modelling complex liquid transportation fuels: chemical ... · chemical kinetic model prediction...

Modelling Complex Liquid Transportation Fuels:Chemical Compositions to Combustion Properties

to Highly Reduced Kinetic Models

Stephen Dooley

University of Limerick

Ireland

“Data Collection and Mining toward the Virtual Chemistry of Smart Energy Carriers”,

SMARTCAT Workgroup 4 Workshop

5-6 April 2016, University Federico II of Naples, Italy

1

State of the Art in Liquid Fuel Kinetic Model

• Experiment proves the surrogate concept to be of high fidelity.• Fidelity of current modeling approaches has NOT been fully evaluated.

2

Challenges: None of the categories are perfect yet!

How fundamentally has the model been constructed?

How many initial fuel components are necessary?

How comprehensively has the model been validated?

How robust are the small fragment chemistries and the initial fuel component chemistries?

How small does the model need to be?

How can even smaller reduced models be derived?

What are the eventual limitations, accuracy vs. cost?

Multi-componentLiquid Fuel Kinetic Model

Model Reduction Methods

•Restricted T & P

•Direct Relation Graph•Path Flux Analysis•Computational Singular Perturbation

•Lumping•…

Sub-component chemistries;

n-alkanes, iso- or weakly branched alkanes, cyclo-

alkanes, aromatics…

Core;C0 – C4 chemistry subset

“Useful” Liquid Fuel

Combustion Model for……..

CFD, Fuel Properties,

Comprehension, etc

Determination of Chemical Quantities

Rate Rules

High level quantum chemistry

Experiments

2

1) Metcalfe W. K., Dooley S., Dryer F. L., Energy & Fuels 25 (2011) 4915–4936.2) Won S. H., Dooley S., Dryer F. L., Ju Y., Proc. Combust. Inst. 33 (2011) 1163–1170.3) Diévart P., Won S. H., Kim H. H., Ju Y., Dooley S., Dryer F. L., Wang W., Oehlschlaeger M. A, Fuel. (2013).4) Westbrook C. K., Pitz W. J., Herbinet O., Curran H. J., Silke E. J., Combust. Flame, 156 (2009) 181–199.5) Mehl M., Pitz W. J., Westbrook C. K., Curran H. J., Proc. Combust. Inst. 33 (2011) 193–200. 6) Jahangirian S., Dooley S., Haas F. M., Dryer F. L., Combust. Flame 159 (2012) 30–43.7) Oehlschlaeger, M. A., Steinberg, J, Westbrook, C. K., Pitz, W. J., 156 (2009) 2165-2172.

3

8) P. Dagaut, A. El Bakali, Fuel 85 (2006) 944–956. 9) P. Gokulakrishnan, G. Gaines, et al. Eng. Gas Turb. Power 129 (2007) 655–664. 10) E. Ranzi, M. Dente, G. Bozzano, A. Goldaniga, T. Faravelli, PECS 27 (2001) 99–139.11) R. Bounaceur, I. Da Costa, R. Fournet, F. Battin-Leclerc, IJCK 2005, 37, 25–49.

Chemical Kinetic/Transport Model Construction

Instructions:1) Evaluate state-of-art kinetic models for surrogate fuel components.2) Assimilate state-of-art.3) Test performance Vs.*Pure components.*Pure component mixtures.*Real fuels.4) Do not adjust scientific construct

for better performance.

S. Dooley, S.H . Won, F. M. Haas, J. Santner, Y. Ju, F.L. Dryer, T. Farouk, “Severely Reduced Kinetic Models for Alternative Aviation Fuels” American Institute for Aeronautics and Astronautics, Joint Propulsion Meeting, Cleveland, Ohio, USA, 29th July 2014.

S. Dooley, F.L. Dryer, T. Farouk, S.H. Won, “Reduced Kinetic Models for the Combustion of Jet Propulsion Fuels” American Institute for Aeronautics and Astronautics, Texas, USA, 7th January 2013.

