Environmental Engineering Reference
In-Depth Information
E
RT
2
R
=−
p mm
exp
(3.6)
fu
fu
ox
The frequency coefficient
F
and the activation energy
E
are constants to be
defined through experiments. Many researchers have tried to define the values for
different kinds of fuel. Among them, Coffee
6
has examined the values to represent
the burning velocity in terms of equivalence ratio of methane-air mixtures.
Instead of mass fractions in Equation 3.6, he used volumetric concentrations as
follows.
[
]
=×
d
CH
24 355
,
[
] [
]
02
.
13
.
4
12
25 10
.
CH
O
exp
(3.7)
4
2
dt
T
where [ ] denotes molar concentration, mol/cm
3
.
This model was originally proposed for representing the burning velocity of
methane-air mixtures at room temperature. Of course, although the expression is
not always suitable for mixtures at any temperature, it provides a guideline for the
reaction model for HiTAC.
3.2.4.2
Four-Step Reaction Model (Jones and Lindstedt)
In a reduced mechanism, a number of minor elementary reactions and intermediate
chemical species are eliminated to create an apparent simplified reaction scheme
either through extracting dominant reactions from the detailed chemistry or com-
bining several elementary reactions by assuming partial equilibrium among them.
For this reason a single reduced reaction model cannot always be effective for a
variety of objects. Note that the accuracy of obtained simulation results might not
be reliable unless the most suitable model for the present object is selected.
This four-step model was built by extracting six species and simplifying them
into four steps of reactions from detailed chemistry. It has been reported that the
model is applicable either to diffusion or premixed laminar flames and that the
obtained burning velocity and flame structure, i.e., temperature and species distri-
butions inside the flame, conform well to actual measurements.
7
The original four-
step reaction mechanism was proposed for generic saturated lower-hydrocarbon
fuels, and in the case of methane, they can be written as follows:
CH
+
H O
CO
+
3
H
(R3)
4
2
2
1
2
CH
+
O
CO
+
2
H
(R4)
4
2
2
1
2
HOHO
2
+
(R5)
2
2
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