SIMPLEC) was used for pressure–velocity coupling, and the advection scheme was a second-order upwind difference scheme. To ensure the convergence of the calculation results, the residuals of all variables should be less than 10−4.

c. Validation results

Figure 3 shows the distributions of normalized wind velocity (u/UH, w/UH), temperature (TTf)/ΔT, turbulent kinetic energy ( k/UH2), and concentration [C/C0, where C0 is the reference gas concentration: C0=[(Cgas×QV)/(UH×H2)]] in the vertical section (y/H = 0) and horizontal section (z/H = 0.025 and 0.25). According to the vertical distribution of streamwise velocity u/UH (Fig. 3a), on the line before the building (x/H = −0.625) and the line at the top of the building (x/H = −0.25), SKE conforms well to those of the experiment. Judging from the velocity distribution in the wake region, SKE overestimates the reattachment length behind the building. According to the vertical distribution of vertical velocity w/UH (Fig. 3b), on the line before the building (x/H = −0.625), the simulated vertical velocity below the stagnation point is basically consistent with the experimental value, whereas above the stagnation point it is clearly larger. On the line at the top of the building (x/H = −0.25), the trend of the SKE result was basically consistent with the experimental results but larger. In the wake region, the numerical simulation basically reproduces the vertical velocity distribution, but the overall velocity was smaller. The reason is that SKE cannot reproduce the periodic fluctuations in the wake region, and the momentum transfer in the lateral direction is underestimated. As a result, the reattachment behind the building is longer than that in the experiment.

Fig. 3.
Fig. 3.

Normalized (a),(b) wind velocity, (c) temperature, (d) TKE, and (e)–(g) concentration distribution (EXP indicates wind-tunnel experiments; SKE means the standard k–ε turbulence model). In (a)–(e) the vertical dotted line represents the vertical position of y/H = 0, −0.625, −0.25, 0.25, 0.625, 1.0, 1.5, and 2.0; in (f) it is the plane of z/H = 0.025; in (g) it is the plane of z/H = 0.25.

Citation: Journal of Applied Meteorology and Climatology 61, 12; 10.1175/JAMC-D-21-0233.1

On the basis of the normalized temperature distribution, as shown in Fig. 3c, the numerical simulation accurately reproduces the vertical temperature distribution. In addition, heat exchange between the laboratory environment and wind-tunnel equipment is unavoidable in wind-tunnel experiments but can be excluded in numerical simulations; thus, it is easy to predict that the thermal effect in numerical simulations will be more obvious than that in experiments. Thus, the near-ground temperature is larger than the experimental result.

Figure 3d shows the distribution of turbulent kinetic energy. It is clear that the peak turbulent kinetic energy calculated by SKE is located at the top of the building, while the maximum values of the experiment are located at the wake region of the building. The value of turbulent kinetic energy in the recirculating flow region is clearly smaller than the experimental results because the abovementioned periodic fluctuation is not reproduced, and the momentum transfer in the lateral direction (y direction) was underestimated.

Judging from the normalized concentration distribution of the vertical section, as shown in Fig. 3e, on the line at the top of the building (x/H = −0.25), SKE grossly underestimates the dispersion. In the wake of the building, it also underestimates pollutant concentrations when z/H > 1.4 (lower concentration region), and they are close to those in the experiment within the wake region. According to the concentration of the near ground of z/H = 0.025, as shown in Fig. 3f, SKE underestimates the width of the pollutant plume because of the underestimation of velocity fluctuation in the lateral direction. This corresponds to the previously discussed periodic fluctuation not being reproduced. Yoshie et al. (2011) used the LES model but obtained the same results. The reason may be that the ground and building block surfaces were not completely smooth but were set as absolutely smooth walls in the numerical simulation. In the plane of z/H = 0.25 (Fig. 3g), concentration prediction by SKE is accurate at higher concentrations (e.g., C/C0 > 1.0).

In general, because this study mainly focuses on the influence of the thermal effect on dispersion and the results of the SKE model are acceptable, it is used in the following research.

3. Simulation setup

Except for ground temperature, the building model, gas source, computational domain, grid settings, other boundary conditions and numerical simulation methods are consistent with the validation case. A nondimensional number, the bulk Richardson number Rib, represents temperature stratification. It is expressed as
Rib=g(THTf)HT0UH2.
Table 1 shows the case settings. Of note, both velocity and temperature vertical profiles conform to logarithmic profiles, according to the Monin–Obukhov theory for the boundary layer (Monin and Obukhov 1954). However, this study aims to investigate the effect of ground temperature on dispersion. To exclude the influence of the inflow wind profile and temperature gradient on pollutant dispersion (the inflow profiles were consistent with the wind-tunnel experiment, as shown in section 2 and Fig. 1), only the ground temperature was the variable for all cases.
Table 1

Ground temperature setting.