4

S. Dooley, S.H. Won, J. Heyne, T.I. Farouk, Y. Ju, F.L. Dryer, K. Kumar, X. Hui, C.-J. Sung, H. Wang, M.A. Oehlschlaeger, T.A. Litzinger, R.J. Santoro, T. Malewicki, K. Brezinsky, Combust. Flame 2012 159: 1444—1466.S. Dooley, S.H. Won, M. Chaos, J. Heyne, Y. Ju, F.L. Dryer, K. Kumar, C.J. Sung, H. Wang, M. Oehlschlaeger, R.J. Santoro, T.A. Litzinger, Combust. Flame 2010 157: 2333-2339.

Chemical Kinetic Model “Prediction”Ignition Delay Laminar Burning Velocity

Surrogate Component Temperature PressureEquivalence

RatioTemperature Pressure

Equivalence Ratio

n-heptane 600-1400K 1 -20 atm 0.5, 1.0, 1.5 298 – 343K 1 atm ~0.6-1.4

n-decane 600-1400K 1 -20 atm 0.5, 1.0, 1.5 343 -400K 1 atm ~0.6-1.4

n-dodecane 600-1400K 1 -20 atm 0.5, 1.0, 1.5 400K 1 atm ~0.6-1.4

n-tetradecane 600-1400K 1 -20 atm 0.5, 1.0, 1.5 400K 1 atm ~0.6-1.4

n-hexadecane 600-1400K 1 -20 atm 0.5, 1.0, 1.5 400K 1 atm ~0.6-1.4

iso-octane 600-1600K 1 -40 atm 0.5, 1.0, 1.5 298 – 400K 1 atm ~0.6-1.4

iso-cetane 600-1600K 10 -40 atm 0.5, 1.0 400K 1 atm ~0.6-1.4

Toluene 900-1600K 1 -40 atm 0.5, 1.0, 1.5 298 – 400K 1 atm ~0.6-1.4

1,3,5 trimethyl benzene 900-1700K 1 -20 atm 0.5, 1.0, 1.5 343 – 400K 1 atm ~0.6-1.4

n-propyl benzene 700-1400K 1 -20 atm 0.5, 1.0, 1.5 343 – 400K 1 atm ~0.6-1.4

n-dodecane/iso-octane 700-1400K 20 atm 1.0 n/a n/a n/a

n-hexadecane/iso-cetane

700-1400K 20 atm 1.0 n/a n/a n/a

n-decane/iso-octane/toluene

700-1400K 20 atm 1.0 400 – 450K 1 atm ~0.6-1.4

n-dodecane/iso-octane/

1,3,5 trimethyl benzene/n-propyl benzene

700-1400K 20 atm 1.0 400 – 450K 1 atm ~0.6-1.4

S. Dooley, S.H, Won, F. M. Haas, J. Santner, Y. Ju, F.L. Dryer, T. Farouk, Joint Propulsion Meeting, Cleveland, Ohio, USA, 29th July 2014. S. Dooley, F.L. Dryer, T. Farouk, S.H. Won, American Institute for Aeronautics and Astronautics, Texas, USA, 29th January 2013.

5


Chemical Kinetic Model “Prediction”Ignition Delay Laminar Burning Velocity

Surrogate Component Temperature PressureEquivalence

RatioTemperature Pressure

Equivalence Ratio

n-heptane 600-1400K 1 -20 atm 0.5, 1.0, 1.5 298 – 343K 1 atm ~0.6-1.4

n-decane 600-1400K 1 -20 atm 0.5, 1.0, 1.5 343 -400K 1 atm ~0.6-1.4

n-dodecane 600-1400K 1 -20 atm 0.5, 1.0, 1.5 400K 1 atm ~0.6-1.4

n-tetradecane 600-1400K 1 -20 atm 0.5, 1.0, 1.5 400K 1 atm ~0.6-1.4

n-hexadecane 600-1400K 1 -20 atm 0.5, 1.0, 1.5 400K 1 atm ~0.6-1.4

iso-octane 600-1600K 1 -40 atm 0.5, 1.0, 1.5 298 – 400K 1 atm ~0.6-1.4

iso-cetane 600-1600K 10 -40 atm 0.5, 1.0 400K 1 atm ~0.6-1.4

Toluene 900-1600K 1 -40 atm 0.5, 1.0, 1.5 298 – 400K 1 atm ~0.6-1.4

1,3,5 trimethyl benzene 900-1700K 1 -20 atm 0.5, 1.0, 1.5 343 – 400K 1 atm ~0.6-1.4

