reaction models of fundamental combustion properties1 reaction models of fundamental combustion...

1

Reaction Models of Fundamental Combustion Properties

Hai Wang

University of Southern California

2009 Fuel Summit, USC

Baptiste Sirjean David Sheen Enoch Dames

3

• JetSurF 0.2 → JetSurF 1.0 • updated kinetic parameters

• uncertainty quantification

• lumped, simplified model (with C. K. Law & T.-F. Lu)

• JetSurF 1.1 – n-butyl-, n-propyl-, ethyl-and methyl-cyclohexanes and cyclohexane.

4

• JetSurF 1.0 – n-alkane (C1 to C12)http://melchior.usc.edu/JetSurF/JetSurF1.0

• Quantum tunneling in the isomerization of n-alkyl radical

• Model uncertainty quantification/propagation

• Lumped model of high-temperature n-alkane thermal cracking

• JetSurF 1.1 – n-butylcyclohexanehttp://melchior.usc.edu/JetSurF/JetSurF1.1

• Reaction kinetics of benzene + O(3P)in collaboration with C. Taatjes: photoionization mass spectrometry and master equation modeling

• Transport properties of long-chain moleculesin collaboration with A. Violi & J. Manion

5

Role of Tunneling in n-alkyl Radicals Isomerizations

• n-alkyl radical (C5 to C8) unimolecular decomposition

W.Tsang, J.A. Walker, J.A. Manion Proc. Combust. Inst. 31 (2007) 141

• H-transfer reactions: low A-factors & Ea from low temperaturedata (300 – 500K)

+ C2H5

+ C2H4

+ C3H6 + CH3

+ C3H7

6

Role of Tunneling in n-alkyl Radicals Isomerizations

W.Tsang, J.A. Walker, J.A. Manion Proc. Combust. Inst. 31 (2007) 141

Endrenyi and Le Roy (1966)

Watkins (1971)

• Tunneling must be considered to reconcile low and high temperature data

7

Tunneling in Reaction Rate Theory

• Transition State Theory: transmission coefficient κ(T)RTEaAeTTk /)()(

• Approximations:– One dimensional assumption:

0)]([82

2

2

2

sVE

hm

x

– Potential Energy Surface expressed as a function V(s)

• Wigner (1932): parabola function

• Skodje and Truhlar (1981): truncated parabola

• Eckart (1917) & Johnston and Heicklen (1966): « Eckart potential »

8

Computational Methods

• One dimensional tunneling transmission coefficient κ(T):- Wigner, Skodje & Truhlar, and Eckart (CSE-Online - Truong et al.)

• Multi-dimensional tunneling transmission coefficient κ(T):- Small Curvature Tunneling (SCT) - Large Curvature Tunneling (LCT) (Polyrate - Truhlar et al.)

Truong et al., http://therate.hec.utah.edu/

Hessian required for each points along the Minimum Energy Path

Computationally expensive

9

PES: n-heptyl radicals H-shifts

0.0

-3.2-2.9 -3.0

21.8

14.4

22.8

14.8

H H

HH

Ener

gy (k

cal/m

ol)

0.0

20.0

10.0

E (0K, ZPE scaled) - kcal/mol

CBS-QB3

10

100

101

102

103

400 800 1200 1600 2000

1-heptyl -> 2-heptyl

Wigner Skodge & Truhlar Eckart

Tran

smis

sion

Coe

ffici

ent, (

T)

Temperature, T (K)

100

101

102

103

104

400 800 1200 1600 2000


Wigner Skodje & Truhlar Eckart

Tran

smis

sion

Coe

ffici

ent, (

T)

Temperature, T (K)

100

101

102

103

104

105

106

400 800 1200 1600 2000


Wigner Skodje & Truhlar Eckart

Tran

smis

sion

Coe

ffici

ent, (

T)

Temperature, T (K)

100

101

102

103

104

105

106

400 800 1200 1600 2000


WignerSkodje & TruhlarEckart

Tran

smis

sion

Coe

ffici

ent, (

T)

