中國機械工程學會第二十一屆全國學術研討會論文集
中華民國九十三年十一月二十六日、二十七日
國立中山大學
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Effects of Gravity on Ignition and Subsequent Transition to Flame Spread
Over a Horizontal Thin Solid Sheet
Tzung-Hsien Lin ,Chau-Sung Wang
Department of Mechanical Engineering,
Southern Taiwan University of Technology, Yung Kang, Tainan 710
the experimental studies, Olson et al. [1] and Olson [2]
Abstract
A numerical study was made for the buoyancy
effects on the ignition and subsequent flame spread over
a thin solid fuel flatly lay on the floor in elevated
gravity environments. Ignition was initiated in the
middle of the sheet to give two flame fronts propagate
in opposite directions. By varying the gravity level, and
consequently Damkohler number, seven cases of flame
spread over a thin solid fuel at 23.3 % oxygen mass
concentration in a range of 1-7 times normal Earth
gravity were conducted. The time of ignition delay
increase slightly with increase gravity within the
used a drop-tower to investigate the forced, opposed
flow and quiescent flame spread in microgravity. The
rate of flame spread was measured, and a low
velocity-quenching limit was found to exist in low
oxygen environments. Quiescent flame spread in
microgravity experiments conducted on Space Shuttle
facilities were presented by Bhattacharjee et al. [3]. The
flame
spread
rate
was
determined
using
a
frame-by-frame analysis of the film, and the solid
surface temperature was measured.
In
purely buoyant
flow
flame
spread
computational range. The rate of flame spread was
experiments, Altenkirch et al. [4] investigated the
found decrease with increasing gravity level due to the
buoyancy effects on downward spreading flames over
Damkohler number effects. At gravity = 4 g, the flames
thermally thin fuel. The parameter variation was
were decelerated eventually stagnated. Flame blow off
determined by performing flame spread experiments in
extinction was predicted at gravity = 5 g after few
a closed chamber, which was swung on a centrifuge to
stagnant time. The greater the gravity the weaker the
generate a gravitational acceleration above that of the
flame structure as well as the rate of flame spread.
Earth. The rates of flame spread were obtained as the
Because of the short fuel vapor resident time in high
5-cm spacing, divided by the elapsed time, was
gravity environment, the fuel reaction rate reduced
measured using an electrical clock. They found that an
cause the flame shrike and temperature drops even to
increase in the buoyancy level caused the flame spread
reach extinction.
rate to drop until no propagation was possible,
indicating that an increasing gravity level tends to
Keyword: gravity、 Damkohler number
increase induced flow intensity such that it retards
downward flame spreading.
1. Introduction
Intense
investigations
have
theoretical
and
recently been
Lin and Chen [5] developed the foundation of
experimental
conducted
the present study, which is a time-dependent combustion
on
model of the ignition of a downward flame. In this work,
downward flame spread over a solid thin fuel surface. In
attention was focused on both the solid and gas phase
中國機械工程學會第二十一屆全國學術研討會論文集
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response at the moments before and after ignition. The
figure. In this study the gravity levels were varied above
ignition mechanism of a vertical thin solid fuel in a
the normal gravity. The ignition and subsequent flame
normal gravitational environment, subjected to an
spread behaviors in elevated gravitational field were
external radiant flux as the ignition source, was
examined.
explored. Although the rate of flame spread was
The mathematical model of the physical problem
predicted, the flame diminished after a short period
described proceed include unsteady gas-phase and
because the burn out regime (ash) was retained
solid-phase governing equations which coupled each
throughout the computation time. This caused a large
other. The governing equations are described as follows:
amount of heat to stay at the flame tail and thus
decreased the flame spread rate.
By assuming that the
2.1 Governing Equations
ash was not retained, a moving boundary condition to
The gas phase model consist of two-dimensional,
account for ash removal was applied in this work. This
time-dependent
latter procedure has been found successful for the direct
Navier-Stokes, energy and species equations. The
simulation of a propagating downward flame.
combustion is described by a one-step overall
The main purpose of this work is to predict
the rate of flame spread and the blow off extinction limit
of a thin fuel at various gravity levels using an unsteady
combustion model. By varying the Damkohler number
through varying the gravity level, a series of parametric
studies was performed to examine the effects of
this time-dependent combustion model the spread rate
will be obtained directly from the history of the flame
front position, and the extinction phenomena at the
blowoff
limit
will
be
depicted.
steady model, developed by Duh and Chen [6], and the
data measured by Altenkirch et al. [4], will verify the
elliptic
solid phase is modeled by an unsteady energy and
mass conservation equations, which coupled with the
gas phase through the energy feed back term from the
gas phase. The solid pyrolysis is described by
first-order Arrhenius expression.
The nondimensional governing equations for the
gas
phase
are
summarized
in
Table
1. The
dimensionless solid-phase governing equations can be
expressed as follows for mass conservation:
ms  
A quantitative
comparison between the results obtained from the
complete
chemical reaction with finite rate global kinetics. The
buoyancy on both the ignition delay time and the flame
spread behavior over a horizontal thin solid fuel. For
continuity,
 s
E
 A s  s exp( s ).
t
Ts
(1)
and for energy conservation:
s
Ts
 2Ts
 s
 msL  1  CTs  1
t
x 2
developed time-dependent model.