Table 1

4. Results and discussion

a. Velocity field and flow field structure

Figure 4 shows the normalized streamwise velocity (u/UH) distributions and the streamline distributions of the vertical profiles (y/H = 0) and near-ground profiles (z/H = 0.025). It was easy to see that with the increase in ground temperature, the reattachment length behind the building significantly decreased. For example, when Rib = −0.09, −0.39, and −0.81, the length was 1.6, 1.4, and 1.1 H, respectively. In addition, the higher was the ground temperature, the more obvious was the upward deflection of the streamline in the reverse flow region, especially when z/H < 0.5. This suggested that rising temperature changed the flow.

Fig. 4.
Fig. 4.

Normalized streamwise velocity (u/UH) distributions (color shading) and streamlines of the (right) vertical profiles (y/H = 0) and (left) near-ground profiles (z/H = 0.025).

Citation: Journal of Applied Meteorology and Climatology 61, 12; 10.1175/JAMC-D-21-0233.1

Figure 5 shows the vertical distributions of u/UH at different positions (x/H = −0.75, 0.25, 0.5, 1, 1.5, and 2) in the vertical section (y/H = 0) for all cases. As mentioned above, the inflow conditions were the same in all cases, except for the ground temperature. On the line before the building (x/H = −0.75), the streamwise velocity in all cases was visually consistent in all cases, indicating that the ground temperature had little effect. This can be also seen from the velocity and streamline in front of the building in Fig. 4. In the wake region, the influence of the ground temperature on the flow became apparent. On the line relatively close to the leeward wall (x/H = 0.25), the leeward wall forced the flow to the top of the building, and the streamwise velocity did not significantly change with temperature but still showed that the higher was the ground temperature, the smaller was the velocity gradient. On the line of x/H = 0.5, the influence of temperature on the flow (especially when z/H < 0.5) increased, and the reverse flow velocity (|u/UH|) increased with increasing temperature. For example, when Rib = −0.09, −0.39, and −0.81, the near-ground u/UH was −0.31, −0.25, and −0.20, respectively. On the line of x/H = 1.0, where it was still within the reverse flow region, the reverse flow velocity (|u/UH|) increased with increasing temperature. For example, when Rib = −0.09, −0.39, and −0.81, the near-ground u/UH was −0.21, −0.13, and −0.06, respectively. On the line of x/H = 1.5, for the case of Rib = −0.39, −0.53, −0.67, and −0.81, the streamwise velocity was positive at all heights, while for the case of Rib = −0.09 and −0.25, the near-ground velocity was negative, which indicated that the length of the reverse flow region was related to the ground temperature. On the line of x/H = 2.0, the streamwise velocity was positive for all cases, and the near-ground (z/H < 0.5) velocity was positively correlated with temperature but was negatively correlated near the top of the building (0.5 < z/H < 1.5).

Fig. 5.
Fig. 5.

Vertical distributions of u/UH at different positions (x/H = −0.75, 0.25, 0.5, 1, 1.5, and 2) in the vertical section (y/H = 0).

Citation: Journal of Applied Meteorology and Climatology 61, 12; 10.1175/JAMC-D-21-0233.1

Figure 6 illustrates the normalized vertical velocity (w/UH) distributions and streamline distributions of the vertical profiles (y/H = 0). In the wake region, the vertical upward velocity increased with increasing temperature, while the vertical downdraft velocity decreased. This also confirmed that the temperature changed the flow.

Fig. 6.
Fig. 6.

Normalized vertical velocity (w/UH) distributions (color shading) and streamlines of the vertical profiles (y/H = 0).

Citation: Journal of Applied Meteorology and Climatology 61, 12; 10.1175/JAMC-D-21-0233.1