Temperature, T (K)

One-Dimensional Tunneling

11

Multi- vs One-dimensional Tunneling

100

101

102

400 800 1200 1600 2000


Wigner EckartSCT

Tran

smis

sion

Coe

ffici

ent, (

T)

Temperature, T (K)

100

101

102

103

400 800 1200 1600 2000


Wigner EckartSCT

Tran

smis

sion

Coe

ffici

ent, (

T)

Temperature, T (K)

Eckart good approximation for 300 < T < 2000 K

Wigner good for this system with T > 800 K

12

Small Curvature Tunneling

100

101

102

103

300 400 500 600 700 800 900 1000

1-heptyl -> 2-heptyl (7)1-heptyl -> 3-heptyl (6)1-heptyl -> 4-heptyl (5)2-heptyl -> 3-heptyl (5)

Tran

sfer

t Coe

ffici

ent, (

T)

Temperature, T (K)

In agreement with experiments

13

Sensitivity Analysis of Eckart κ(T): Variation of Imaginary Frequency

100

101

102

103

104

200 400 600 800 1000 1200


Eckart Eckart 90% imaginary frequencyEckart 110% of imaginary frequency

Tran

smis

sion

Coe

ffici

ent, (

T)

Temperature, T (K)

Uncertainty Propagation

David A. Sheen and Hai Wang

15

JetSurF (Version 0.2) Release date: September 08, 2008

Main page JetSurF 0.2 Download Performance How to Cite

20

30

40

50

60

70

0.6 0.8 1.0 1.2 1.4 1.6

Lam

inar

Fla

me

Spee

d, c

m/s

Equivalence Ratio,

n-Dodecane-Air (p = 1 atm, Tu = 403 K)

Data taken from X.Q. You, F.N. Egolfopoulos, H. Wang, “Detailed and Simplified Kinetic Models of n‐Dodecane Oxidation: The Role of Fuel Cracking in Aliphatic Hydrocarbon Combustion,” Proc. Combust. Inst. doi:10.1016/j.proci.2008.06.041 (2009). Symbols: experimental data taken with the counterflow twin‐flame technique with nonlinear extrapolation through detailed numerical simulations. Line: JetSurF (v0.2 prediction).

16

Kinetic Parameter Uncertainties

Baulch, et al. (2005)

~50%

H + O2 ↔ OH + O (R1)

• Logarithmic sensitivity coefficient= 0.24 (ethylene-air, = 1, p = 1 atm)

•±5% (±4 cm/s) uncertainty in predicted flame speed due to R1 alone

• Key question (Sheen et al. 2009): How do we propagate uncertainties in rate constants in combustion simulations?

• Uncertainty factor ~1.25

17

Propagation of Uncertainty

0

1 1...i ij ij

m m m

i j j kj k j

kk

x x

nominal value

1st order coefficients2nd order coefficients

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


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)

19


Main page JetSurF 1.0 download Performance How to cite Symbols: Data from S.S. Vasu, D.F. Davidson, Z. Hong, V. Vasudevan, R.K. Hanson, “n‐Dodecane Oxidation at High Pressures: Measurements of Ignition Delay Times and OH Concentration Time Histories,” Proc. Combust. Inst. 32 (2009) 173‐180. Onset of OH emission. Lines: Nominal prediction with JetSurF v1.0. Blue symbols: Uncertainty in JetSurF v1.0 predictions using Monte Carlo simulation. The nominal predictions do not represent the mean of statistical uncertainties because the uncertainty calculations used an unoptimized H2/CO sub model.

