Theories and Applications of Chem. Eng., 2002, Vol. 8, No. 1
화학공학의
이론과
응용
제
8
권
제
1
호
2002
년
화염의
농도와
온도
계산
정옥진
,
김
영한
동아대학교
화학공학과
Numerical Calculation of Concentration and Temperature in a Flame
Ok Jin Joung
and
Young Han Kim
Dept. of Chem. Eng., Dong

A University
Introduction
The analysis of combustion processes is difficult, because fast and
complex reactions are involved in the
process. Moreover, its highly exothermic reaction makes the measurement of composition and temperature in a
flame complicated.
An electrostatic measurement system is simple and inexpensive to be implemented in the fla
me analysis. It
detects only a local composition in the flame, but new data
acquisition
system connected to a personal computer
getting multiple measurements at the same moment solves the problem of spatially limited detection. The ion
measurement in a lam
inar flame was conducted by Shcherbakov et al. [1], and in turbulent flames Furukawa et al.
[2] measured the flame using an electrostatic probe. Also, numerical analysis of the turbulent flame was
conducted by McKentry et al. [3].
In this study, a numerica
l calculation using a set of partial differential equations of mass and energy balances
is conducted to compare with the experimental measurement. The numerical simulation is carried out for a
relatively simple laminar flame, since the comparison is easier
than a turbulent flame.
Numerical Analysis
A detailed description of the burner used in this study is given in Figure 1. Fittings of a half