Figure 7 shows the vertical distribution of w/UH at different positions (x/H = −0.75, 0.25, 0.5, 1, 1.5, and 2) in the vertical section (y/H = 0). On the windward side of the building (x/H = −0.75), due to the high ground temperature, the buoyancy action was opposite to the downdraft direction, causing the downward speed to decrease. The difference was small, but the higher was the temperature, the greater was the upward velocity near the ground. For example, when Rib = −0.09, −0.39, and −0.81, the maximum near-ground (z/H = 0.05) w/UH was 0.01, 0.02, and 0.03, respectively. In the wake region, the influence of the ground temperature on the vertical velocity became apparent. The leeward side of the building (x/H = 0.25) was the emission location. As the emission velocity (UP/UH) was 0.32, the vertical velocity near the ground (z/H < 0.1) was mainly affected by the emission momentum. As the height increased, the influence of airflow in the recirculation zone gradually replaced the influence of emission momentum, thus causing the vertical upward velocity to increase with the temperature of the ground. On the line of x/H = 0.5, it was clear that the vertical upward velocity was the largest, while the vertical downdraft velocity was the minimum under the highest temperature condition. For example, when Rib = −0.09, −0.39, and −0.81, the maximal vertical upward velocity w/UH was −0.01, −0.05, and −0.11, respectively. With increasing downstream distance (x/H = 1.0, 1.5, and 2.0), the vertical motion gradually weakens. On the lines of x/H = 1.5 and 2.0, there was not even a vertical upward flow when Rib = −0.09. In a ward, the vertical movement increased with increasing ground temperature. Given that the pollution source was located in the recirculation zone, it was easy to infer that strong vertical movement could aid in the vertical dispersion of pollutants.

Fig. 7.
Fig. 7.

Vertical distributions of w/UH at different positions (x/H = −0.75, 0.25, 0.5, 1, 1.5, and 2) in the vertical section (y/H = 0).

Citation: Journal of Applied Meteorology and Climatology 61, 12; 10.1175/JAMC-D-21-0233.1

b. Normalized concentration field (C/C0)

Figure 8 presents the normalized concentration (C/C0) distributions of the vertical profile (y/H = 0) and near-ground profiles (z/H = 0.025). Of note, the density of the pollutant (ethylene) is similar to that of air; thus, it can be considered as a neutrally buoyant gas, which allows us to exclude the buoyancy effect of the gas itself. It was clear in all cases that the contaminants were concentrated between the source and the leeward wall of the building and were low downstream of the source. This occurred because the pollution source was located in the recirculation zone. After discharge, pollutants first migrated upstream, then to the leeward side of the building, and finally downstream with the airflow. The pollutant dispersion was sensitive to ground temperature. The plume depth increased with increasing ground temperature, while the plume width decreased with temperature. This result was directly related to the flow field. With the increase in ground temperature, the vertical upward movement of flow was enhanced, along with the increase in the upward dispersion of pollutants, resulting in increasing plume depth. For the near-ground plane, the vortex centers got closer to each other as the temperature increased, which reduced the horizontal dispersion and then the plume width.

Fig. 8.
Fig. 8.

Normalized C/C0 distributions of the (bottom) vertical profiles (y/H = 0) and (top) near-ground profiles (z/H = 0.025).

Citation: Journal of Applied Meteorology and Climatology 61, 12; 10.1175/JAMC-D-21-0233.1

Figures 9 and 10 show the distributions of C/C0 at different positions (x/H = −0.25, 0.25, 0.5, 1, 1.5, and 2) in the vertical section (y/H = 0) and near-ground plane (z/H = 0.025). At the top of the building (x/H = −0.25), although the concentration was very low, temperature stratification had a clear influence. For example, when Rib = −0.09, −0.39, and −0.81, the maximum C/C0 on the top of the building was 0.007, 0.013, and 0.028, respectively. However, the near-ground concentration was the opposite of the highest concentration when Rib = −0.09. This indicated that vertical airflow was more intense when the ground temperature was higher and then reduced the lateral dispersion. In the wake region, the concentration was much higher than that at the top building. On the line of x/H = 0.25, which was the discharge outlet, the pollutant concentration reached its maximum value. The concentration near the ground was mainly affected by the initial discharge momentum of the pollutant source [as mentioned above, the discharge velocity of the pollutant source (UP/UH) was 0.32 near the ground, which was greater than the airflow velocity]. However, with increasing height, the pollutant concentration rapidly decreased due to the strong vertical velocity and the turbulence intensity. On the line of x/H = 0.5, the vertical concentration distribution showed a positive correlation with ground temperature, while the horizontal concentration distribution showed a double peak. For example, when Rib = −0.09, the maximal near-ground concentration (C/C0) was 10.49 at y/H = ±0.30, and the axis concentration (y/H = 0) was 4.72. When Rib = −0.39, the maximal near-ground concentration (C/C0) was 13.14 at y/H = ±0.20, and the axis concentration (y/H = 0) was 7.40. When Rib = −0.81, the maximal near-ground concentration (C/C0) was 11.74 at y/H = ±0.13, and the axis concentration (y/H = 0) was 9.02. The positions of the two peak concentrations are close to each other with increasing ground temperature. With increasing downstream distance (x/H = 1.0, 1.5, and 2.0), the airflow was gradually not affected by the building, and the higher was the ground temperature, the faster was the recovery, the concentration decreased, and the temperature had less influence on the concentration. For example, on the line of x/H = 2.0, the horizontal bimodal concentration distribution changed to a unimodal distribution for all cases.

