ICAT, November 13-14 2008

Outline

• Background, motivation and goals

• Kinetic Models

• Validation against shock tube experiments

• Comparison against HCCI experiments with PRFs

• Conclusions

Background and problem statement

Mechanisms for pollutant formation and ignition characteristics need to be compact for integration with complex fluid flow calculations

Reduced chemistry for:

• Variable components of fuel mixtures,

• Varying conditions.

is necessary for HCCI simulations and development.

Conflict between chemical and physical complexity

Chemical Information in Combustion Calculations

Multi-D flow modelMax 100 reactionsSimple fuels

Homogeneous model~1000 reactionsPractical fuel mixtures

Great span between high/low values, slow/fast processes: stiffness

additional numerical problems

3D flow calculation: ~106 computational cells

Turbulent flow: ~101 differential equations for independent variables

Detailed Chemistry: ~102 extra differential equations

Kinetic Models

The detailed mechanism : The latest reaction mechanism for PRFs from the LLNL 4238 reactions and 1034 species, most of them reversible. The detailed mechanism has been developed for wide range of engine applications.

The skeletal mechanism : 386 reactions and 63 species. The skeletal mechanism has been developed for SI knocking conditions by using an automatic reduction method.

Here both mechanisms will be validated for HCCI conditions by using shock tube and real engine experiments

Measure-ment

Fitting tomeasurements

Pro:

• Compact and reliable

Con:

• Restricted range of conditions• Equipment intensive• Easily measurable species only

Methods for reducing mechanisms

Fittedmechanism

Detailedmechanism

Systematic reduction

Skeletalmechanism

Pro:

• Versatility of detailed mechanism • Standard procedure for recalculation• Automation possibility

Con:

• Expertise and labour intensive

The automatic reduction method:Sensitivity and reaction flow analyses

Removal of redundant reaction paths

A measure of redundance: Reaction flow - transfer rate of atomic species between molecules

N H 3

N 2N H

N

H N O

N O

C N H N C O

C H 3 N H 2

C H 2 N H

C H N H

H C N

N 2 O

N 2

N 2 H

N O

N O

N O

N O

N O

N O

C H 2 N H 2

N C O

N H 2

' ''

1

''

1

R

R

N aj

k jk ik aka k

ij N

k ikk

nr

nf

r

'' '

1

'

1

R

R

N aj

k jk ik aka k

ij N

k ikk

nr

nc

r

sN

i

akik

ak nn

1

'

Species sensitivity analysis and necessity index

A species with low reaction flow is not necessarily redundant!Influence on important combustion parameters has to be measured

Sensitivity and reaction flow in one: species necessity

cA,E

A

B

CD

E fE,A

,0max , , ; 1, , 1,a ai i j ij j ij s aN N N f N c j N a N

,01,max ( )

s

jii

k N jk

SN

S

,

1

RNkj

A j kk k j

d AS r

dr c

Conditions and parameter ranges

Two intake conditions are compared;

(i) high intake temperature and low intake pressure

(ii) low intake temperature and high intake pressure

Experimental data for PRF 94 and PRF 84: Andrae, Johansson, Björnbom, Risberg, Kalghatgi, Combust. Flame, 140:267-86, (2005).

0.01

0.1

1

10

100

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Exp. PRF 0

LLNL PRF 0

63 sp PRF 0

Exp. PRF 100

LLNL PRF 100

63 sp PRF 100

Exp. PRF 90

63 sp PRF 90

Exp. PRF 80

63 sp PRF 80

Exp. PRF 60

63 sp PRF 60

Ign

itio

n d

ela

y, m

s

1000/T, 1/K

Model validation against shock tube ignition delay times from Fieweger.