n-propyl benzene 700-1400K 1 -20 atm 0.5, 1.0, 1.5 343 – 400K 1 atm ~0.6-1.4

n-dodecane/iso-octane 700-1400K 20 atm 1.0 n/a n/a n/a

n-hexadecane/iso-cetane

700-1400K 20 atm 1.0 n/a n/a n/a

n-decane/iso-octane/toluene

700-1400K 20 atm 1.0 400 – 450K 1 atm ~0.6-1.4

n-dodecane/iso-octane/

1,3,5 trimethyl benzene/n-propyl benzene

700-1400K 20 atm 1.0 400 – 450K 1 atm ~0.6-1.4

S. Dooley, S.H, Won, F. M. Haas, J. Santner, Y. Ju, F.L. Dryer, T. Farouk, Joint Propulsion Meeting, Cleveland, Ohio, USA, 29th July 2014. S. Dooley, F.L. Dryer, T. Farouk, S.H. Won, American Institute for Aeronautics and Astronautics, Texas, USA, 29th January 2013.

Chemical Kinetic Model “Prediction”• Ignition delay measurements by M. Oehlschlaeger1

– Shell SPK, Sasol IPK, S-8, Jet A.

– Surrogates formulated by Combustion Property Target technique 2 .

• Simulation gives same conclusion as experiment, regarding relative reactivity of each real fuel.

• Quantitatively offset to longer IDTs.

1) H. Wang, M. A. Oehlschlaeger, Fuel 98 (2012) 249-258.

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

50

100

1000

10000

50000

Detailed Model + Surrogate Fuels

Jet-A, POSF 4658

IPK, Iso Paraffinic Kerosene

S-8, Coal-to-Liquid

SPK, Gas-to-Liquid

Ign

itio

n d

ela

y tim

e,

/ s

1000K / T

20 atm, stoichiometric fuel in air

1300 1200 1100 1000 900 800 700 Temperature / K

General paradigm1) Real fuel definition2) Surrogate fuel formulation3) Model construction4) Chemical kinetic model reduction5) Kinetic model “prediction”

6

Group additivity type analysis performedon 1st and 2nd generation surrogate fuelsshows high degree of Commonality ofChemical Groups on a mass basis.

Example: n-propylbenzene =>

Each Molecular structure may contain

several of the same groups and thus the

molecules themselves do not represent

linearly independent parameters.

Benzyl

CH2

CH3

0 20 40 60 80 100

A

ltern

ative 2n

d G

enera

tion S

urr

ogate

1st

Gen. Surrogate

2nd

Gen. Surrogate

#2

#3

#4

#5

#6

#7

Mass %

CH2 CH

3 Benzyl-type

42.7/33.0/24.3%, nC10/iC8/toluene

40.4/29.5/7.3/22.8% , nC12/iC8/135TMB/nPB

39.3/31.6/13.8/15.3

40.1/31.3/27.7/0.7

35.4/33.2/0.0/31.4

36.1/33.3/1.6/28.9

39.6/30.3/14.5/15.6

28.9/31.3/12.0/17.7

Molecular group mass comparisons for 1st Gen (n-decane/iso-octane/toluene 42.7/33.0/24.3 mole %), 2nd gen(n-dodecane/iso-octane/1,3,5 trimethylbenzene/n-propylbenzene 40.41/29.48/7.28/22.83 mole %) and six~equally possible alternative 2nd gen POSF 4658 surrogate fuel mixtures.

Dooley et al. Combust Flame 159:1444-466 (2012).

Prevaporized Combustion is Controlled by Chemical Functional Groups

1 x Benzyl

+ 1 x CH2

+ 1 x CH3

7

• Nuclear Magnetic Resonance (NMR) spectroscopy can identify the atomic detail comprising a fuel.

• NMR is already used to provide information that constrains industry fuel properties.

Nuclear Magnetic Resonance for Fuels

8

Example 1H NMR spectra of gasoline.

Courtesy, J.C. Edwards, NMR Associates (2014)

• 1) Test the applicability of assembling simple functional group compositions of real fuels from the atom types identified by NMR.

