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Burning Rate, Kinetic Coupling,and Mechanism Reduction
Yiguang Ju Mechanical and Aerospace Engineering
Princeton University
2007 AFOSR MURI Kick-Off MeetingGeneration of Comprehensive Surrogate Kinetic
Models andValidation Databases for Simulating Large
Molecular WeightHydrocarbon Fuels
Holiday Inn, Princeton100 Independence Way
Princeton, NJ 08540
September 17, 2007
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Outline
•Identification of research problems
•Research targets
•Experimental and analytical methods
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ParaffinsIso-paraffins Cycloparaffins Aromatics Naphthalenes
Fuel Component SelectionLimited understanding
DetailedModel B
DetailedModel C
DetailedModel D
DetailedModel A
Thermodynamic/Transport/Reaction -Rate Parameter Determination
Experimental Data• Ignition (RCM,ST)• Speciation (FR, ST)• Flames (HP/HT)
burning rateignitionextinctiondiffusion
• Soot characteristics (HPDC)
Minimization / Optimization / Validation
Greater understanding
Kinetic Coupling
Density Ignition criteriaViscosity C/H Ratio
Heat Release RateHeat Capacity
Flame TemperatureSooting Character
etc …
Surrogate Composition Formulation(emulation of physical/chemical properties)
JetFuels
SURROGATE FUEL
Validation
SingleComponents
Single Componentsand
Mixtures
Comparison
REDUCED MECHANISMSFor specificapplications
II
III
I
VI
V
IV
•Burning rate•Diffusion-Kinetic coupling•Mechanism reduction
Research Targets &
Where We Fitin The Roadmap
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Problems: Burning Rates at High Pressures
ms.flow speed
lengtht
msSα
dflame speeyDiffusivitt
r
Lf
3100
30
11
102
3
22
===
====−
DME, Ф = 0.77, 10 atm Kobayashi et al. 10 atmQin & Ju, 2005
Yuan, Ju & Law, 2005
Relevant to ICE?
KaMSS
au
u −=10
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Research Tasks
• Accurate measurements of flame speeds at elevated pressures by using spherical flames
• Understanding and modeling of transport-kinetic coupling
• Development of efficient reduced mechanism by considering transport-kinetic coupling
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Experimental Methods: Flame Speed Measurements
• Challenges and methodologies to measure flame speeds at high pressures and temperatures accurately
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Flame Speed Measurement: Spherical Flames1.
Constant volume method:
(High pressure & high temperature)without stretch correction but large pressure increase
Lewis (1934), Metghalchi (1980), Farrell (2004)…Assumption: Non-flame curvature (stretch) effect!
)3()()(
1)(3
/10
0
200
dtdP
PP
PPRRRS u
efu
γ
−=
)4()(11123/1
/10
000
0 −
⎥⎦
⎤⎢⎣
⎡−−
−⎟⎟⎠
⎞⎜⎜⎝
⎛+−≈
− γ
γγ PP
PPPP
PP
RL
SSS
e
eeu
u
uu
What if the stretch effect is not zero?Flame speed error will be:
Lu
: Markstein length from pressure history
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Constant Volume Method:Stretch Corrected Flame Speed (SCFS) (H2 /air)
Chen et al. 2007
0.5
1
1.5
2
0 0.2 0.4 0.6 0.8 1Normalized flame radius, Rf /R0
Flam
e sp
eeds
nom
arliz
ed b
y S
L0 PREMIXwithout stretch correctionstretch corrected flame speed
1.0 1.01 1.02 1.05 1.1 1.2 1.5 2 3 4 5
Normalized pressure, P/P0
(Su0)
(Su)(SL)
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Flame Speed Measurement: Spherical Flames:12.
Constant pressure method
(High pressure)
What if the burned gas velocity is not zero?Flame speed error will be:
with stretch correction & small pressure increase
Bradley (1972), Faeth (1992), Law (2000), Ju (2005), Peterson (2007)…
)1(/ ubfu VS ρρ=
)2(ˆˆ
f
b
u
uu
Vu
SSS
=−
≡ε
Assumption: Burned gas velocity is zero!
