7ISFS, July 11-15, 2011
Towards a predictive
combustion chemistry model
Hai Wang
University of Southern California
1
Combustion Kinetics of Jet Fuels
Applications
Gas-turbine engines:
CFD-based design
Pollutant emission
Hypersonics:
Ignition
Flame holding
2
Jet Fuels Composition (courtesy of Tim Edwards)
4658
3327
4734
4572
4765
3773
World
survey
Jet A
composite
blend
JP-7
F-T Jet
RP-1
Coal-based
jet fuel
DCL
JP-8
Jet A, Jet A1, JP-8, JP5, TS-1
Paraffins (n- + i-)
55.2
67.9
99.7
57.6
0.6
57.2
58.8
Cycloparaffins
17.2
21.2
<0.2
24.8
46.4
17.4
10.9
Dicycloparaffins
7.8
9.4
0.3
12.4
47.0
6.1
9.3
Tricycloparaffins
0.6
0.6
<0.2
1.9
4.6
0.6
1.1
Alkylbenzenes
12.7
0.7
<0.2
2.1
0.3
13.5
13.4
Indanes/Tetralins
4.9
<0.2
<0.2
0.3
1.1
3.4
4.9
Indenes
<0.2
<0.2
<0.2
<0.2
<0.2
<0.2
<0.2
Naphthalene
<0.2
<0.2
<0.2
<0.2
<0.2
<0.2
0.13
Naphthalenes
1.3
<0.2
<0.2
0.3
<0.2
1.7
1.55
Acenaphthenes
<0.2
<0.2
<0.2
<0.2
<0.2
<0.2
<0.2
Acenaphthylenes
<0.2
<0.2
<0.2
0.4
<0.2
<0.2
<0.2
Tricyclic Aromatics
<0.2
<0.2
<0.2
<0.2
<0.2
<0.2
<0.2
3
Surrogate Strategy
• A mixture of 4 to 5 neat hydrocarbons as the
surrogate to mimic the chemical and physical
behaviors of real jet fuels:
– boiling and evaporation characteristics
– C/H ratio
– A possible set of surrogate components
Staight-chain alkane:
Cyclo alkane:
Brached-chain alkane:
One-ring aromatics:
Two ring compounds:
n-dodecane
n-butylcyclohexane
2,7-dimethyl octane
n-propylbenzene
tetralin/a-methyl naphthalene?
4
Model Hierarchy
Aliphatics
Aromatics
Products
CH4
CHxOy, C2-4Hx Oxidation
H2O, CO2
CO-H2 Oxidation
H2, CO
C2H2, soot
H2 Oxidation
……
5
Performance Requirements
• Ignition (homogeneous vs. diffusive)
• Steady burning
• Extinction
• Premixed vs. nonpremixed flames
• Pressure and concentration variations
• Global responses (flame speed, ignition, extinction)
• Detailed flame structure (major, minor species, NO,
soot precursors)
6
Law, Sung, Wang, Lu, AIAA J, 2005.
Model Parameters
• Reaction Pathways and Rate Constants
T-dependence
P-dependence
• Thermochemical properties
Enthalpy of formation, specific heat,
entropy
• Transport Properties
Lennard-Jones Parameters
7
Sample Reaction Model
TABLE 2. Detailed Kinetic Modela
c
No.
reactionb
k = A Tnexp(–E/RT)
A
n
E
references/
comments
Reactions of propene
1
