EcoEngines Chemical Kinetics

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© 2006 Edward S. Blurock, Gladys Moréac, Lund University - All rights reserved.

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Chemical KineticsChemical Kinetics

An EC funded NoE on Energy Conversion in Engines

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Module B, Section 3This course was developed by:• Edward S. Blurock (Lund University)• Gladys Moréac (Lund University)

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Motivation

Chemical kinetics:

–Description of chemical oxidation behavior of commercial fuels.

–Detail is needed to describe:

- fuel oxidation

- pollutant formation

- CO emission

- NOx formation

- chemistry behind knock,etc.

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Purpose of PresentationAn outline of the state of the art in modeling

complex chemistry.– Many techniques will be presented– Too little time to present details

What you should get out of the presentation– That the methods presented exist– What the methods accomplish, their purpose– For more detail follow the key references given

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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…)

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Examples of model componentsGasoline:

- PRF (Primary Reference Fuels): iso-octane, n-heptane

- mono-aromatic: toluene, benzene, propylbenzene...

Diesel:

- PRF and/or linear alkanes

- Poly-aromatic: α-methylnaphthalene...

Kerosene:

- PRF and/or linear alkanes

- Poly-aromatic

- Naphtenes: propyl-cyclohexane...

Biofuels: Conventional fuels + additives (ETBE, MTBE, methanol...)

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Examples of chemical modelGlobal: One or very few reactions.

“Shell Model” (5 species, 8 reactions).Halstead, M. P.; Kirsch, L. J.; Prothero, A.; Quinn, C. P., Proc. Roy. Soc. London, A346, 515-538 (1975).

Reduced/Lumped: Valid under a limited set of conditions (T, P..)

- n-heptane oxidation and pyrolysis mechanism (41 species, 266 reactions)Held, T. J.; Marchese, A. J.; Dryer, F. L., Combust. Sci. Technol., 123, 107-146 (1997).

- n-decane oxidation mechanism (98-273 species and 644-1282 reactions)Glaude, P. A.; Battin-Leclerc, F.; Fournet, R.; Warth, V.; Côme, G. M.; Scacchi, G., Combust. Flame, 122,

451-462 (2000)

Detailed: Valid under a wide range of conditions.

- n-heptane oxidation mechanism (550 species and 2450 reactions)Curran, H. J.; Gaffuri, P.; Pitz, W. J.; Westbrook, C. K. Combust.Flame, 114, 149-177 (1998).

- n-decane oxidation mechanism (506 species and 3684 reactions)Moréac, G., Blurock, E. S., Mauss, F.; to be published in Combust. Sci. Technol. (2006)

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Mechanism structureWhether produced by hand or generated automatically,

the structure of the mechanism is the same

Species: Hydrocarbon Fuel, oxidizer, intermediates, products...

Reactions: How the species react with each other

Pathways: Succesive set of reactions

Sub-mechanisms: Blocks of related reactions from a pathway

Detailed mechanism: Combined set of sub-mechanisms

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Reaction Pathway

R + O2 = ●R +O2H

●R + O2 = ●ROO

●ROO = ●QOOH

●QOOH + O2 = ●OOQOOH

●OOQOOH = ●OQOOH + OH

●OQOOH = products + OH

CH3CH2CH2CH3 + O2 = ●CH2CH2CH2CH3 + O2H

●CH2CH2CH2CH3 + O2 = ●OOCH2CH2CH2CH3

●OOCH2CH2CH2CH3 = HOOCH2●CHCH2CH3

HOOCH2●CHCH2CH3 + O2= HOOCH2CH(OO)CH2CH3

HOOCH2CH(OO)CH2CH3 = HCOCH(OOH)CH2CH3 + OH

HCOCH(OOH)CH2CH3 = products + OH

Generic: Example:

Classic low temperature alkane pathway

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Sub-MechanismA pathway generates a sub-mechanism tree of reactions

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Outline

Detailed Mechanism Generation– Reactive Center and Reaction Generation– Complete Mechanism Generation– Optimization

Mechanism Reduction– Skeletal – Time Scale Analysis– Lumping– Adaptive Chemistry

Rate coefficient Optimization– Automatic Reaction Coefficient Optimization

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Detailed Mechanism GenerationSingle Reaction Generation

– Generic Reaction Classes Definition of Reactive Center and Environment

– Application of Reaction Class to SpeciesRecognition of reactive centerApplication of bond/valence changes

Reaction Pathways– Sub-Mechanisms

Complete Mechanism Generation– Exhaustive Application of Reaction Classes

Filtering of unwanted reactions– Controlled Generation

Generate only a fixed path of reactions

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Why Detailed Mechanism Generation?