Fig. 9.
Fig. 9.

Vertical distributions of C/C0 at different positions (x/H = −0.25, 0.25, 0.5, 1, 1.5, and 2) in the vertical section (y/H = 0).

Citation: Journal of Applied Meteorology and Climatology 61, 12; 10.1175/JAMC-D-21-0233.1

Fig. 10.
Fig. 10.

Horizontal distributions of C/C0 at different positions (x/H = −0.25, 0.25, 0.5, 1, 1.5, and 2) in the near-ground section (z/H = 0.025).

Citation: Journal of Applied Meteorology and Climatology 61, 12; 10.1175/JAMC-D-21-0233.1

c. Normalized concentration fluxes

To gain insight into the mechanisms that contribute to concentration transportation, concentration fluxes must be considered. Scalar transport of concentration included convective and turbulent diffusion effects, which were expressed by convection as the mean scalar fluxes and turbulent diffusion fluxes, respectively. The normalized vertical convective fluxes were expressed as wC/(UHC0), while the vertical turbulent diffusion fluxes were expressed as wC′/(UHC0). The turbulent diffusion fluxes were calculated as
wC=ϑtSct×cz.
In Eq. (11), ϑt is the turbulent viscosity and Sct is the turbulent Schmidt number.

Figure 11 shows the vertical direction normalized convective flux wC/(UHC0) and turbulent diffusion flux wC′/(UHC0) distributions of the plane (y/H = 0). Both convective transport and turbulent transport played an important role in vertical dispersion, and both increased with increasing ground temperature.

Fig. 11.
Fig. 11.

Normalized flux distributions of the vertical plane (y/H = 0).

Citation: Journal of Applied Meteorology and Climatology 61, 12; 10.1175/JAMC-D-21-0233.1

Figure 12 shows the vertical direction of the wC/(UHC0) and wC′/(UHC0)distributions of the line (y/H = 0, x/H = 0.25 and 0.5). On the line of x/H = 0.25, the convection fluxes near the ground were large and dominant. On the one hand, because the ground was the discharge location of the pollution source, it was mainly affected by the initial discharge momentum of the pollution source (as mentioned above, the discharge velocity of the pollutant source (UP/UH) was 0.32 near the ground, which was greater than the airflow velocity). On the other hand, turbulent mass transport was limited by the presence of the ground, which was consistent with the results of Gousseau et al. (2011). As the height increased, the convection fluxes rapidly decreased and reached approximately 1 above z/H = 0.2 and then decreased slowly to almost 0 at and above the height of the building. However, the turbulent fluxes were minor at the ground level and then rapidly increased as the height increased, reaching a maximum value at z/H = 0.05, and subsequently decreased with increasing height, with a second peak value appearing at the top of the building. Turbulent fluxes played a dominant role at the top of and above the building, indicating that turbulent motion was primarily responsible for the dispersion of pollutants above the building. In addition, both convective and turbulent fluxes increase as the ground temperature increases, indicating that temperature changes the flow. On the line of x/H = 0.5, the influence of temperature on convective fluxes was greater than that on turbulent fluxes. When Rib = −0.09, turbulent motion and convective motion had similar and counteracting effects. When Rib = −0.39, convective motion was clearly greater than turbulent motion below z/H = 0.7, with a maximal wC/(UHC0) of 0.40 and a maximal wC′/(UHC0) of 0.12. Above z/H = 0.7, the two had counteracting effects. When Rib = −0.81, convective motion was more clearly greater than turbulent motion below z/H = 0.8, with a maximal wC/(UHC0) of 1.02 and a maximal wC′/(UHC0) of 0.17. Above z/H = 0.8, the two had counteracting effects. This means that the increase in temperature mainly increased the vertical upward convection fluxes.

Fig. 12.
Fig. 12.

Normalized flux distribution of the line [y/H = 0, x/H = (left) 0.25 and (right) 0.5].

Citation: Journal of Applied Meteorology and Climatology 61, 12; 10.1175/JAMC-D-21-0233.1

5. Conclusions

The effect of temperature on flow and pollutant dispersion around an isolated building was investigated by CFD. The accuracy in simulating the thermal effect on the flow and dispersion was assessed by comparing it with wind-tunnel experimental data. Then, the thermal effect on dispersion was analyzed. The main conclusions were as follows:

  1. In comparison with the wind-tunnel experimental results, the calculated reattachment behind the building by the standard k–ε turbulence model is longer than that in the experiment because it cannot reproduce the periodic fluctuations in the wake region and the momentum transfer in the lateral direction is underestimated. Despite this, the temperature and concentration of the numerical simulation are in good agreement with the experimental results.