aC3H5 + H (+M) = C3H6 (+M)
2
CH3 + C2H3 (+M) = C3H6 (+M)
3
4
5
6
7
8
9
10
11
12
13
14
C3H6 + H = C2H4 + CH3
C3H6 + H = aC3H5 + H2
C3H6 + H = CH3CCH2 + H2
C3H6 + O = CH2CO + CH3 + H
C3H6 + O = C2H5 + HCO
C3H6 + O = aC3H5 + OH
C3H6 + O = CH3CCH2 + OH
C3H6 + OH = aC3H5 + H2O
C3H6 + OH = CH3CCH2 + H2O
C3H6 + HO2 = aC3H5 + H2O2
C3H6 + CH3 = aC3H5 + CH4
C3H6 + CH3 = CH3CCH2 + CH4
2.001014
1.331060
–12.0
5968
a=0.020 T***=1097 T*=1097 T**=6860
2.501013
4.271058
–11.94
9770
***
*
a= 0.175 T =1341 T =60000 T**=10140
1.601022
–2.39 11180
1.701005
2.5
2490
05
4.0010
2.5
9790
1.201008
1.65
327
3.501007
1.65
–972
1.801011
0.7
5880
6.001010
0.7
7630
06
3.1010
2.0
–298
1.101006
2.0
1450
9.601003
2.6
13910
2.201000
3.5
5675
8.4010–01
3.5
11660
k∞, d
k0
e
k∞, f
k0
e
1 atm, g
[33]
[33]
[33]
[33]
[33]
[33]
[33]
[33]
[33]
[33]
[33]
Reactions of allyl
15
16
17
18
19
20
21
CH3 + C2H2 = aC3H5
CH3 + C2H3 = aC3H5 + H
aC3H5 + H = aC3H4 + H2
aC3H5 + O = C2H3CHO + H
aC3H5 + OH = C2H3CHO + H + H
aC3H5 + OH = aC3H4 + H2O
aC3H5 + O2 = aC3H4 + HO2
2.681053
1.501024
1.801013
6.001013
4.201032
6.001012
4.991015
–12.82
–2.83
35730
18618
–5.16
30126
–1.4
22428
1 atm, [24]
1 atm, f
[33]
[33]
1 atm, [33]
[33]
[36]
8
9
Selected Fundamental Problems
1. Reaction kinetics of
CO + HO2 → CO2 + OH
2. Quantum tunneling in H-shift of
alkyl radicals
3. Kinetic model uncertainty prediction/
minimization
10
CO + HO2 → CO2 + OH
• RCM results suggest k(CO + HO2) should
be reduced by a factor of 3 from Mueller et al.
Ignition Delay Time (ms)
15
T s a ng a n d H am p s o n 30
109
10
5
0
Ignition Delay Time (ms)
25
107
M u e lle r e t a l.31
105
L lo yd 2 9
Pc = 30 Bar
Tc = 1010.5 K
20
15
10
5
0
103
5
101
0 .5
1 .0
1 .5
2 .0
1 0 0 0 K /T
2 .5
3 .0
3 .5
Ignition Delay Time (ms)
k 1 (c m 3 /m o l-s )
1 0 11
Pc = 15 Bar
Tc = 1028.5 K
Pc = 50 Bar
Tc = 1044 K
4
3
2
1
0
0.0
0.2
0.4
0.6
RCO
0.8
1.0
11
Mittal, Sung, Yetter Int. J. Chem. Kinet. 2006
CO + HO2 → Products
±0.5
CCSD(T)/CBS Potential energy in kcal/mol
Energies (kcal/mol) at 0 K relative to CO + HO2•
Products/
G3B3
transition state
a
CCSD(T)/ CCSD(T)/ CCSD(T)/ FCC/CBS
cc-pVTZ cc-pVQZa
CBS
CO2+OH
-63.3
-59.9
-61.0
-61.8
-61.7
HOOC•O
6.3
8.1
7.2
6.5
6.0
TS1
18.3
18.8
18.3
17.9
17.3
TS2
12.0
14.4
13.4
12.7
11.8
TS3
19.3
19.9
19.3
18.9
18.2
TS4
15.5
17.2
16.4
15.8
