行政院國家科學委員會補助專題研究計畫
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對衝水霧流與地板上固體燃料火焰的交互作用
Interaction Between Opposite Water Mist Flow and Flame Over a Solid Fuel on the
Floor
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計畫編號：NSC 94－2212－E－218－015－
執行期間： 94 年 8 月 1 日至 95 年 7 月 31 日
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執行單位：南台科技大學機械工程系暨研究所
中
華
民
國
95 年
10 月
16 日
中文摘要
large amount of heat from the flame. It was
found that, increase the mist concentration
本研究在建立二維的暫態燃燒數值模式，研
究在靜止正常重力狀態下，置於地板上的固
體燃料火焰，受流場中的水霧濃度含量增加
與水霧液滴穿透流場到達燃料表面而冷卻
燃料的影響，使火焰溫度下降而導致熄滅的
熄滅機制，建立數值模式。數值模式中加入
水蒸汽的物種方程式，用以估計水霧吸熱蒸
發後，流場中水蒸汽濃度的變化，由於水蒸
汽濃度的增加不止稀釋了火焰中燃料和氧
的濃度，還吸收了大量的燃燒熱。研究發
results the flame size shrike and the flame
temperature decrease. The flame stick on the
fuel surface and the flames tip collapse in one
as the flame spread rate decrease. Further
increase the concentration of the mist, the
flame extinction phenomena occurred when
the critical mist concentration reaches.
現，在水霧通過火燄時吸收大部分的燃燒
熱，因而使火燄尺寸縮小和溫度降低，隨水
霧濃度的增加，火焰傳播速率減慢，兩火燄
尾端倒塌而結合在一起，火燄縮收而貼緊在
2. Introduction
燃料表面，達臨界水霧濃度時地板上燃燒火
燄發生息滅現象。
關鍵詞：固體燃料、火焰、水霧濃度、熄滅
on downward flame spread over a solid thin
fuel surface. In the experimental studies,
Olson et al. [1] and Olson [2] used a
drop-tower to investigate the forced, opposed
flow and quiescent flame spread in
microgravity. The rate of flame spread was
1. Abstract
Keywords: solid fuel, flame, mist
concentration, extinction
Intense theoretical and experimental
investigations have recently been conducted
This study develops a two-dimensional
unsteady combustion model for a thin solid
fuel burning and extinction on the floor in a
quiescent, normal gravity environment. The
extinction mechanism is increase the mist
concentration and so the penetration amount
of the mist reaches the hot fuel surface, the
flame temperature decreases which eventually
cause the flame extinction. In unsteady
combustion model, vapor and oxidizer species
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
energy equations were accounted. From these
energy
equations
the
variations
of
concentration of vapor and oxidizer in the
flow field are estimated. The vapor and
oxidizer in flame not only dilute the fuel and
oxygen but also absorbs a lot of combustion
heat from the flame. The interaction with hot
air induced by the flame will occur
continuously when mist flow through the flow
field. The evaporation of the mist extracts a
experiments, Altenkirch et al. [4] investigated
the buoyancy effects on downward spreading
flames over thermally thin fuel. The parameter
variation was determined by performing flame
spread experiments in a closed chamber,
which was swung on a centrifuge to generate a
gravitational acceleration above that of the
Earth. The rates of flame spread were obtained
as the 5-cm spacing, divided by the elapsed
time, was measured using an electrical clock.
They found that an increase in the buoyancy
level caused the flame spread rate to drop until
no propagation was possible, indicating that
3. MATHEMATICAL MODEL
an increasing gravity level tends to increase
induced flow intensity such that it retards
downward flame spreading.
Lin and Chen [5] developed the
foundation of the present study, which is a
time-dependent combustion model of the
ignition of a downward flame. In this work,
attention was focused on both the solid and
gas phase response at the moments before and
after ignition. The ignition mechanism of a
two flames initiated at the center of a thin
solid fuel sheet and propagate outward from
the center in a quiescent gravitational
environment. Both the left and right flames
are opposite mode because the flame spread
and the entrained flow directions are in
opposite. Initially, the entrained flow along
the fuel surface but it turns to flow upward
due to heated in the flame zone, as shown in
the figure. In this study the gravity levels were
vertical thin solid fuel in a normal
gravitational environment, subjected to an
external radiant flux as the ignition source,
was explored. Although the rate of flame
varied above the normal gravity. The ignition
and subsequent flame spread behaviors in
elevated gravitational field were examined.
The mathematical model of the physical
spread was predicted, the flame diminished
after a short period because the burn out
regime (ash) was retained throughout the
computation time. This caused a large amount
of heat to stay at the flame tail and thus
decreased the flame spread rate.
By
problem described proceed include unsteady
gas-phase
and
solid-phase
governing
equations which coupled each other. The
governing equations are described as follows:
assuming that the ash was not retained, a
moving boundary condition to account for ash
removal was applied in this work. This latter
procedure has been found successful for the
direct simulation of a propagating downward
flame.
The main purpose of this work is to
predict the rate of flame spread and the
extinction limit of a thin fuel at various vapor
concentration using an unsteady combustion
The gas phase model consist of
two-dimensional, time-dependent continuity,
complete elliptic Navier-Stokes, energy and
species equations. The combustion is
described by a one-step overall chemical
reaction with finite rate global kinetics. The
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
model. For 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 vapor
concentration limit will be depicted. A
quantitative comparison between the results
obtained from the steady model, developed by
Duh and Chen [6] will verify the developed
time-dependent model.
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:
Figure 1 shows schematic diagram of
2.1 Governing Equations
ms  
(1)
 s
E
 A s  s exp( s ).
t
Ts
and for energy conservation:
s
Ts
 Ts
 s
 msL  1  CTs  1
t
x 2
2

