Click to edit Master title style Reaction Mechanisms of Click to edit … · 2008. 10. 27. ·...

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Reaction Mechanisms of Surrogate Fuels

C. K. Law, Princeton University

Fuels SummitSeptember 8-10, 2008

Topics of Presentation:1. Flame speed determination in counterflow2. Flame speed determination in propagating

spherical flame3. Reduced mechanisms



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1. Determination of Laminar Flame Speeds using the Counterflow

(n-Heptane)



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Schematic of Counterflow Apparatus



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Matrix of Experimental Conditions

• Pressure: 0.5, 1.0, 1.5, 2.0 atmospheres• Temperature: 298, 350K• O2 concentration: 21, 18%• Equivalence ratio: 0.7 – 1.4



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Raw Data & Density Scaling

10

20

30

40

50

60

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

Flam

e Sp

eed,

Suo

(cm

/s)

Equivalence Ratio, φ

1 atm, 298 K (Davis & Law [1])

0.5 atm, 350 K

1 atm, 350 K

1.5 atm, 350 K

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


1 atm, 298 K (Davis & Law [1])0.5 atm, 350 K

1 atm, 350 K

1.5 atm, 350 K

Mas

s Fl

ux, f

(kg/

m2 -

s)

Data reduction throughmass flux: f =Raw Data on o

uusρous



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Pressure Scaling

-4

-3

-2

-1

0

-1 .0 -0 .5 0 .0 0 .5 1 .0

2ln[

f (kg

/m2 -

s)]

ln [p (a tm )]

φ = 0 .8 , p = 1 -2 a tm

n = 1 .5

n = 1 .3φ = 1 .4 , p = 1 -2 a tm

φ = 0 .6 , p = 0 .5 -1 a tm

n = 1 .4

φ = 1 , p = 0 .5 -1 a tm

n = 1 .7

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

1 atm, 298 K1 atm, 350 K1.5 atm, 350 K0.5 atm, 350 K

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


Scal

ed M

ass

Flux

, (f x

p-n

/2) (

kg/m

2 -s)

Determination of reaction order based on calculation

Final correlation (n=1.5)



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Comparison with Wang Mechanism

10

20

30

40

50

60

70

80

0.6 0.8 1.0 1.2 1.4 1.6

1 2981 3501.5 3500.5 3502 350

Flam

e Sp

eed,

Suo

(cm

/s)


p (atm) Tu (K)

1.5 atm, 350 K

1 atm, 350 K



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2. Determination of Laminar Flame Speeds using the Constant-

Pressure Bomb



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(Novel) Experimental Apparatus

• Double chamber design allows: – Constant pressure

during flame propagation– High pressure (~60 atm.)

• Heating pads over outer wall allows vaporization of liquid fuel at constant temperature



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Issues on Data Accuracy

• Mixture stoichiometry for pre-vaporized liquid fuels

• Residual ignition energy• Chamber confinement and geometry

effects• Nonlinear flame evolution, especially for

Le>1 flames, characteristic of lean hydrocarbon/air mixtures (C>2)



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Mixture Stoichiometry• Heated chamber ensures fuel vaporization• Thorough mixing of all tubings and

chamber• Equivalence ratio triple checked

– Calculated volume of fuel relative to chamber volume

– Measured partial pressure of fuel– Gas sampled and analyzed with gas

chromatograph



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Residual Ignition Energy

50 100 150 200 250 300 350 400 450 5000

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40

60

80

100

120

140

160

κ (1/s)

s b (cm

/s)

Quasi-Steady Propagation

Increasing Ignition Energy



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Chamber Diameter Increased with Mk II Design

0 100 200 300 400 5000

50

100

150

200

250

κ (1/s)

Sb (c

m/s

)n-Butane/air, 1 atm, φ=0.85

Smaller Chamber

Larger Chamber Diameter



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Chamber Confinement & Geometry

0 50 100 150 200 250 3000

20

40

60

80

100

120

140

160

180

200

220

κ (1/s)

