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FLUENT CFD software (FLUENT ver.14, 2012) was used to simulate wind flow and odor dispersion around various configurations of cubic buildings. The Reynolds-averaged conservation equations for mass and momentum were used to simulate the processes of interest. Mass and momentum conservation equations are written as follows;

where u_j is the velocity of j component, t is the time, x_j is the j coordinate, ρ is the air density, μ is the dynamic viscosity; g_i is the gravitational body force;

is the Reynolds stress; μ_t is the turbulent viscosity.

The turbulence kinetic energy, k, and the specific dissipation rate, ω, are obtained from the following transport equations (FLUENT ver.14, 2012):

and

In these equations, G~k represents the generation of turbulence kinetic energy due to mean velocity gradients, G_ω represents the generation of ω, Γ_k and Γ_ω represent the effective diffusivity of k and ω, respectively. Y_k and Y_ω represent the dissipation of k and ω due to turbulence. D_ω represents the cross-diffusion term. S_k and S_ω are user-defined source terms.

Hydrogen sulfide (H₂S) was selected as an odorous fluid and was also presumed to flow along with clean dry air. According to Lin et al. (2009), the modeled fluid was defined as clean air and H₂S and its mass fraction at the odor source is defined as;

where Y_s is the odor mass fraction at the inlet of the system boundary, which is the ratio of the odorous gas mass to that of the total air mass in 1.0 m³ and is dimensionless P_a is the atmospheric pressure of 101,325 Pa at sea level, T the temperature in K; M the molecular weight of dry air or 0.028966 kg/mol; R is the universal gas constant of 8.31432 J/(mol·K); O_cg the odor source concentration in OU/m³, and m_H2S the mass of H₂S required to produce one odor unit, expressed as kg/OU, and m_H2S=7.0×10^-9 kg/OU. An odor unit (OU) is defined as the number of times an odorous air sample needs to be diluted with clean air to be no longer detectable by 50% of a team of panelists. This diluted concentration is also referred to as the threshold level (Lin et al., 2007).

The advection - diffusion (AD) module was applied to study the species transport process by analyzing the mass fraction of pollutants in the mixture. FLUENT analyzes the mass diffusion process based on the following equations (Riddle et al., 2004):

where J_i is the diffusion flux of the mixture (kg/m²s), ρ is the density of the mixture (kg/m³), D is the mass diffusion coefficient of the pollutant in the mixture (m²/s), y is the mass fraction of the pollutant (kg/kg), μ_t is the turbulent viscosity (kg·s/m). Sc_t is the Turbulent Schmidt number.

Fig. 1 shows the computational domain and boundary conditions. The domain was conceived following the COST Action 732 (Franke et al., 2007) and AIJ (Tominaga et al., 2008) guidelines. Its dimensions are equal to 25H×11H×6H (H=10 m is building height) in the streamwise (x), lateral (z) and vertical (y) directions, respectively. Atmospheric stability was fixed to be in a neutral condition in this study. To compare the experiments by Li and Meroney (1983) and to test the effect of the same building in streamwise direction, cubic building was selected in this study. The three kinds of building configurations used in this study are shown in Table 1. Each configuration has five different emission conditions, namely 1000 OU/s, 2000 OU/s, 3000 OU/s, 4000 OU/s and 5000 OU/s, respectively. So, simulation cases comprise a total of 15 cases. For all cases a single wind direction perpendicular to the building face was considered.

Fig. 1. 
Computational domain and boundary conditions.

Case	Building configuration	Remark
I	B1 (Isolated building)
II	B1 and B2 downstream of B1
III	B1, B2 downstream of B1 and B3 downstream of B2

Inlet velocity profile of the horizontal wind velocity in a neutral stability condition is defined as (Pieterse and Harms, 2013);

As illustrated by Lin et al. (2007) the vertical profile of temperature can be defined as follows;

Where, T(z) is the air temperature (K) at z, γ_d is the dry adiabatic lapse rate of 0.01 K/m. z_s is a height of 1.35 m above the earth’s surface; T_s is the air temperature at z_s in K.