T
 qex .
 Pr Gr y w
(2)
2. MATHEMATICAL MODEL
Figure 1 shows schematic diagram of two flames
initiated at the center of a thin solid fuel sheet and
propagate outward from the center in a quiescent
2.2 Boundary and Initial Conditions
2.2.1Boundary conditions in dimensionless form
are, for gas phase:
gravitational environment. Both the left and right flames
At x=xmin and x=xmax:
are opposite mode because the flame spread and the
u  0, v  0, T  1, YF  0, YO  YO , P  P .
entrained flow directions are in opposite. Initially, the
At y=0
entrained flow along the fuel surface but it turns to flow
u  0, T  Ts , m w   w v w
upward due to heated in the flame zone, as shown in the
(3)
中國機械工程學會第二十一屆全國學術研討會論文集
中華民國九十三年十一月二十六日、二十七日
mw  mw YFw 
YF
Pr Le Gr y
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physical time.

(4)
w
3. RESULTS AND DISCUSSION
mw YOw 
YO
Pr Le Gr y

The ignition delay time as a function of gravity level
.
was shown in Figure 2. The ignition delay time was
w
defined as the time elapse from the external radiation
At y=ymax:
u v T YF YO




 0, P  P .
x x x
x
x
applied to the instance of local maximum fuel reaction
(5)
rate exceeds 1
10-4 g/cm3/s. The choice of this
ignition criterion is because of we defined this value of
and for the solid phase:
contour in fuel reaction rate distribution as a visible
At x=xmin:
 s  1, Ts  1.
(6)
At x=xmax:
 s  1, Ts  1.
(7)
2.2.2 Initial conditions in dimensionless form
are, for the gas phase:
At t0:
u  0, v  0, T  1, YF  0, YO  YO , P  P .
(8)
and for the solid phase
flame boundary. As shown in the Figure2, the ignition
delay time increase slightly with increasing in gravity
level. This is because of higher buoyancy force enhance
the convection to carry more amount of fuel vapor
downstream. Therefore, it is need more time to
accumulate enough fuel vapors to form a flammable
mixture. The same trend of increase was found in the
work of Nakamura [8] for gravity near normal gravity.
Figure 3 shows the time histories of both right and
At t0:
 s  1, Ts  1.
(9)
left flames propagate in different gravities. The gravity
varies from normal earth up to five times of normal
gravity with increment of one. In this unsteady flame
2.3 Computational Grid
model the rate of flame spread can obtain from the slope
The strong coupling between pressure and velocity
of the loci of flames propagate. As shown in the figure,
in the full unsteady Navier-Stokes equations in gas
the rate of flame spread in 1g environment is about 0.29
phase are solved using the SIMPLE algorithm [7]. The
cm/s but it decrease with the increasing in gravity due to
detail computational procedure can be referred to Ref
the Damkohler number effects [9]. Comparing to the
[5]. A non-uniform grid of exponential distribution in
downward flame spread ([4], [6], [10]), the rate of flame
the gas phase was used with the grid points being
spread in this horizontal direction is faster then that in
concentrated near the gas-solid interface, where ignition
downward. This result coincides with the experimental
is likely, to capture the significant change in the
observations in the work of Hirano et al. [11]. Also, the
temperatures and flow field. A grid test has been