Detailed mechanisms of large hydrocarbons:

Too large and too complex now to do by hand

Hundreds to thousands of species and reactions

Automation is another level of thinking:

Not thinking of individual species and reactions

Rather classes of species and reactions

Chemical classes:

Groups of reactions and species with similar properties

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Single Reaction Generation

Reaction Center

The set of bonds and atom valences that change in the course of a reaction

Examples:

Generic Loss of Radical to Form Olefin

Generic Group Replaced by an Oxygen

●C C A ●C C ●A

●C C O ●C C ●O

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Single Reaction GenerationReaction Pattern

Supplemented with the Environment around Reactive Center

(Functional Groups which can effect reaction rate)

Peroxyl Group Influence on bonding

Include Bonding of Carbon

RcRa

RdRb

●C C O O H

RcRa

RdRb

C C ●O O H

●C C O O H

C C ●O O H+

+

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Determines how the bonding and atom valences are changed in the course of the reaction

The Reactive Center Changes

The surrounding functional

Groups are unchanged

Correspondence Between Reactants and Products

RcRa

RdRb

●C C O O H

RcRa

RdRb

C C ●O O H

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Reaction Formation

Match Reactant of Reaction Pattern with Reactant

RcRa

RdRb

●C C O O H

HH

H

●C C O O HC CH

HH

HH

Reaction Pattern

Reactant

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CH3CH2●CHCH2OOH CH3CH2CHCH2

●OOH+

HH

H

●C C O O HC CH

HH

HH

●O O H

HH

H

C CC CH

HH

HH

+

RcRa

RdRb

●C C O O H

RcRa

RdRb

C C O H●O+

Application to form a specific reaction:

Reaction pattern:

Chemical formula in the mechanism:

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Mechanism GenerationSingle Reaction Generation







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Reaction Pathway

R + O2 = ●R +O2H

●R + O2 = ●ROO

●ROO = ●QOOH

●QOOH + O2 = ●OOQOOH

●OOQOOH = ●OQOOH + OH

●OQOOH = products + OH

CH3CH2CH2CH3 + O2 = ●CH2CH2CH2CH3 + O2H

●CH2CH2CH2CH3 + O2 = ●OOCH2CH2CH2CH3

●OOCH2CH2CH2CH3 = HOOCH2●CHCH2CH3

HOOCH2●CHCH2CH3 + O2= HOOCH2CH(OO)CH2CH3

HOOCH2CH(OO)CH2CH3 = HCOCH(OOH)CH2CH3 + OH

HCOCH(OOH)CH2CH3 = products + OH

Generic: Example:

Classic low temperature alkane pathway

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Reaction PathwayA pathway generates a sub-mechanism tree of reactions

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Detailed Mechanism GenerationSingle Reaction Generation







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Combinatorial ExplosionThe number of combinations of applications of reaction

classes can increase rapidly with species size

n-butanen-hexane

n-decane

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Everything can react with everything in a multitude of ways !

A large part of detailed mechanism production

is deciding what is important and what is not

How to avoid the combinatorial explosion?– Filtering of unreasonable reactions– Controlled generation of only the wanted reactions

Combinatorial Explosion

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Exhaustive with Filtering

Examples:

De Witt, M.J., Dooling, D.J., Broadbelt, L.J, Ind. Eng. Chem. Res., 39, 2228-2237 (2000)–Tetradecane pyrolysis: large extensive mechanisms

Grenda J.M., Androulaktis, I.P., Dean, A.M., Green Jr., W.H., Ind. Eng. Chem. Res,42, 1000-1010 (2003)

–Pressure dependent reactions through cycloalkyl intermediates–Use of Quantum Rice-Ramsperger-Kassel (QRRK) for pressure dependence

Product pool

Generate

next reaction

Filter out

End if no products

Seed molecule

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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 stepSeed molecule

Generate

Second step. . .

