1

Reaction Models of Fundamental Combustion Properties 

Hai Wang

Enoch Dames, David Sheen* & Rei Tangko

University of Southern California

* Currently at NIST

2011 Fuel Summit, ANL

2

H. Wang, E. Dames, B. Sirjean, D. A. Sheen, R. Tangko, A. Violi, J. Y. W. Lai, F. N. Egolfopoulos,  D. F. Davidson, R. K. Hanson, C. T. Bowman, C. K. Law, W. Tsang, N. P. Cernansky, D. L. Miller, R. P. Lindstedt, A high‐temperature chemical kinetic model of n‐alkane (up to n‐dodecane), cyclohexane, and methyl‐, ethyl‐, n‐propyl and n‐butyl‐cyclohexane oxidation at high temperatures, JetSurF version 2.0, September 19, 2010 (http://melchior.usc.edu/JetSurF/JetSurF2.0).

3

USC Mech II (http://ignis.usc.edu/Mechanisms/USC‐Mec h II/USC_Mech II.htm)

H2, CO, CH4, C2H6, C2H4, C2H2, allene, propyne, C3H6, C3H8, 1,3‐C4H6, 1‐butene, 2‐butene, isobutene, n‐C4H10, i‐C4H10, cyclopentadiene, benzene, toluene

Validation data: > 150 sets

JetSurF 1.0 (http://melchior.usc.edu/JetSurF/JetSurF1.0/Index.html)

n‐CmH2m+2 (5 ≤m ≤ 12)Validation data: > 41 sets

JetSurF 2.0 (http://melchior.usc.edu/JetSurF/JetSurF2.0/Index.html)

cyclohexane, methyl‐, ethylene, n‐propyl, n‐butyl‐cyclohexane

Validation data : > 47 sets

4

1. n‐Dodecane oxidation revisited –Uncertainty analysis by MUM‐PCE.

2. Mechanism of one‐ring aromatics oxidation.

5

1. n‐Dodecane oxidation revisited –Uncertainty analysis by MUM‐PCE.

2. Mechanism of one‐ring aromatics oxidation.

6

Uncertainty Matters ‐ Example (1)The Hubble Constant

• dark matter• big freeze versus big crunch

7

Uncertainty Matters ‐ Example (2)Global Radiative Forcing

8

Uncertainty Matters ‐ Example (3)Chicago Weather

9

Multispecies Time‐History Data and JetSurF PredictionsDavidson, Hong, Pilla, Farooq, Cook & Hanson, Combustion and Flame (2010)

10 100 100010

100

1000

Mol

e Fr

actio

n [p

pm]

Time [s]

1494K, 2.15atm300ppm heptane, =1

H2O

CO2

OH

C2H4

Solid lines: experiments; dashed lines: JetSurF 1.0

Species uncertainty: ±5%

T5 uncertainty: ±10 K

10

10-5

10-4

10-3

Mol

e Fr

actio

n

C2H4

10-5

10-4

10-3

Mol

e Fr

actio

n

C2H4

10-5

10-4

10-3

Mol

e Fr

actio

n

OH

10-5

10-4

10-3

Mol

e Fr

actio

n

OH

10-5

10-4

10-3

Mol

e Fr

actio

n

H2O

10-5

10-4

10-3

Mol

e Fr

actio

n

H2O

10-5

10-4

10-3

10-5 10-4 10-3

Mol

e Fr

actio

n

CO2

Time (s)

10-5

10-4

10-3

10-5 10-4 10-3

Mol

e Fr

actio

n

CO2

Time (s)

Predictions of As‐Compiled and Uncertainty‐Minimized Models

Unconstrained Constrained

11

Effect on predicted laminar flame speed (n‐heptane‐air)

Prior knowledge (kinetic uncertainty as is)

Model constrained by Stanford species profiles

Model constrained by species profiles+ flame speeds

Need flame speed data with 2 < 2 cm/s

12

Model constrained by species profiles Model constrained by flame speeds

CH3, CH2, secondary chain branching, fuel breakup

H chain branching

What did the Stanford data offer?

13

What did the Stanford data offer?