Isooctane validation against shock tube ignition delay times

T5

K

p5

atm

Experimentti / ms

LLNLti / ms

Rel.Err.%

Skeletalti / ms

Rel.Err.%

855 56.4 1719 3118 81% 1951 13%

867 59.3 1755 2762 57% 1711 -3%

894 58.5 1193 2460 106% 1580 32%

927 55.7 1067 1897 78% 1411 32%

975 51.2 871 1070 23% 950 9%

984 18.1 1511 2562 70% 2250 49%

995 16.3 1535 2460 60% 2073 35%

1006 51.1 625 690 10% 634 1%

1015 47.8 505 650 29% 600 19%

1043 17.1 927 1291 39% 1009 9%

1077 18.4 604 804 33% 624 3%

1098 47.5 222 231 4% 219 -1%

1109 15.9 516 647 25% 501 -3%

1159 14.9 214 374 75% 330 54%

n-heptane validation against shock tube ignition delay times

T5

K

p5

atm

Experimentti / ms

LLNLti / ms

Rel.Err.%

Skeletalti / ms

Rel.Err.%

806 20.0 1.38 1.17 -15% 1.08 -22%

850 19.9 1.65 1.29 -22% 1.34 -19%

906 19.8 1.84 2.30 25% 2.49 36%

909 53.9 0.25 0.36 42% 0.25 -2%

923 60.0 0.24 0.32 32% 0.22 -10%

926 60.6 0.23 0.32 38% 0.21 -10%

932 55.4 0.32 0.39 21% 0.27 -16%

985 48.6 0.36 0.70 92% 0.42 15%

1007 57.7 0.23 0.53 128% 0.29 25%

1012 18.1 0.94 2.14 127% 1.27 35%

1013 53.6 0.29 0.58 99% 0.32 9%

1023 54.2 0.26 0.54 108% 0.29 11%

1027 59.1 0.24 0.47 99% 0.25 5%

1048 16.7 0.85 1.49 75% 0.83 -3%

1057 50.0 0.19 0.45 131% 0.24 24%

1063 53.1 0.18 0.39 118% 0.21 17%

1115 52.3 0.10 0.22 117% 0.13 27%

Comparison against HCCI experiments with PRFs

20

30

40

50

60

70

80

90

-20 -15 -10 -5 0 5 10 15

ExperimentLLNL-1034 species63 species

PRF 84-1 bar

Pre

ssur

e [b

ar]

Crank Angle Degree ATDC

Experimental [27] and calculated pressures for PRF 84 in a HCCI Engine: po=1.0 bar, To=393 K, f = 0.2857, Engine speed = 900 rpm, e = 16.7, Vd =1.95 dm3.

Calculations start at -99 degrees ATDC at 472 K and 1.74 bar [28].

10

20

30

40

50

60

70

-30 -20 -10 0 10 20

Experiment

LLNL-1034 species

63 species

Pre

ssur

e [b

ar]

Crank Angle Degree ATDC

PRF 94-1 bar

Experimental [27] and calculated pressures for PRF 94 in a HCCI Engine: po=1.0 bar, To=393 K, f = 0.2857, Engine speed = 900 rpm, e = 16.7, Vd =1.95 dm3.

Calculations start at -99 degrees ATDC at 455 K and 1.37 bar [28].

40

60

80

100

120

140

160

180

-20 -15 -10 -5 0 5 10

ExperimentLLNL-1034 species63 species

Pre

ssur

e [b

ar]

PRF 84-2 bar

Crank Angle Degree ATDC

Experimental [27] and calculated pressures for PRF 84 in a HCCI Engine. po=2.0 bar, To=313 K, f = 0.25, Engine speed = 900 rpm, e = 16.7, Vd = 1.95

dm3. Calculations start at -99 degrees ATDC at 415 K and 3.34 bar [28].

20

40

60

80

100

120

140

160

180

-20 -15 -10 -5 0 5 10 15 20

Experiment

LLNL-1034 species

63 species

Pre

ssur

e [b

ar]

PRF 94-2 bar

Crank Angle Degree ATDC

Experimental [27] and calculated pressures for PRF 94 in a HCCI Engine.po=2.0 bar, To=313 K, f = 0.25, Engine speed = 900 rpm, e = 16.7, Vd = 1.95

dm3. Calculations start at -99 degrees ATDC at 415 K and 3.34 bar [28].

