EFFECTS OF ELEVATED GRAVITY ON PROPAGATING FLAME OVER A
THIN SOLID SHEET
Tzung-Hsien Lin Sheng-Wen Tsay
Department of Mechanical Engineering,
Southern Taiwan University of Technology, Yung Kang, Tainan 710, Taiwan
ABSTRACT
spread over a solid thin fuel surface. In the experimental
A numerical study was made for the buoyancy
studies, Olson et al. [1] and Olson [2] used a drop-tower
effects on the ignition and subsequent flame spread over
to investigate the forced, opposed flow and quiescent
a thin solid fuel flatly lay on the floor in elevated
flame spread in microgravity. The rate of flame spread
gravity environments. Ignition was initiated in the
was measured, and a low velocity-quenching limit was
middle of the sheet to give two flame fronts propagate
found to exist in low oxygen environments. Quiescent
in opposite directions. By varying the gravity level, and
flame spread in microgravity experiments conducted on
consequently Damkohler number, seven cases of flame
Space Shuttle facilities were presented by Bhattacharjee
spread over a thin solid fuel at 23.3 % oxygen mass
et al. [3]. The flame spread rate was determined using a
concentration in a range of 1-7 times normal Earth
frame-by-frame analysis of the film, and the solid
gravity were conducted. The time of ignition delay
surface temperature was measured.
increase slightly with increase gravity within the
In purely buoyant flow flame spread experiments,
computational range. The rate of flame spread was
Altenkirch et al. [4] investigated the buoyancy effects
found decrease with increasing gravity level due to the
on downward spreading flames over thermally thin fuel.
Damkohler number effects. At gravity = 4 g, the flames
The parameter variation was determined by performing
were decelerated eventually stagnated. Flame blow off
flame spread experiments in a closed chamber, which
extinction was predicted at gravity = 5 g after few
was swung on a centrifuge to generate a gravitational
stagnant time. The greater the gravity the weaker the
acceleration above that of the Earth. The rates of flame
flame structure as well as the rate of flame spread.
spread were obtained as the 5-cm spacing, divided by
Because of the short fuel vapor resident time in high
the elapsed time, was measured using an electrical clock.
gravity environment, the fuel reaction rate reduced
They found that an increase in the buoyancy level
cause the flame shrike and temperature drops even to
caused the flame spread rate to drop until no
reach extinction.
propagation was possible, indicating that an increasing
gravity level tends to increase induced flow intensity
Keyword: gravity、 Damkohler number
such that it retards downward flame spreading.
Lin and Chen [5] developed the foundation of the
1. INTRODUCTION
present study, which is a time-dependent combustion
Intense theoretical and experimental investigations
model of the ignition of a downward flame. In this work,
have recently been conducted on downward flame
attention was focused on both the solid and gas phase
response at the moments before and after ignition. The
entrained flow along the fuel surface but it turns to flow
ignition mechanism of a vertical thin solid fuel in a
upward due to heated in the flame zone, as shown in the
normal gravitational environment, subjected to an
figure. In this study the gravity levels were varied above
external radiant flux as the ignition source, was
the normal gravity. The ignition and subsequent flame
explored. Although the rate of flame spread was
spread behaviors in elevated gravitational field were
predicted, the flame diminished after a short period
examined.
because the burn out regime (ash) was retained
The mathematical model of the physical problem
throughout the computation time. This caused a large
described proceed include unsteady gas-phase and
amount of heat to stay at the flame tail and thus
solid-phase governing equations which coupled each
decreased the flame spread rate.
other. The governing equations are described as follows:
By assuming that the
ash was not retained, a moving boundary condition to
account for ash removal was applied in this work. This
2.1 Governing Equations
latter procedure has been found successful for the direct
simulation of a propagating downward flame.
The gas phase model consist of two-dimensional,
time-dependent
continuity,
complete
elliptic
The main purpose of this work is to predict the rate
Navier-Stokes, energy and species equations. The
of flame spread and the blow off extinction limit of a
combustion is described by a one-step overall chemical
thin fuel at various gravity levels using an unsteady
reaction with finite rate global kinetics. The solid phase
combustion model. By varying the Damkohler number
is
through varying the gravity level, a series of parametric
conservation equations, which coupled with the gas
studies was performed to examine the effects of
phase through the energy feed back term from the gas
buoyancy on both the ignition delay time and the flame
phase. The solid pyrolysis is described by first-order
spread behavior over a horizontal thin solid fuel. For
Arrhenius expression.
modeled
by an unsteady energy and
mass
this time-dependent combustion model the spread rate
The nondimensional governing equations for the
will be obtained directly from the history of the flame
gas phase are summarized in Table 1. The dimensionless
front position, and the extinction phenomena at the
solid-phase governing equations can be expressed as
blowoff
follows for mass conservation:
limit
will
be
depicted.
A quantitative
comparison between the results obtained from the
steady model, developed by Duh and Chen [6], and the
data measured by Altenkirch et al. [4], will verify the
developed time-dependent model.
ms  
 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
2. MATHEMATICAL MODEL

