The document discusses chemical kinetics modeling of combustion reactions. It describes the need for detailed chemical kinetic models to understand fuel oxidation, pollutant formation, and combustion chemistry phenomena. Complex fuel mixtures require the use of reduced model fuels and reaction mechanisms. Detailed mechanisms are generated using generic reaction classes and can involve hundreds to thousands of species and reactions. Mechanism reduction techniques like lumping and skeletal reduction are used to reduce mechanism size and computational cost for modeling applications.

4. Why Model fuels ? Example of composition of a commercial diesel fuel, from Dagaut,P., PCCP, 4 , 2079-2094 (2002). Real fuel : - Diesel, Gasoline, Biofuels or Kerosene Fuels - Too complex to model using all the components Model Fuel : Reproduce the oxidation characteristics of a real fuel (Diesel, Gasoline, Kerosene Fuels…)

8. Reaction Pathway Generic: Example: Classic low temperature alkane pathway R + O 2 = ● R +O 2 H ● R + O 2 = ● ROO ● ROO = ● QOOH ● QOOH + O 2 = ● OOQOOH ● OOQOOH = ● OQOOH + OH ● OQOOH = products + OH CH 3 CH 2 CH 2 CH 3 + O 2 = ● CH 2 CH 2 CH 2 CH 3 + O 2 H ● CH 2 CH 2 CH 2 CH 3 + O 2 = ● OOCH 2 CH 2 CH 2 CH 3 ● OOCH 2 CH 2 CH 2 CH 3 = HOOCH 2 ● CHCH 2 CH 3 HOOCH 2 ● CHCH 2 CH 3 + O 2 = HOOCH 2 CH(OO)CH 2 CH 3 HOOCH 2 CH(OO)CH 2 CH 3 = HCOCH(OOH)CH 2 CH 3 + OH HCOCH(OOH)CH 2 CH 3 = products + OH

9. Sub-Mechanism A pathway generates a sub-mechanism tree of reactions

17. Single Reaction Generation Application to form a specific reaction: Reaction pattern: Chemical formula in the mechanism: CH 3 CH 2 ● CHCH 2 OOH CH 3 CH 2 CHCH 2 ● OOH + H H H ● C C O O H C C H H H H H ● O O H H H H C C C C H H H H H + R c R a R d R b ● C C O O H R c R a R d R b C C O H ● O +

19. Reaction Pathway Generic: Example: Classic low temperature alkane pathway R + O 2 = ● R +O 2 H ● R + O 2 = ● ROO ● ROO = ● QOOH ● QOOH + O 2 = ● OOQOOH ● OOQOOH = ● OQOOH + OH ● OQOOH = products + OH CH 3 CH 2 CH 2 CH 3 + O 2 = ● CH 2 CH 2 CH 2 CH 3 + O 2 H ● CH 2 CH 2 CH 2 CH 3 + O 2 = ● OOCH 2 CH 2 CH 2 CH 3 ● OOCH 2 CH 2 CH 2 CH 3 = HOOCH 2 ● CHCH 2 CH 3 HOOCH 2 ● CHCH 2 CH 3 + O 2 = HOOCH 2 CH(OO)CH 2 CH 3 HOOCH 2 CH(OO)CH 2 CH 3 = HCOCH(OOH)CH 2 CH 3 + OH HCOCH(OOH)CH 2 CH 3 = products + OH

20. Reaction Pathway A pathway generates a sub-mechanism tree of reactions

25. Controlled Generation Only products of last step are used in next step Examples: Moréac, G., Blurock, E. S.;Automatic generation of a detailed mechanism for the oxidation of n-decane, to be published in Comb. Sci. Technol. (2006) Blurock, E. S., Detailed Mechanism Generation 1: Generalized Reactive Properties as Reaction Class Substructures. J. Chem. Inf. Comp. Sci., 44 , 1336-1347 (2004) Product pool Generate first step Seed molecule Generate Second step . . .