What causes non-zero burned gas velocity?Compression, non-symmetric flow, radiation…Q U
b
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Constant Pressure Method: Compression Induced Burned Gas Velocity
Chen & Ju 2007
Q Ub
Nomalized spatial coordinate, r/R0
Nor
mal
ized
flow
velo
city
,a*U
/SL
0 0.25 0.5 0.75 1-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8Velocity distribution V(r)
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-30%
-20%
-10%
0%
10%
to Rf/R0
S u0 /S
L-1
from =0.1from =0.2from =0.3
0.2 0.3 0.4 0.5
use "Su=a*dRf/dt"neglect the compression effect
compression corrected flame speeduse "Su=a*(dRf/dt-Ub)"
Rf/R0
Rf/R0
Rf/R0
Constant Pressure Method:
Compression Corrected Flame Speed (CCFS)
Flame speed correction:
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What If a Cylindrical Chamber is Used?
Princeton 8.3 cm 8.3 cm diadia. by 13 cm length,. by 13 cm length,10 cm dia. by 15 cm length,10 cm dia. by 15 cm length,
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Outer Chamber
Inner Chamber
Mercury Lamp
Focus Lens
Collimating Lens
Decollimating Lens
Pinhole
High-Speed VideoCamera
Knife Edge
Permanentmagnet
Gas Releasing HolesQuartz Window
Tungsten Wire
Iron Plate
Pressure Sensor & GaugesOuter Chamber
Inner Chamber
Mercury Lamp
Focus Lens
Collimating Lens
Decollimating Lens
Pinhole
High-Speed VideoCamera
Knife Edge
Permanentmagnet
Gas Releasing HolesQuartz Window
Tungsten Wire
Iron Plate
Pressure Sensor & Gauges
Non-symmetrical flow induced burned gas velocity!
-5 -4 -3 -2 -1 0 1 2 3 4 5-5
-4
-3
-2
-1
0
1
2
3
4
5
Axial direction, z (cm)
Rad
ial d
irect
ion,
r (c
m)
What If a Cylindrical Chamber is Used?
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High Pressure Flame Speed (Su
) MeasurementEffect of non-spherical flow, ub
≠0
?)1(*
=Δ⋅−=
−
f
f
u
uu
uu
sss σ
0
50
100
150
200
250
0 1000 2000 3000 4000Stretch (1/s)
Flame speed (cm/s)
0.5 cm
1.01.52.02.53.0
3.5
4.0
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How to Improve Measurements: Potential Flow Model
Potential flow:
Ring source
Point source
{ } γγηγηπ
φπ
dzyx
tqr
tm⋅
+⋅−+⋅−+
⋅= ∫
2
02/1222 )]sin([)]cos([
)(4
)(
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Prediction of Fame Speed Using Potential Flow
0
50
100
150
200
250
0 1000 2000 3000 4000Stretch (1/s)
Flame speed (cm/s)
Cylindrical Model (Rw=5 cm)
Cylindrical Experiment (Rw=5 cm)
Unconfined ModelUnconfined Model
Cylindrical Model
Rw = 5 cm
Cylindrical Experiment
Rw = 5 cm
Stretch (s-1)
Flam
e Sp
eed
(cm
-s-1
)
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Flow-Corrected Flame Speed
M.P. Burke, Y. Ju, F.L. Dryer, Eastern States Meeting, Virginia 2007
150160170180190200210220230240250
0 500 1000 1500 2000 2500 3000 3500Stretch (1/s)
Cal
cula
ted
flam
e sp
eed
(cm
/s)
Uncorrected
Flow Corrected
⎟⎟⎠
⎞⎜⎜⎝
⎛−⋅= b
f
u
bu u
dtdr
sρρ
dtdr
s f
u
bu ⋅=
ρρ
wfw rrr 5.01.0 <<
H2
-air, Φ=3.0,1atm
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X
Y
-1.5 -1 -0.5 0 0.5 1 1.5
-1.5
-1
-0.5
0
0.5
1
1.5
X
Y
-1 -0.5 0 0.5 1
-1
-0.5
0
0.5
1
Le=0.25 Le=2.0
•1D steady-state and transient simulation of counterflow flames
•2D direct simulation of transient spherical flame propagation
Modeling Approaches
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How to Improve Measurements (Radiation Effects): One-Dimensional Direct Modeling
Temperature distribution Radiation heat loss distribution
Flame
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Improving Measurements (Multi-Dimensional Effect):Adaptive Direct Modeling
X (mm)
Y(m
m)
-10 -5 0 5 10-10
-5
0
5
10
X (mm)
Y(m
m)
-10 -5 0 5-10
-5
0
5
10
Q3.75E+103.50E+103.25E+103.00E+102.75E+102.50E+102.25E+102.00E+101.75E+101.50E+101.25E+101.00E+107.51E+095.00E+092.50E+09
A
B
D
C
a. Adaptive unstructured grid b. Grids for spherical flames
c. Spherical flame propagation
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Research Goal
