Kinetic effects of blended n-alkane and aromatic fuel mixtures on the extinction limits of diffusion Flames

& A new dynamic multi time scale algorithm andA new dynamic multi-time scale algorithm and

path flux analysis method for mechanism reduction

Sang Hee Won, Wenting Sun, Xiaolong Gou, Yiguang Ju*

Department of Mechanical and Aerospace EngineeringPrinceton University

Sept.14-17, 2009

Introduction: Surrogate Fuel Model DevelopmentS th ti f l h t b d b bl di ith j t f l• Synthetic fuels have to be used by blending with jet fuel: – normal, branched, and cyclo alkanes, and aromatics

• MURI team selected surrogate jet fuel components• MURI team selected surrogate jet fuel components– n-decane, methyl-cyclohexane, n-propyl- and trimethyl- benzenes,

toluene…By matching H/C ratio, sooting index, burning rates, ignition time…

• Example: Gasoline Surrogate model (PRF+1)– Blending of toluene to n-heptane and iso-octane to match both

burning and soot formation targets• Challenge 1:• Challenge 1:

How does the kinetic coupling between aromatics and alkanesaffect burning rate and extinction limit? g

How can we predict burning limits, flame speeds from mixing rule?• Challenge 2: g

How to generate robust, efficient, & user friendly reduced kinetic models?

1. Experimental Studies of Kinetic Effects of Diffusion Flame Extinction Limits

(Fuel Vaporization and Counterflow Burner)

• Experimental setup of the measurements of n-decane/aromatics extinction limits– Using FTIR measurements to check thermal decomposition and

concentration variation: Concentration fluctuation < 1%concentration variation: Concentration fluctuation < 1%

Heater & insulation

Nitrogen

Heater & insulationHeater

Fuel

T1 T2

To burner

Schematics of evaporation system

Experimental Measurements of OH Concentration b i l i d d flby using laser induced fluorescence

• Nd:YAG Laser : Quanta-Ray (532 nm), Cobra-stretch dye laser• ICCD Camera : PIMAX-Gen II (Princeton Instrument)• PLIF: Q1(6) transition (282.93 nm), linear regime, beam height 80 mm

Quenching correction n decaneQuenching correction n‐decane

OH PLIF(a)

blended fuelOH

OH PLIF( )

blended fuelPAH

OH PLIF(b)

Schematic photo for Rayleigh scattering and PLIF PAH PLIF(c)

Extinction limits of toluene blended n-decane–air Mixtures

224n-decane80% n-decane & 20% toluene60% n-decane & 40% toluene/s

]

192

40% n-decane & 60% toluenetolueneJet-A, Ref [5]JP-8, Ref [5]ra

te [

1/

160

stra

in r

n-decane

128

nctio

n s n-decane

l

96Extin toluene

0.15 0.2 0.25 0.3 0.35

Fuel mass fraction YFF

Validation of n-decane-toluene mechanism: Extinction Limits

250

s]

n-decane (present)n-decane (Seshadri, 2007)

LIF tested condition

200e

a E[1

/s toluene (present)toluene (Seshadri, 2007)calculation (present)80% n-decane + 20% toluene60% n-decane + 40% toluene

150

rain

rate 60% n-decane + 40% toluene

40% n-decane +60% toluene

100ctio

n st

rEx

tinc

500.02 0.06 0.1 0.14

Fuel mole fraction Xf Chaos et al. 2005

Kinetic coupling between toluene fragment H abstraction reactions with chain-branching reactions

C6H5CH3+H<=>C6H5CH2+H2n-decane, Xf = 0.0580% n-decane + 20% toluene, Xf = 0.06

C6H5O+H(+M)<=>C6H5OH(+M)

C6H5CH2+H<=>C6H5CH360% n-decane + 40% toluene, Xf = 0.08toluene, Xf = 0.10

CH3+H(+M)=CH4(+M)

( ) ( )

HCO+M=H+CO+M

H+O2(+M)=HO2(+M)

H+O2=O+OH

CO+OH=CO2+H

-0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7

Sensitivity of extinction strain rate

Kinetic coupling between toluene fragment H abstraction reactions with chain-branching reactions

1500

1800

1.00E-04

1.50E-04

]