As presented in Pieterse and Harms (2013) the profile for the turbulent kinetic energy k and the turbulent dissipation of inlet ε for the neutral stratified atmospheric boundary layer is defined as follows;

In terms of overall grid resolution, Tominaga et al. (2008) advised a grid-convergence study until the prediction result does not change significantly any more with increasing grid resolution. To perform the grid sensitivity study, a one-building configuration case was selected. According to Blocken (2015), Franke et al. (2004) state that the grid should be fine enough to capture the important physical phenomena like shear layers and vortical structures with sufficient resolution. For urban and building models, they advise to use at least 10 cells per cube root of the building volume, and 10 cells in between every two buildings. So, three grids with cubical cells of 1.0, 0.5 and 0.4 m around building surfaces corresponding to cell counts of 10, 20 and 25 along the building height and facet were generated. Franke et al. (2004) advised to keep the stretching ratio below 1.3 in regions of high gradients, to limit the truncation error. Franke et al. (2004) also advised the use of hexahedral cells over tetrahedral cells, as hexahedral yield smaller truncation errors and better iterative convergence. To this end, outside the building block array an expansion ratio of 1.1 was applied to the cells resulting in final grids of 269,630, 664,000 and 938,720 hexahedral cells, respectively. The grid sensitivity study presented the comparison of the mean horizontal wind velocity U along vertical profiles at two locations with different flow regimes. The first profile (Fig. 2(a)) was located upstream of one building configuration; the second velocity profile (Fig. 2(b)) was located in the leeward wake region of a one-building configuration. As can be seen in Fig. 2, the profiles indicate some grid dependency, which becomes smaller on the finer grids. For both locations, very little quantitative differences are present between the 0.4 m-grid and the 0.5 m-grid whereas for the 1.0 m-grid in comparison to the 0.5 m-grid even qualitative differences are found. This suggests the 0.5 m-grid with a cell count of 20 per building height is appropriate for reliably predicting flows around an isolated cubic building.

Fig. 2. 
Mean horizontal wind velocities U (m/s) on different grids at the upstream (a) and downstream wake region (b), Δ is mesh size, H (=10 m) is building height. Vertical red dotted line shows the z-position.

Gromke and Blocken (2015) state that the turbulent Schmidt number (Sct) is a fitting parameter, similar to the constants in turbulence models, which differs for different configurations. Studies on pollutant dispersion around isolated buildings using classical turbulence closure schemes for the Reynolds-averaged Navier-Stokes (RANS) equations suggest values for the Turbulent Schmidt number (here after S_ct) ranging from 0.1 to 1.3 (Chavez et al., 2011; Blocken et al., 2008). According to Tominaga and Stathopoulos (2009), a smaller value of Sct such as 0.3 tends to provide better predictions of concentration distribution around plumes in open country and around a single building, where the turbulent momentum diffusion is often underestimated when using RANS models.

This variability suggests the need for careful consideration about the appropriate S_ct number for each single study case. Therefore, pollutant dispersion around isolated cubic buildings was simulated with different values for S_ct and validated against wind tunnel data in this study.

Fig. 3 compares the contours of the dimensionless concentration, K, on the roof surface obtained with the present CFD and two experiments (Li and Meroney, 1983). In this study, dimensionless concentration K was defined as:

Fig. 3. 
Comparison of dimensionless concentration K on centerline of roof, leeward and sidewall.

where Q_e is the plume flow rate (m³/s), c is mass fraction of tracer gas, H is the cube size (m), and U_H is mean x-velocity at building height. Although a higher S_ct appears to provide a better prediction of the downwind dispersion along the rooftop centerline (Fig. 3(a)), there are no noticeable differences for the upwind dispersion. However, S_ct=0.1 produces a better result than other S_ct results for the lateral direction (Fig. 3(b)). From this result, it can be concluded that S_ct=0.1 is the best number to use in this case.

