Westbrook Dryer 1981 PDF
Westbrook Dryer 1981 PDF
Westbrook Dryer 1981 PDF
31-43
0010-2202/81/2702-0031$06.50/0
Abstract-Simplified reaction mechanisms for the oxidation of hydrocarbon fuels have been examined
using a numerical laminar flame model. The types of mechanisms studied include one and two global reaction
steps as well as quasi-global mechanisms. Reaction rate parameters were varied in order to provide the best
agreement between computed and experimentally observed flame speeds in selected mixtures of fuel and air.
The influences of the various reaction rate parameters on the laminar flame properties have been identified, and
a simple procedure to determine the best values for the reaction rate parameters is demonstrated. Fuels studied
include II-paraffins from methane to II-decane, some methyl-substituted II-paraffins, acetylene, and representative olefin, alcohol and aromatic hydrocarbons. Results show that the often-employed choice of simultaneous
first order fuel and oxidizer dependence for global rate expressions cannot yield the correct dependence of
flame speed on equivalence ratio or pressure and cannot correctly predict the rich flammability limit. However, the best choice of rate parameters suitably reproduces rich and lean flammability limits as well as the
dependence of the flame speed on pressure and equivalence ratio for all of the fuels examined. Two-step and
quasi-global approaches also yield information on flame temperature and burned gas composition. However,
none of the simplified mechanisms studied accurately describes the chemical structure of the flame itself.
INTRODUCTION
32
= ao TI/2/C,ot
o, = alTl/2/(Cto t Wi)
D7'
(I)
where {nt} are determined by the choice of fuel.
This global reaction is often a convenient way of
approximating the effects of the many elementary
reactions which actually occur. Its rate must therefore represent an appropriate average of all of the
individual reaction rates involved. The rate expression of the single reaction is usually expressed
k ov = AT" exp( -Ea/RT)[Fuel]n[Oxidizer]b.
(2)
33
70,-----------,---------,-------,-------,----------,
_ _I
Equivalence ratio -
FIGURE I Variation of flame speed with equivalence ratio for /I-octane in air, computed using the singlestep reaction rates indicated. Experimental values for the lean and rich flammability limits (.pL'=O.5 and
.p11'=4.3) for the observed flame speed at .p=I (open circle), and for the maximum flame speed (open square)
are also indicated.
rich mixtures. Only for the special case ofa stoichiometric fuel-air mixture, for which the rate parameters were evaluated, does Eq. (3) predict the
proper flame speed. The inadequacy of the assumption of a =b = I was observed for all of the hydrocarbon fuels examined in this study. As a result, we
conclude that this rate expression should not be used
in models for any combustion problems in which the
fuel-air equivalence ratio varies with time or
position.
It was found that significant improvements in
predicted flame speeds could be obtained with different choices for the concentration exponents a
and b. The flame speed depends strongly on the fuel
concentration exponent a for rich mixtures and on
the oxygen concentration exponent b for lean mixtures. The best agreement between computed and
experimental results was obtained with
34
S = Sop-x
(5)
S" aP<u+b-2l/2
(6)
35
TABLE I
Single-step reaction rate parameters giving best agreement between experimental flammability limits
<PR') and computed flammability limits (h and <PR). Units are cm-sec-molc-kcal-Kelvins
Fuel
e;
CH4
CH.
C,H.
C3H.
C.HI0
CSH12
C.H'4
C,Hl'
C.Hl.
C.H,.
C.H.o
CloH ..
CH,OH
C.HsOH
C.H.
C7H.
C,H.
C.H.
C,H,
1.3 x 10
8.3 x lOs
1.1 x 101 '
8.6 x 1011
7.4xlO l l
6.4 x 1011
5.7x 1011
5.1 x 1011
4.6 x 1011
7.2 x 101 '
4.2 x 1011
3.8x 1011
3.2 x 101
1.5 x 101 '
2.0 x 1011
1.6 x 1011
2.0 x 101
4.2 x 1011
6.5 x 101
48.4
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
40.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
(J
-0.3
-0.3
0.1
0.1
0.15
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.15
-0.1
-0.1
0.1
-0.1
0.5
('h' and
<PI:
<pc
<PR'
<PR
1.3
1.3
1.65
1.65
1.6
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.6
1.85
1.85
1.65
1.85
1.25
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.4
0.5
0.3
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.4
0.5
0.3
1.6
1.6
2.7
2.8
3.3
3.6
4.0
4.5
4.3
4.3
4.3
4.2
4.1
3.4
3.4
3.2
6.7
2.8
>10.0
1.6
1.6
3.1
3.2
3.4
3.7
4.1
4.5
4.5
4.5
4.5
4.5
4.0
3.6
3.6
3.5
6.5
3.0
>10.0
36
TABLE II
Single-step and detailed reaction rate parameters for
methane-air, corresponding to curves in Figure 2.