  2. With the increase in ground temperature, the reattachment length behind the building significantly decreases, and the vertical upward velocity increases, suggesting that increasing temperature changes the flow.

  3. The pollutant distribution is sensitive to ground temperature even when the source is located within the recirculation zone of the building. The plume depth grows with the increasing ground temperature, while the plume width decreases with the temperature.

  4. Both convective transport and turbulent transport play an important role in vertical dispersion, and both increase with increasing ground temperature. The influence of ground temperature on convective motion is even more obvious than that on turbulent motion.

Data availability statement.

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

REFERENCES

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    • Crossref
    • Search Google Scholar
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    • Crossref
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    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mavroidis, I., R. F. Griffiths, and D. J. Hall, 2003: Field and wind tunnel investigations of plume dispersion around single surface obstacles. Atmos. Environ., 37, 29032918, https://doi.org/10.1016/S1352-2310(03)00300-5.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Monin, A. S., and A. M. Obukhov, 1954: Basic laws of turbulent mixing in the surface layer of the atmosphere. Tr. Geofiz. Inst., Akad. Nauk SSSR, 24, 163187.

    • Search Google Scholar
    • Export Citation
  • Monin, A. S., and A. M. Yaglom, 1971: Statistical Fluid Mechanics. MIT Press, 782 pp.

  • Pasquill, F., and F. B. Smith, 1983: Atmospheric Diffusion. Ellis Horwood, 437 pp.

  • Repetto, M. P., 2011: Neutral and non-neutral atmosphere: Probabilistic characterization and wind-induced response of structures. J. Wind Eng. Ind. Aerodyn., 99, 969978, https://doi.org/10.1016/j.jweia.2011.06.010.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Santos, J. M., R. F. Griffiths, N. C. Reis Jr., and I. Mavroidis, 2009a: Experimental investigation of averaging time effects on building influenced atmospheric dispersion under different meteorological stability conditions. Build. Environ., 44, 12951305, https://doi.org/10.1016/j.buildenv.2008.09.020.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Santos, J. M., N. C. Reis Jr., E. V. Goulart, and I. Mavroidis, 2009b: Numerical simulation of flow and dispersion around an isolated cubical building: The effect of the atmospheric stratification. Atmos. Environ., 43, 54845492, https://doi.org/10.1016/j.atmosenv.2009.07.020.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sessa, V., Z.-T. Xie, and S. Herring, 2020: Thermal stratification effects on turbulence and dispersion in internal and external boundary layers. Bound.-Layer Meteor., 176, 6183, https://doi.org/10.1007/s10546-020-00524-x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers, 666 pp.

    • Crossref
    • Export Citation
  • Tomas, J. M., M. J. B. M. Pourquie, and H. J. J. Jonker, 2016: Stable stratification effects on flow and pollutant dispersion in boundary layers entering a generic urban environment. Bound.-Layer Meteor., 159, 221239, https://doi.org/10.1007/s10546-015-0124-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tominaga, Y., A. Mochida, R. Yoshie, H. Kataoka, T. Nozu, M. Yoshikawa, and T. Shirasawa, 2008: AIJ guidelines for practical applications of CFD to pedestrian wind environment around buildings. J. Wind Eng. Ind. Aerodyn., 96, 17491761, https://doi.org/10.1016/j.jweia.2008.02.058.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tsalicoglou, C., J. Allegrini, and J. Carmeliet, 2020: Non-isothermal flow between heated building models. J. Wind Eng. Ind. Aerodyn., 204, 104248, https://doi.org/10.1016/j.jweia.2020.104248.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Uehara, K., S. Murakami, S. Oikawa, and S. Wakamatsu, 2000: Wind tunnel experiments on how thermal stratification affects flow in and above urban street canyons. Atmos. Environ., 34, 15531562, https://doi.org/10.1016/S1352-2310(99)00410-0.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wood, C. R., and Coauthors, 2010: Turbulent flow at 190 m height above London during 2006–2008: A climatology and the applicability of similarity theory. Bound.-Layer Meteor., 137, 7796, https://doi.org/10.1007/s10546-010-9516-x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xie, X. M., C.-H. Liu, D. Y. C. Leung, and M. K. H. Leung, 2006: Characteristics of air exchange in a street canyon with ground heating. Atmos. Environ., 40, 63966409, https://doi.org/10.1016/j.atmosenv.2006.05.050.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xie, X. M., C.-H. Liu, and D. Y. C. Leung, 2007: Impact of building facades and ground heating on wind flow and pollutant transport in street canyons. Atmos. Environ., 41, 90309049, https://doi.org/10.1016/j.atmosenv.2007.08.027.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yassin, M. F., 2013a: A wind tunnel study on the effect of thermal stability on flow and dispersion of rooftop stack emissions in the near wake of a building. Atmos. Environ., 65, 89100, https://doi.org/10.1016/j.atmosenv.2012.10.013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yassin, M. F., 2013b: Experimental study on contamination of building exhaust emissions in urban environment under changes of stack locations and atmospheric stability. Energy Build., 62, 68–77, https://doi.org/10.1016/j.enbuild.2012.10.061.