15.3
34.1
34.0
HCO+O2
33.3
33.1
33.7
With CCSD(T)/cc-pVTZ zero-point energies.
(5e,5o)
CASPT2/CBS
(9e,8o)
(11e,10o)
Literature
value
-61.6±0.1
17.1
18.2
18.4
33.6±0.1
12
CO + HO2 → Products
±0.5
CCSD(T)/CBS Potential energy in kcal/mol
Theoretical Treatment and Assumptions
•
•
•
•
Monte Carlo solution of master equation of collision energy transfer
Exponential down model for collision energy transfer
RRKM microcanonical rate constants
1-D hindered internal rotation by inverse Laplace Transform of
rotational partition function
13
CO + OH → Products
Pressure Dependency – Overall Rate Coefficient
3 00
2 00
15 0
10 0
80
(a) 98 K
-1 -1
5 00
-12
k
3
25 0 0
k (cm molecule s )
10
T e m p e ra tu re (K )
10
-13
10
-12
10
-13
(b) 190 K
k
(c) 250 K
k
-1 -1
k (cm molecule s )
-1
-1
k (cm m o le cu le s )
65 0 B a r
10
3
k
-1 2
3
-1 -1
k (cm molecule s )
1 00 B ar
-12
HOCO
CO2 + H
3
10 Bar
10
1 Bar
HOCO
10
-13
-1 -1
-1 3
CO2 + H
k0
(d) 298 K
10
-12
10
-13
k
3
10
k (cm molecule s )
1 T o rr
0
2
4
6
8
1 0 0 0 K /T
Joshi, Wang, Int. J. Chem. Kinet. (2006)
10
12
10
-3
10
-2
10
-1
10
0
10
1
P (Bar)
10
2
10
3
10
4
10
5
14
CO + HO2 → CO2 + OH
1 0 11
upperlimit
k 1 (c m 3 /m o l-s )
1 0 10
T sa n g a n d H a m p s o n 30
109
M u e lle r e t a l.31
T h is w o rk
108
107
lowerlimit
106
0 .6
0 .8
1 .0
1 0 0 0 K /T
1 .2
1 .4
15
CO + HO2 → CO2 + OH
Ignition Delay Time (ms)
15
Pc = 15 Bar
Tc = 1028.5 K
10
Now we get the ignition
delay times right
5
0
Ignition Delay Time (ms)
25
Pc = 30 Bar
Tc = 1010.5 K
20
15
10
5
0
Ignition Delay Time (ms)
5
Pc = 50 Bar
Tc = 1044 K
4
3
2
1
0
0.0
0.2
0.4
0.6
RCO
0.8
1.0
16
Role of Tunneling in n-alkyl Radical Isomerization/b-Scission
• Example: n-heptane + (H, O, OH, ..) → heptyls + (H2, OH, H2O)
2C2H4 + C3H7
+ CH3
+ C3H7
2C2H4 + C3H7
+ C2H5
• Isomerization determines the C1-C6 fragment distribution, and
hence the main flame chemistry.
17
Role of Tunneling in n-alkyl Radical Isomerization
• Tunneling must be considered to reconcile low and high
temperature data → tunneling affects the post-cracking
kinetics
18
W.Tsang, J.A. Walker, J.A. Manion Proc. Combust. Inst. 31 (2007) 141
Tunneling in Reaction Rate Theory
• Transition State Theory: transmission coefficient κ(T)
k  (T )   (T ) Ae
Ea / RT
• Approximations:
– One dimensional assumption:
 