CPU time was found to decrease two orders of magnitude when using the skeletal mechanism compared to the detailed one.

Computational Gain

possibility for further reduction

QSSA

ONLINE REDUCTION

…….

Species lifetimes and reduction by QSSA

Species lifetime from Jacobian of chemical source terms:

iii J

1

r

f33

r3f33

k

k

]H[

]OH[]CH[]OCH[

0k]H[]OCH[k]OH[]CH[]OCH[t

A fast reversible reaction with a short-lived species

CH3 + OH CH3O + H

An explicit algebraic expression (which is easily calculated) => the species can be removed from the set of differential equations:

Quasi Steady-State Assumption (QSSA):

Software Chain

Detailedmechanism

(data)

Skeletalmechanism

(data)

Reactionflow andsensitivityanalysis

Range of testcalculations

(simplified model)

Removal of redundant reactions

Reduced mechanism

(code)

CFD code(PDF, RIF)

Quasi steady-state approximations (QSSA)

Chemicaland physicallifetime plussensitivity analysis

Range of testcalculations

(simplified model)

State variablesand major concentrations

Source terms

Detailedmechanism

(data)

Skeletalmechanism

(data)

Software Chain

Reduced mechanism

(code)

Reactionflow andsensitivityanalysis

Range of testcalculations

(two-zone model)

Removal of redundant reactions

Range of testcalculations

(two-zone model)

Chemicaland physicallifetime plussensitivity analysis

Quasi steady-state approximations (QSSA)

CFD code(PDF, RIF)

State variablesand major concentrations

Source terms

Summary and conclusions

• A method for automatic reduction of detailed reaction mechanisms has been

developed and tested with a two-zone model for knocking combustion in an SI engine fuelled with PRF.

• Reaction flow, species sensitivity and lifetime analysis were calculated for a whole range of engine operating characteristics and used for ranking species by importance.

• The detailed mechanism was reduced to a skeletal one with 62 species, yielding <0.25 CAD error in ignition delay.

• The skeletal mechanism was in turn reduced to 17 species by QSSA, with an ignition delay error of <1 CAD.

• The observed errors increase monotonously with increasing degree of reduction, indicating the relevance of the ranking measures

Summary and conclusions

Error occurring by using the smaller mechanisms may be larger compared to detailed mechanisms in wide range, but it would be reduced dramatically for specified problems.

The detailed mechanism: generated to model precisely fuel oxidation and autoignition over a large range in chemical

features, includes several hundred of species and several thousand of reactions. their usage in multi-dimensional simulations is not possible.

The skeletal mechanism: the skeletal mechanism have been successfully validated to experimental data for isooctane, n-

heptane and mixtures of the two fuels obtained from shock tube experiments

skeletal mechanism reduces the computational difficulties and the CPU time during the multi-dimensional simulations. Here CPU time was found to decrease two orders of magnitude when using the skeletal mechanism compared to the detailed one.

skeletal mechanism gives good agreement with experimental results.

skeletal mechanism can be used in engine simulations within the range of the validation for future efforts in the field of HCCI combustion and engine development.

Acknowledgements

The authors would like to acknowledge financial support from:

Shell Global Solutions (UK), Chester, United Kingdom

European Community (EC), FP6 Marie Curie Program

This work has been financed under the European Commission Marie Curie Transfer of Knowledge Scheme (FP6) pursuant to Contract MTKI-CT-2004-509777 and was performed within a framework of a research and technological development program with the title SUSTAINABLE FUELUBE.

Thanks for your attention. I would like to invite you to

International Conference on Fuels and Combustion in Engines

in Istanbul, September 2009

For more information

fce@sakarya.edu.tr

www.fce.sakarya.edu.tr