60 % n-decane + 40 % toluene near extinction, Xf = 0.1, a = 176 1/s

1200

1500

5.00E-05 Tem

ole/

cm3 s

C6H5CH2+ H = C6H5CH3

900

-5.00E-05

0.00E+00

mperaturra

te [m

o

overall decomposition of n-decane

600-1.00E-04

5.00E 05 re [K]

actio

n r

C10H22=C2H5+C8H17 1

of n decane

overall decomposition of toluene

0

300

-2 00E-04

-1.50E-04Re

C10H22=C2H5+C8H17-1C10H22=nC3H7+C7H15-1C10H22=CH3+C9H19-1C6H5CH3+H<=>C6H5CH2+H2C6H5CH3+OH<=>C6H5CH2+H2OC6H5CH3+H<=>A1+CH3

0.1 mm

0-2.00E-040.85 0.9 0.95 1 1.05 1.1

Axial coordinate [cm]

Validation of Kinetic Mechanism (OH concentration)( )

2E-082

O

80% n-decane + 20% toluene,Xf = 0.07

1.8E-081.8O

H conc[a.u

.]

1.6E-081.6

centrationt

ensi

ty [

1.4E-081.4

on [mole/

OH

LIF

in

80% n-decane + 20% toluene,

1E 08

1.2E-08

1

1.2

/cm3]

O

n-decane, Xf = 0.05

,Xf = 0.06

1E-08150 100 150 200

Strain rate a [1/s] OH and HOver prediction of H abstraction?Over prediction of H abstraction?

Thermal and Kinetic effects on Extinction Limits

4E-081800 Ma]

Xf = 0.100.09

N2/n-decane4E-081800 M

a]

Toluene/n-decane

3E-08

1600

1700

ax. concentrure

T max

[K]

0.08

0.06

[OH]

3E-08

1600

1700

ax. concentrure

T max

[K]

[OH]

increasing toluene blending

1E-08

2E-08

1400

1500

ration [molex.

tem

pera

tu

[H]1E-08

2E-08

1400

1500

ration [molex.

tem

pera

tu

n-decane

[H]80% n-decane+ 20% toluene

extinction limit

01300

1400

2.5 3.5 4.5 5.5

e/cm3]M

ax

M h t l t / t i t [J/ 3]

n-decane

decreasing fuel mole fraction

extinction limit01300

1400

2.5 3.5 4.5 5.5

e/cm3]

Max

Ma heat release rate / strain rate [J/cm3]

toluene Xf = 0.1

[ ]+ 20% toluene60% n-decane+ 40% toluene 40% n-decane

+ 60% toluene

Max. heat release rate / strain rate [J/cm3] Max. heat release rate / strain rate [J/cm3]

Low dimensional correlation between strain rate and heat release200

1000

1200

Max

of rem3 s

] overall heat release rateheat release rate from CO + OH = CO2 + H

n-decane

150

800

000

x. heat reeaction ra

te [J

/cm

80% n-decane+ 20% toluene

60% n-decaneextinction

100600

elease raC

O + O

Helea

se r 60% n-decane

+ 40% toluene

40% n-decane+ 60% toluene

50

400

ate [J/cmH = C

O2.

heat

re

toluene

00

200

m3s]

+ H Max

.

0 100 200 300 400

Strain rate a [1/s]

50% h t l i l di tl i OH~50% heat release involves directly in OH

Linear Correlations between OH concentration and extinction limit

2E-08

cm3 ] near extinction

1.5E-08

[mol

e/c

n-decane

80% n-decane20% l

1E-08

trat

ion [OH] + 20% toluene

60% n-decane+ 40% toluene

40% n-decane+ 60% toluene

5E-09conc

ent

toluene+ 60% toluene

0

Max

. c

[H]

00 100 200 300 400

Extinction strain rate aE [1/s]

Linear correlation of extinction limits for toluene-n-decane mixtures

300

/s]

n-decane80% n-decane + 20% toluene60% n-decane + 40% toluene

250at

e a E

[1/

40% n-decance + 60% toluenetoluenelinear fit

R² = 9.703E-01200

stra

in ra

100

150

nctio

n s

50

100

Exti

500.001 0.0013 0.0016 0.0019 0.0022 0.0025

Xf ·(H/C ratio)2 / mean fuel molecular weight

Update of toluene kinetic mechanismp

500n-decane_exp.toluene exp.