2
x
2
8 m
2

h
2
[ E  V ( s )]   0
– Potential Energy Surface expressed as a function V(s)
• Wigner (1932): parabola function
• Eckart (1917) & Johnston and Heicklen (1966): « Eckart potential »
19
Various Approximations
• One dimensional tunneling transmission coefficient κ(T):
- Wigner, Skodje & Truhlar, and Eckart
• Multi-dimensional tunneling transmission coefficient κ(T):
- Small Curvature Tunneling (SCT)
Hessian required for each points along
the Minimum Energy Path
Computationally expensive
20
Truong et al., http://therate.hec.utah.edu/
PES: n-heptyl radicals H-shifts
CBS-QB3
H
H
22.8
21.8
E nerg y (k cal/m o l)
20.0
H
1 4.8
H
1 4.4
10.0
0.0
0.0
-2.9
-3 .2
-3.0
21
E (0K, ZPE corrected)
Multi- vs One-dimensional Tunneling
103
1 -he p ty l -> 3-h ep ty l
1 01
T ra ns m iss ion C oe ffic ien t,  (T )
T ra n s m is s io n C o e ffic ie n t,  (T )
1 02
W ig ner
E ck a rt
SCT
1 00
40 0
80 0
12 0 0
16 0 0
2000
T e m p e r a ture , T (K )
1 -h e p tyl -> 4 -he p tyl
102
W ig n e r
E ck a rt
SCT
101
100
400
800
1200
1600
2000
Te m p e ra tu re , T (K )
Eckart  good approximation for 300 < T < 2000 K
Wigner  good for T > 800 K
22
Sensitivity Analysis of Eckart κ(T):
Variation of Imaginary Frequency
T ra ns m iss ion C oe ffic ien t,  (T )
104
1 -h e p tyl -> 4 -he p tyl
103
E ck a rt
102
E ck a rt 9 0 % im a g in a ry fre q u e n cy
E ck a rt 1 1 0 % o f im a g in a ry fr e qu e n c y
101
100
200
400
600
800
1000
1200
Te m p e ra tu re , T (K )
23
It’s all about the accuracy of the potential energy!
JetSurF 1.0 Validation – Species
Concentrations behind reflected shock waves
H. Wang, E. Dames, B. Sirjean, D. A. Sheen, R. Tangko, A. Violi, J. Y. W. Lai, F. N. Egolfopoulos, D. F. Davidson, R. K.
Hanson, C. T. Bowman, C. K. Law, W. Tsang, N. P. Cernansky, D. L. Miller, R. P. Lindstedt, A high-temperature chemical
kinetic model of n-alkane (up to n-dodecane), cyclohexane, and methyl-, ethyl-, n-propyl and n-butyl-cyclohexane
oxidation at high temperatures, JetSurF version 2.0, September 19, 2010
(http://melchior.usc.edu/JetSurF/JetSurF2.0).
Mole Fraction [ppm]
1494K, 2.15atm
1000 300ppm heptane, =1
CO2
C2H4
100
H2O
OH
10
10
100
1000
Time [s]
Plot stolen from Ron Hanson. Solid line: experiments; dashed line: JetSurF
24
Kinetic Parameter Uncertainties
H + O2 ↔ OH + O (R1)
• Uncertainty factor ~1.25
• Logarithmic sensitivity coefficient
= 0.24 (ethylene-air,  = 1, p = 1 atm)
• ±5% (±4 cm/s) uncertainty in
predicted flame speed due to R1
alone
~50%
• Key question (Sheen et al. 2009):
How do we propagate
uncertainties in rate constants in
combustion simulations?
25
Baulch, et al. (2005)
Propagation of Uncertainty
2nd order coefficients
1st order coefficients
0
xi  xi
m

a
j 1
m
ij
j 
m
b
ij k
 j  k  ...
k 1 j  k
basis random variable
nominal value
Data structure that describes a chemical model
+ associated uncertainty
 r  x    r ,0 
N
a
N
r ,i xi

i 1
N
b
r , ij
xi x j
i 1 j  i
Represents some
physics model,
e.g. PREMIX
1-atm C2H4-air mixtures

 r  x, ξ    r x
0
m
   aˆ
i 1
m
r ,i
i 
m
  bˆ
i 1
ji
r , ij
 i j
L a m in a r F la m e S p e e d , s u 0 (c m /s )
80
60
40
20
E g o lfo p o u lo s & L a w (1 9 9 0)
F a e th & co -w o rk ers (1 99 8 )
L a w & c o -w o rk e rs (20 0 5 )
0 .5
Predictions of a chemical model (e.g. laminar flame speed)
+ associated uncertainty
1 .0
1 .5
2 .0
E q u ivale n c e R atio , 
26
Sheen et al. (2009)
Prediction Uncertainties in As-Compiled Model
M o le F ra c tio n
C 2H 4
1 0 -4
1 0 -4
1 0 -3
M o le F ra c tio n
1 0 -5
1 0 -5
OH
1 0 -3
T im e (s )
1 0 -4
1 0 -4
1 0 -3
M o le F ra c tio n
1 0 -5
1 0 -5
H 2O
1 0 -3
T im e (s )
1 0 -4
1 0 -5
1 0 -5
CO2
1 0 -3
1 0 -4
1 0 -3
M o le F ra c tio n
M o le F ra c tio n
M o le F ra c tio n
M o le F ra c tio n
M o le F ra c tio n
C 2H 4
1 0 -3
T im e (s )
1 0 -4
1 0 -5
1 0 -5
1 0 -4
T im e (s )
1 0 -3
1 0 -3
Good nominal
prediction with
significant
uncertainty!
1 0 -4
1 0 -5
1 0 -5
OH
1 0 -3
1 0 -4
1 0 -3
T im e (s )
1 0 -4
1 0 -5
1 0 -5
H 2O
1 0 -3
1 0 -4
1 0 -3
T im e (s )
1 0 -4
1 0 -5
1 0 -5
CO2
1 0 -3
1 0 -4
1 0 -3
T im e (s )
1 0 -4
1 0 -5
1 0 -5
1 0 -4
T im e (s )
1 0 -3
27
Method of Uncertainty Minimization
k2
x  x0  αξ
Chemical model
+ associated uncertainty
h1
k1
 r  x    r ,0 
N
a
N
r ,i xi
i 1