    • Crossref
    • Export Citation
  • Yee, E., and C. A. Biltoft, 2004: Concentration fluctuation measurements in a plume dispersion through a regular array of obstacles. Bound.-Layer Meteor., 111, 363415, https://doi.org/10.1023/B:BOUN.0000016496.83909.ee.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yoshie, R., G. Y. Jiang, T. Shirasawa, and J. Chung, 2011: CFD simulations of gas dispersion around high-rise building in non-isothermal boundary layer. J. Wind Eng. Ind. Aerodyn., 99, 279288, https://doi.org/10.1016/j.jweia.2011.01.006.

    • Crossref
    • Search Google Scholar
    • Export Citation
Save
  • Allegrini, J., 2018: A wind tunnel study on three-dimensional buoyant flows in street canyons with different roof shapes and building lengths. Build. Environ., 143, 7188, https://doi.org/10.1016/j.buildenv.2018.06.056.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Allegrini, J., V. Dorer, and J. Carmeliet, 2013: Wind tunnel measurements of buoyant flows in street canyons. Build. Environ., 59, 315326, https://doi.org/10.1016/j.buildenv.2012.08.029.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Allegrini, J., V. Dorer, and J. Carmeliet, 2014: Buoyant flows in street canyons: Validation of CFD simulations with wind tunnel measurements. Build. Environ., 72, 6374, https://doi.org/10.1016/j.buildenv.2013.10.021.

    • Search Google Scholar
    • Export Citation
  • Biltoft, C. A., 2001: Customer report for mock urban setting test. DPG Doc. WDTC-FR-01-121, 55 pp., https://my.mech.utah.edu/∼pardyjak/documents/MUSTCustReport.pdf.

    • Crossref
    • Export Citation
  • Duan, G., and K. Ngan, 2019: Sensitivity of turbulent flow around a 3-D building array to urban boundary-layer stability. J. Wind Eng. Ind. Aerodyn., 193, 103958, https://doi.org/10.1016/j.jweia.2019.103958.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Duan, G., and K. Ngan, 2020: Influence of thermal stability on the ventilation of a 3-D building array. Build. Environ., 183, 106969, https://doi.org/10.1016/j.buildenv.2020.106969.

    • Search Google Scholar
    • Export Citation
  • Franke, J., A. Hellsten, H. Schlünzen, and B. Carissimo, 2007: Best Practice Guideline for the CFD Simulation of Flows in the Urban Environment. Meteorological Institute, 52 pp.

    • Crossref
    • Export Citation
  • Gousseau, P., B. Blocken, and G. J. F. van Heijst, 2011: CFD simulation of pollutant dispersion around isolated buildings: On the role of convective and turbulent mass fluxes in the prediction accuracy. J. Hazard. Mater., 194, 422434, https://doi.org/10.1016/j.jhazmat.2011.08.008.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Higson, H. L., R. F. Griffiths, C. D. Jones, and C. Biltoft, 1995: Effect of atmospheric stability on concentration fluctuations and wake retention times for dispersion in the vicinity of an isolated building. Environmetrics, 6, 571581, https://doi.org/10.1002/env.3170060604.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Huang, X.-T., Y.-D. Huang, N. Xu, Y. Luo, and P.-Y. Cui, 2020: Thermal effects on the dispersion of rooftop stack emission in the wake of a tall building within suburban areas by wind-tunnel experiments. J. Wind Eng. Ind. Aerodyn., 205, 104295, https://doi.org/10.1016/j.jweia.2020.104295.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Huang, Y.-D., N. Xu, S.-Q. Ren, L.-B. Qian, and P.-Y. Cui, 2021: Numerical investigation of the thermal effect on flow and dispersion of rooftop stack emissions with wind tunnel experimental validations. Environ. Sci. Pollut. Res., 28, 11 61811 636, https://doi.org/10.1007/s11356-020-11304-y.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jiang, G. Y., and R. Yoshie, 2018: Large-eddy simulation of flow and pollutant dispersion in a 3D urban street model located in an unstable boundary layer. Build. Environ., 142, 4757, https://doi.org/10.1016/j.buildenv.2018.06.015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kanda, I., and Y. Yamao, 2016: Passive scalar diffusion in and above urban-like roughness under weakly stable and unstable thermal stratification conditions. J. Wind Eng. Ind. Aerodyn., 148, 1833, https://doi.org/10.1016/j.jweia.2015.11.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kim, J.-J., and J.-J. Baik, 2001: Urban street-canyon flows with bottom heating. Atmos. Environ., 35, 33953404, https://doi.org/10.1016/S1352-2310(01)00135-2.

