Theoretical models implemented in software SIRANE

The flow in a street canyon consists of a recirculation in the plane transverse to the street and a longitudinal flow along the street.

The details of this flow depends on the geometry of the street and wind (speed and direction).

Due to the movement of recirculation which confines the transverse flow to the street, the average speed \(U_{street}\) is necessarily oriented along the street. It is assumed that this longitudinal flow results from a balance between the driving by the external flow and the friction on the sides of the street. With these assumptions, we can show that (Soulhac et al., 2008) depends :

• Wind velocity (quantified by the friction velocity \(u^*\)).
• Wind direction with respect to the street axis \(\varphi\).
• Height \(H\) and width \(W\) of the street.
• The roughness of the walls of buildings \(z_{0,bat}\)

The mass balance of pollutant within the street ensures the balance of different streams :

• The source of pollutants due to traffic on the street
• Advective flow of pollutants imported by the upstream intersection.
• Advective flux of pollutants discharged from the downstream intersection.
• The turbulent flow of pollutants exchanged with the atmosphere outside the top of the street.

Writing this balance can express the average concentration within the street.

In SIRANE software, modeling of flow in an intersection aims to determine how pollutant flows are exchanged between the various intersecting streets. Detailed numerical simulations (Soulhac et al., 2009) have helped to highlight the two main behaviors taken into account in modeling an intersection:

• Horizontal air flow from street to street.
• The vertical movements between the interior and the exterior of the canopy.

The calculation of pollutant flows from street to street involves determining the convective flux \(P_{i,j}\) exchange between \(i\) street and \(j\) street intersections. For this, we assume that the currents from upstream streets do not intersect and behave purely two-dimensional (see figure on the right).

The vertical structure of the atmosphere in the boundary layer surface is modeled using the theory of similarity Monin-Obukhov. The velocity profile is described by the equation: \[u(z)=\frac{u_\star}{\kappa} \left [ ln \left (\frac{z-d}{z_0} \right ) - \psi_m \left ( \frac{z-d}{L_{MO}} \right ) \right ] \] with :

• \(z\) altitude above ground.
• \(u*\) friction velocity.
• \(\kappa\) Karman constant.
• \(z_0\) est la aerodynamic roughness of the area.
• \(d\) displacement thickness of the area.
• \(\psi_m\) universal function.
• \(L_{MO}\) Monin-Obukhov length.

The values ​​of these parameters are determined by SIRANE from meteorological data and site characteristics, using parameterizations of meteorological preprocessor.

To properly describe the pollution at disctrit scale, it is necessary to take into account the transport of pollutants above roof level.

Pollutants above this level is derived from sources above the buildings, or turbulent diffusion of pollutants present in the streets through street-atmosphere interface.

These two terms are both treated as sources flow in the external flow. Conversely, pollutants that diffuse from the atmosphere to the streets are treated as sources negative flow.

In SIRANE software, transport of pollutants in the atmosphere is represented using a Gaussian plume model. Each intersection and every street becomes the source of a plume responsible of a concentration distribution given by equation panache.