N
b
r , ij
least-squares minimization
xi x j
i 1 j  i
 x
Physics model
*
0

 M  obs    x   2
r
0 

 r ,0
 m in  

2
x0
obs
 r 1
 r 
N

n 1
x 
2
0 ,n
 n 
2




Covariance matrix

 r  x, ξ    r x
0
m
   aˆ
i 1
m
 
r ,i i
m
  bˆ
i 1
ji

r , ij i j

 



n
r 1
1
 
obs
r
2

* *T
*T
T * T
T
 b x 0 x 0 b  ax 0 b  b x 0 a  aa   4 I 

α 
*
Predictions
+ associated uncertainty
1
1/ 2
28
Predictions of As-Compiled and Uncertainty-Minimized Models
Unconstrained
Constrained
M o le F ra c tio n
C 2H 4
1 0 -4
1 0 -4
1 0 -3
M o le F ra c tio n
1 0 -5
1 0 -5
OH
1 0 -3
T im e (s )
1 0 -4
1 0 -4
1 0 -3
M o le F ra c tio n
1 0 -5
1 0 -5
H 2O
-3
10
T im e (s )
1 0 -4
1 0 -5
1 0 -5
CO2
1 0 -3
1 0 -4
1 0 -3
M o le F ra c tio n
M o le F ra c tio n
M o le F ra c tio n
M o le F ra c tio n
M o le F ra c tio n
C 2H 4
1 0 -3
T im e (s )
1 0 -4
1 0 -5
1 0 -5
1 0 -4
T im e (s )
1 0 -3
1 0 -3
1 0 -4
1 0 -5
1 0 -5
OH
1 0 -3
1 0 -4
1 0 -3
T im e (s )
1 0 -4
1 0 -5
1 0 -5
H 2O
-3
10
1 0 -4
1 0 -3
T im e (s )
1 0 -4
1 0 -5
1 0 -5
CO2
1 0 -3
1 0 -4
1 0 -3
T im e (s )
1 0 -4
1 0 -5
1 0 -5
1 0 -4
T im e (s )
1 0 -3
29
Effect on predicted laminar flame speed
Considering no experiments
Model constrained by species profiles
Model constrained by species profiles
+ flame speeds
30
Effect on predicted laminar flame speed
U n c e rta in ty in S p e c ie s V a lu e , 2 
20%
 s (c m /s )
4
10%
7%
obs
5%
3
C H 3 (S e ries 2 ) o n ly
O H (S e rie s 1 ) o n ly
A ll m ulti-s p ec ie s (S e rie s 1 & 2 )
2
0
5
10
1 /(2 
15
obs
)
20
31
What did uncertainty minimization do?
32
Acknowledgements
Previous students/postdocs
• Ameya Joshi
• Xiaoqing You
• Scott G. Davis
• Alexander Laskin
Current students/postdocs
• David Sheen
• Enoch Dames
• Baptiste Sirjean
Collaborators
• Stephen Klippenstein (ANL)
• Chung-King Law (Princeton)
• Fokion Egolfopoulos (USC)
• Elke Goos (DLR)
The JetSurF team
Ron Hanson (Stanford)
Tom Bowman (Stanford)
Heinz Pitsch (Stanford)
Wing Tsang (NIST)
Angela Violi (UMich)
Peter Lindstedt (Imperial Col.)
Nick Cernansky (Drexel)
David Miller (Drexel)
Financial Support
AFOSR, AFRL, SERDP, DOE,
NSF
33