400e

a E[1

/s] toluene_exp.

n-decane_num.updated toluene_num.previous toluene_num.

300

rain

rate

200

nctio

n st

r

0

100

Extin

00 0.05 0.1 0.15 0.2 0.25

Fuel mole fraction Xf

2. A Dynamic Multi-Time Scale (MTS) Method with2. A Dynamic Multi Time Scale (MTS) Method with Path Flux Analysis (PFA) for Mechanism Reduction

– Dynamic (Hybrid) Multi Timescale Method (MTS/HMTS) – A Path Flux Analysis (PFA) Method for Mechanism Reduction– Validations of MTS using ignition, steady/unsteady flames

Reduced mechanisms generated by existing approaches remainReduced mechanisms generated by existing approaches remain •Very large •Broad reaction timescale distributions and physical interests•Quasi steady assumption ILDM only apply to limited conditions•Quasi-steady assumption, ILDM only apply to limited conditions.

Can we develop a simple, rigorous, time accurate method?

Multi Timescale (MTS) Method

35

40

t = 0.1 ms

The Basic Idea of Multi-Time Scale Method: timescale changes!

25

30

35

spec

ies

t = 0.2 ms t = 0.3 ms

ΔtF

10

15

20

Num

ber o

f FastestGroup

Medial Groups

ΔtMk

t

kk eKY τ−

=

-1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -130

5

Log10

(characteristic time / s)

Groups

Sl tΔtS g

10( )Slowest

Group

0Ti

Δt1 2

Diagram of multi time scale scheme

ΔtF is the time step of the fastest group, ΔtM is the time step of the medial group and Δt is the time step of the slowest group

Time

group, and ΔtS is the time step of the slowest group

MTS to HMTSHybrid Multi Timescale (HMTS) Method

ΔtF = basetImplicit Euler Method

Fastest Group

Intermediate Groups

ΔtM

Fastest Groups

Intermediate Groups

ΔtM

base

E li it

Groups

ΔtS

Groups

ΔtS Explicit Euler Method

Slowest Group

0 t

ΔtSSlowest Group

0 t

ΔtS

0.06

ctio

n VODE MTSHMTS 1

0 Time tbase0 Time t

0.04m

ass

frac HMTS-1

HMTS-3 HMTS-5

0.02

C10

H22

m

0.0 0.1 0.2 0.30.00

C

Time /ms

Validation by homogeneous ignition

Ignition in

n-decane/air 121 species (M. Chaos, IJCK, 2007)

Ignition inhomogeneous

mixture

5 2 62.8temperature 2.0

) VODE

100

105

2.22.42.6

OH

tion

CO2

1000

K)

1.0

1.5

time

(ms) MTS

HMTS1atm

10-10

10-5

1 61.82.0

Mas

s fra

ct ODE MTSHMTS m

pera

ture

(

0 0

0.5

20atm

tion

dela

y 0 1 2 3 4 5

10-20

10-15

1.21.41.6

C10H22

M HMTS T

em0.5 0.6 0.7 0.8 0.9

-0.5

0.0

Igni

Temperature and species profiles

0 1 2 3 4 5Time (0.1 ms)

Ignition delay time for n decane air

1000/Initial temperature (1/K)

Temperature and species profiles Ignition delay time for n-decane-air

Computation efficiency: comparison with ODE solverp y p

Normalized by the computation time of ODE solver

1.5 ODE

1.5 ODE

1.0

ratio

MTS HMTS 1.0

ratio

MTS HMTS

0.5

CP

U ti

me

0.5

CP

U ti

me

0.5 0.6 0.7 0.8 0.90.0

C

0.5 0.6 0.7 0.8 0.90.0

1000/I iti l t t (1/K)C

1atm

1000/Initial temperature (1/K) 1000/Initial temperature (1/K)

20atm

7~10 times faster

Validation by propagation of unsteady spherical flamesy p p g y pDetailed Mechanism

Outwardly propagating spherical n-decane flames (ASURF-1D Princeton)

Flame front

Ignition pointIgnition point

Can we further reduce the computation time?