rate of flame spread in horizontal direction obtained
conducted to ensure that the solutions are independent
from this present unsteady flame model is near that
of grid size. The grid numbers of the entire
obtained from the steady flame model [12], which using
computational domain were 238 for x, 153 for y
the integration of mass blowing rate from the solid
direction,
surface to calculate the rate of flame spread. The case
the
corresponding
nondimensional
and
of4-g in Figure 3 shows that the rate of flame spread
dimensional computational area was 61.2450.16
cm2. The nondimensional time step for
computation was 13 corresponding 0.0712 s of the
was decelerated and eventually reaches zero after 4 s;
computational domain was 445.36363.21,
the flame fronts almost no further advance, in other
words, flame was stagnated. This is because of that, in
中國機械工程學會第二十一屆全國學術研討會論文集
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this buoyancy level, the gas residence time becomes too
Figure 7 at 4.70 s. Finally, the flat flame shrinks and the
small for the completion of the exothermic chemical
temperature drops continuously to become a point flame
reaction to maintain the flame spread process at a
and disappear eventually, as shown at 5.06 s and 5.34 s
constant rate, the blow off extinction may occurs
in Figure 6 and Figure 7, respectively.
somewhere. Consequently, as expected, the blow off
extinction occurs in the case of gravity = 5 g when the
flames propagate little distance at 4.77 s after the
external radiation applied. The blow off extinction
process will be illustrated later.
The
flames
shape,
flow
velocities
vector
distributions and temperature contours after 2 s of
ignition occurs at various gravities are shown in the
Figure 4 and Figure 5, respectively. As shown in the
figures, the flame structure in 1-g gravity is strongest
because the flame length and flame temperature are
greatest. While the flame structure in 4-g gravity is
weakest because the flame length and temperature are
weakest. The weaker of the flame is due to the shorter
of the gas residence time caused by the greater of the
buoyant flow. This can be confirmed from the 4-g plot
of Figure 4 in which the buoyant flow velocity vectors
are the biggest compare to the other cases. The
maximum buoyant flow velocity in 4-g case within the
region show in the plot is about 236 cm/s compare to
the that in 1-g case of 137 cm/s. Figure 4 also shows the
flame in normal gravity propagate farthest within 2 s
indicates that the rate of flame spread is fastest.
The blow off extinction process in 5-g case is
illustrated in Figure 6 and Figure 7. Figure 6 shows
enlarge view for the sequence of gas-phase fuel reaction
rate during the blow off extinction process while Figure
7 shows enlarge view for the sequence of gas-phase
temperature. At gravity = 5g the buoyancy flow is
strong enough such that the fuel vapor resident time in
the flame is too short for exothermic chemical reaction
completion. Consequently,
the vigorous chemical
reaction was reduced and the left and right straight
flames shrinks into one flat flame after some stagnated
times as shown in Figure 6 at 4.70 s. Meanwhile, the