    • Search Google Scholar
    • Export Citation
  • Launder, B. E., and D. B. Spalding, 1972: Lectures in Mathematical Models of Turbulence. Academic Press, 169 pp.

    • Crossref
    • Export Citation
  • Li, X.-X., R. Britter, and L. K. Norford, 2016: Effect of stable stratification on dispersion within urban street canyons: A large-eddy simulation. Atmos. Environ., 144, 4759, https://doi.org/10.1016/j.atmosenv.2016.08.069.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marucci, D., and M. Carpentieri, 2020: Dispersion in an array of buildings in stable and convective atmospheric conditions. Atmos. Environ., 222, 117100, https://doi.org/10.1016/j.atmosenv.2019.117100.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Masoumi-Verki, S., P. Gholamalipour, F. Haghighat, and U. Eicker, 2021: Embedded LES of thermal stratification effects on the airflow and concentration fields around an isolated high-rise building: Spectral and POD analyses. Build. Environ., 206, 108388, https://doi.org/10.1016/j.buildenv.2021.108388.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mavroidis, I., R. F. Griffiths, C. D. Jones, and C. A. Biltoft, 1999: Experimental investigation of the residence of contaminants in the wake of an obstacle under different stability conditions. Atmos. Environ., 33, 939949, https://doi.org/10.1016/S1352-2310(98)00219-2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mavroidis, I., R. F. Griffiths, and D. J. Hall, 2003: Field and wind tunnel investigations of plume dispersion around single surface obstacles. Atmos. Environ., 37, 29032918, https://doi.org/10.1016/S1352-2310(03)00300-5.

    • Search Google Scholar
    • Export Citation
  • Monin, A. S., and A. M. Obukhov, 1954: Basic laws of turbulent mixing in the surface layer of the atmosphere. Tr. Geofiz. Inst., Akad. Nauk SSSR, 24, 163187.

    • Search Google Scholar
    • Export Citation
  • Monin, A. S., and A. M. Yaglom, 1971: Statistical Fluid Mechanics. MIT Press, 782 pp.

  • Pasquill, F., and F. B. Smith, 1983: Atmospheric Diffusion. Ellis Horwood, 437 pp.

    • Crossref
    • Export Citation
  • Repetto, M. P., 2011: Neutral and non-neutral atmosphere: Probabilistic characterization and wind-induced response of structures. J. Wind Eng. Ind. Aerodyn., 99, 969978, https://doi.org/10.1016/j.jweia.2011.06.010.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Santos, J. M., R. F. Griffiths, N. C. Reis Jr., and I. Mavroidis, 2009a: Experimental investigation of averaging time effects on building influenced atmospheric dispersion under different meteorological stability conditions. Build. Environ., 44, 12951305, https://doi.org/10.1016/j.buildenv.2008.09.020.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Santos, J. M., N. C. Reis Jr., E. V. Goulart, and I. Mavroidis, 2009b: Numerical simulation of flow and dispersion around an isolated cubical building: The effect of the atmospheric stratification. Atmos. Environ., 43, 54845492, https://doi.org/10.1016/j.atmosenv.2009.07.020.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sessa, V., Z.-T. Xie, and S. Herring, 2020: Thermal stratification effects on turbulence and dispersion in internal and external boundary layers. Bound.-Layer Meteor., 176, 6183, https://doi.org/10.1007/s10546-020-00524-x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers, 666 pp.