A Path Flux Analysis (PFA) Method forM h i R d ti

p

Mechanism Reduction

Reaction path, DRG & DRGEP

∑ δ 1 if the th elementary reactioni⎧

•Only direct relation;•r is not conservative;•Multi-path reaction?

AA

ABAB

Ii iiA

Ii BiiiAAB CP

CPv

vr

++

=≡∑∑

=

=

,1 ,

,1 ,

ω

δωDRG: ,

1 if the th elementary reaction involves speceis B0 otherwise

B i

iδ

⎧⎪= ⎨⎪⎩ A

)()(,1 , ABABIi BiiiA

AB CPCP

CP

vr −

=≡∑ =

δω CAB PAB

•Net reaction rate;

Mi

),max(),max( AAAAAB CPCPDRGEP:

)(max BMAMMpathsallAB ii

i

rrr ⋅≡

;•Consider strongest indirect path•Catalytic reactions? B

Path Flux Analysis Method• Both forward and backward

flfluxes• Both direct and indirect relations

r are conservativeM lti ti fl

A B

1pro st ABAB

Pr − = 1con st ABAB

Cr − =

• Multi-generation fluxes• Multi-reaction pathways

max( , )ABA A

rP C max( , )AB

A AP C

A M B

∑=− ×=

IiBMAMndpro

ABii

CPP

CPP

r,1

2 ])max()max(

[ ∑=− ×=

IiBMAMndcon

ABii

CPC

CPC

r,1

2 ])max()max(

[

ndconndprostconstpro 2211 −−−− +++

MMAA iiCPCP ),max(),max( MMAA ii

CPCP ),max(),max(

ndconAB

ndproAB

stconAB

stproABAB rrrrr 2211 +++=

22

Validation by n-decane homogeneous ignitionIgnition delay times Perfect Stirred Reactor

23

Skeletal mechanisms of different sizesComparison of PFA with DRG

0 01T0=1200 K

0.01

g (s)

detail DRG PFA

1E-3

τ ig

1 atm

50 60 70 80 90

1E-3

20

τ ig (s

)

50 60 70 80 901E-4

20 atm

Number of species in skeletal mechnism

24

Integration of HMTS & PFA : Comparison of ODE & HTMS

Outwardly propagating spherical n-decane/air flame

Reduced mechanism

Flame front

1.00

n decane air φ 1

Outwardly propagating spherical n decane/air flame Flame front

0.75

on (c

m) n-decane-air,φ=1

Reduced mechanism

0.50 t loc

atio

0.25

me

front

ODEHMTS

0 000 0 002 0 004 0 006 0 0080.00

Flam

HMTSIgnition point

0.000 0.002 0.004 0.006 0.008Time (s)

ConclusionKi ti li ff t t l th ti ti li it f bl d d lk d• Kinetic coupling affects strongly the extinction limits of blended alkane and aromatic fuel mixtures.

• Measurements of aromatic fuel fragments and OH concentration are important g pto develop validated kinetic mechanisms for blended fuel mixtures.

• The extinction limits of toluene blended n-decane mixtures are found linearly d d t th i OH t ti ti di l i ddependent on the maximum OH concentration, suggesting as a radical index.

• A simple linear correlation between extinction limits and fuel properties is obtained for n-decane/toluene blended fuel mixtures.obtained for n decane/toluene blended fuel mixtures.

• A new dynamic multi-timescale (MTS) model and a hybrid MTS model are developed. Both MTS and HMTS methods have excellent accuracy and i d i ffi i f i i i d fl i h d il d h iimproved computation efficiency for ignition and flames with detailed chemistry.

• A Path flux analysis (PFA) method is developed for mechanism reduction. The method has better model accuracy in a broad temperature and pressure ranges.method has better model accuracy in a broad temperature and pressure ranges.

• The integration of MTS/HMTS with PFA mechanism reduction can dramatically enhance the computation efficiency.

F t kFuture work:•Kinetic effects on extinction limits of n-decane/n-dodecanewith trymethylbenzene n propylbenzenewith trymethylbenzene, n-propylbenzene•Development of radical index to construct extinction correlation•Experimental data of flame speeds at elevated pressures •Reduced mechanism development using MTS/PFA for aromatic fuels

Thanks Dr. Tishkoff for the MURI research grantg