inch size are
utilized to assemble a burner. As fuel of the burner n

butane gas is provided through 1/8 inch tubin
g installed in
the center of the burner. Air is separately fed for the combustion.
For the simplicity of the computation, a couple of assumptions are made in the development of system
equations. Because gas is supplied as a laminar flow in vertical directi
on, no significant radial gas flow is
expected and radial transport of mass and energy is dominated by diffusion. In addition, axial gas flow is large
enough to ignore axial diffusion, and the flow is steady and constant.
With the assumptions, a material b
alance in steady state is formulated as
A
z
r
r
c
r
r
r
D
z
c
v
]
[
1
(1)
B. C.
0
r
c
at
r
= 0
c
= 0 at
r
=
R
c = c
0
at
z = 0, r=0
c= 0
at
z=0, r>0
and an energy balance is
A
r
c
z
p
r
H
r
c
r
r
r
k
z
T
v
C
)
(
]
[
1
(2)
B. C.
0
r
T
at
r
= 0
0
r
T
at
r
=
R
T = T
0
at
z = 0
The mechanism of chemical reaction of a combustion process is very complicated. Because the approximate
composition and temperature profiles are studied here, a first order simple reacti
on mechanism is utilized in the
analysis.
The material balance in dimensionless form is
'
]
'
'
'
[
'
'
1
'
'
2
c
v
L
k
r
c
r
r
r
v
R
D
L
z
c
z
z
(3)
Theories and Applications of Chem. Eng., 2002, Vol. 8, No. 1
화학공학의
이론과
응용
제
8
권
제
1
호
2002
년
where the primes indicate the dimensionless variables as below.
0
'
c
c
c
,
L
z
z
'
,
and
R
r
r
'
And the energy balance is
'
)
(
)
(
]
'
[
'
'
0
0
2
c
v
L
k
T
T
C
c
H
r
T
r
r
v
R
L
C
k
z
T
z
m
p
r
z
p
c
(4)
where
0
0
'
T
T
T
T
T
m
Though the system is described in cylindrical coordinate, a two dimensional rectangular grid containing
the center axis is used in the formulation of the finite diff
erence equations from Eqs. (3) and (4). An explicit
technique is implemented here to solve the set of parabolic partial differential equations. The concentration and
temperature are simultaneously found at the same axial position. The grid sizes in radial
and axial directions are
determined to satisfy the stability criterion.
The average size of flame is 2 cm in radius, and axial velocity is obtained air flow rate of 4 liters per
minute. Fuel flow is too small to be included. Physical properties are ta
ken from those of air. Kinetic information
is from a reference [4]. Table 1 lists the parameters used in this study.
Results and discussion
For a typical case of a laminar flame, fuel concentration and temperature distributions are calculated from
the pro
cedure explained in the section of numerical analysis. The parameters listed in Table 1 for the
computation of concentration and temperature are from the case of
experimental
result shown in Figure 1. Figure
2 shows the fuel concentration distribution in d
imensionless position of the flame. The numbers given on the
curves are dimensionless concentrations. Because fuel burns from outside of the flame, high concentration is
observed in the center and the concentration decreases as flame goes up. Temperature d
istribution is given in
Figure 3. Again, the numbers on the curves are dimensionless temperatures. The highest temperature is observed
at the center and one third of axial location. The temperature diminishes as moving away from the center.
Though the loca
tion of the highest temperature is different from the current measurement of the experiment, the
patterns of both distributions of ion from the experiment and temperature from the numerical calculation are
similar. In spite that complex chemical reactions
are involved in combustion process, high temperature indicates
high rate of exothermic reaction and ion generation. This explains the similarity of the temperature and ion
concentration distributions. The difference in location of the center of circular pa
ttern is from the discrepancy in
parameters used in the numerical calculation and the experiment. The gas flow rate in the numerical computation
is determined from the supplied air flow rate, but secondary air supply from the surrounding of flame is
signif
icant in actual experiment. Including the secondary supply to the flow to increase the flow rate by 50 %
moves the center upward as shown in the difference between Figures 3 and 4. This is an example to explain the
discrepancy in some of the parameters use
d in the simulation.
The circular patterns below the center is similar in the distributions of calculated temperature and measured
ion concentration, but those above the center are quite different. While the high concentration ions are consumed
by reaction
and are not detected above the center, the heat generated from reaction moves upward to be sensed as
shown in the distribution.
Because the distribution of ions explains combustion process the best, many studies dealing the combustion
pursue an efficient
means to measure the distribution. For example, the combustion process in an internal engine
for automobile is directly related to the efficiency of the engine. The confined structure of the engine prevents
from optical measurement of the ions, and therefo
re the technique utilizing an electrostatic probe is useful to
such an application. It is simple to fabricate and is also inexpensive compared with laser instruments.
Conclusion
A numerical analysis is carried out to compare the computed distribution of c
oncentration and temperature
with the experimental outcome.
The distribution of ion in the flames is measured with different fuel supply rates. The analysis of the
distributions gives the optimum ratio of fuel and air supply. The result of the numerical te
mperature calculation
Theories and Applications of Chem. Eng., 2002, Vol. 8, No. 1
화학공학의
이론과
응용
제
8
권
제
1
호
2002
년
shows a similar pattern with the ion distribution measured experimentally. In other words, either measurement of
temperature or ion distribution gives identical information for the analysis of a flame.
REFERENCES
[1] Shcherbakov, N.D
., Ospanov, B. S. and Fialkov, B. S.,
Combust. Explos. Shock Waves,
24
, 313 (1988).
[2] Furukawa, J., Hirano, T. and Williams, F. A.,
Combust. and Flame,
113
, 487 (1998).
[3] McKenty, F., Gravel, L. and Camarero, R.,
Korean J. Chem. Eng
.,
16
, 482 (1999).
[
4] Librovich, B. V., Makhviladze, G. M., Roberts, J. P. and Yakush, S. E.,
Combust. and Flame
, 118, 669
(1999).
Table 1. Parameters for numerical
calculation
symbol
value
L
4 cm
D
0.225 cm
2
/s
R
1 cm
v
z
21.2 cm/s
k
c
1.2 x 10

5
cal/(cm
C s
)
E
A
1.25 x 10
5
J/mol
T
m
1000
C
T
0
256
C
c
0
1 x 10

3
g/cm
3
1.16 x 10

3
g/cm
3
C
p
0.272 cal/g
C

H
r
1.09 x 10
4
cal/g
Figure
1
. Distribution of current
measurement in
microamperes for fuel supply
of 30 cm
3
/minute.
0
0.2
0.4
0.6
0.8
1
0
1
2
3
4
5
6
x 10
3
radial distance ()
concentration ()
0.1
0.2
0.3
0.4
Figure 2. Calculated di
stribution of dimensionless fuel
concentration. (Numbers on the curves are
dimensionless axial distance.)
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
radial distance ()
height ()
0.001
0.005
0.01
0.05
0.1
0.15
0.2
Figure
3
. Calculated distribution of dimensionless
temperature.
0.1
0.2
0.3
0.4
0.5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
radial distance ()
height ()
0.0005
0.001
0.005
0.01
0.015
0.02
0.025
Figure 4. Calculated distribution of dimensionless
temperature with i
ncreased gas velocity.
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