    • Crossref
    • Export Citation
  • Tomas, J. M., M. J. B. M. Pourquie, and H. J. J. Jonker, 2016: Stable stratification effects on flow and pollutant dispersion in boundary layers entering a generic urban environment. Bound.-Layer Meteor., 159, 221239, https://doi.org/10.1007/s10546-015-0124-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tominaga, Y., A. Mochida, R. Yoshie, H. Kataoka, T. Nozu, M. Yoshikawa, and T. Shirasawa, 2008: AIJ guidelines for practical applications of CFD to pedestrian wind environment around buildings. J. Wind Eng. Ind. Aerodyn., 96, 17491761, https://doi.org/10.1016/j.jweia.2008.02.058.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tsalicoglou, C., J. Allegrini, and J. Carmeliet, 2020: Non-isothermal flow between heated building models. J. Wind Eng. Ind. Aerodyn., 204, 104248, https://doi.org/10.1016/j.jweia.2020.104248.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Uehara, K., S. Murakami, S. Oikawa, and S. Wakamatsu, 2000: Wind tunnel experiments on how thermal stratification affects flow in and above urban street canyons. Atmos. Environ., 34, 15531562, https://doi.org/10.1016/S1352-2310(99)00410-0.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wood, C. R., and Coauthors, 2010: Turbulent flow at 190 m height above London during 2006–2008: A climatology and the applicability of similarity theory. Bound.-Layer Meteor., 137, 7796, https://doi.org/10.1007/s10546-010-9516-x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xie, X. M., C.-H. Liu, D. Y. C. Leung, and M. K. H. Leung, 2006: Characteristics of air exchange in a street canyon with ground heating. Atmos. Environ., 40, 63966409, https://doi.org/10.1016/j.atmosenv.2006.05.050.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xie, X. M., C.-H. Liu, and D. Y. C. Leung, 2007: Impact of building facades and ground heating on wind flow and pollutant transport in street canyons. Atmos. Environ., 41, 90309049, https://doi.org/10.1016/j.atmosenv.2007.08.027.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yassin, M. F., 2013a: A wind tunnel study on the effect of thermal stability on flow and dispersion of rooftop stack emissions in the near wake of a building. Atmos. Environ., 65, 89100, https://doi.org/10.1016/j.atmosenv.2012.10.013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yassin, M. F., 2013b: Experimental study on contamination of building exhaust emissions in urban environment under changes of stack locations and atmospheric stability. Energy Build., 62, 68–77, https://doi.org/10.1016/j.enbuild.2012.10.061.

    • Crossref
    • Export Citation
  • Yee, E., and C. A. Biltoft, 2004: Concentration fluctuation measurements in a plume dispersion through a regular array of obstacles. Bound.-Layer Meteor., 111, 363415, https://doi.org/10.1023/B:BOUN.0000016496.83909.ee.

    • Search Google Scholar
    • Export Citation
  • Yoshie, R., G. Y. Jiang, T. Shirasawa, and J. Chung, 2011: CFD simulations of gas dispersion around high-rise building in non-isothermal boundary layer. J. Wind Eng. Ind. Aerodyn., 99, 279288, https://doi.org/10.1016/j.jweia.2011.01.006.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Approaching flow for the wind-tunnel experiment.

  • Fig. 2.

    Computational (a) domain and (b) grid.

  • Fig. 3.

    Normalized (a),(b) wind velocity, (c) temperature, (d) TKE, and (e)–(g) concentration distribution (EXP indicates wind-tunnel experiments; SKE means the standard k–ε turbulence model). In (a)–(e) the vertical dotted line represents the vertical position of y/H = 0, −0.625, −0.25, 0.25, 0.625, 1.0, 1.5, and 2.0; in (f) it is the plane of z/H = 0.025; in (g) it is the plane of z/H = 0.25.

  • Fig. 4.

    Normalized streamwise velocity (u/UH) distributions (color shading) and streamlines of the (right) vertical profiles (y/H = 0) and (left) near-ground profiles (z/H = 0.025).

  • Fig. 5.

    Vertical distributions of u/UH at different positions (x/H = −0.75, 0.25, 0.5, 1, 1.5, and 2) in the vertical section (y/H = 0).

  • Fig. 6.

    Normalized vertical velocity (w/UH) distributions (color shading) and streamlines of the vertical profiles (y/H = 0).

  • Fig. 7.

    Vertical distributions of w/UH at different positions (x/H = −0.75, 0.25, 0.5, 1, 1.5, and 2) in the vertical section (y/H = 0).

  • Fig. 8.

    Normalized C/C0 distributions of the (bottom) vertical profiles (y/H = 0) and (top) near-ground profiles (z/H = 0.025).

  • Fig. 9.

    Vertical distributions of C/C0 at different positions (x/H = −0.25, 0.25, 0.5, 1, 1.5, and 2) in the vertical section (y/H = 0).

  • Fig. 10.

    Horizontal distributions of C/C0 at different positions (x/H = −0.25, 0.25, 0.5, 1, 1.5, and 2) in the near-ground section (z/H = 0.025).

  • Fig. 11.

    Normalized flux distributions of the vertical plane (y/H = 0).

  • Fig. 12.

    Normalized flux distribution of the line [y/H = 0, x/H = (left) 0.25 and (right) 0.5].

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