14

2

3

4

0 5 10 15 20

1/(2 obs)

20% 10% 7% 5%

Uncertainty in Species Value, 2 obs

CH3 (Series 2) only

OH (Series 1) only

All multi-species (Series 1 & 2)

s (

cm/s

)

Effect on predicted laminar flame speed (n‐heptane‐air)

15

10-6

10-5

10-4

10-3

10-2

10-5 10-4 10-3

Mol

e Fr

actio

n

Time(s)

457 ppm nC12

H26

/ 7500 ppm O2 / Ar

T5 = 1410 K, p

5 = 2.15 atm

H2O

CO2

C2H

4

OH

nC12

H26

Multispecies Time‐History Data and JetSurF PredictionsDavidson, Hong, Pilla, Farooq, Cook, Hanson, Proc. Combust. Inst. (2011)

Dashed line: Expt. Data

Solid lines: JetSurF 1.0

16

Multispecies Time‐History Data and JetSurF PredictionsDavidson, Hong, Pilla, Farooq, Cook, Hanson, Proc. Combust. Inst. (2011)

10-6

10-5

10-4

10-3

464 ppm nC12H26 / 7577 ppm O2 / ArT5 = 1405 K, p5 = 2.35 atm

Mol

e Fr

actio

n

nC12H26

10-6

10-5

10-4

10-3

10-5 10-4 10-3

Mol

e Fr

actio

n

C2H4

Time (s)

10-6

10-5

10-4

10-3

Mol

e Fr

actio

n

OH

10-6

10-5

10-4

10-3

10-5 10-4 10-3M

ole

Frac

tion

H2O

Time (s)

10-6

10-5

10-4

10-3

10-5 10-4 10-3

Mol

e Fr

actio

nCO2

Time (s)

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Global Combustion Properties

JetSurF is consistently too slow for n‐dodecane oxidation

18

Potential Causes for the Problems

• Bad group additivity estimates for the thermochemistry of alkyl radicals impact cracked product distribution (odd versus even numbered C atoms), leading to slower oxidation rates. 

No.  e.g., implementing recent results by Truhlar did not lead to appreciable changes in model predictions.

• Rate constant uncertainties?

Likely.  MUM‐PCE analysis show that the two sets of data can be reconciled by the same model (JetSurF)……to an extent

n‐heptane and n‐dodecane share the same group additivity parameters and rate rules.

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10-6

10-5

10-4

10-3

10-2

10-5 10-4 10-3

Mol

e Fr

actio

n

Time(s)

457 ppm n-C12H26 / 7500 ppm O2 / ArT5 = 1410 K, p5 = 2.15 atm

n-C12H26

C2H4

OH

Define Experimental Uncertainty

Solid line: nominal

Dotted line: ±20%

Dashed line: ±10K in T5

20

Ethylene No. P5 (atm) T5 (K) Conditions

Oxidation C2H4 Species Profiles4 6 3-3.5 1221-1267 K 0.5-2.0

Pyrolysis C2H4 Species Profiles5 10 2.58-3.14 1392-1895 K 1% in Ar

Case n-Dodecane No. P0/P5(atm)

T0/T5 (K) Conditions

Oxidation

OH, H2O, CO2, C2H4, nC12H26

Species Profiles1 11 2.26-2.41 1392-1418 K 1.0

Flame Speed2 4 1 403 K 0.6-1.4Ignition Delay3 2 22.7-30.9 907-1117 K 0.5-1.0

Pyrolysis C2H4, nC12H26 Species Profiles1 6 2.1-2.7 1201-1391 K 380-430 ppm in Ar

1D.F Davidson et al. (2011).  2X. You et al. (2009). 3S.S. Vasu et al. (2009). 4Ren et al. (2011). 5Pilla et al. (2011). 6Davidson et al. (2010)

n-Heptane No. P5 (atm) T5 (K) Conditions

OxidationOH, H2O, CO2

Species Profiles6 15 2.15-2.35 1365-1480 K 1.0

Pyrolysis C2H4 Species Profiles5 8 2.67-3.2 1247-1874 K 300 ppm in Ar

Summary of Experiments Used for Constraint

2121

Heptane and Dodecane Species Time Histories

10-6

10-5

10-4

10-3

5 5

Mol

e Fr

actio

nC2H4

10-6

10-5

10-4

10-3

5 5

Mol

e Fr

actio

n

C2H4

10-6

10-5

10-4

10-3

Mol

e Fr

actio

n

OH

10-6

10-5

10-4

10-3

Mol

e Fr

actio

n

OH

10-6

10-5

10-4

10-3

Mol

e Fr

actio

n

H2O

10-6

10-5

10-4

10-3M

ole

Frac

tion

H2O

Heptane Dodecane

10-5 10-4 10-3

Time (s)10-5 10-4 10-3

Time (s)

2222

101

102

103

104

0.565%n-C12H26-20.89%O2-78.55%N2= 0.5, p5 = 20atm

Igni

tion

Del

ay,

s

101

102

103

104

0.7 0.8 0.9 1.0 1.1 1.2

1.123%n-C12H26-20.77%O2-78.1%N2= 1, p5 = 20atm

Igni

tion

Del

ay,

s

1000 K / T

20

30

40

50

60

70

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

Equivalence Ratio,

Lam

inar

Fla

me

Spee

d

s uo (cm

/s)

n-C12

H26

/air at p = 1 atm and Tu = 403 K

n‐Dodecane Global Combustion Properties 

23

SummarySummary

• The multi‐species time histories of n‐heptane and n‐dodecane can be reconciled within the uncertainties of JetSurF (to an extent).