• Measure the flame speeds and Markstein lengths of surrogate fuel components up to 30 atm in a wide range of equivalence ratios
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2. Models for Transport-Kinetic Coupling
Transport-coupling regimes:• Diffusion of reactants modifies fuel flux
n-heptane, n-dodecane, oxygen…• Diffusion of intermediate species
modifies local C/H ratio, e.g. H2
,CH4
,C2
H4• Diffusion of radicals modifies kinetic
reaction rate (via H abstraction)e.g. H, O, …
Kinetic coupling between straight chain and aromatic molecules
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Sensitivity of Transport Properties: Flame Temperature
0 20 40 60 80 100 120
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
nC7H16 C6H5CH3
iC4H8
iC8H18
C3H6pC3H4
C2H6
C2H2C2H4
CH4
CO2
CO
O
H2O
H
Sen
sitiv
ity o
f fla
me
tem
pera
ture
on
diffu
sivi
ty
Species number
O2
Extinction of PRF + Toluene
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Lewis Number, Le
Crit
ical
Igni
tion
Pow
er,Q
c
0.5 1 1.5 2 2.510-2
10-1
100
101
102
103
h=0.00h=0.01
(a)
Q ?
Lewis Number, Le
Crit
ical
Igni
tion
Pow
er,Q
c
0.5 1 1.5 2 2.510-2
10-1
100
101
102
103
h=0.00h=0.01
(a)
Q ?
Effect of Reactant Transport on Minimum Ignition Energy
Fuel molecular size
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Experimental Measurements Using Steady StateCounterflow Flames
• Extinction limit & temperature• Species (reactants, intermediate species, and radicals (O, H, OH)
Understanding of transport-kinetic coupling
Numerical modeling
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Modeling of Transport-Kinetic Coupling inTransient Mixing & Ignition Process
Tem
pera
ture
, spe
cies
, and
vel
ocity
0 L
T
YO
YF
V
0 L
T
YOYF
V
0 L
T
YO
YF
V
a.Homogeneous ignition b. Frozen diffusionignition
c. diffusion ignition
•Kinetic ignition delay•Transport-kinetic coupling (No mixing delay time)
Transport-kinetic coupling (with mixing delay time)
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Mechanism Reduction
Current strategies• Reaction Rate Analysis (Peters et al.)• Graph relation analysis (Lu et al.)• Intrinsic Low Dimension Method (Mass & Pope)• Computational Singular Perturbation (Lam et al.)• High Dimensional Fitting
(Franklach et al.)
•Lead to similar size of reduced mechanism•Reduced mechanism remains large•Homogeneous system, diffusion flux is not included
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Our Approach
Path analysis (including diffusion flux, forspecies & reaction reduction)
CSP time scale analysis (fast & slow species)
In-situ adaptive HDMR (fitting)
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High Dimensional Modeling Representation: Piecewise Reusable Implementation of Solution
Mapping
))(( 11 nnr
nn t SySyy +Δ+= ++
nnHDMR
n ttf Syy Δ+Δ=+ ),(1
)x,...,x,x()x,(xf)(xf+ f = (x)f N21..12i
jijii
ii0HDMR Nj
f++∑∑≥
Explicit time marching: need to calculate minor species
HDMR fitting:
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Time (s)
Tem
pera
ture
(K)
0.0E+00 2.0E-04 4.0E-04
1000
1500
2000
2500
HDMRODE
Example: Ignition of Methane-Air
Li, Chen, Ju, Rabitz et al., 2007
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Conclusions• Accurate measurement of flame speeds at high
pressures by using a spherical bomb remains challenging. Physical processes such as flow compression, non-symmetrical flow motion, stretch, and radiation need to be included for accurate measurements.
• There are three different types of transport-kinetic couplings. New models to describe mixing and transport-kinetic coupling in non-premixed and transient ignition process are needed. Advanced computation methods and experimental data are needed to gain quantitative understanding of transport-
kinetic coupling.• New methodologies to generate computationally
efficient reduced mechanisms are needed. Adaptive HDMR and time splitting method are attractive approaches.