Sb (c

m/s

)Flame Radius of 1.8 cm

Useful data forextrapolation

Systematically change boundary conditions and determine radius at which boundary conditions influence propagation



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Linear & Nonlinear Extrapolations

ob

bob

bob

b

sL

ss

ss κ2ln

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−=⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

κbobb Lss −=Linear:

Nonlinear:

•Easy to use•Generally adopted in determinations of laminar flame speeds•Used in most of this study as its accuracy is adequate

•Potentially more accurate•Potential complications from initial and unsteady effects•Needs further study



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Range of Extrapolation (Lean Pentane)

0 200 400 600 800 1000

100

150

200

250

κ (1/s)

s b (cm

/s)

UsefulData

BoundaryInfluence

Transient Ignition

Linear Extrapolation

Nonlinear Extrapolation



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Range of Extrapolation (Rich Pentane)

0 100 200 300 400 500 600 700 80050

100

150

200

κ (1/s)

s b (cm

/s)

Transient IgnitionUsefulData

BoundaryInfluence

Nonlinear Extrapolation

Linear Extrapolation



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Linear vs. Nonlinear Extrapolation



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Comparison with USC Data (1 atm)



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3. An Integrated Approach for Systematic

Reduction of Large Kinetic Mechanisms



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Need for Mechanism Reduction

• Detailed mechanisms are

– (Supposedly) accurate and comprehensive

– Large and stiff

• Drastically reduced mechanisms are necessary for large-scale simulations of large hydrocarbons and their mixtures



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Major Challenges in Computational Simulation Involving Complex Fuels

101 102 103 104

102

103

104

before 2000 2000 to 2005 after 2005

iso-ocatane (LLNL)

iso-ocatane (ENSIC-CNRS)

n-butane (LLNL)

CH4 (Konnov)

neo-pentane (LLNL)

C2H4 (San Diego)CH4 (Leeds)

Methyl Decanoate(LLNL)

C16 (LLNL)

C14 (LLNL)C12 (LLNL)

C10 (LLNL)

USC C1-C4USC C2H4

PRF

n-heptane (LLNL)

skeletal iso-octane (Lu & Law)skeletal n-heptane (Lu & Law)

1,3-ButadieneDME (Curran)C1-C3 (Qin et al)

GRI3.0Num

ber o

f rea

ctio

ns

Number of species

GRI1.2 pre-20002000 – 2005post-2005

Number of Species

Num

ber o

f Rea

ctio

ns

nC7H16

C11H22O2

1000 2000 300010-15

10-12

10-9

10-6

Sho

rtest

Spe

cies

Tim

e S

cale

, Sec

Temperature

Ethylene,p = 1 atmT0 = 1000K

n-Heptane, p = 50 atmT0 = 800K

Typical flow time

Large Size Chemical Stiffness

, K

, I

I ≈ 5K

• High simulation cost- Size- Stiffness

• Massive output



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Strategy for Static Mechanism & Stiffness Reduction

Directed Relation Graph (DRG)

Detailed mechanism561 species

DRG Aided Sensitivity Analysis

Reduced mechanism52 species, 48 global-steps

Analytic QSS solution

Unimportant ReactionElimination

Isomer Lumping

Skeletal mechanism78 species, 359 reactions



“Skeletal” mechanism68 species, 283 reactions

QSS ReductionReduced mechanism

52 species, 48 global-steps

QSS Graph

Diffusive Species Bundling

Reduced mechanism52 species

14 diffusive species



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Demonstration of Reduction Strategies & Efficiency

• Candidate fuel: n-Heptane

• LLNL-Westbrook mechanism

• K = 561 Species

• I = 2539 (~ 5K) Elementary reactions

• Final reduced mechanism

• K = 55 Species

• K – M = 55 – 4 = 51 Lumped reactions

(M = No. of elements)



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Homogeneous ApplicationsIgnition Delay PSR Extinction