Same units as Table I
ED
Set 1
Set 2
Set 3
Set 4
SetS
1.3
1.3
0.8
1.0
--Set 1
------ Set 2
- - - - Set 3
- - - Set4
--SetS
1.5
Equivalence ratio -
One-step
Detailed mechanism
Two-step mechanism
mechanism
1>
0.8
1.0
1.2
Tad
1990
2220
2140
[COl/[C0 2]
[H2]/[H20]
0.03
0.11
0.69
0.005
0.02
0.15
Tad
Tad
[COl/[C0 2]
2017
2320
2260
1975
2250
2200
0.08
0.14
0.43
In addition to the fact that the burned gas contains these incompletely oxidized species, it is also
well recognized that typical hydrocarbons burn in
a sequential manner. That is, the fuel is partially
oxidized to CO and H 2, which are not appreciably
consumed until all of the hydrocarbon species have
disappeared (Dryer and Westbrook, (979). Dryer
and Glassman used this observation to construct a
two-reaction model for methane oxidation in a
turbulent flow reactor
CH4+3/202 = CO+2H20
CO + 1/202 = CO 2,
(8)
111)
JI1
(9a)
(9b)
The rate of the CO oxidation reaction has been
taken from Dryer and Glassman and has the
value
k9b = 1014.6 exp( -40/ RT)
x [COP[H20jO.5[02]O.25
(10)
In order to reproduce both the proper heat of reaction and pressure dependence of the [CO]/[C02]
equilibrium, a reverse reaction was defined for
38
TABLE IV
Pam meters for two-step and quasi-global reaction mechanisms giving best agreement between experimental
and computed flammability limits. Same units as Table I
Two-step mechanism
A
e.
e;
2.8 x 10'
1.5 x 10'
1.3 x 1012
1.0 x 1012
8.8 x 10"
7.8x to
7.0 X 10"
6.3 X 1011
5.7 x 1011
9.6 X 1012
5.2x 10'1
4.7 X lOll
3.7 x 1012
1.8 x 10'2
2.4 x 1011
1.9 x 1011
2.4 x 1012
5.0x 1011
7.8 x 10'2
48.4
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
40.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
-0.3
-0.3
0.1
0.1
0.15
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.15
-0.1
-0.1
0.1
-0.1
0.5
1.3
1.3
1.65
1.65
1.6
1.5
4.0 x 10'
2.3x 10'
2.0 x 1012
1.5x 1012
1.3 x 10'2
1.2 x 1012
1.1 x 1012
1.0 x 1012
9.4x io
1.5 x 1013
8.8 x 1011
8.0x 1011
7.3 x 10'2
3.6 x 10'2
4.3 x 10"
3.4 x 10"
4.3 x 10'2
8.0 x 10"
1.2 x 101'
48.4
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
40.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
30.0
-0.3
-0.3
0.1
0.1
0.15
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.15
-0.1
-0.1
0.1
-0.1
0.5
Fuel
CH,
CH,
C,Ha
C,H,
C,HIO
C,H'2
CoHI4
C,Hlo
C,H"
C,HI'
CUH::lO
C loH22
CH,OH
C2H,OH
CoHo
C,H,
C2H,
CaH.
C,H2
Quasi-global mechanism
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.6
1.85
1.85
1.65
1.85
1.25
(II)
1.3
1.3
1.65
1.65
1.6
1.5.
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.6
1.85
1.85
1.65
1.85
1.25
n
C llHz m+-Oz=nCO+rnH z.
2
(12)
39
reactions and rate parameters used for the He-OaCO mechanism are given in Table V. The computed
flame speeds as functions of equivalence ratio and
pressure are essentially indistinguishable from those
found from the single-step and two-step mechanisms discussed earlier. The principal advantage is
the further improvement in the burned gas composition and temperature, although the flame structure and species concentrations in the flame zone
cannot presently be predicted well by the quasiglobal mechanism.
TABLE V
Reaction mechanism used in quasi-global mechanism for
CO-H.-O. system. Reverse rates computed from relevant
equilibrium constants. Same units as Table 1
Reaction
H+O.=O+OH
H.+O=H+OH
0+ H.O=OH +OH
OH+H.=H+H.O
H+O.+M=HO.+M
O+HO.=O.+OH
H+HO.=OH+OH
H+HO.=H.+O.
OH+HO.=H.O+O.
HO.+H02=H.0.+O.
H.O.+M
=OH+OH+M
HO.+H.=H.O.+H
H.O.+OH=H.O+ HO.