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Outline


Mechanism Reduction– Skeletal – Time Scale Analysis– Lumping– Adaptive Chemistry


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Mechanism Reduction

• Reduce the effective number of species and reactions in the differential equations to solve for source terms

• Computational Cost in a mechanism is – Number of Species: squared increase (building Jacobian)– Number of Reactions: linear increase (evaluating

exponential)

• Used to calculate the chemical source terms within larger more complex computations (Computational Fluid Dynamics)

Key reference:Tomlin, A.S.; Turanyi, T.; Pilling, M.J. “Mathematical tools for the construction, investigation and reduction of combustion mechanisms” in “Low temperature combustion and auto-ignition; Comprehensive Chemical Kinetics”, 35, Pilling, M.J. Ed.; Elsevier: Amsterdam, 293-437 (1997).

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Mechanism ReductionGoal: To reproduce the details of the complex mechanism in an

equivalent small mechanism.

Techniques:– Condense: Condense the information to a computationally

compact form (Lumping)– Limit Conditions: Under a limited set of conditions, eliminate

unused portions of the mechanism are eliminated (Skeletal,POSM)

– Tabulation: In local regions of source term space, approximations are tabulated (PRISM, ISAT, Flamelets)

– Reformulate: Reformulation of the source term equations to computationally simpler form (QSSA, CSP)

– Progress Variables: Use of a reduced number of coordinates to access source term state information

– Combinations: Hybrids of the above

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Outline


Mechanism Reduction– Lumping– Skeleton– Time Scale Analysis– Adaptive Chemistry


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Species Lumping

Mechanism is reduced through combination of species to a smaller number of lumped species

Chemical Lumping:– Based on species structure and/or reactivity

Formal Lumping: – Mathematical transformation between lumped and unlumped

(for example, linear combination of species concentrations)

Li, G.; Rabitz, H. Chem. Eng. Sci., 44, 1413-1430, 1989.

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Example of Chemical LumpingSchematic representation for the lumping of four different

5-ring alkylperoxy radicals

5r-C7H14OOH

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Lumped species in n-heptane Mechanism

6r-QOOH Species RO2 Species

p = 40bar, = 1.0, T = 800K

0

5 10-5

1 10-4

2 10-4

0.27 0.29 0.31 0.33 0.35

1-C7H

15O

22-C

7H

15O

23-C

7H

15O

24-C

7H

15O

2Added SpeciesL-C

7H

15O

2

Con

cen

trat

ion

[m

ole

/cm

3]

t [msec]

0

4 10-7

8 10-7

1 10-6

2 10-6

0.27 0.29 0.31 0.33 0.35

C7H

14OOH1-3

C7H

14OOH2-4

C7H

14OOH3-1

C7H

14OOH3-5

C7H

14OOH4-2

Added Species6r-C

7H

14OOH

Con

cen

trat

ion

[m

ole

/cm

3]

t [msec]

Concentration of Species Lumped Together Add to Single Lumped Species

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1362 reactions142 species

n-C7H16

L-C7H15

L-C7H15O2

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

A1-2 A4-3

B3-4

C4-3

D4-3

n-C7H16

4- C7H15O2

1-C7H15 4-C7H15

1-C7H15O2 2- C7H15O2 3- C7H15O2

2-C7H15 3-C7H15

A1-3 A1-4 A1-5 A2-1 A2-3 A2-4 A2-5 A2-6 A3-2 A3-4 A3-5 A3-6 A3-7 A3-1 A4-2 A4-1

B1-3 B1-4 B1-5 B1-2 B1-2 B2-3 B2-4 B2-5 B2-6 B1-3 B2-3 B3-4 B3-5 B2-5 B1-5 B1-4 B2-4

C1-3 C1-4 C1-5 C2-1 C2-3 C2-4 C2-5 C2-6 C3-1 C3-2 C3-4 C3-5 C3-6 C3-7 C4-1 C4-2

D1-3 D1-4 D1-5 D2-1 D2-3 D2-4 D2-5 D2-6 D3-1 D3-2 D3-4 D3-5 D3-6 D3-7 D4-1 D4-2 D1-2

C1-2

1624 reactions203 speciesDetailed

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Lumped Mechanism – Same As Detailed

