A New Algorithm to Solve Condensation/Evaporation Growth and Coagulation of Nanoparticles
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A New Algorithm to Solve Condensation/Evaporation Growth and Coagulation of Nanoparticles
Marion Devilliers1,2, Christian Seigneur2, Edouard Debry1, Karine Sartelet2
1 National Institute of Industrial Environment and Risk (INERIS), Verneuil en Halatte, France
2 Atmospheric Environnement Center (CEREA), Joint Laboratory École des Ponts ParisTech/EDF R&D, Université Paris-Est, France
European Geosciences UnionGeneral Assembly 2011 Vienna | Austria | 05 April 2011
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Nanoparticles : a health concern
• Definition : at least one of the dimensions of the particle is less than 100 nm
• Potential adverse effects on human health
• Multiple sources :– indoor air (domestic activities)– outdoor air (road traffic, ...)
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Objectives of this study
• To be accurate with both number (important for nanoparticles) and mass (important for fine and coarse particles)
• To correctly account for phenomena specific to nanoparticles such as Kelvin effect, van der Waals forces, electric forces for charged particles, and fractal aspect
→ development of an aerosol model suitable for both indoor and outdoor applications
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The sectional approach
• Development of a 0D model with particle size distribution discretized in N sections
• Each section is characterized by a representative mean diameter, a number concentration and/or a mass concentration of particles
• Hypotheses are:– temperature and particle density are constant– all particles have the same composition– particles are spherical
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Initial distribution : regional pollution
number distribution volume distribution
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Initial distribution : diesel vehicles
number distribution volume distribution
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Condensation/EvaporationThe volume variation at each time step for the section i is
calculated using the following formula:
with the Kelvin effect calculated as follows:
and the partial gas pressure being updated at every time step because of mass conservation
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Redistribution of the particles
• To keep the representative diameter in the section, particles which are too large or too small are moved to the next or the previous section
• To redistribute particles among sections, different schemes have been tested and compared
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Standard redistribution schemesEuler-Mass:
Euler-Number:
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Advanced redistribution schemes
• Moving-Diameter redistribution when diameter changes
section (based on Jacobson scheme)
• Full-Moving no redistribution, cannot be used in 3D but here as the reference (with 500 sections)
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New schemes
• Euler-Hybrid number redistribution for nanoparticles,
mass redistribution for fine and coarse particles
• Euler-Coupleredistribution conserving both mass and
number
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Results : regional pollution
Moving-Diameterand Euler-Hybridshow the best results
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Results : diesel vehicles
• Moving-Diameter shows the best results• Euler-Hybrid is better than the other Euler schemes
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Performance statistics
Comparing to our reference using the formula (for the number) :
Distribution Error Euler-Mass
Euler-Number
Euler-Hybrid
Euler-Couple
Moving-Diameter
Regional pollution
logN 1.24 0.32 0.30 0.41 0.19
M 0.21 0.72 0.05 0.15 0.14
Diesel vehicules
logN 0.89 0.92 0.81 0.80 0.29
M 0.63 1.41 0.63 1.21 1.24
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Coagulation
Coagulation has been added to the model that simulate c/e with the Euler-Hybrid scheme(using a splitting method)
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Future work
• Comparison of different coagulation kernels:– integrated over the section– based on representative diameter
• Van der Waals forces will be taken into account for coagulation
• A new other scheme: Euler - Irregular using a finer discretization for nanoparticles
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Thank you for your attention