Figure 1 shows schematic diagram of two flames

T
 qex .
 Pr Gr y w
(2)
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
gravitational environment. Both the left and right flames
I. Boundary conditions in dimensionless form are, for
are opposite mode because the flame spread and the
gas phase:
entrained flow directions are in opposite. Initially, the
At x=xmin and x=xmax:
u  0, v  0, T  1, YF  0, YO  YO , P  P .
(3)
dimensional computational area was 61.2450.16 cm2.
At y=0:
The nondimensional time step for computation was 13
u  0, T  Ts , m w   w v w
corresponding 0.0712 s of the physical time.
mw  mw YFw 
mw YOw 
YF
Pr Le Gr y

YO
Pr Le Gr y

(4)
3. RESULTS AND DISCUSSION
w
The ignition delay time as a function of gravity
.
level was shown in Figure 2. The ignition delay time
w
At y=ymax:
was defined as the time elapse from the external
u v T YF YO




 0, P  P .
x x x
x
x
(5)
radiation applied to the instance of local maximum fuel
reaction rate exceeds 110-4 g/cm3/s. The choice of this
and for the solid phase:
ignition criterion is because of we defined this value of
At x=xmin:
contour in fuel reaction rate distribution as a visible
 s  1, Ts  1.
(6)
At x=xmax:
flame boundary. As shown in the Figure2, the ignition
delay time increase slightly with increasing in gravity
 s  1, Ts  1.
(7)
level. This is because of higher buoyancy force enhance
II. Initial conditions in dimensionless form are, for the
the convection to carry more amount of fuel vapor
gas phase:
downstream. Therefore, it is need more time to
At t0:
accumulate enough fuel vapors to form a flammable
u  0, v  0, T  1, YF  0, YO  YO , P  P .
(8)
and for the solid phase:
mixture. The same trend of increase was found in the
work of Nakamura [8] for gravity near normal gravity.
At t0:
Figure 3 shows the time histories of both right and
 s  1, Ts  1.
(9)
left flames propagate in different gravities. The gravity
varies from normal earth up to five times of normal
2.3 Computational Grid
gravity with increment of one. In this unsteady flame
The strong coupling between pressure and velocity
model the rate of flame spread can obtain from the slope
in the full unsteady Navier-Stokes equations in gas
of the loci of flames propagate. As shown in the figure,
phase are solved using the SIMPLE algorithm [7]. The
the rate of flame spread in 1g environment is about 0.29
detail computational procedure can be referred to Ref
cm/s but it decrease with the increasing in gravity due to
[5]. A non-uniform grid of exponential distribution in
the Damkohler number effects [9]. Comparing to the
the gas phase was used with the grid points being
downward flame spread ([4], [6], [10]), the rate of flame
concentrated near the gas-solid interface, where ignition
spread in this horizontal direction is faster then that in
is likely, to capture the significant change in the
downward. This result coincides with the experimental
temperatures and flow field. A grid test has been
observations in the work of Hirano et al. [11]. Also, the
conducted to ensure that the solutions are independent
rate of flame spread in horizontal direction obtained
of grid size. The grid numbers of the entire
from this present unsteady flame model is near that
computational domain were 238 for x, 153 for y
obtained from the steady flame model [12], which using
direction,
the integration of mass blowing rate from the solid
the
computational
corresponding
domain
was
nondimensional
445.36363.21,
and
surface to calculate the rate of flame spread. The case of
4-g in Figure 3 shows that the rate of flame spread was
the flame is too short for exothermic chemical reaction
decelerated and eventually reaches zero after 4 s; the
completion. Consequently,
flame fronts almost no further advance, in other words,
reaction was reduced and the left and right straight
flame was stagnated. This is because of that, in this
flames shrinks into one flat flame after some stagnated
buoyancy level, the gas residence time becomes too
times as shown in Figure 6 at 4.70 s. Meanwhile, the
small for the completion of the exothermic chemical
amount of heat release from the chemical reaction
reaction to maintain the flame spread process at a
reduced cause the flame temperature drops as shown in
constant rate, the blow off extinction may occurs
Figure 7 at 4.70 s. Finally, the flat flame shrinks and the
somewhere. Consequently, as expected, the blow off
temperature drops continuously to become a point flame
extinction occurs in the case of gravity = 5 g when the