• Not enough data to pinpoint rate rules that need to be expanded. 

24

1. n‐Dodecane oxidation revisited –Uncertainty analysis by MUM‐PCE.

2. Mechanism of one‐ring aromatics oxidation.

25

102

103

0.67 0.75 0.82 0.90

orthometapara

1000 K / T

Xylene Isomers, = 1.0, P5 = 10atm

1.962% xylene, 20.60% O2, and 77.44% N2

Ji, Dames, Wang, and Egolfopoulos, Combust. Flame, submitted.

Igni

tion

Del

ay T

ime

(s)

> >

10

20

30

40

50

0.6 0.8 1 1.2 1.4 1.6Equivalence Ratio

Lam

inar

Fla

me

Spee

d, c

m/s

Tu = 353 K, P = 1 atm

Shen and Oehlschlaeger, Combust. Flame, 2009. 

Xylene Relative Reactivity Revisited Xylene Relative Reactivity Revisited –– High High Temperature MechanismTemperature Mechanism

26

+ H

+ CH3

+ H

+ H +M, H, O, O

H

+M

+M, H, O, OH

+M, H, O, OH

+ H

+ CH3

+ H

+ CH3

+ H

+ H

+ H

+ H +M, H, O, O

H

+M

+M, H, O, OH

+M, H, O, OH

Initial Pathways (Initial Pathways (oo‐‐Xylene)Xylene)

• Radical‐radical recombination

• O2 addition at 1012 cm3 mol‐1 s‐1 (da Silva and Bozzelli 2010)• H or CH3 elimination to a benzyne: 70 ‐ 80 kcal/mol

• ‘H‐hopping’ isomerization: 60 kcal/mol

• Isomerization to resonantly stabilized benzylic radical, Ea = ?

27

22‐‐Methylphenyl Methylphenyl PESPESaa

42.8

-22.3

62.2

Relativ

e En

ergy (kcal/mol)

0 0

+ CH3

+ H86.0a

79.1a

+ Hc

86.8b

3mp 2mp

TS-1-3

TS-1-2

benzyl

42.8

-22.3

62.2

Relativ

e En

ergy (kcal/mol)

0 0

+ CH3

+ H86.0a

79.1a

+ Hc

86.8b

42.8

-22.3

62.2

Relativ

e En

ergy (kcal/mol)

0 0

+ CH3

+ H86.0a

79.1a

+ Hc

86.8b

3mp 2mp

TS-1-3

TS-1-2

benzyl

aDetermined at B97X-D/6-311G(2d,p) level of theorybCavallotti, Mancarella, Rota, and Carra, JPCA 2007.cIntermediate channels not shown.

28

103

104

105

106

107

108

109

0.5 0.6 0.7 0.8 0.9 1

k0.1k1k10k50kinf

k, 1

/s

P (atm)

103

104

105

106

107

108

109

0.5 0.6 0.7 0.8 0.9 1

103

104

105

106

107

108

109

0.5 0.6 0.7 0.8 0.9 11000 K / T

k, 1

/s

103

104

105

106

107

108

109

0.5 0.6 0.7 0.8 0.9 11000 K / T

RRKM/Master Equation ResultsRRKM/Master Equation Results

29

43.1

42.1

42.7

42.1

42.8

Eo (kcal/mol)ProductReactant

43.1

42.1

42.7

42.1

42.8

Eo (kcal/mol)ProductReactant

Comparison of Energy Barrier HeightsComparison of Energy Barrier Heights

42.7

-22.7

62.2

Relative Energy (kcal/mol)

0 0MX5 MX6

TS-6-5

TS-6-1

MX1

42.7

-22.7

62.2

Relative Energy (kcal/mol)

0 0MX5 MX6

TS-6-5

TS-6-1

MX1

30

100

102

104

106

108

0.5 0.6 0.7 0.8 0.9 1

k

, 1/s

1000K / T

8

2000 1600 1400 1200 1000

T (K)

