Computational Fluid Dynamics models

Eulerian and Lagrangian models have become uniquely efficient tools for atmospheric dispersion simulations from meso- to macroscale. These models are tightly connected to numerical weather prognostic (NWP) models that provide wind field and other meteorological data in order to perform dispersion calculations. Grid resolution of NWP models is in a range of 1 to 10 km, however, several dispersion problems are concentrated on a smaller scale.

Most importantly, in case of urban air pollution, source and receptor points are often located within a few hundred meters from each other, surrounded by a very complex geometry. Wind field datasets from NWP models have far too coarse resolution to represent the wind field within an urban area, thus existing Eulerian and Lagrangian dis-persion models cannot be used.

As urban air quality has become a more and more important part of environmental and health protection, two ap-proaches have been developed to provide air quality forecasts within urban areas: a statistical and a dynamic (CFD) approach. The former tried to determine a statistical correlation between meteorological data and air quality measurement time series. In the years when computational performance did not allow running fine resolution flow simulations for urban areas, this approach provided valuable air quality forecasts for many populated cities.

However, the method had the disadvantage that it required detailed and long-term air quality measurement data, thus it was not applicable for fast-developing cities that lacked earlier measurements. Furthermore, changes in the city structure or even impact studies of planned buildings’ effect on air quality couldn’t be simulated.

The more and more efficient computers led to the rapid development of the Computational Fluid Dynamics (CFD) technology, a general purpose engineering tool for numerical flow simulation. They provide a tool to solve various partial differential equations (PDEs) that enables the user to define the governing equations that best fit to their needs. The basic form of the Navier–Stokes-equation for turbulent incompressible fluids

(10.38) ,

where is the wind field, is density,pis pressure, is the eddy viscosity and is the gravitational acceleration vector. Equation (10.38) is very similar to the one solved in numerical weather prognostic (NWP) models, however, the coordinate system, grid, boundary conditions and physical parameterizations are completely different (Figures 10.9, 10.10).

Dispersion of air pollutants

Figure 10.9: Horizontal cross section of the wind field (m/s) and turbulent diffusion coefficient (m²/s) at 10 m height around the buildings of the Paks Nuclear Power Plant, assuming 10 m/s south-westerly wind. On the lee

side, turbulent diffusion dominates over advection.

The flexibility of CFD models’ application for different purposes led to their large dominance on all areas of mechanical and environmental engineering as well as microscale dispersion modelling (Balczó et al., 2011).

CFD models consist of four main parts:

1. a mesh generator, that splits the computational domain to cells with a user-defined resolution;

2. a PDE solver, that solves a selected form of the Navier–Stokes and other attached (e.g. dispersion) equations;

3. turbulence model;

4. a visualization tool to create 3D plots and slices of the computed fields.

Key parameters of a CFD model are the mesh, the solver and the turbulence model. While in engineering cases the computationally most efficient tetrahedral mesh and finite element solvers are used, atmospheric simulations are often carried out on hexahedral mesh and/or using finite volume solvers.

Figure 10.10: Horizontal cross section of concentration field after a hypothetical release from the southern tower at 10 m height at Paks Nuclear Power Plant. If advection dominates at the source point, crosswind dispersion is weak (westerly wind, right). If the source point is in downwash area, cross- and upwind dispersion is significant

(easterly wind, left).

As CFD models are often used around complex geometry, a fine grid resolution is required to explicitly calculate turbulence to a very low scale that results in a very large computational cost. However, subgrid-scale turbulence still has to be estimated, which in most cases is assumed to be isotropic. Among the various turbulence models for CFD, the k-e approach has become the most popular for both engineering and atmospheric applications. However, in the atmosphere, anisotropy of turbulence can cause large errors in k-e results, thus modified atmosphere-oriented

Dispersion of air pollutants

CFD-based street canyon models are widely used to predict air quality in urban and industrial areas. Atmospheric dispersion and even chemical reactions can be simulated together with the flow on the same grid. Another solution is to use the CFD tools only to provide a stationary wind field, and modify an existing Eulerian or Lagrangian dispersion model to carry out transport simulations using the CFD-based wind data. General purpose computational fluid dynamics packages like ANSYS’s Fluent and the open-source OpenFOAM are often used for atmospheric studies, furthermore, several CFD softwares have been designed specifically for atmospheric dispersion and wind engineering studies like the German MISKAM or the French MERCURE.

Baklanov (2000) pointed out several weaknesses that made CFD results less reliable as the scale increased. The convective boundary layer (CBL) usually extends over 1 km and the very fine grid resolution does not allow running the simulation in its whole height within a reasonable computational time. It makes very difficult to take into account atmospheric stability parameters that are dominant in convective cases. Another difficulty is to provide proper boundary conditions for wind and turbulence parameters either from measurement or NWP data. Although nesting CFD into NWP models is difficult due to their different coordinates, governing equations and variables, Tewari et al., 2010 presented promising results using WRF and a three-dimensional CFD code.

While numerical weather prognostic (NWP) and computational fluid dynamics (CFD) models provide reliable wind data for all scales of atmospheric dispersion simulations, their connection proved to be difficult. While recent developments of NWPs achieve more and more detailed resolution, CFD models with enhanced computational capacity, parallel computing and LES simulation for anisotropic turbulence are becoming even better for PBL simulations. Either the modification of an NWP model to perform microscale simulations, or an extension of a CFD software for atmospheric studies holds large possibilities and gaps, and is a direction of extensive research from both meteorological and environmental engineering side (Table 10.6).

Table 10.6: Recommended approaches for different scales and applications of atmospheric dispersion modelling 100 – 1000 km

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