M.K. Neophytou1&2, D. Goussis2, E. Mastorakos1, R.E. Britter1

1 University of Cambridge, Department of Engineering, Trumpington Street, Cambridge CB2 1PZ, UK

2 Institute of Chemical Engineering and High Temperature Processes, F.O.R.T.H., Patras 26500, Greece

The development of a The development of a scale-adaptive reactive pollutant dispersion scale-adaptive reactive pollutant dispersion

modelmodel

1. INTRODUCTION

The dispersion of reactive pollutants involves physical and chemical processes that occur over a wide

range of spatial and temporal scales.

2. SCALE-VARIANT APPROACHES

An appropriate modelling basis for model “nesting” must address the scale-variant nature of both the chemical and the physical processes involved in the dispersion.

For the physical processes, such common modelling approaches are the Reynolds-Averaged-Navier-Stokes and the Large-Eddy Simulations, or even more sophisticated approaches can be used such as the Conditional Moment Closure [2]. For the chemical processes however, modelling has little addressed so far the transformations on a time scale basis.

For the aims of this work, we employ the Computational Singular Perturbation (CSP) Analysis[3]. CSP is a rigorous time scale analysis technique that is currently used to model turbulent reacting flows in combustion, and has only very recently been applied to realistic pollution chemistry[4]. CSP performs an eigenvalue analysis and algorithmically identifies the time scale of the reacting species; what determines the “fast-” and “slow-” reacting species is the associated time scale of the turbulent mixing. In the modelling of reactive pollutant dispersion, CSP analysis has the potential to adjust itself naturally to a change of time scale, while being consistent in itself in the chemical reduction across a change of scale.

This project has benefited from the EU Programme STOPP and is currently being funded by the UK-EPSRC Programme DAPPLE

5. CONCLUDING REMARKS AND FURTHER WORK

1. A rigorous time scale analysis has been applied to resolve a typical scale range of atmospheric chemical processes.

2. If we compare the chemical time scales with the physical time scales, there are two regimes of mixing-chemistry interaction that can be identified, in which:

the chemical time scales are faster than the mixing scale processes, thus they reach a quasi-steady equilibrium before the reactants start dispersing, and thereby certain approximations can be made about the chemical compositions of the reactants and products;

the mixing time scale is faster than the chemical time scale, and the reactants well-mixed before they have undergone any transformation

3. This scale-adaptive reactive model can be incorporated into dispersion models.

References:

1. Britter RE & Hanna SR, (2003) Flow and dispersion in urban areas, Annual Review of Fluid Mechanics, 35:469-96.

2. Klimenko AY & Bilger RW (1998) Conditional Moment Closure for turbulent combustion, Prog. Energy Combust. Sci. 25:595-687

3. Massias, Diamantis, Mastorakos & Goussis (1999). An algorithm for the construction of global reduced mechanisms with CSP data. Combus. Flame 117, 685-708

4. Neophytou MK, Goussis D, van Loon M, Mastorakos E (2003), Reduced chemical mechanisms for atmospheric pollution using Computational Singular Perturbation Analysis, Atmospheric Environment – submitted.

5. Gery, Whitten, Killus, Dodge (1989). A photochemical kinetics mechanism for urban and regional scale computer modelling. J. Geophys. Res. 94, D10, 12925-56

Imagine yourself standing inside a street canyon in your home city. How much of what you breathe there, has actually come from the street itself, and how much from the surrounding neighbourhood and the surrounding city?

To address such questions, pollutant dispersion modelling points towards a “nesting” of the various individual models that address dispersion, each at a particular scale[1]. However, when the chemical reactions of pollutants (which have their own time scales) are considered, a “nesting” task needs to address the interaction between the mixing process and the chemistry at all scales.

4. A TIME SCALE ANALYSIS FOR CHEMISTRY

3. A TIME-SCALE ESTIMATE FOR PHYSICS

Characteristic spatial scales of the physical processes can be translated into characteristic temporal scales using a representative wind advection speed. For a typical wind speed (U) of 5m/s, for example, time scales will range from 6.7x10-1 min (for the street canyon) up to 6.7x102 min (for the regional scale).

Test Case CSP analysis for the chemical processes is performed for an urban scenario in which the initial VOC/NOx ratio is 10.. The Carbon Bond Mechanism (CBM-IV), which consists of 81 reactions and 32 species[5], is used to describe the detailed atmospheric chemistry. A box model is considered in which there are no advection or diffusion processes involved; finite concentrations of species are released and evolve in time due to the CBM-IV chemistry. Initial conditions are taken from a set of measurements at the Marylebone area in Central London, UK.

Results

Time scales of reacting chemical species overall range from an order of 10-4 min up to 10+8 min. Figure 3 shows the diurnal variation of the local time scales for selected species of interest in the CBM-IV mechanism in an urban scenario.

Regional(~ 200 km)

City(~ 20 km)

Neighbourhood(~ 2 km)

Street Canyon(~ 0.2 km)

Physical space/time scales Chemical time scales

regional time scale

canyon time scale

regional time scale

canyon time scale

regional time scale

canyon time scale

Reactive Pollutant Dispersion

physical processes(e.g. wind advection, diffusion)

chemical processes(e.g. reactions, emissions)

Figure 2: Aerial photo of the Marylebone area in London (UK)illustrating thestreet canyon and neighbourhood scales

Figure 1: Reactive pollutant dispersion involves dynamical and chemical processes over a wide range of scales.

Figure 3: Diurnal variation of the local time scales of chemicalspecies in atmospheric chemistry subject to urban conditions.