31. Example of Chemical Lumping Schematic representation for the lumping of four different 5-ring alkylperoxy radicals 5r-C 7 H 14 OOH

32. Lumped species in n -heptane Mechanism 6r-QOOH Species R O 2 Species p = 40bar,  = 1.0, T = 800K Concentration of Species Lumped Together Add to Single Lumped Species

33. 1362 reactions 142 species n -C 7 H 16 L-C 7 H 15 L-C 7 H 15 O 2 A-5r B-5r C-5r D-5r A-6r B-6r C-6r D-6r A-7r B-7r C-7r D-7r A-8r B-8r C-8r D-8r L = Lumped species, 5r, 6r, 7r and 8r represent the size of the ring Lumped Mechanism : n -heptane 1624 reactions 203 species Detailed

34. Lumped Mechanism – Same As Detailed Davis and Law Laminar flame speed for n -heptane/air mixture at p=1 bar and T i =298 K Experimental data (symbols) Detailed mechanism (solid line) Lumped mechanism (dashed line)

40. Skeleton Mechanism : n -heptane 470 reactions 64 species N -C 7 H 16 L-C 7 H 15 L-C 7 H 15 O 2 A-5r B-5r C-5r D-5r A-6r B-6r C-6r D-6r A-7r B-7r C-7r D-7r Lumped n - C 7 H 16 L - C 7 H 15 L - C 7 H 15 O 2 A - 5r B - 5r C - 5r D - 5r A - 6r B - 6r C - 6r D - 6r A - 7r B - 7r C - 7r D - 7r A - 8r B - 8r C - 8r D - 8r L = Lumped species, 5r, 6r, 7r and 8r represent the size of the ring 1362 reactions 142 species n - C 7 H 16 L - C 7 H 15 L - C 7 H 15 O 2 A - 5r B - 5r C - 5r D - 5r A - 6r B - 6r C - 6r D - 6r A - 7r B - 7r C - 7r D - 7r A - 8r B - 8r C - 8r D - 8r L = Lumped species, 5r, 6r, 7r and 8r represent the size of the ring n - C 7 H 16 L - C 7 H 15 L - C 7 H 15 O 2 A - 5r B - 5r C - 5r D - 5r A - 6r B - 6r C - 6r D - 6r A - 7r B - 7r C - 7r D - 7r A - 8r B - 8r C - 8r D - 8r n - C 7 H 16 L - C 7 H 15 L - C 7 H 15 O 2 A - 5r B - 5r C - 5r D - 5r A - 6r B - 6r C - 6r D - 6r A - 7r B - 7r C - 7r D - 7r A - 8r B - 8r C - 8r D - 8r L = Lumped species, 5r, 6r, 7r and 8r represent the size of the ring 1362 reactions 142 species 1624 reactions 203 species Detailed

47. Example: Library Probability Density Function ( PDF ) A stochastic method that uses distribution functions to describe the fluctuating scalars in a turbulent field. Pope, S. B. PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11 ,119-92 (1985). Flamelets “ Thin diffusion layers embedded in a turbulent non- reactive flow field.” Peters, N., Turbulent combustion, Cambridge University Press, Cambridge, (2000).

49. Example of Adaptive Chemistry Two-zone zero-dimensional stochastic reactor model (SRM) for SI-Engine calculations. Each particle in the PDF (Probability Density Function) calls a different phase at each time-step during the calculation. The basic idea behind the SRM is to divide the mass within the cylinder into an arbitrary number of particles, and to use a Stochastic Monte Carlo process with an operator splitting algorithm.

51. Optimization of Rate Coefficients Frequency Factor Temperature Exponent Activation Energy

52. Optimization of Rate Coefficients Frenklach, M.; Wang H.; Rabinovitz, M. J., Prog. Energy Combustion Sci., 18 , 47-73 (1992). Function to Optimize Model – Experimental Data Response Surface y

53. Reduction-Optimization Cycle