Comparison of HighComparison of High‐‐Pressure Limit Rate CoefficientPressure Limit Rate Coefficient

●

●

●

●

31

146146120Research Octane Number (da Silva and Bozzelli, 2010)

Type of substituted one-ring aromatic

Xylene Relative Reactivity Revisited Xylene Relative Reactivity Revisited –– High Temperature MechanismHigh Temperature Mechanism

o- m- p-102

103

0.67 0.75 0.82 0.90

orthometapara

1000 K / T

Xylene Isomers, = 1.0, P5 = 10atm

1.962% xylene, 20.60% O2, and 77.44% N2

10

20

30

40

50

0.6 0.8 1 1.2 1.4 1.6Equivalence Ratio

Lam

inar

Fla

me

Spee

d, c

m/s

Tu = 353 K, P = 1 atm

Igni

tion

Del

ay T

ime

(s)

Ji, Dames, Wang, and Egolfopoulos, Combust. Flame, submitted.

Shen and Oehlschlaeger, Combust. Flame, 2009. 

: sites where H‐abstraction may result in a phenylic radical with relatively long lifetime.: sites where H‐abstraction may result in facile H‐shift to a benzylic radical.: benzyl‐type radical site. 

The degree of difficulty for H shift to benzylic radical impact the fuel reactivity.

32

Back Up Slides

33

Propagation of Uncertainty

0

1 1...i ij ij

m m m

i j j kj k j

kk

x x

basis random variable

Data structure that describes a chemical model + associated uncertainty

,0 , ,1 1

N N N

r r r i i r ij i ji i j i

a x b x x

x

Predictions of a chemical model (e.g. laminar flame speed)+ associated uncertainty

0, ,

1 1

ˆˆ,m m m

r r r i i r ij i ji i j i

x ξ x

Represents some physics model,e.g. PREMIX

1‐atm C2H4‐air mixtures

20

40

60

80

0.5 1.0 1.5 2.0

Egolfopoulos & Law (1990)Faeth & co-workers (1998)Law & co-workers (2005)La

min

ar F

lam

e Sp

eed,

su0 (

cm/s

)

Equivalence Ratio,

Sheen et al. (2009)

34

20

40

60

80

0.5 1.0 1.5 2.0

Egolfopoulos & Law (1990)Faeth & co-workers (1998)Law & co-workers (2005)La

min

ar F

lam

e Sp

eed,

su0 (

cm/s

)

Equivalence Ratio,

Method of Uncertainty Minimization (MUM‐PCE)

obs obs obs,0r r r r ξ

2* obs, ,2obs1 1 1

1 ˆˆminM M M M

r ir r i r ijr i i j ir

α

α

0

20obs

,00 *2obs1

minM r r

r r

x

xx

0, ,

1 1

ˆˆ,m m m

r r r i i r ij i ji i j i

x ξ x 0

1i i

m

i jj

jx x

1‐atm C2H4‐air mixtures

20

40

60

80

0.5 1.0 1.5 2.0

Egolfopoulos & Law (1990)Faeth & co-workers (1998)Law & co-workers (2005)La

min

ar F

lam

e Sp

eed,

su0 (

cm/s

)

Equivalence Ratio,

“best” model

least‐squares minimization

model + uncertainty

prediction + uncertainty

Sheen, et al. (2009)

35

2* * obs, ,2,... obs1 1 1

1 ˆˆ,... min ...M M M M

r ir r i r ijr i i j ir

α β

α β

0

1 1...i ij ij

m m m

i j j kj k j

kk

x x

20

40

60

80

0.5 1.0 1.5 2.0

Egolfopoulos & Law (1990)Faeth & co-workers (1998)Law & co-workers (2005)La

min

ar F

lam

e Sp

eed,

su0 (

cm/s

)

Equivalence Ratio,

Method of Uncertainty Minimization (MUM‐PCE)

obs obs obs,0r r r r ξ

0

20obs

,00 *2obs1

minM r r

r r

x

xx

0, ,

1 1

ˆˆ,m m m

r r r i i r ij i ji i j i

x ξ x

1‐atm C2H4‐air mixtures

20

40

60

80

0.5 1.0 1.5 2.0

Egolfopoulos & Law (1990)Faeth & co-workers (1998)Law & co-workers (2005)La

min

ar F

lam

e Sp

eed,

su0 (

cm/s

)

Equivalence Ratio,

“best” model

least‐squares minimization

model + uncertainty

prediction + uncertainty

Sheen, et al. (2009)