A CFD Study of Near-field Odor Dispersion around a Cubic Building from Rooftop Emissions
Abstract
Odor dispersion around a cubic building from rooftop odor emissions was investigated using computational fluid dynamics (CFD). The Shear Stress Transport (here after SST) k-ω model in FLUENT CFD code was used to simulate the flow and odor dispersion around a cubic building. The CFD simulations were performed for three different configurations of cubic buildings comprised of one building, two buildings or three buildings. Five test emission rates were assumed as 1000 OU/s, 2000 OU/s, 3000 OU/s, 4000 OU/s and 5000 OU/s, respectively. Experimental data from wind tunnels obtained by previous studies are used to validate the numerical result of an isolated cubic building. The simulated flow and concentration results of neutral stability condition were compared with the wind tunnel experiments. The profile of streamline velocity and concentration simulation results show a reasonable level of agreement with wind tunnel data. In case of a two-building configuration, the result of emission rate 1000 OU/s illustrates the same plume behavior as a one-building configuration. However, the plume tends to the cover rooftop surface and windward facet of a downstream building as the emission rate increases. In case of a three-building configuration, low emission rates (<4000 OU/s) form a similar plume zone to that of a two-building configuration. However, the addition of a third building, with an emission rate of 5000 OU/s, creates a much greater odorous plume zone on the surface of second building in comparison with a two-building configuration.
Keywords:
CFD model, SST k-ω model, Odor dispersion, Cubic building, Rooftop emission1. INTRODUCTION
A large number of industrial, institutional, university and hospital laboratories, as well as manufacturing facilities, emit a wide range of potentially harmful pollutants (e.g., toxic and odorous chemicals) from rooftop stacks to urban environments. Therefore, the dispersion of potential hazardous exhaust from these stacks is of great concern when addressing possible consequences of such releases on human health and safety, as well as the environment in the stack vicinity (Yassin, 2013). Among these pollutants, exposure to unpleasant odors is one of the most frequent causes of air quality complaints in both industrial and urban areas. Odor nuisance is most frequently associated with discontinuous emissions generated by restaurants, fast food outlets and bars, which may occur for short/prolonged times, occasionally or on a repetitive basis depending on the actual operating hours of the facility (Pettarin et al., 2015).
Once odors are emitted from a source, their transport, dispersion and fate in the environment is controlled by a complex interaction that depends on the strength of emissions, meteorological conditions, topographic features around the site, stack height and near-field buildings. Therefore, it is difficult to predict odor dispersion with certainty due to the complex interaction between atmospheric flow and flow around buildings.
Near-field pollutant dispersion in the built environment is characterized by the complex interaction of plumes with flow fields perturbed by building obstacles. The dispersion field consists of local emission sources and the dispersion of the emissions in nearby individual buildings and the surrounding neighborhood (Tominaga and Stathopoulos, 2016).
The main assessment tools in urban physics are field measurements, full-scale and reduced-scale laboratory measurements and numerical simulation methods including Computational Fluid Dynamics (CFD) (Blocken, 2015). In the past two decades, micro-scale Computational Fluid Dynamics (CFD) simulation has been widely used as an emerging analysis method for pollutant dispersion around buildings and in urban areas, sometimes in lieu of wind tunnel tests. The CFD simulation method consists of solving the transport (advection and diffusion) equation of concentration based on the velocity field obtained from the Navier-Stokes equations. CFD can provide detailed information about the relevant flow and concentration variables throughout the calculation domain. However, it is difficult to implement various dispersion processes such as atmospheric stratification, buoyancy, chemistry etc. to the model, whereas they are easily applied to the operational models (Tominaga and Stathopoulos, 2013).
Odor dispersion in the atmosphere has been the subject of numerous investigations, while there has been less research done on odor dispersion around buildings. Odor dispersion under steady winds and constant emissions in the presence of few buildings has been evaluated using the Re-Normalization Group (RNG) k-ε model by Maizi et al. (2010). Dourado et al. (2014) presented a fluctuating plume model. However, the model appears to over-predict dispersion if compared to the wind tunnel data. In spite of the increasing number of applications based on dispersion models, this modeling approach has not yet been adequately validated to be confidently used for odor impact assessment. Moreover, we are not aware of applications of odor dispersion models to more complex urban environments (Pettarin et al., 2015).
The SST k-ω accounts for the principal turbulent shear stress and uses the across-diffusion term in the ω equation to blend both the k-ω model and k-ε model and to ensure that the model equations behave appropriately in both the near-wall and far-field zones. Thus, the SST k-ω model offers a superior simulation performance as compared with the individual k-ω and k-ε models (Menter et al., 2003). Recently, The SST k-ω model is increasingly being used to predict pollutant dispersion around barriers and isolated building (e.g., Kim and Jeong, 2015; Kim et al., 2014; Ramponi and Blocken, 2012; Lin et al., 2009).
In this respect, the aim of this paper is to investigate the influence of upstream rooftop odor emissions on near-field buildings. For this purpose, the CFD simulations were performed for three building cases, namely, an isolated cubic building, two cubic buildings and three cubic buildings, respectively. The SST k-ω model was used to simulate the flow and odor dispersion around cubic buildings in this study.
