reaction models of combustion properties4 • version 1.0+1.1 →jetsurf 2.0 n‐butyl‐,...

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Reaction Models of Fundamental Combustion Properties

Hai Wang

Enoch Dames, David Sheen & Rei Tangko

University of Southern California

2010 Fuel Summit, Princeton

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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).

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• Version 1.0+1.1 → JetSurF 2.0 n‐butyl‐, n‐propyl‐, ethyl‐ and methyl‐cyclohexanes and cyclohexane.

n‐pentane to n‐dodecane

Some branched chain HCs + aromatics

• Key Revisions from version 1.0+1.1• Low temperature chemistry of cyclohexane and

methylcyclohexane added• H‐abstraction rates from Violi• ……

• Validation test sets > 200 (documented online)http://melchior.use.edu/JetSurF

JetSurF Status

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Multispecies Time‐History DataDavidson, 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

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Multispecies Time Histories

Solid lines: experiments; dashed lines: JetSurF 1.0

10-6

10-5

10-4

10-3

10-5 10-4 10-3

Mol

e Fr

actio

n

Time (s)

OH

H2O

CO2

10-4

10-3

10-5 10-4 10-3

Mol

e Fr

actio

n

Time (s)

C2H4

nC7H16

300 ppm n-C7H16 - 3300 ppm O2 in Ar, T5 = 1365 K, p5 = 2.35 atm

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What can we learn from the multispecies time‐histories?

• The model is accurate, but is it precise?

•Given the ~±5% experimental accuracy, can the data be utilized to improve model precision?

• To what extent the data improve model precision?


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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


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)

9

10-5

10-4

10-3

Mol

e Fr

actio

n

C2H4

10-5

10-4

10-3

10-5 10-4 10-3

Mol

e Fr

actio

n

OH

Time (s)

10-5

10-4

10-3H2O

10-5

10-4

10-3

10-5 10-4 10-3

CO2

Time (s)

300 ppm nC7H16 / 3300 ppm O2 / Ar (T5 = 1494 K, p5 = 2.15 atm)

Multispecies Time Histories(Model Uncertainties)

JetSurF 1.0 is quite accurate

10

10-5

10-4

10-3

Mol

e Fr

actio

n

C2H4

10-5

10-4

10-3

10-5 10-4 10-3

Mol

e Fr

actio

n

OH

Time (s)

10-5

10-4

10-3H2O

10-5

10-4

10-3

10-5 10-4 10-3

CO2

Time (s)


JetSurF 1.0 is quite accurate… but aren’t we lucky!


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Even less precise towards lower T5.

10-6

10-5

10-4

10-3

Mol

e Fr

actio

nC2H4

10-6

10-5

10-4

10-3

10-5 10-4 10-3

Mol

e Fr

actio

n

OH

Time (s)

10-6

10-5

10-4

10-3H2O

10-6

10-5

10-4

10-3

10-5 10-4 10-3

CO2

Time (s)


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10-5

10-4

10-3

10-5 10-4 10-3

Mol

e Fr

actio

n

Time (s)

C2H4

H2O

OH

CO2

300 ppm nC7H16 / 3300 ppm O2 / ArT5 = 1494 K, p5 = 2.15 atm



10-6

10-5

10-4

10-3

10-4 10-3

Mol

e Fr

actio

n

Time (s)


C2H4

H2O

OH CO2

Analyses of Experimental Uncertainties

Dashed lines: ±10K T5 uncertainty; dotted lines: ±20% uncertainty on species concentration

13

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

0, ,

1 1

ˆˆ,m m m


x ξ x 0

1i i

m

i jj

jx x


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

Sheen, et al. (2009)

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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


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


x ξ x


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

Sheen, et al. (2009)

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10-5

10-4

10-3

Mol

e Fr

actio

n

C2H4

10-5

10-4

10-3

10-5 10-4 10-3

Mol

e Fr

actio

n

OH

Time (s)

10-5

10-4

10-3H2O

10-5

10-4

10-3

10-5 10-4 10-3

CO2

Time (s)

Model Precision Improved by the data



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(a)

(b)

(a)

(b)

Impact on Flame Speed Predictions


0.7 0.9 1.1 1.3 1.5

Equivalence Ratio,

Flam

e Sp

eed

(cm

/s)

n‐heptane‐air mixtures (p = 1 atm, T0 = 353 K)

unconstrained – prior model

constrained – posterior modelOH, H2O, CO2 ( = 1, T5 = 1365 * 1495 K)

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Multispecies Time HistoriesEffect of Experimental Uncertainties


1

2

3

4

0 5 10 15 20

1/(2 obs)

= 1.0

s (

cm/s

)uo

= 1.4

20% 10% 7% 5%

Uncertainty in Species Value, 2 obs

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)

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Multispecies Time HistoriesEffect of Experimental Uncertainties

(a)

(b)

(c)

(a)

(b)

(c)

0.7 0.9 1.1 1.3 1.5

Equivalence Ratio,

Flam

e Sp

eed

(cm

/s)



posterior model (±20%)

posterior model (±5% - hypothetical)

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(d)(d)

(a)

(b)

(a)

(b)

Model is Accurate, and (Looks) Precise (Too)with constrained joint parameter uncertainties

Equivalence Ratio,

Flam

e Sp

eed

(cm

/s)



2 sets of OH, H2O, CO2 profiles

2 sets of OH, H2O, CO2 profilesFlame speedIgnition delay

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102

103

104

Igni

tion

Del

ay,

(s) 0.4% nC7H16 / 4.4 % O2 / Ar (p5 = 1 atm)

102

103

104

0.60 0.65 0.70 0.75

1000 K/T

Igni

tion

Del

ay,

(s)

Open diamond: Smith et al. (2005); filled circles: Davidson et. al. (2010)

Model is Accurate, and (Looks) Precise (Too)with constrained joint parameter uncertainties

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Multispecies Global Multispecies+properties Global properties

Joint Parameter Uncertainties

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JetSurF (Version 1.1) Release date: September 15, 2009

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

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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

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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

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Cyclohexane Low‐Temperature Chemistry

Miller, Taatjes (2009)

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Cyclohexane Ring‐Opening Reaction

CH3

CH2

k (s–1) = 5×1016 exp[ –88 (kcal/mol) / RT] (Tsang 1978)

CH3

CH2

CH3

C:H

H2.C

C.H2

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Methylcyclohexane Ring‐Opening Reaction

CH3

CH2

CH3

CH3

CH3

CH3

CH3

CH3

• •

CH2

CH3

CH3

CH3

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Ring‐Opening Reactions

CBS‐QB3 energy

→ Ho = 89.8 kcal/mol

→ Ho = 79.0 kcal/mol

CH3

C:H

CH3CH3

CH3

••

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Ea = 71 kcal/mol

Ea = 88 kcal/mol

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Summary

• JetSurF 2.0 is available online (still needs work).

•Major improvement from version 1.1• Added low temperature of cyclohexane

• Unresolved problems

• Low‐temperature chemistry for n‐butylcyclohexane not yet implemented

• Kinetics of alkylated cyclohexane thermal decomposition (ring opening through the carbene mechanism) currently unavailble)

reaction models of combustion properties4 • version 1.0+1.1 →jetsurf 2.0 n‐butyl‐,...

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