CO+OH~CO.+H
CO+O.~CO.+O
CO+O+M~CO.+M
CO+ HO.=CO.+OH
OH+M=O+H+M
O.+M=O+O+M
H.+M~H+H+M
H.O+M=H+OH+M
Eo
II
2.2 x 1014
1.8 x 10' 0
6.8 x 10"
2.2x 10' 3
1.5 x 10"
5.0 x 101
2.5 x 1014
2.5 x 1013
5.0 x 1013
1.0 x 10"
0.0
1.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
16.8
8.9
18.4
5.1
-1.0
1.0
1.9
0.7
1.0
1.0
1.2 x 1017
7.3 x io
1.0 x 101 3
1.5 x 10'
3.1 x io
5.9x 10"
1.5 x 10'4
8.0 x 101
5.lxI0 15
2.2 x 10'4
2.2 x 10'0
0.0
0.0
0.0
1.3
0.0
0.0
0.0
-1.0
0.0
0.0
0.0
45.5
18.7
1.8
-0.8
37.6
14.1
23.7
103,7
115.0
96.0
105.0
Both the strengths and weaknesses of the quasiglobal approach can be illustrated by comparing
species and temperature profiles computed with a
quasi-global reaction mechanism with those computed with a full detailed mechanism. This was
done for the case of a stoichiometric methanol-air
mixture at atmospheric pressure, using a detailed
mechanism taken from our previous study (Westbrook and Dryer, 1980a). Both models correctly
reproduced the observed laminar flame speed of
44cmJsec. Computed results are summarized in
Figures 3 and 4. The temperature and fuel concen-
40
2500 ,...----,----------,--------~------____,r__=---...,
0.12
I
Temperature
2000 - -
---
\
\
0.08
.,e
.0
1!
"~
..
....
1l.
f-
,
\
Q 1500
.E
I
___ I I
- -- ...
"0
:;;
1000
CO X 2
- --
0.04
500
-2
-1
Relative flame position (mm)
0.008 OH_-
-.:::=-e 0.006 e
'fi
"0
:;; 0.004 -
..-
--
-".:!'-
-----
o
0.002
-2
-...;::""--
-,
'"
!
-1
. Relative flame position tmrn]
F.IGURE 4 Concentration profiles for H, 0, and OH radicals as functions of relative flame position for the
same flame models as in Figure 3.
41
DISCUSSION
The procedures described here can be applied to any
type offuel molecule to develop and validate simplified reaction mechanisms. We have illustrated the
basic method with some hydrocarbon fuels of common interest, but other fuels, including non-hydrocarbons, can be treated in the same way. As an
example, flame speeds for methyl-substituted nparaffins are several centimeters per second smaller
than for straight-chain molecules of the same overall
composition and their flammability limits are
slightly narrower (Dugger el al.). Thus the flame
speed at atmospheric pressure for a stoichiometric
mixture of isooctane (2,2,4-trimethyl pentane) in air
is about 36cm/sec while that for n-octane is about
40em/sec. The rich flammability limit for isooctane
is <PR' =3.6 and about 4.25 for n-octane. If the rate
parameters for n-octane in Table I are used, but the
pre-exponential A is multiplied by 0.81 (i.e. (36/40)2),
then the single-step reaction mechanism reproduces
the experimental data well for isooctane. This
scaling of the pre-exponential can be done for many
of the methyl-substituted paraffin fuels.
For each set of reaction rate parameters, the preexponential terms tabulated here should be regarded
as approximate values if they are used in other numerical models. In addition to rate parameters,
flame speeds depend on thermodynamic and transport properties which may be treated somewhat
differently in other models. The activation energies
and concentration exponents derived here should
be valid for other models. Therefore, for use in
other codes, the parameters presented here should
be used as initial estimates, with comparisons between computed and experimental data for some
reference condition serving to calibrate the preexponential factor A.
The most significant result of the modeling work
discussed in this paper is the development of a
systematic, direct means of determining rate parameters for global reactions which can be used to
model flame propagation. In contrast with other
simplified reaction rate expressions in common use,
the rates derived in this manner correctly reproduce experimental flame speeds over wide ranges of
equivalence ratio and pressure. This avoids the
problem demonstrated for rate expressions which
assume that the fuel consumption reaction is first
order in fuel and oxidizer concentrations. With
those parameters flame speeds and flammability
limits for fuel-rich mixtures are seriously overestimated.
42
ACKNOWLEDGEMENT
We acknowledge with pleasure valuable discussions with
Professor Forman Williams. This work was performed in
part under the auspices of the U.S. Department of Energy
by the Lawrence Livermore National Laboratory under
contract number W-7405-ENG-48.
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43
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