• 2) Analyze this information as constraining toward the accurate prediction of complex combustion properties, can this approach be competitive with “fundamental” chemical kinetic models?

• 3) Analyze this information for utility toward identifying the important functional groups dictating different combustion properties

=> inform toward fuel design.

Objectives

9

Calibration Data Set of Measured Combustion

Behaviors of Defined Chemical

Compositions

Training Algorithm

Magnitude of Dependence of Combustion Behaviour

on each Chemical Functionality

Inputs Outputs

tignition ≡ f (T, xCH2, xCH3 xBenzyl)

Methodology

10



Compositions

Training Algorithm

Chemical Functionality Definitions



Inputs

Knowledge of Combustion Kinetics

Outputs


Methodology

11



Compositions

Training Algorithm

Atom TypeComposition of Real Fuels




Inputs

NMR


Outputs


Methodology

12



Compositions

Training Algorithm





Inputs

NMR


Quantitative Predictions of Real Fuel Combustion Behaviours

Outputs

Identification of Functional Group Definitions most constraining

to tested Combustion Response


Methodology

1

2

13

• Select homogenous gas phase ignition delay as candidate test data set.

=> large body of data exists across fuels, temperature, pressure.

=> ignition delay is richly responsive to chemical structure

=> homogenous ignition delay is phenomenalogically related to legal quantities of cetane and octane numbers.

• Minimize potential imprecisions in facility-to-facility data sets by selecting data from only one laboratory - M. A. Oehlschlaeger at RPI.

• Reference condition is 20 atm, phi 1.0 in air.

Methodology

14

[1] S. H. Won, S. Dooley, P. S. Veloo, H. Wang, M. A. Oehlschlaeger, F. L. Dryer and Y. Ju, Combust. Flame 161 (2014) 826–834.

[2] S. Dooley, S. H. Won, M. Chaos, J. Heyne, Y. Ju, F. L. Dryer, K. Kumar, C.-J. Sung, H. Wang, M. A. Oehlschlaeger, R. J. Santoro and T. A. Litzinger, Combust.Flame 157 (2010) 2333–2339.

[3] S. Dooley, S. H. Won, J. Heyne, T. I. Farouk, Y. Ju, F. L. Dryer, K. Kumar, X. Hui, C.-J. Sung, H. Wang, M. A. Oehlschlaeger, V. Iyer, S. Iyer, T. A. Litzinger, R. J.Santoro, T. Malewicki and K. Brezinsky, Combust. Flame 159 (2012) 1444–1466.

[4] S. Dooley, S. H. Won, S. Jahangirian, Y. Ju, F. L. Dryer, H. Wang and M. A. Oehlschlaeger, Combust. Flame 159 (2012) 3014–3020.

[6] S. M. Sarathy, C. K. Westbrook, M. Mehl, W. J. Pitz, C. Togbe, P. Dagaut, H. Wang, M. A. Oehlschlaeger, U. Niemann, K. Seshadri, P. S. Veloo, C. Ji, F. N.Egolfopoulos and T. Lu, Combust. Flame 158 (2011) 2338–2357.

[7] H. Wang, M. A. Oehlschlaeger, S. Dooley F.L. Dryer, United States Combustion Meeting, Atlanta Georgia, 2011.

[8] H. Wang, M. A. Oehlschlaeger, Fuel 98 (2012) 249–258.

[9] S.H. Won, F. M. Haas, A. Tekawade, G. K., M. A. Oehlschlaeger, S. Dooley, F. L. Dryer, 9th U. S. National Combustion Meeting, 2015, Cincinnati, Ohio.

Methodology – High Temperatures

15

• To simplify mathematical model, ignition delay is divided into regions of Arrhenius and non Arrhenius behaviors, ~ 1000 K.

Model 1 – “High” Temperatures

f1(T) ≡ Ln(τ) ≡ a0 + a1/T

+ a2 xCH2 + a3 xCH3 + a4 xBZY

+ a5 xCH2/T + a6 xCH3/T + a7 xBZY/T

+ a8 xCH2 xCH3

• Trained to pure components (x7) and mixtures of pure components (x4).