101

102

103

104

0.70 0.80 0.90 1.00 1.10 1.20

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

Igni

tion

Del

ay,

s

1000 K / T

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

20

40

60

80

0.5 1.0 1.5 2.0


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

nominal value

uncertainty

0, ,

1 1

ˆˆ,m m m


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


min

ar F

lam

e Sp

eed,

su0 (

cm/s

)

Equivalence Ratio,

“best” model

least-squares minimization

model + uncertainty

prediction + uncertainty

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

Sheen, et al. (2009)


Main page JetSurF 1.1 download Performance How to cite How to Cite JetSurF 1.1: B. Sirjean, E. Dames, D. A. Sheen, F. N. Egolfopoulos, H. Wang, D. F. Davidson, R. K. Hanson, H. Pitsch, C. T. Bowman, C. K. Law, W. Tsang, N. P. Cernansky, D. L. Miller, A. Violi, R. P. Lindstedt, A high‐temperature chemical kinetic model of n‐alkane, cyclohexane, and methyl‐, ethyl‐, n‐propyl and n‐butyl‐cyclohexane oxidation at high temperatures, JetSurF version 1.1, September 15, 2009 (http://melchior.usc.edu/JetSurF/JetSurF1.1). Note: Detailed reaction model development is inherently a work in progress. The current release is for the purpose of discussion and evaluation. Although the model predicts a large body of experimental data, it should be used with caution. The release is meant to be used for modeling the pyrolysis and oxidation of n‐alkane (up to n‐dodecane) at high temperatures only.

22

Detailed Kinetic Model for High-Temperature Oxidation of Cycloalkanes

• Butyl-cyclohexane, methylcyclohexane, and cyclohexane

• All C6 cyclic alkanes from cyclohexane to butylcyclohexane

Shock Tube Laminar Flame Speed

Flow Reactor/Perfectly Stirred Reactor

Cyclohexane

Methylcyclohexane

Ethylcyclohexane

Propylcyclohexane

Butylcyclohexane

Dagaut and co-workers (2000), Sirjean et al. (2007), Westbrook and co-worker (2007) Curran and co-worker (2006)

Dagaut and co-worker (2001)

Detailed Chemical Kinetic Models

23

High-Temperature Combustion Chemistry of Cycloalkanes (I)

• Initial C-C bond fission

+ CH3

+ C2H5

+ C3H7

+ C4H9

HH

NoBack rate constant from nC3H7 + iC3H7 = C6H14 [1]

Alkyl group (Ct-Cs)

NoRing opening of c-C6H12 [2]Cyclic structure (Cs-Cs)

NoRing opening of c-C6H12 [2]Ea lowered by 1 kcal/mol

(BDEn-hexane – BDE 2-methylpentane)Cyclic structure (Ct-Cs)

NoBack rate constant from

2 C2H5 = n-C4H10Alkyl group (Cs-Cs)


CH3 + C2H5 = C3H8Alkyl group (Cp-Cs)

Pressure fall-of

Source and Method of Rate EstimationC-C bond fission

NoBack rate constant from nC3H7 + iC3H7 = C6H14 [1]

Alkyl group (Ct-Cs)

NoRing opening of c-C6H12 [2]Cyclic structure (Cs-Cs)

NoRing opening of c-C6H12 [2]Ea lowered by 1 kcal/mol

(BDEn-hexane – BDE 2-methylpentane)Cyclic structure (Ct-Cs)


2 C2H5 = n-C4H10Alkyl group (Cs-Cs)


CH3 + C2H5 = C3H8Alkyl group (Cp-Cs)

Pressure fall-of

Source and Method of Rate EstimationC-C bond fission

[1] Tsang, W., J. Phys. Chem. Ref. Data 1988, 17, 887[2] Tsang, W., International Symposium on Combustion, 2008, Montreal, Canada

24

High-Temperature Combustion Chemistry of Cycloalkanes (III)

• H-abstraction by H, O2, OH, O, CH3, HO2Cycloalkanes

N/AH, O2, CH3, HO2 : C3H8 + X = C3H7 + HXO : Cohen’s method OH : Michael et al. (cycloalkanes)

Cyclic structure (Secondary H)

N/AH, O2, OH, HO2, O, CH3 : i-C4H10 + X = t-C4H9 + HXOH : Michael et al. (cycloalkanes)