and disappear eventually, as shown at 5.06 s and 5.34 s
flames propagate little distance at 4.77 s after the
in Figure 6 and Figure 7, respectively.
the vigorous chemical
external radiation applied. The blow off extinction
4. CONCLUSIONS
process will be illustrated later.
The
flames
shape,
flow
velocities
vector
A numerical study was made for the buoyancy
distributions and temperature contours after 2 s of
effects on the ignition and subsequent flame spread over
ignition occurs at various gravities are shown in the
a thin solid fuel flatly lay on the floor in elevated
Figure 4 and Figure 5, respectively. As shown in the
gravity environments. In this present time-dependent
figures, the flame structure in 1-g gravity is strongest
model we can readily simulate the flame propagation
because the flame length and flame temperature are
behavior over a thin fuel surface.
greatest. While the flame structure in 4-g gravity is
By varying the gravity level, and consequently Da,
weakest because the flame length and temperature are
we conducted seven cases of flame spread over a thin
weakest. The weaker of the flame is due to the shorter
solid fuel at 23.3 % oxygen mass concentration in a
of the gas residence time caused by the greater of the
range of 1-7 times normal Earth gravity. The
buoyant flow. This can be confirmed from the 4-g plot
computational results shown that the time of ignition
of Figure 4 in which the buoyant flow velocity vectors
delay increase slightly with increase gravity within the
are the biggest compare to the other cases. The
computational range. The time histories of flame front
maximum buoyant flow velocity in 4-g case within the
positions was plotted for various gravity, then the rate of
region show in the plot is about 236 cm/s compare to
flame spread was the slope of the flame propagation loci.
the that in 1-g case of 137 cm/s. Figure 4 also shows the
The rate of flame spread was found decrease with
flame in normal gravity propagate farthest within 2 s
increasing gravity level due to the Damkohler number
indicates that the rate of flame spread is fastest.
effects. At gravity = 4 g, the flames were decelerated
The blow off extinction process in 5-g case is
illustrated in Figure 6 and Figure 7. Figure 6 shows
eventually stagnated. Flame blow off extinction was
predicted at gravity = 5 g at 4.77 s after ignition occurs.
enlarge view for the sequence of gas-phase fuel reaction
The temperature and flame length in normal gravity
rate during the blow off extinction process while Figure
were greatest indicated that it was the strongest flame.
7 shows enlarge view for the sequence of gas-phase
In the case of 4 g, the induced buoyant flow velocity
temperature. At gravity = 5g the buoyancy flow is
reaches a value of 236 cm/s compare the 137 cm/s in
strong enough such that the fuel vapor resident time in
normal gravity, but the temperature and flame size were
lowest indicated that it was the weakest flame. The
Combust. Sci. Technol., vol. 77, pp. 291-305, 1991.
flame in normal gravity propagate farthest within 2 s
[7]S. V. Patankar, Numerical Heat Transfer and Fluid
indicates that the rate of flame spread is fastest.
Flow, McGraw-Hill, New York, USA, 1980.
In case of 4-g gravity, the rate of flame spread
[8]Nakamura, Y., Yamashita, H., and Takeno, T.,
decelerates to become stagnated at the final stage of
Combust. Flame 120:34 (2000).
propagates. The blow off extinction may occur some
[9]A. C. Fernandez-Pello and T. Hirano, Controlling
where for time greater than 6 s. At gravity = 5 g, the left
Mechanisms of Flame Spread, Combust. Sci. Technol.,
and right straight flames shrinks into one flat flame after
vol.
some stagnated times at 4.70 s. Meanwhile, the amount
[10]Lin, T. H., Num. Heat Transfer A 40:841 (2001).
of heat release from the chemical reaction reduced cause
[11]Hirano, T., Noreikis, S. E., and Waterman, T. E.,
the flame temperature drops. The flat flame shrinks and
Combust. Flame 22353 (1974).
the temperature drops continuously to become a point
[12]Chen, C. H., and Chan, S. C. Combust. Sci.
flame and disappear eventually.
Technol., 107:59 (1995).
32, pp. 1-31, 1983.
5. ACKNOWLEDGMENTS
The author would like to thank the National
Science
Council of the
Taiwan
for
financially
Table 1
supporting this research under Contract No. NSC




   u   v               S
t
x
y
 x  x  y  y 
90-2212-E-218-006.
6. REFERENCES
[1]S. L. Olson, P. V. Ferkul and J. S. T’ien,
Twenty-Second
Combustion,
Symposium
pp.
Gas Phase Governing Equations
1213-1222,
(international)
The
Equation