amount of heat release from the chemical reaction
reduced cause the flame temperature drops as shown in
4. CONCLUSIONS
1
A numerical study was made for the buoyancy
effects on the ignition and subsequent flame spread over
a thin solid fuel flatly lay on the floor in elevated
gravity environments. In this present time-dependent
model we can readily simulate the flame propagation
behavior over a thin fuel surface.
By varying the gravity level, and consequently Da,
we conducted seven cases of flame spread over a thin
solid fuel at 23.3 % oxygen mass concentration in a
range of 1-7 times normal Earth gravity. The
computational results shown that the time of ignition
delay increase slightly with increase gravity within the
computational range. The time histories of flame front
positions was plotted for various gravity, then the rate of
flame spread was the slope of the flame propagation loci.
The rate of flame spread was found decrease with
increasing gravity level due to the Damkohler number
effects. At gravity = 4 g, the flames were decelerated
eventually stagnated. Flame blow off extinction was
predicted at gravity = 5 g at 4.77 s after ignition occurs.
The temperature and flame length in normal gravity
were greatest indicated that it was the strongest flame.
In the case of 4 g, the induced buoyant flow velocity
reaches a value of 236 cm/s compare the 137 cm/s in
normal gravity, but the temperature and flame size were
lowest indicated that it was the weakest flame. The
flame in normal gravity propagate farthest within 2 s
indicates that the rate of flame spread is fastest.
In case of 4-g gravity, the rate of flame spread
decelerates to become stagnated at the final stage of
propagates. The blow off extinction may occur some
where for time greater than 6 s. At gravity = 5 g, the left
and right straight flames shrinks into one flat flame after
some stagnated times at 4.70 s. Meanwhile, the amount
中國機械工程學會第二十一屆全國學術研討會論文集
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of heat release from the chemical reaction reduced cause
the flame temperature drops. The flat flame shrinks and
the temperature drops continuously to become a point
高重力場對薄燃料火焰傳播之效應
flame and disappear eventually.
林宗賢 王朝松
南台科技大學機械工程系
5. ACKNOWLEDGMENTS
摘要
The author would like to thank the National
Science
Council of the
Taiwan
for
financially
supporting this research under Contract No. NSC
90-2212-E-218-006.
本文以數值方法研究在高重力場中，浮力對引
燃和火焰傳播之效應。引燃開始於燃料中央，造成兩
個朝相反方向傳播之火焰。藉由改變不同的重力，也
6. REFERENCES
因此改變 Damkohler number，在 1 到 7 倍的正常重
[1]S. L. Olson, P. V. Ferkul and J. S. T’ien,
力場和 23.3%的氧濃度環境中，研究 7 種薄燃料的火
Twenty-Second
on
焰。引燃延遲時間隨重力場增加而微小的增加。研究
Combustion, pp. 1213-1222, The Combustion Institute,
發現火焰傳播速度會因 Damkohler number 效應，隨
Pittsburgh, 1988.
重力的增加而減少。在重力等於 4g 的時候，火焰會
[2]S. L. Olson, Combust. Sci. Technol., vol. 76, pp.
慢慢的減速最後停滯。在重力等於 5g 的時候，預測
233-249, 1991.
到火焰將在短時間的停滯後熄滅。較大的重力將伴隨
[3]S. Bhattacharjee, R. A. Altenkirch, and K. Sacksteder,
著較弱的火焰結構和火焰傳播速度。由於在高重力環
Combust. Sci. Technol., vol. 91, pp. 225-242, 1993.
境下，燃氣駐留時間減少，將導致火焰減弱且溫度下
[4]K. A. Altenkirch, R. Eichhorn, and P. C. Shang,
降，甚至使火焰熄滅。
Symposium
(international)
Combust. Flame, vol. 37, pp. 71-83, 1980.