Davis and Law

Laminar flame speed for n-heptane/air mixture at p=1 bar and Ti=298 K

Experimental data (symbols)Detailed mechanism (solid line)

Lumped mechanism (dashed line)

10

20

30

40

50

0.6 0.8 1.0 1.2 1.4 1.6 1.8

Davis & LawLund_CalculationsB

SL [

cm/s

ec]

n-heptane-air

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Outline


Mechanism Reduction– Lumping– Skeletal– Time Scale Analysis– Adaptive Chemistry


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Mechanism Reduction: Skeletal

Reduction through elimination of Reactions and Species

Under a limited set of conditions(which can be quite extensive),

unused species and reactions of the mechanism are eliminated if they are considered inert

under those conditions

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Skeletal Mechanisms: Criteria

Local Sensitivity (Expensive to calculate):

How does a small perturbation of an input parameter affect an output parameter

Example: How does a rate constant affect the temperature k/T

Reaction Flow Analysis:

The flux through a given reaction or molecule (related to reaction rates)

Heat Release:

When combined with reaction rates, a non-computationally expensive indicators of necessity of reactions

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Finding skeletal mechanisms

Examples of semi-automated methods that use knowledge

gained by derived criteria:

Necessity Parameter: Combination of sensitivity and flowsSoyhan, H.S.; Mauss, F.; Sorusbay, C., Combust. Flame, 125, 906-919 (2001).

Directed Relation Graph: Uses of flow analysisLu, T; Law, C. K., Combust. Flame, 144, 24-36 (2006).

Heat Release/Rates: Criteria for elimination of reactionsWang, H.; Frenklach, M., Combust. Flame, 87, 365-370 (1991).

Principle Component Analysis: Linear combination of speciesVajda, S.; Valko, P.; Turányi, T., Int. J. Chem. Kinet., 17, 55-81 (1985).

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Fully automated optimization methods:

Binary Optimization (inclusion or exclusion of reaction/species):– Integer Programming

Androulakis, I.P., AICHE, 46, 361-371 (2000).

– Genetic AlgorithmsEdwards, K.; Edgar, T.F.; Manousiouthakis, V.I. Computers Chem Engng., 22, 239-

246 (1998).

Direct Simulation: Motivated by Stochastic ModelingMosbach, S.; Su, H. Kraft, M., Proc. Combust. Institute, 30, 1301-1308

(2005).

Finding skeletal mechanisms

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Skeleton Mechanism : n-heptane

N-C7H16

L-C7H15

L-C7H15O2

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-C7H16

L-C7H15

L-C7H15O2

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-C7H16

L-C7H15

L-C7H15O2

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-C7H16

L-C7H15

L-C7H15O2

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-C7H16

L-C7H15

L-C7H15O2

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



470 reactions

64 species

A1-2 A4-3

B3-4

C4-3

D4-3

n-C7H16

4- C7H15O2

1-C7H15 4-C7H15

1-C7H15O2 2- C7H15O2 3- C7H15O2

2-C7H15 3-C7H15

A1-3 A1-4 A1-5 A2-1 A2-3 A2-4 A2-5 A2-6 A3-2 A3-4 A3-5 A3-6 A3-7 A3-1 A4-2 A4-1

B1-3 B1-4 B1-5 B1-2 B1-2 B2-3 B2-4 B2-5 B2-6 B1-3 B2-3 B3-4 B3-5 B2-5 B1-5 B1-4 B2-4

C1-3 C1-4 C1-5 C2-1 C2-3 C2-4 C2-5 C2-6 C3-1 C3-2 C3-4 C3-5 C3-6 C3-7 C4-1 C4-2

D1-3 D1-4 D1-5 D2-1 D2-3 D2-4 D2-5 D2-6 D3-1 D3-2 D3-4 D3-5 D3-6 D3-7 D4-1 D4-2 D1-2

C1-2

1624 reactions203 speciesDetailed

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Outline




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Separation of fast and slow processesFast processes of full phase space fall into (slow) lower dimensional manifoldDecoupling (two sets of equations) of system into fast and slow modes

Quasi-Steady State Assumption (QSSA):– Some Species fall into (close to)

equilibrium (dC/dt=0) within time scale considered

– Close to Equilibrium, they move along the same path in composition space (reduced dimension).