S
Continuity
1

0
x-Mom.
u
y-Mom.
v
Energy
T
Fuel
YF
Oxidizer
YO
on
Combustion
Institute, Pittsburgh, 1988.
[2]S. L. Olson, Combust. Sci. Technol., vol. 76, pp.
233-249, 1991.
[3]S. Bhattacharjee, R. A. Altenkirch, and K.
Sacksteder, Combust. Sci. Technol., vol. 91, pp.
225-242, 1993.
[4]K. A. Altenkirch, R. Eichhorn, and P. C. Shang,
Combust. Flame, vol. 37, pp. 71-83, 1980.
[5]T. H. Lin, and C. H. Chen, Numerical Analysis of
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 Flame Spread over a Thermally Thin Fuel,


Gr

Gr

Pr Gr

Pr GrLe

Pr GrLe

p
 Su
x
 
p
 Sv  
y
   F
F
 q
F

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 
y
Entrained flow
x
Thin solid fuel sheet
Fig. 1. Schematic diagram of two flames propagate
Flame Front Position (cm)
Flame
Entrained flow
1g
2g
3g
4g
5g
2
Gravity
1
flame blowoff extinction
0
-1
outward from the center of a thin solid fuel sheet
on the floor in a quiescent gravitational
-2
environment.
0
1
2
3
4
5
6
Time (s)
Fig. 3. Time histories of flame front positions at
various gravity levels.
2.5
2.0
Gravity = 2 g
Gravity = 3 g
Gravity = 4 g
1.5
1.8
y
(cm)
Symbol Plot
Linear Fit
1.6
Igition Delay Time (s)
Gravity = 1 g
2.0
1.0
0.5
1.4
0.0
2.5
1.2
2.0
1.0
1.5
y
(cm)
0.8
1.0
0.6
0.5
0.4
0.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
-1.5
1.5
-1.0
-0.5
0.2
Fig.
0.0
0
2
4
6
8
4.
Flames
0.0
0.5
1.0
1.5
x (cm)
x (cm)
and
flow
velocity
vector
distributions at various gravity levels after 2 s of
2
Gravity (980 cm/s )
Fig. 2. Ignition delay time at various gravity level.
ignition occur. The flame shapes shown are the fuel
reaction rate contour of 10-4 g/cm3/s.
2.5
2.0
0.6
Gravity = 2 g
Gravity = 1 g
Time = 4.70 s
0.4
y
(cm)
1.5
y
(cm)
0.2
1.0
0.5
0.0
-0.8
0.6
0.0
2.5
2.0
Gravity = 3 g
Gravity = 4 g
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
Time = 4.77 s
0.4
y
(cm)
1.5
y
(cm)
0.2
1.0
1400
0.5
0.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5
-1.0
-0.5
x (cm)
0.0
0.5
1.0
0.0
-0.8
0.6
1.5
x (cm)
0.4
Fig. 5. Temperature distributions at various gravity
0.0
-0.8
0.6
Time = 4.70 s
y
(cm)
0.4
0.2
0.4
-0.2
0.0
Time = 5.06 s
700
800
900
0.2
0.6
0.0
-0.8
0.6
-0.4
y
(cm)
levels after 2 s of ignition occur.
0.4
-0.6
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
0.6
0.8
Time = 5.34 s
y
(cm)
0.2
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0.0
-0.8
Time = 4.77 s
-0.6
-0.4
-0.2
x (cm)
y
(cm)
Fig. 7. Sequence for the blow off extinction process.
0.2
Shown are the temperature contours in case of 5 times
0.0
-0.8
0.6
0.4
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
normal gravity.
Time = 5.06 s
高重力場對薄燃料火焰傳播之效應
y
(cm)
0.2
-4
0.0
-0.8
0.6
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
Time = 5.34 s
0.4
摘要
y
(cm)
本文以數值方法研究在高重力場中，浮力對引燃和火
0.2
0.0
-0.8
林宗賢 蔡昇彣*
南台科技大學機械工程系
焰傳播之效應。引燃開始於燃料中央，造成兩個朝相
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
x (cm) Reference Vectors (cm/s)
80
反方向傳播之火焰。藉由改變不同的重力，也因此改
變 Damkohler number，在 1 到 7 倍的正常重力場和
Fig. 6. Sequence for the blow off extinction process.
23.3%的氧濃度環境中，研究 7 種薄燃料的火焰。引
Shown are the reaction rate contours in case of 5 times
燃延遲時間隨重力場增加而微小的增加。研究發現火
normal gravity. The contours shown are the quantity of
焰傳播速度會因 Damkohler number 效應，隨重力的
take log10.
增加而減少。在重力等於 4g 的時候，火焰會慢慢的
減速最後停滯。在重力等於 5g 的時候，預測到火焰
將在短時間的停滯後熄滅。較大的重力將伴隨著較弱
的火焰結構和火焰傳播速度。由於在高重力環境下，
燃氣駐留時間減少，將導致火焰減弱且溫度下降，甚
至使火焰熄滅。
關鍵字: 重力 、