2. MATERIALS AND METHODS
2. 1 Numerical Method
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;
$$$\frac{\partial {u}_{i}}{\partial {x}_{j}}=0$$$ | (1) |
$$$\frac{\partial {u}_{i}}{\partial t}+{u}_{j}\frac{\partial {u}_{i}}{\partial {x}_{j}}=-\frac{1}{\rho}\frac{\partial p}{\partial {x}_{i}}+\frac{\mu}{\rho}\frac{{\partial}^{2}{u}_{i}}{\partial {x}_{j}\partial {x}_{j}}-\frac{\partial}{\partial {x}_{j}}\left(\overline{{u}_{i}\text{'}{u}_{j}\text{'}}\right)+{g}_{i}$$$ | (2) |
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;
$$$-\overline{{u}_{i}\text{'}{u}_{j}\text{'}}=-\frac{1}{\rho}{\mu}_{t}\left(\frac{\partial {u}_{i}}{\partial {x}_{j}}+\frac{\partial {u}_{j}}{\partial {u}_{i}}\right)-\frac{2}{3}k{\delta}_{ij}$$$ | (3) |
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):
$$$\frac{\partial}{\partial t}\left(\rho k\right)+\frac{\partial}{\partial {x}_{i}}\left(\rho k{u}_{i}\right)=\frac{\partial}{\partial {x}_{j}}\left({\mathrm{\Gamma}}_{k}\frac{\partial k}{\partial {x}_{j}}\right)+{\stackrel{~}{G}}_{k}-{Y}_{k}+{S}_{k}$$$ | (4) |
and
$$$\begin{array}{c}\frac{\partial}{\partial t}\left(\rho \omega \right)+\frac{\partial}{\partial {x}_{j}}\left(\rho \omega {u}_{j}\right)\hfill \\ =\frac{\partial}{\partial {x}_{j}}\left({\mathrm{\Gamma}}_{\omega}\frac{\partial \omega}{\partial {x}_{j}}\right)+{G}_{\omega}-{Y}_{\omega}+{D}_{\omega}+{S}_{\omega}\hfill \end{array}$$$ | (5) |
In these equations, $$ {\stackrel{~}{G}}_{k}$$ 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.
2. 2 Evaluation of Odor Intensity
Hydrogen sulfide (H_{2}S) 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 H_{2}S and its mass fraction at the odor source is defined as;
$$${Y}_{s}=\frac{{O}_{cg}\times {m}_{H2S}}{\left({P}_{a}M/RT\right)+{O}_{cg}\times {m}_{H2S}}$$$ | (6) |
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 m^{3} 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/m^{3}, and m_{H}_{2}_{S} the mass of H_{2}S required to produce one odor unit, expressed as kg/OU, and m_{H}_{2}_{S}=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):
$$${J}_{i}=-\left(\rho D+\frac{{\mu}_{t}}{S{c}_{t}}\right)\text{\u2207}y$$$ | (7) |
where J_{i} is the diffusion flux of the mixture (kg/m^{2}s), ρ is the density of the mixture (kg/m^{3}), D is the mass diffusion coefficient of the pollutant in the mixture (m^{2}/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.
2. 3 Computational Domain and Boundary Condition
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.
Inlet velocity profile of the horizontal wind velocity in a neutral stability condition is defined as (Pieterse and Harms, 2013);
$$$u=\frac{{u}_{*}}{\kappa}ln\frac{z}{{z}_{0}}$$$ | (8) |
As illustrated by Lin et al. (2007) the vertical profile of temperature can be defined as follows;
$$$T\left(z\right)=-{\gamma}_{d}\left(z+{z}_{s}\right)+{T}_{s}$$$ | (9) |
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;
$$$k\left(z\right)=5.48{u}_{*}^{2}$$$ | (10) |
$$$\epsilon \left(z\right)=\frac{{u}_{*}^{3}}{\kappa z}$$$ | (11) |
3. QUALITY ASSESSMENT AND ASSURANCE STUDIES
3. 1 Grid Sensitivity Study
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.
3. 2 Turbulent Schmidt Number Analysis
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:
$$$K=\frac{c{H}^{2}{U}_{H}}{{Q}_{e}}$$$ | (12) |
where Q_{e} is the plume flow rate (m^{3}/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.
3. 3 Assessment of the SST k-ω Turbulence Model
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.
4. EFFECTS OF DOWNSTREAM BUILDINGS ON FLOW AND ODOR DISPERSION
4. 1 Effect of Downstream Building on Flow Field
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.
4. 2 Influence of Odor Dispersion on Downstream Building
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/m^{3} (Brancher et al., 2017), 1000 OU/s was selected as the basic emission concentration in this study. Because 1 OU/m^{3} is referred to as the threshold level (Lin et al., 2007), 1 OU/m^{3} 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. 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. 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.
5. CONCLUSION
The effect of downstream buildings on near-field odor dispersion from rooftop odor emissions was investigated using computational fluid dynamics (CFD). The simulated flow and concentration results of neutral stability condition were compared with the wind tunnel experiments. Although more comparisons are needed to derive firmer conclusions, this study has produced the following conclusions:
- (1) The horizontal mean velocity simulation results of a one-building configuration showed a reasonable level of agreement with wind tunnel data.
- (2) The result of the SST k-ω model with the Schmidt number S_{ct}=0.1 reveals good agreement with wind tunnel result for the concentration field.
- (3) In the case of a one-building configuration, as the odor emission rate increases, the odor plume touched the rooftop surface and was dragged downstream of the building. However, some odor plume moves to the building’s side facet but most of the odor plume moves to the building rooftop and leeward facet.
- (4) In the case of a two-building configuration, the plume tends to cover the rooftop surface and windward facet of the downstream building as the emission rate increases. The results clearly indicate that the increasing emission rate has a great impact on the second building.
- (5) In the case of a three-building configuration, the addition of a third building, 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.
Acknowledgments
This work was supported by Kyonggi University Research Grant 2015.
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