Cyclic structure (Tertiary H)

N/AH, O2, CH3, HO2 : C3H8 + X = C3H7 + HXO : Cohen’s method OH : Michael et al. (n-alkanes)

Alkyl group

Pressure fall-ofSource and Method of Rate EstimationH-abstraction

N/AH, O2, CH3, HO2 : C3H8 + X = C3H7 + HXO : Cohen’s method OH : Michael et al. (cycloalkanes)

Cyclic structure (Secondary H)

N/AH, O2, OH, HO2, O, CH3 : i-C4H10 + X = t-C4H9 + HXOH : Michael et al. (cycloalkanes)

Cyclic structure (Tertiary H)

N/AH, O2, CH3, HO2 : C3H8 + X = C3H7 + HXO : Cohen’s method OH : Michael et al. (n-alkanes)

Alkyl group

Pressure fall-ofSource and Method of Rate EstimationH-abstraction

25

High-Temperature Combustion Chemistry of Cycloalkanes (V)

• C-C bond beta-scission in cycloalkyl radicals Cycloalkyl radicals n-alkyl radicals

+ +

+

+

26

C-C bond beta-scission Source and Method of Rate Estimation

Pressure fall-of

Alkyl group (Cp-Cs)Analogous rate constant of alkyl

radical isomer Yes

Alkyl group (Cs-Cs)Analogous rate constant of alkyl

radical isomer Yes

Alkyl group (Ct-Cs)2-methyl-pent-4-yl radical

-scission [1]Yes

Cyclic structure (Ct-Cs)Ring opening of c-C6H11 [2]Ea lowered by 1 kcal/mol

(BDEn-hexane – BDE 2-methylpentane)Yes

Cyclic structure (Cs-Cs) Ring opening of c-C6H11 [2] Yes

• Rate constants:

High-Temperature Combustion Chemistry of Cycloalkanes (VI)

[1] McGivern, W.S., Awan, I.A., Tsang, W., Manion, J.A., J. Phys. Chem. A, 2008, 112,6908[2] Tsang, W., International Symposium on Combustion, 2008, Montreal, Canada

27

High-Temperature Combustion Chemistry of Cycloalkanes (VII)

• Mutual isomerization of cycloalkyl radicals Cycloalkyl radicals n-alkyl radicals

H

H

H

28

High-Temperature Combustion Chemistry of Cycloalkanes (VIII)

• B3LYP/6-311G(d,p) PES + TST Theory + Eckart Tunneling

0.0

-4.8 -4.2-4.3

-6.7

-3.8 -3.7-3.7

20.7 21.3

30.0

13.7 12.5

27.4

20.420.8

13.6

21.022.8

20.3

16.5

16.9

29

Additional Features of JetSurF 1.1

• Branched alkenes decomposition reactions:– Initial C-C bond fission– Retro-ene reactions– Chemically activated reactions with H (analogous to C3H6+H)

• Branched alkenyl radicals decomposition:– C-C bond fission reactions and mutual isomerization pressure

dependant rates:

Tsang and co-workers, n-alkyls (C5 to C8), branched alkyl (2-meythylpentyl) and alkenyl radicals (C4 to C6)

• 352 species and 2083 reactions

30


Main page JetSurF 1.1 download Performance How to cite

Performance That We Know: Validation tests for the base model, including JetSurF version 1.0 and USC‐Mech II, can be found at their respective web sites. For n‐butylcyclohexane and its related fuel compounds, the current validation tests include

Laminar flame speeds

Cyclohexane‐, methylcyclohexane‐ and n‐butylcyclohexane‐air mixtures, p = 1 atm, Tu = 353 K. Egolfopoulos (2009)

Cyclohexane‐air mixtures, p = 1 atm, Tu = 298 K. Davis & Law (1998).

n‐Propylcyclohexane‐air mixtures, p = 1 atm, Tu = 403 K. Dubois et al. (2008).