[5]T. H. Lin, and C. H. Chen, Numerical Analysis of
關鍵字: 重力 、
Ignition and Transition to Downward Flame Spread
Over a Thermally-Thin Solid Fuel, I. J. Trans.
Phenomena, vol. 1, pp. 255-275, 1999.
[6]F. C. Duh, and C. H. Chen, A theory for Downward
y
Flame Spread over a Thermally Thin Fuel, Combust.
Gravity
Sci. Technol., vol. 77, pp. 291-305, 1991.
[7]S. V. Patankar, Numerical Heat Transfer and Fluid
Flame
Flow, McGraw-Hill, New York, USA, 1980.
[8]Nakamura, Y., Yamashita, H., and Takeno, T.,
Combust. Flame 120:34 (2000).
Entrained flow
Entrained flow
[9]A. C. Fernandez-Pello and T. Hirano, Controlling
Mechanisms of Flame Spread, Combust. Sci. Technol.,
vol.
32, pp. 1-31, 1983.
[10]Lin, T. H., Num. Heat Transfer A 40:841 (2001).
[11]Hirano, T., Noreikis, S. E., and Waterman, T. E.,
Combust. Flame 22353 (1974).
[12]Chen, C. H., and Chan, S. C. Combust. Sci.
Technol., 107:59 (1995).
x
Thin solid fuel sheet
Fig. 1. Schematic diagram of two flames propagate
outward from the center of a thin solid fuel sheet on the
floor in a quiescent gravitational environment.
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2.5
2.0
Gravity = 1 g
Gravity = 2 g
Gravity = 3 g
Gravity = 4 g
2.0
1.8
Igition Delay Time (s)
1.5
Symbol Plot
Linear Fit
1.6
y
(cm)
1.0
1.4
0.5
1.2
0.0
2.5
1.0
2.0
0.8
1.5
y
(cm)
1.0
0.6
0.5
0.4
0.0
-1.5
0.2
-1.0
-0.5
0.0
0.5
-1.5
1.5
1.0
-1.0
-0.5
0.0
0.5
1.0
1.5
x (cm)
x (cm)
0.0
0
2
4
6
8
Gravity (980 cm/s2)
Fig. 2. Ignition delay time at various gravity level.
Fig.
4.
Flames
and
flow
velocity
vector
distributions at various gravity levels after 2 s of
ignition occur. The flame shapes shown are the fuel
reaction rate contour of 10-4 g/cm3/s.
Flame Front Position (cm)
2.5
1g
2g
3g
4g
5g
2
1
2.0
Gravity = 1 g
Gravity = 2 g
Gravity = 3 g
Gravity = 4 g
1.5
y
(cm)
1.0
0.5
0.0
2.5
flame blowoff extinction
0
2.0
1.5
y
(cm)
-1
1.0
0.5
0.0
-1.5
-2
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5
-1.0
-0.5
x (cm)
0
1
2
3
4
5
Time (s)
Fig. 3. Time histories of flame front positions at
0.0
0.5
1.0
1.5
x (cm)
6
Fig. 5. Temperature distributions at various gravity
levels after 2 s of ignition occur.
various gravity levels.
0.6
0.4
Time = 4.70 s
y
(cm)
0.2
0.0
-0.8
0.6
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
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Fig. 7. Sequence for the blow off extinction process.
Shown are the temperature contours in case of 5 times
Fig. 6. Sequence for the blow off extinction process.
normal gravity.
Shown are the reaction rate contours in case of 5 times
normal gravity. The contours shown are the quantity of
Table 1
take log10.
Gas Phase Governing Equations




   u   v               S
t
x
y

x

x

y

y



 
0.6
Time = 4.70 s
0.4
y
(cm)
0.2
0.0
-0.8
0.6
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
Equation


S
Continuity
1

0
x-Mom.
u

y-Mom.
v
p
 Su
x
 
p

 Sv  
y
   F
Energy
T
Fuel
YF
Gr

Gr

Pr Gr

Pr GrLe

F
 q
F

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Oxidizer
YO

Pr GrLe
F
f
where
Su 
1    u     v  2    v 

 



3 x  Gr x  y  Gr x  3 x  Gr y 
Sv 
1    v     u  2    u 






3 y  Gr y  x  Gr y  3 y  Gr x 
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