Methodology - NMR

16

• From NMR functional groups assignments are made for 4 real aviation fuels,

• Jet-A, IPK, S-8 and SPK.

• 1H and 13C spectra of each fuel were obtained with a JEOL 400 MHz NMR ECX-400.

• Carbon atom types are quantified by relating quantitative hydrogen atom signal tocarbon atom signal. i.e. (the 1H (13C) approach).



Compositions

Training Algorithm





Inputs

NMR



Outputs




Methodology

1

2

17



Compositions

Training Algorithm





Inputs

NMR



Outputs




Methodology

1

2

18

?

Testing - High Temperatures

19

H. Wang, M. A. Oehlschlaeger, Fuel 98 (2012) 249–258.

0.8 0.9 1.0

100

1000

Kinetic NMR

Model Model

Jet-A POSF 4658

Syntroleum S8 4734

Shell SPK 5729

IPK Sasol 7629

Ign

itio

n d

ela

y t

ime

/

s

1000K/T

• When supplied with the NMR determined CH2, CH3 and Benzyl groupfractions the low temperature model also closely predicts themeasurements (symbols) of Wang & Oehlschlaeger at 20 atm, phi in air.

• The model suggest Jet-A to bemarginally slower to ignite thanthe synthetic fuels, which itsuggests to be closelyequivalent.

Testing - High Temperatures

20


0.8 0.9 1.0

100

1000

Kinetic NMR

Model Model

Jet-A POSF 4658

Syntroleum S8 4734

Shell SPK 5729

IPK Sasol 7629

Ign

itio

n d

ela

y t

ime

/

s

1000K/T

• Surrogate fuel formulation –detailed kinetic modelpredictions are less accuratethan NMR based model.

• The model suggest Jet-A to bemarginally slower to ignite thanthe synthetic fuels, which itsuggests to be closelyequivalent.


Testing - Low Temperatures

21

1.0 1.2 1.4 1.6

1000

10000

1.0 1.2 1.4 1.6

1000

10000

1.0 1.2 1.4 1.6

1000

10000

1.0 1.2 1.4 1.6

1000

10000

Sasol IPK 7629

Model R2 = 0.93

Kinetic model

Jet-A POSF 4658,

Model R2 = 0.78

Kinetic model

S8 4734,

Model R2 = 0.89

Kinetic model

Ignitio

n d

ela

y t

ime /

s

Shell SPK 5729,

Model R2 = 0.79

Kinetic model

1000K/T



• Surrogate fuelformulation – detailedkinetic modelpredictions are inferiorto NMR based real fuelmodel.

Importance of Functional Groups?

22

• Local sensitivity analysis conducted on each model definition.

• High temperature ignition is relatively insensitive to tested ranges ofchemical composition, low temperature ignition is much more sensitive.

Karla Dussan, Stephen Dooley, Frederick L. Dryer, Sang Hee Won, “Nuclear Magnetic Resonance Orientated

Functional Group Regression for Liquid Fuel Combustion Properties” PROCI 2016 under review.

• Surrogate fuelformulation – detailedkinetic modelpredictions are inferiorto NMR based real fuelmodel.

High Temperature

Low Temperature

High Temperature

Low Temperature

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

Usin

g C

H2

Sensitivity coefficient

Benzyl

CH3

CH2 CH

2CH

2CH

2

Usin

g C

H2C

H2C

H2

Functional Groups

23

Karla Dussan, Stephen Dooley, Frederick L. Dryer, Sang Hee Won, “Nuclear Magnetic Resonance Orientated

Functional Group Regression for Liquid Fuel Combustion Properties” PROCI 2016 under review.

• The model can differentiate as to which functional group definition is moredictating to a particular combustion behaviour.

• Example case study: -CH2- verses -CH2- CH2--CH2-

Summary

• Surrogate fuel – detailed chemical kinetic models show high fidelity in prediction of complex liquid fuel combustion properties, but are quantitatively inaccurate.

• Functional group representations of complex liquid fuels can make combustion property predictions of high fidelity and high accuracy (but at limited range of conditions).

• Data Needs:

– 1) Ranking of most constraining functionalities for the oxidation of a liquid hydrocarbon mixture.

– 2) Compositional data of real liquid hydrocarbon fuels.