Ignition delay times behind reflected shock waves

n‐Butylcyclohexane‐oxygen‐argon, p5 = 1.5 atm. Davidson & Hanson (2009).

Cyclohexane‐oxygen‐argon mixtures, p5 = 1.5 and 3 atm. Davidson & Hanson (2009).

Cyclohexane‐oxygen‐nitrogen mixtures, p5 = 15 & 50 atm. Daley et al. (2008).

Cyclohexane‐oxygen‐nitrogen mixtures, p5 = 8 atm. Sirjean et al. (2007).

Methylcyclohexane‐oxygen‐argon mixtures, p5 = 1.5 and 3 atm. Davidson & Hanson (2009).

Methylcyclohexane‐oxygen‐nitrogen mixtures, p5 = 20 atm. Vasu et al. (2009).

31


Main page JetSurF 1.1 download Performance How to cite

10

20

30

40

50

60

0.6 0.8 1.0 1.2 1.4 1.6

Lam

inar

Fla

me

Spee

d (c

m/s

)

Equivalence Ratio,

Cyclohexane-Air (p = 1 atm, T0 = 353 K)

10

20

30

40

50

60

0.6 0.8 1.0 1.2 1.4 1.6

Lam

inar

Fla

me

Spee

d (c

m/s

)

Equivalence Ratio,

Methylcyclohexane-Air (p = 1 atm, T0 = 353 K)

10

20

30

40

50

60

0.6 0.8 1.0 1.2 1.4 1.6

Lam

inar

Fla

me

Spee

d (c

m/s

)

Equivalence Ratio,

Butylcyclohexane-Air (p = 1 atm, T0 = 353 K)

10

20

30

40

50

60

70

0.6 0.8 1.0 1.2 1.4 1.6

Lam

inar

Fla

me

Spee

d (c

m/s

)

Equivalence Ratio,

n-Propylcyclohexane-air (p = 1 atm, T0 = 403 K)Flame Speed comparisons. Data are preliminary and not shown here

32


Main page JetSurF 1.1 download Performance How to cite Symbols: Data from D.F. Davidson, R.F. Hanson, “Cycloalkane Ignition Studies,” unpublished, June 29, 2009. Onset of OH emission. Lines: JetSurF v1.1 predictions

102

103

0.65 0.70 0.75 0.80

0.22% n-butylcyclohexane - 4% O2 in Ar = 0.83, p5 = 1.5 atm

Igni

tion

Del

ay (

s)

1000 K / T

102

103

0.67 0.70 0.72 0.75 0.77 0.80 0.82 0.85

0.234% n-butylcyclohexane - 4%O2 in Ar0.88p5 = 3 atm

Igni

tion

Del

ay (

s)

1000 K / T

102

103

0.65 0.70 0.75 0.80 0.85

0.119%n-butylcyclohexane - 4%O2 in Ar0.45p5 = 1.5 atm

Igni

tion

Del

ay (

s)

1000 K / T

Ignition delay comparisons. Data are preliminary and not shown here

33


Main page JetSurF 1.1 download Performance How to cite Symbols: Data from D.F. Davidson, R.F. Hanson, “Cycloalkane Ignition Studies,” unpublished, June 29, 2009. Onset of OH emission. Lines: JetSurF v1.1 predictions.

102

103

0.65 0.70 0.75

0.381% methylcyclohexane - 4%O2 in Ar1p5 = 1.5 atm

Igni

tion

Del

ay (

s)

1000 K / T

102

103

0.65 0.70 0.75 0.80

0.381% methylcyclohexane - 4%O2 in Ar1p5 = 3 atm

Igni

tion

Del

ay (

s)

1000 K / T

102

103

0.65 0.70 0.75 0.80

0.191% methylcyclohexane - 4%O2 in Ar0.5p5 = 1.5 atm

Igni

tion

Del

ay (

s)

