# Design of Road-Side Barriers to Mitigate Air Pollution near Roads
## 2 Methodology
### Simulation of the Dispersion Phenomena (the NR-CFD Model)
This methodology was adopted for the present work to describe the turbulence within the chosen atmospheric stability condition, and the \(k\) and \(\varepsilon\) average values reported by them were also used for the inlet boundary condition. _Simulation of the pollutant dispersion:_ Vehicle transit over roads generates pollutants that are emitted both directly from the vehicle's tailpipe and from the road-wheels interaction. Attempting to deal with the complexity of the real air pollutant dispersion, researchers have subdivided its study in three phases [39]: From the source (tailpipe or wheel-road interaction) to the ambient near the vehicle, where solid and gas phase pollutants maintain their characteristics with a dilution ratio of up to 1000:1. Then, from the vehicle to the road, where pollutants mix with other sources of pollutants with a dilution ratio of up to 10:1, and then from the road to the ambient downwind the road. Focusing this work on the last phase, a uniform concentration on the road was assumed as a net result of the multiple vehicles crossing by the same position over a long time, regardless of the exact source of the pollutants. For comparative purposes, an arbitrary emission of \(E\) = 1 g s\({}^{-1}\) m\({}^{-2}\) was chosen, verifying that results do not depend on the emission rate [22]. Chemical reactions were not considered in this model, which is acceptable for the case of inert pollutants or pollutants with a mean lifetime significantly longer than the residence time within the computational domain. In our case, for a wind speed of 1 m/s, the residence time of gas-phase pollutants in the computational domain is -5.5 min. In order to model gas-phase pollutants dispersion, a species transport model was added to our CFD simulation. It solves the conservation equations for each of the chemical species in the computational domain and predicts their local mass fraction across said domain [40]. Thus, the model integrates a convection-diffusion equation (Equation (1)), as well as a mass diffusion flux equation for turbulent flows (Equation (2)) during the iterative solution process. \[\frac{d(\rho Y_{i})}{dt}+\
abla\ (\rho uY_{i})\ =\ -\
abla\ J_{i}+R_{i}+S_{i} \tag{1}\]  
\[J_{i}\ =\ -\bigg{(}\rho D_{i,m}+\frac{H_{t}}{Sc_{t}}\bigg{)}\
abla Y_{i}-D_{T,i} \frac{\
abla T}{T} \tag{2}\]  
In Equations (1) and (2), \(u\) is the fluid velocity field, \(Y_{i}\) is the local mass fraction for species \(i\), \(J_{i}\) is the diffusion flux of species \(i\), \(R_{i}\) is the net production rate of species \(i\) by chemical reaction, \(S_{i}\) is the generation rate from the dispersed phase plus user-defined sources, \(\rho\) is the bulk fluid density, \(\mu_{i}\) is the turbulent viscosity, \(D_{i,m}\) is mass diffusion coefficient for species \(i\) in the mixture (defined as \(9\times 10^{-6}\) m\({}^{2}\) s\({}^{-1}\) for free SF\({}_{6}\)-air diffusion [41], \(D_{T,i}\) is the thermal (Soret) diffusion coefficient for specie \(i\), which can be neglected for the present case, and \(T\) is the bulk fluid temperature [40]. Bold symbols are vectors. For the present model, the species considered were dry air and SF\({}_{6}\). This last one is a tracer gas known for its high density compared to air and its easily detectable nature even at low concentrations. This gas-phase pollutant surrogate was chosen to directly compare the NR-CFD model to the experimental results of the NRTS08 campaign. _Other details of the CFD model:_ The solver used for the present study was the commercial software ANSYS FLUENT v2020. A pressure-based solver was used with a coupled scheme, in which, the mass and momentum equations are solved simultaneously while the other equations (energy, species transport and turbulence) are solved segregated. Even though the effects of the gravity were included in the simulation, no evidence of a strong influence of this term was observed in the solution. Second order schemes were used in the spatial discretization of all the equations.