24

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

50

100

1000

10000

50000

Jet-A

1st Generation Surrogate

Detailed Model

1154

651

461

348

233

211

171

167

144

Ign

itio

n d

ela

y tim

e,

/ s

1000K / T

(n-decane/iso-octane/toluene)

1300 1200 1100 1000 900 800 700 Temperature / K

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

50

100

1000

10000

50000

Detailed Model

1291

965

810

695

558

425

402

384

315

231

219

Jet-A

2nd Generation Surrogate(n-dodecane/iso-octane/

n-propyl benzene/trimethyl benzene)

Ign

itio

n d

ela

y tim

e,

/ s

1000K / T

1300 1200 1100 1000 900 800 700 Temperature / K

25

• In order to emulate detailed model over entire temperature range:– 1st generation composition (3 components) requires 233-461 species.

– 2nd generation composition (4 components) requires 315-558species (+ > 35%).

• In order to emulate detailed model only at high temperature, 1100 K+ :– 1st generation composition requires 144 species.

– 2nd generation composition requires 219 species (+ 52%).


Chemical Kinetic Model “Prediction”

Chemical Kinetic Model Reduction

1) Figure adapted from Lu, Law, Progress in Energy and Combustion Science 35 (2009) 192-215.

Approximate current upper limits for

affordable numerical

simulations

• Can real fuel gas phase combustion properties be computed or predicted by a scientifically developed modelling strategy?

26

3147 Species

Convention Reduction Methods

Fully realistic approach shows genuine limitations.

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

50

100

1000

10000

50000

Jet-A


Detailed Model

1154

651

461

348

233

211

171

167

144

Ign

itio

n d

ela

y tim

e,

/ s

1000K / T


1300 1200 1100 1000 900 800 700 Temperature / K

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

50

100

1000

10000

50000

Detailed Model

1291

965

810

695

558

425

402

384

315

231

219

Jet-A



Ign

itio

n d

ela

y tim

e,

/ s

1000K / T

1300 1200 1100 1000 900 800 700 Temperature / K

27







Methodology – Low Temperatures

28

• To simplify mathematical model, ignition delay is divided into regions of Arrhenius and non Arrhenius behaviors, ~ 1000 K.

Model 2 – “Low” Temperatures

f1(T) ≡ Ln(τ) ≡ a0 + a11/T + a12/T2 + a13/T3



+ a8 xCH2 xCH3

• Trained to pure components (x8) and mixtures of pure components (x4).

1.0 1.2 1.4 1.6

1000

10000

100000R2

-

-

0.894

0.975

0.900

0.875

0.917

-

n-propyl benzene

Iso-octane

Iso-dodecane

n-dodecane

2,6,10-trimethyldodecane

2-methylheptane

n-octane

n-heptane

Ign

itio

n d

ela

y tim

e /

s

1000K/T

1.0 1.2 1.4 1.6

1000

10000

R2

0.893

0.949

0.559

0.764

2nd Gen surrogate

nC10/iC8/Toluene

nC16/iC16

nC12/iC8

Ign

itio

n d

ela

y tim

e /

s

1000K/T

29

• Analysis of Terms


f1(T) ≡ Ln(τ) ≡ a0 + a1/T



+ a8 xCH2 xCH3 Model 1

Coefficient Estimate SE tStat pValue

a0 -9.4685 8.6041 -1.1005 0.27303

a1 14.653* 8.7069 1.6829 0.094639

a2 4.4604 8.0507 0.55403 0.58045

a3 2.4829 11.892 0.2088 0.83491

a4 1.9255 8.1896 0.23511 0.81447

a5 -3.5834* 8.1419 -0.44012 0.66054

a6 -1.287* 12.02 -0.10707 0.91489

a7 -0.9154* 8.288 -0.11045 0.91221

a8 -3.805 0.56926 -6.6842 5.2E-10

Number of observations 148

Root Mean Squared Error 0.150

R-squared 0.969 Adjusted R-Squared 0.967

F-statistic vs. constant model

• Analysis of terms showsbenzyl fraction andmethylene-to-methylto be the importantchemical terms.