– Their solution can be calculated algebraically instead of solving the differential equations

Time Scale Analysis

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Time Scale AnalysisSeparation of solution in terms of fast and slow time scales

Quasi-Steady State Approximation:Solving algebraically QSSA species

Atkins, P., Physical Chemistry. Academic Press, New York, 927–935 (1994).

Identification of QSSA species through ‘Importance’Lovas, T.; Nilsson, D.; Mauss, F., Proc. of Combustion Symposium, 28, 1809-

1816 (2002).

Eigenvalues of Jacobian Matrix:Eigenvalues determine fast and slow reacting species– Intrinsic Low Dimensional Manifold (IDLM):

Mass, U.; Pope, S.B., Combust. Flame, 88, 903-914 (1992).

– Computational Singular Perturbation (CSP):Lam, S.H.;Goussis, D.A., Int. J. Chem. Kinet., 26, 461-486 (1994).

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Outline




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Adaptive Chemistry

Principle:– A combustion process is composed of several regions

Method:– Each region has its own representation of the chemistry– At each time step the phase chemistry is used

The methods differentiate by:– Representation of the chemical phases– Determination of the phases– Optimization of the phase chemistry– Recognition of which phase should be used

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Example: Polynomial BasedPrinciple:

– The phase is represented by a polynomial

– Phases are accumulated dynamically building up a library

– Search of phase through a tree structure

ISAT: 1st degree polynomial approximation established through Jacobian matrix. Phase size based on curvature.

Pope, S., Combust. Theory Modelling, 1, 41-63 (1997).

PRISM: 2nd degree polynomial established through factorial design. Phase size is fixed in coordinate space.

Tonse, S.; Moriarty, N.; Brown, N.; Frenklach, M., Israel J. of Chem., 39, 97-106 (1999).

APTAB: PRISM approximation based on accumulated ISAT points (no factorial design).

Ngozi, N.; Blurock, E.S.; Mauss, F., Proc. Symp. (Med.) Combust., 4 (2005).

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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).

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Skeletal Mechanism BasedPrinciple:

– Small number of phases– each is a skeletal mechanism

A Priori Optimized:– Each region/phase is set up before the calculation– Each phase is optimized (global optimization)

Bhattacharjee, B.; Schwer, D.A.; Barton, P.I.; Green, W.H., Combust. Flame, 135, 191-208 (2003).

Machine Learning Based:– Each phase is determined by a cluster of species importance– Each phase is minimized with respect to species importance– Phase recognition by a machine learning deduced decision tree

Tunér, M.; Blurock, E.S.; Mauss, F., SAE 2005-01-3813 (2005).

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Example of Adaptive ChemistryTwo-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.

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Outline




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Optimization of Rate Coefficients

Frequency Factor Temperature Exponent

Activation Energy

S

kki

N

ik

nkik RTETAcr exp,

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Optimization of Rate Coefficients

j

N

i

N

jiiij

N

ii

N

iii XXXX

R RR

i

R

20φy

N

rr

obsrr

1

2θyyθΨ

Frenklach, M.; Wang H.; Rabinovitz, M. J., Prog. Energy Combustion Sci., 18, 47-73 (1992).

Function to Optimize

Model – Experimental Data

Response Surface

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Reduction-Optimization Cycle

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1

2

3

4

5

6

25 30 35 40 45 50 55 60

Tim

e [s

ec]

Erro

r [CA

D]

# Species

CPU Time

Reduction

Op

timiz

atio

n

Op

timiz

atio

n

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Needs for future

– Fundamental experimental data needed:

Shock tube

RCM auto-ignition

engines

JSR, PFR species concentrations

Flames species concentrations and velocities

– New mechanism for the oxidation of future fuels (biofuels...)

– Computer technology will enable more detailed chemical models

EcoEngines Chemical Kinetics

Technology

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