1000 K / T

Ignition delay comparisons. Data are preliminary and not shown here

35


Main page JetSurF 1.1 download Performance How to cite Symbols: Data S. Zeppieri, K. Brezinsky, I. Glassman, “Pyrolysis Studies of Methylcyclohexane and Oxidation Studies of Methylcyclohexane and Methylcyclohexane/Toluene Blends,” Combustion and Flame 108 (1997) 266‐286. Lines: JetSurF v1.1 predictions

0

500

1000

1500

2000

2500

0 10 20 30 40 50 60 70 80

1815 ppm methylcyclohexane - 14660 ppm O2 T = 1160 K, p = 1 atm

MethylcyclohexaneCH4C2H4

Time (ms)

Mol

e Fr

actio

n (p

pm)

0

2000

4000

6000

8000

10000

12000

0 10 20 30 40 50 60 70 80


CO

CO2

Time (ms)

Mol

e Fr

actio

n (p

pm)

0

200

400

600

800

0 20 40 60 80


C3H61,3-C4H6Isoprene (CH2=C(CH3)-CH=CH2)

Mol

e Fr

actio

n (p

pm)

Time (ms)

0

50

100

150

200

250

300

350

0 20 40 60 80

C2H6Allene (aC3H4)

Mol

e Fr

actio

n (p

pm)

Time (ms)


36


Main page JetSurF 1.1 download Performance How to cite Symbols: Data from S. M. Daley, A. M. Berkowitz, M. A. Oehlschlaeger, “A shock tube study of cyclopentane and cyclohexane ignition at elevated pressures,” International Journal of Chemical Kinetics, 40 (2008) 624‐634. Onset of OH* emission. Lines: JetSurF v1.1 predictions.

101

102

103

104

0.75 0.80 0.85 0.90 0.95 1.00

0.5802% cyclohexane - 20.89%O2 in N2 0.25p5 = 15 atm

Igni

tion

Del

ay (

s)

1000 K / T

101

102

103

104

0.75 0.80 0.85 0.90 0.95 1.00 1.05


Igni

tion

Del

ay (

s)

1000 K / T

101

102

103

104

0.80 0.85 0.90 0.95 1.00 1.05 1.10


Igni

tion

Del

ay (

s)

1000 K / T

101

102

103

104

0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10


Igni

tion

Del

ay (

s)

1000 K / T

37


Main page JetSurF 1.1 download Performance How to cite Symbols: Data from J. Vanderover, M. A. Oehlschlaeger, “Ignition Time Measurements for Methylcyclohexane and Ethylcyclohexane‐Air Mixtures at Elevated Pressures,” International Journal of Chemical Kinetics 41 (2009) 82‐91. Onset of OH emission. Lines: JetSurF v1.1 predictions

101

102

103

104

0.75 0.80 0.85 0.90 0.95

0.4977% methylcyclohexane - 20.90%O2 in N20.25p5 = 15 atm

Igni

tion

Del

ay (

s)

1000 K / T

101

102

103

104

0.75 0.80 0.85 0.90 0.95 1.00 1.05


Igni

tion

Del

ay (

s)

1000 K / T

101

102

103

104

0.75 0.80 0.85 0.90 0.95 1.00 1.05


Igni

tion

Del

ay (

s)

1000 K / T

101

102

103

104

105

0.80 0.85 0.90 0.95 1.00 1.05 1.10

0.9905% methylcyclohexane - 20.80%O2 in N21p5 = 50 atm

Igni

tion

Del

ay (

s)

1000 K / T

38


Main page JetSurF 1.1 download Performance How to cite Symbols: Data from J. Vanderover, M. A. Oehlschlaeger, “Ignition Time Measurements for Methylcyclohexane and Ethylcyclohexane‐Air Mixtures at Elevated Pressures,” International Journal of Chemical Kinetics 41 (2009) 82‐91. Onset of OH emission. Lines: JetSurF v1.1 predictions

101

102

103

104

105

0.7 0.8 0.9 1.0 1.1

0.4358% ethylcyclohexane - 20.92%O2 in N20.25p5 = 15 atm

Igni

tion

Del

ay (

s)

1000 K / T

101

102

103

104

0.75 0.80 0.85 0.90 0.95 1.00 1.05


Igni

tion

Del

ay (

s)

1000 K / T

101

102

103

104

0.75 0.80 0.85 0.90 0.95 1.00 1.05


Igni

tion

Del

ay (

s)

1000 K / T

101

102

103

104

0.85 0.90 0.95 1.00 1.05


Igni

tion

Del

ay (

s)

1000 K / T

39


What we know about the problem at high pressure?