The next step of the quality assessment addresses the capability of the SST k-ω turbulence model to simulate the flows around isolated buildings. Fig. 4 illustrates the comparison of vertical distribution of streamwise velocity on (a) roof center and (b) behind a cube at centerline. The simulated results showed a good agreement with the wind tunnel results.

Fig. 4. 
Comparison of vertical distribution of streamwise velocity on (a) roof center (X/H=0.5) and (b) behind cube (X/H=1.5) at centerline.

In order to analyze the three different building configurations mentioned previously, a general view of the computational results in terms of velocity and stream line are illustrated in Fig. 5 and Fig. 6. This comparative view of results shows the difference of flow field behavior as the building number increases in the near-field environment. Additional buildings (B2 and B3) induce more low wind speed zones between buildings. These zones are also characterized by the presence of high velocity as can be shown by the streamlines in Fig. 6.

Fig. 5. 
Contours of x-velocity magnitude (m/s) for vent mass flow rate 1000 OU/s (=7.0×10^-6 kg/s). (a) a one-building configuration, (b) a two-building configuration, (c) a three-building configuration.

Fig. 6. 
Streamlines of vertical cross-section (Z=0 m) and plan view at height Y=5 m. (a) a one-building configuration, (b) a two-building configuration, (c) a three-building configuration.

The Malodor Prevention Law recommends the air dilution sensory (ADS) test as a primary means to assess the level of odor pollution in dilution-to-threshold (D/T) ratios in South Korea (Kim, 2016). Under this Law, samples are collected from the vents of odor sources and the emission limit is 1000 D/T (D/T is dilution-to-threshold (D/T) ratios) for facilities in industrial areas. Because values of D/T are theoretically comparable to OU/m³ (Brancher et al., 2017), 1000 OU/s was selected as the basic emission concentration in this study. Because 1 OU/m³ is referred to as the threshold level (Lin et al., 2007), 1 OU/m³ is used to depict the size of an odorous plume zone.

Fig. 7 shows influencing area of the odorous plume zone for a one-building configuration. Overall, as the odor emission rate increases, the odor plume touched the rooftop surface and was dragged downstream of the building. When the emission rate is 3000 OU/s, most of the building’s leeward facet is included in the odorous plume zone. However, most of the building’s side facet is excluded from odorous plume zone.

Fig. 7. 
Influencing area of the odorous plume zone (1 OU/m³) for a one-building configuration. (a) 1000 OU/s, (b) 2000 OU/s, (c) 3000 OU/s, (d) 4000 OU/s, (e) 5000 OU/s.

Fig. 8 presents Influencing area of the odorous plume zone for a two-building configuration. Although an emission rate of 1000 OU/s illustrates the same plume behavior as a one-building configuration (Fig. 7(a)), it was noticed that the plume tends to the cover rooftop surface and windward facet of a downstream building as the emission rate increases to 2000 OU/s (Fig. 8(b)). Again, it was noticed that the side facet of the second building is included in the odorous plume zone at an emission rate of 4000 OU/s. The results clearly indicate that the increasing emission rate has a great impact on the second building.

Fig. 8. 
Influencing area of the odorous plume zone (1 OU/m³) for a two-building configuration. (a) 1000 OU/s, (b) 2000 OU/s, (c) 3000 OU/s, (d) 4000 OU/s, (e) 5000 OU/s.

Fig. 9 shows influencing area of the odorous plume zone of a three-building configuration. In general, it was observed that a low emission rate (<4000 OU/s) has a similar odorous plume zone to that of a two-building configuration. However, the addition of a third building (B3), with an emission rate of 5000 OU/s, creates a much greater odorous plume zone on the surface of the second building in comparison with a two-building configuration. Therefore, most of the second building surface is covered with an odorous plume zone and the leeward facet of the third building is impacted by an odor plume at an emission rate of 5000 OU/s.

Fig. 9. 
Influencing area of the odorous plume zone (1 OU/m³) for a three-building configuration. (a) 1000 OU/s, (b) 2000 OU/s, (c) 3000 OU/s, (d) 4000 OU/s, (e) 5000 OU/s.