1500

1600

1700

1800

1900

2000

1E-6 1E-4 1E-2 1E+0 1E+2

Residence Time, sec

Detailed68-species55-species

1200

1300

1400

1500

1400

1800

2200

Tem

pera

ture

, K

n-heptaneT1 = 300K

φ = 0.5

φ = 1.0

φ = 1.5

p = 50 atm

1

5

50

51

50

51

1E-7

1E-5

1E-3

1E-1

1E+1

Detailed68-species55-species

1E-7

1E-5

1E-3

1E-1

1E+1

Igni

tion

Del

ay, (

sec)

1E-7

1E-5

1E-3

1E-1

1E+1

0.5 1 1.5

1000/T, (1/K)

φ = 0.5

φ = 1.0

φ = 1.5

n-heptane

p = 1 atm5

50

5

50

50

5

1

1



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Laminar Flame Speeds

0.6 0.8 1.0 1.2 1.4 1.6

0

20

40

60

Detailed 78-species 68-species 55-species without bundling 55-species with bundling Davis & Law, 1998 Huang et al, 2004

Lam

inar

Fla

me

Spe

ed, c

m/s

ec

Equivalence Ratio

p = 1 atmT0= 300K

n-heptane



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Reduction of A Monster Mechanism

0

1000

2000

3000

4000

0 0.1 0.2 0.3 0.4 0.5

MD -air

Senkin & PSRp: 1 atmφ: 0.5 ~ 1.5T0: 900 ~ 1300K (senkin) 300K (PSR)

Detailed mechanism(LLNL 2007):

~3000 species ~8500 reactions

Skeletal mechanism: ~700 reactions

125 species

Methyldecanoate, n-C9H19C(=O)OCH3

Relative error tolerance, ε

Num

ber o

f spe

cies



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Mechanism Validation

10-6 10-5 10-4 10-3 10-2 10-1 100800

1000

1200

1400

1600

Tem

pera

ture

, K

Residence Time, s

p = 1 atmφ = 1.0

10-5 10-4 10-3 10-2 10-1 100

1500

2000

2500

0.5

0.7

Tem

pera

ture

, K

Residence Time, s

Methyl Decanoate - AirPSRp = 1 atmT0 = 300K

φ = 1.0

Auto-Ignition PSR



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Summary• Laminar flame speeds measured:

– n-Heptane in the counterflow– n-Pentane in the high-pressure bomb

• Considerable development of the high-pressure bomb technique for experimentation with large hydrocarbons– Fuel pre-vaporization and mixing – Ignition transient & complex flame dynamics– Chamber confinement and asymmetry– Linear vs. nonlinear extrapolation

• Suite of methods developed for reduction of size and stiffness of large mechanisms

• Ready for production mode?– Further improvement of experimental technique– Need guidance on experimental matrix



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Thank You!



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Backup Slides



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Operating Limits of Experimentation by Liquid Fuel Condensation

0.5 1 1.5 2300

320

340

360

380

400

3 atm4 atm5 atm

10 atm15 atm20 atm30 atm

40 atm50 atm

φ

Tem

pera

ture

(K)

n-Octane

0.5 1 1.5 2300

320

340

360

380

400

3 atm5 atm

10 atm15 atm20 atm30 atm40 atm50 atm

φ

Tem

pera

ture

(K)

n-Heptane

0.5 1 1.5 2300

320

340

360

380

400

10 atm15 atm20 atm

30 atm40 atm50 atm

φ

Tem

pera

ture

(K)

n-Hexane

0.5 1 1.5 2300

320

340

360

380

400

20 atm30 atm40 atm50 atm

φ

Tem

pera

ture

(K)

n-Pentane



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Comparisons

• Need to add comparison to Professor Wang’s mechanism



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Reduction of iso-Octane Mechanism

• Original: 857 species, 3605 reactions• Skeletal: 233 species, 676 reactions• Reduced: 78 species, 207 reactions

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