• Impurities: not likely

• Sensitivity towards the rate of H abstraction:

R-cC6H11 + HO2 → products

• No kinetic dead ends

• Missing appropriate FREE-RADICAL CHAIN INITIATION!

Non-equilibrium kinetics upon shock heating?Carbene + O2 → free radicals?

Simplified Chemical Kinetic Models for High-Temperature

Oxidation of C5 to C12 n-alkanes

B. Sirjean, E. Dames, D.A. Sheen, H. Wang

University of Southern California

41

Systematic Simplification of C5-C12 Detailed Model

n-CnH2n+2 with 12 ≥ n ≥ 5

H-abstraction: OH, H, CH3, O, O2, HO2Unimolecular initiation

Chain length ?

1,5 H-shift if ≥ C6

1-alkene simplified

USC Mech II

C0 – C4

Radical type?C5– C12

Primary

Secondary

C5-C6 1-alkenes C-C -scission

Alkyl ≥ C6

Lumped n-alkane C5 to C12 model:9 species & 193 reactions

+Detailed C0 to C4 model (USC Mech II)

111 species & 784 reactions

“Model II”120 species

977 reactions

42

Model Details and Validation

Model n-alkane cracking

H2/CO/C1-C4 based model

Number of species

Number of reactions

I detailed detailed 194 1459

II lumped detailed 120 977

III lumped skeletal 84 499

Standard ofpresentation

43

Validation: Pyrolysis of n-dodecane in a Jet-Stirred Reactor

O. Herbinet, P.M. Marquaire, F. Battin-Leclerc, R. Fournet, Anal. Appl. Pyrolysis 78 (2007) 419

0

20

40

60

80

100

850 900 950 1000 1050

Con

vers

ion,

%

Temperature, K

0

20

40

60

80

100

0 1 2 3 4 5

Con

vers

ion,

%

Residence time, s

873 K

973 K

44

Validation: Laminar Flame Speed

10

20

30

40

50

60

70

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8Equivalence Ratio,

n-Dodecane-air Tu = 403 K, P = 1 atmLa

min

ar F

lam

e Sp

eed

(cm

/s)

45

Validation: Ignition

101

102

103

104

101 102 103 104

Model IModel II

Sim

ulat

ed ig

nitio

n de

lays

, s

Experimental ignition delays, s

Set of experimental data:n-C5H12 (Φ = 1; 0.5 – P5 = 1.9; 1.7 atm)n-C6H14 (Φ = 1; 0.5 – P5 = 1.8; 1.7 atm)n-C7H16 (Φ = 2; 1; 0.5 – P5 = 1 atm)n-C8H18 (Φ = 1; 0.5 – P5 = 2 atm)n-C9H20 (Φ = 1; 0.5 – P5 = 2 atm)n-C10H22 (Φ = 1 – P5 = 1.2; 13 atm)n-C12H26 (Φ = 1; 0.5 – P5 = 20 atm)

S. S. Vasu, D. F. Davidson, Z. Hong, V. Vasudevan, R.K. Hanson, Proc. Combust. Inst. 32 (2009) 173D. F. Davidson, S. C. Ranganath, K.-Y. Lam, M. Liaw, Z. Hong, R. K. Hanson, "Ignition Delay Time Measurements of Normal Alkanes and Simple Oxygenates" Journal of Propulsion and Power, in press (2009)

reaction models of fundamental combustion properties1 reaction models of fundamental combustion...

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