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06 / August / 2010
Markus Sander ms785@cam.ac.uk
Soot Formation
Burner
Flame Condensation of PAHs Coalescense Particle Inception by PAHs Reaction Zone
Temperature
Stochastic model describing the formation of soot particles in - - PowerPoint PPT Presentation
Stochastic model describing the formation of soot particles in - - PowerPoint PPT Presentation
Stochastic model describing the formation of soot particles in flames Markus Sander, Robert IA Patterson, Abhijeet Raj and Markus Kraft 06 / August / 2010 Soot Formation Temperature Reaction Zone Burner Flame Carbon Addition Reactions
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Markus Sander ms785@cam.ac.uk
Using structural information
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Markus Sander ms785@cam.ac.uk
PAH reactions (selection)
S1 S2 S3 S4 S5 S6 Free-edge growth Free-edge desorption 5-member ring addition 5-member ring desorption Armchair growth 5- to 6-member ring Frenklach, Wang, Violi
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Markus Sander ms785@cam.ac.uk
PAH KMC growth simulation
Growth of a PAH molecule – kinetic Monte Carlo (KMC) simulation Seed molecule: Seed molecule: Pyrene Pyrene
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Markus Sander ms785@cam.ac.uk
The PAH-PP Model
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Markus Sander ms785@cam.ac.uk
The Data Structure
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Markus Sander ms785@cam.ac.uk
The Data Structure
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Markus Sander ms785@cam.ac.uk
Data structure: A Binary Tree
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Markus Sander ms785@cam.ac.uk
Jump Processes
Inception: Coagulation: Condensation:
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Markus Sander ms785@cam.ac.uk
Particle Rounding
Coalescence level: Surface change due to particle growth: s: Smoothing factor.
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Markus Sander ms785@cam.ac.uk
PAH Growth inside Particles
- They are notfully accessible to the gasphase.
- Active sites are blocked
PAHs inside particles grow slower then PAHs in the gasphase: The growth of PAHs inside particles is multiplied with the growthfactor g (0<g<1)
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Markus Sander ms785@cam.ac.uk
Parameter Estimation
How to determine the unknown parameters?
1. The parameter range has been determined. 2. Parameters have been calculated using a low discrepency series and the model evaluated at these points. 3. The set of parameters that minimises the objective function has been chosen and further optimised using a response surface method.
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Markus Sander ms785@cam.ac.uk
Parameter Estimation
The median di of the particle size distribution is optimised against experimental vlues by minimising the objective function: Data points in the 3-dimensional parameter space are generated using a Halton low discrepancy series.
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Markus Sander ms785@cam.ac.uk
Parameter Estimation
Further optimisation using a response surface approximation: Mean and variance can be expressed in terms of . Target function:
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Markus Sander ms785@cam.ac.uk
Parameter Estimation
Where to get experimental data from?
From the literature But computers are bad in reading papers! Use a machine readable format to store data.
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Markus Sander ms785@cam.ac.uk
Automated Model Optimisation
A PrIMe XML file for a flame
- M. Frenklach. Transforming data into knowledge Process Informatics
for combustion chemistry. Proc. Combust. Inst., 31:125–140, 2007.
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Markus Sander ms785@cam.ac.uk
Results
Flame A2 Flame B3
Experimental data from:
- B. Zhao, Z. Yang, Z. Li, M. V. Johnston, and H. Wang. Particle size distribution function of incipient soot in laminar
premixed ethylene flames: effect of flame temperature. Proc. Combust. Inst., 30(2):1441–1448, 2005.
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Markus Sander ms785@cam.ac.uk
Results
5 mm HAB 8 mm HAB 10 mm HAB 12 mm HAB
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Markus Sander ms785@cam.ac.uk
Results
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Markus Sander ms785@cam.ac.uk
Conclusion
- A detailed particle model involving the
connectivity of the primary particles has been presented.
- A priori unknown parameters have been
estimated using a combination of a low discrepancy series and a response surface
- ptimisation.
- Results have been validated against
experimental data.
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Markus Sander ms785@cam.ac.uk