30

• Analysis of Terms


f1(T) ≡ Ln(τ) ≡ a0 + a1/T



+ a8 xCH2 xCH3 Model 1


a0 -9.4685 8.6041 -1.1005 0.27303

a1 14.653* 8.7069 1.6829 0.094639

a2 4.4604 8.0507 0.55403 0.58045

a3 2.4829 11.892 0.2088 0.83491

a4 1.9255 8.1896 0.23511 0.81447

a5 -3.5834* 8.1419 -0.44012 0.66054

a6 -1.287* 12.02 -0.10707 0.91489

a7 -0.9154* 8.288 -0.11045 0.91221

a8 -3.805 0.56926 -6.6842 5.2E-10

Number of observations 148

Root Mean Squared Error 0.150





31

• Analysis of Terms at low temperatures shows more descriptors are needed than at high temperatures – as one would expect.


f1(T) ≡ Ln(τ) ≡ a0 + a11/T + a12/T2 + a13/T3



+ a8 xCH2 xCH3

Model 2


a0 -128.2 12.2 -10.43 8.5E-20

a11 409.5* 32.1 12.76 3.2E-26

a12 -406.8* 30.3 -13.39 5.5E-28

a13 133.3* 9.8 13.58 1.7E-28

a2 -0.62 4.7 -0.13 0.89

a3 -7.71 7.8 -0.99 0.32

a4 -4.53 5.11 -0.88 0.37

a5 -0.034* 4.55 -0.007 0.99

a6 9.47* 7.63 1.24 0.21

a7 5.57* 4.91 1.1 0.25

a8 -3.25 0.86 -3.78 2.83E-4Number of

observations172

Root Mean

Squared Error0.193




32

• There is a much larger variance when modeling other functionalities at low temperatures vs. high temperature– as we expect.


f1(T) ≡ Ln(τ) ≡ a0 + a11/T + a12/T2 + a13/T3



+ a8 xCH2 xCH3

Model 2


a0 -128.2 12.2 -10.43 8.5E-20

a11 409.5* 32.1 12.76 3.2E-26

a12 -406.8* 30.3 -13.39 5.5E-28

a13 133.3* 9.8 13.58 1.7E-28

a2 -0.62 4.7 -0.13 0.89

a3 -7.71 7.8 -0.99 0.32

a4 -4.53 5.11 -0.88 0.37

a5 -0.034* 4.55 -0.007 0.99

a6 9.47* 7.63 1.24 0.21

a7 5.57* 4.91 1.1 0.25

a8 -3.25 0.86 -3.78 2.83E-4Number of

observations172

Root Mean

Squared Error0.193



0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

50

100

1000

10000

50000

Jet-A


Detailed Model

1154

651

461

348

233

211

171

167

144

Ign

itio

n d

ela

y tim

e,

/ s

1000K / T


1300 1200 1100 1000 900 800 700 Temperature / K

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

50

100

1000

10000

50000

Detailed Model

1291

965

810

695

558

425

402

384

315

231

219

Jet-A



Ign

itio

n d

ela

y tim

e,

/ s

1000K / T

1300 1200 1100 1000 900 800 700 Temperature / K

33







0.6 0.8 1.0 1.2 1.430

40

50

60

70

Jet-A


1st_461

1st_211

1st_167

1st_144

Lam

inar

Burn

ing V

elo

city,

Su0 /

cm

s-1

Equivalence ratio in "air", 0.6 0.8 1.0 1.2 1.4

30

40

50

60

70

Jet-A

2nd Generation Surrogate

1st_461

2nd_558

2nd_231

2nd_219

Lam

inar

Burn

ing V

elo

city,

Su0 /

cm

s-1

Equivalence ratio in "air",

34

• In order to emulate detailed model performance of atmospheric pressure laminar burning velocities:– 1st generation composition requires 144 species.


X. Hui, C.-J. Sung, Fuel 2013 109: 191-200.S. Dooley, S.H. Won, J. Heyne, T.I. Farouk, Y. Ju, F.L. Dryer, K. Kumar, X. Hui, C.-J. Sung, H. Wang, M.A. Oehlschlaeger, T.A. Litzinger, R.J. Santoro, T. Malewicki, K. Brezinsky, Combust. Flame 2012 159: 1444—1466.


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