A large eddy simulation study of pollutant dispersion in urban areas

Pollutant dispersion in urban areas is nowadays a critical environmental problem. In the present abstract we discuss a recent large-eddy simulation model developed for the study of dispersion at neighborhood scale. The model resolves the incompressible set of equations of motion under the Boussinesq approximation in a curvilinear frame of reference. A body fitted grid is used to reproduce the macroscopic terrain slopes while the immersed boundary method of Roman et al. (Comp. & Fluids, 2009) is used to reproduce complex geometric features, like buildings. Wall shear stresses are reproduced using two different approaches depending on the kind of solid wall. An equilibrium-stress wall-layer model together with a modification of the Smagorinsky SGS model is employed at the body-fitted walls, whereas the equilibrium-stress model of Roman et al. (Phys. Fluids, 2009) has been set over the immersed boundaries. A standard Smagorinsky model is used in the flow field. The governing equations are solved through the fractional step algorithm of Zang et al. (J. Comp. Phys., 1994). The advective terms of momentum equation and advection-diffusion equation of the pollutant concentration are treated using two different strategies. First we use centered second order accurate scheme together with explicit high-order filter to remove spurious wiggles arising close to the sharp corners of the buildings (F-simulations). Second we used a quadratic upwind interpolation (Q-simulations). The first strategy has the advantage to preserve the correct level of turbulent kinetic energy in the flow field, while removing small scale unphysical wiggles. The main drawback of this procedure stands in the empirical calibration required for the frequency of filtering. The second strategy does not require calibration but has the drawback to remove a large amount of turbulent kinetic energy. The model has been massively validated against numerical and experimental literature data. Tests have been performed reproducing cases with increased complexity. First a bottom Ekman layer archetypal of a neutral atmospheric boundary layer has been reproduced and results compared with those of Sullivan and Moeng & Sullivan (J. Atm. Sci, 1994). Successively a wind tunnel experiment of the flow around an isolated obstacle (CEVDAL database) has been reproduced. In this test, emission of a dilute concentration in the downwind side of the obstacle has been also simulated. Third, the flow around an array of low-rising buildings (MUST experiment) has been reproduced with an incidence angle of 41°.

Overall, the validation phase has shown that the Q simulations overestimate the average velocity when held at a constant driving force because of suppression of a noticeable amount of turbulent kinetic energy and a consequent underestimation of the friction coefficient. This problem is less evident when the simulations are carried out at constant flow rate. In this case the average velocity is well predicted while the underestimation of the wall shear stress affects less the characteristics of the mean velocity field. When simulating dispersion of a dye, F simulations tend to spread the pollutant concentration over a larger region because explicit filtering diffuses at a faster rate the concentration itself. This effect is not present in the Q simulations. The main drawback of Q simulations was the prediction of a too low level of turbulent kinetic energy when compared to the reference data.

As an applicative example we finally studied pollutant release in a residential area of the city of Trieste in Italy. The simulated area has the shape of a valley which is confined on one side by the sea (see fig.1 where a schematic of the domain is reported together with the reference coordinate system). The area covered by the simulation has a horizontal extensions of Lx= 1500m and Ly=1000m and a vertical extension Lz=600m. 256x256 equispaced grid nodes were used in the horizontal directions while in the vertical one 60 points were used. They were clustered near the ground with a maximum resolution of 1m. The flow is directed along the x direction, mimicking a south-west sea breeze. The inflow planes at x=0 were generated by a LES pre-simulation over a periodic domain, while at the outflow plane located at x=Lx a zero gradient condition was used together with a damping region to avoid spurious reflections in the domain. At the lateral and at the upper sides free slip conditions were set. The base of the body fitted grid was derived through an interpolation of the terrain elevations. The velocity at the nodes placed close to the fluid IB interface, called IB nodes, has been derived through a linear interpolation of the velocities at the projection nodes. To simulate pollutant dispersion from urban vehicle traffic, we have set a line source placed in the central part of the domain.

The results of the simulations have shown that in Q simulations the dissipative scheme produced a flow field in which the size of the smallest turbulent structures was considerably larger than in the F simulations. The latter ones seem to be preferable since are able to suppress the oscillations and at the same time they furnish a more detailed representation of the small turbulent structures acting at the building scales. Results for the scalar concentration are currently under analysis and will be shown at the workshop.