T

 qex .
 Pr Gr y w
(2)
2.2 Boundary and Initial Conditions
I. Boundary conditions in dimensionless
form are, for gas phase:
At x=xmin and x=xmax:
u  0, v  0, T  1, YF  0, YO  YO , P  P .
(3)
At y=0:
YF
Pr Le Gr y

w
(4)
mw YOw 
YO
Pr Le Gr y
detail computational procedure can be referred
to Ref [5]. A non-uniform grid of exponential
distribution in the gas phase was used with the
grid points being concentrated near the
gas-solid interface, where ignition is likely, to
capture the significant change in the
temperatures and flow field. A grid test has
been conducted to ensure that the solutions are
independent of grid size. The grid numbers of
the entire computational domain were 238 for
x, 153 for y direction, the corresponding
nondimensional computational domain was
u  0, T  Ts , m w   w v w
mw  mw YFw 
and velocity in the full unsteady
Navier-Stokes equations in gas phase are
solved using the SIMPLE algorithm [7]. The

.
w
445.36363.21,
and
dimensional
computational area was 61.2450.16 cm2.
The
nondimensional
time
step
for
computation was 13 corresponding 0.0712 s
of the physical time.
At y=ymax:
u v T YF YO




 0, P  P .
x x x
x
x
(5)
and for the solid phase:
At x=xmin:
 s  1, Ts  1.
(6)
At x=xmax:
 s  1, Ts  1.
(7)
II. 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:
At t0:
 s  1, Ts  1.
(9)
2.3 Computational Grid
The strong coupling between pressure
3. RESULTS AND DISCUSSION
The flames shape, flow velocities vector
distributions and temperature contours after 2
s of ignition occurs at various vapor
concentration are shown in the Figure 2 and
Figure 3, respectively. As shown in the figures,
the flame structure in zero vapor concentration
is strongest because the flame length and
flame temperature are greatest. While the
flame structure in 0.3 vapor concentration is
weakest because the flame length and
temperature are weakest. The weaker of the
flame is due to the decrease of the fuel
concentration caused by the greater of the
vapor concentration. This can be confirmed
from the YH 2 O =0.3 plot in Figure 2 in which
the buoyant flow velocity vectors are the
biggest compare to the other cases. The
maximum buoyant flow velocity in YH 2 O =0.3
case within the region show in the plot is
about 236 cm/s compare to the that in
YH 2 O =0.0 case of 137 cm/s. The extinction
The temperature and flame length in zero
vapor concentration were greatest indicated
that it was the strongest flame. In the case of
process in YH 2 O =0.43 case is illustrated in
YH 2 O =0.43, the temperature and flame size
Figure 4 and Figure 5. Figure 4 shows enlarge
view for the sequence of gas-phase fuel
reaction rate during the extinction process
while Figure 5 shows enlarge view for the
sequence of gas-phase temperature. At vapor
concentration = 0.43 the vapor is strong
enough such that the fuel vapor resident time
in the flame is too short for exothermic
were lowest indicated that it was the weakest
flame. The extinction may occur for flame
propagating time greater than 6 s. At
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
reaction decreases
cause the flame
temperature drops. The flat flame shrinks and
the temperature drops continuously to become
a point flame and disappear eventually.
as shown in Figure 4 at 4.70 s. Meanwhile, the
amount of heat release from the chemical
reaction reduced cause the flame temperature
drops as shown in Figure 5 at 4.70 s. Finally,
the flat flame shrinks and the temperature
drops continuously to become a point flame
5. REFERENCES
[1] S. L. Olson, P. V. Ferkul and J. S. T’ien,
Twenty-Second Symposium (international)
on Combustion, pp. 1213-1222, The
Combustion Institute, Pittsburgh, 1988.
and disappear eventually, as shown at 5.06 s
and 5.34 s in Figure 4 and Figure 5,
respectively.
YH 2 O =0.43 the left and right straight flames
shrinks into one flat flame after some
stagnated times at 4.70 s. Meanwhile, the
amount of heat release from the chemical
4. CONCLUSIONS
A numerical study was made for the
vapor concentration that is the mist effects on
the ignition and subsequent flame spread over
a thin solid fuel flatly lay on the floor in
various vapor concentration environments. In
[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
this present time-dependent model we can
readily simulate the flame extinction behavior
over a thin fuel surface.
By varying the vapor concentration we
conducted five cases of flame spread over a
thin solid fuel at 23.3 % oxygen mass
concentration. The computational results
shows that the flame extinction was predicted
at vapor concentration 0.43 on 4.77 s after
ignition occurs.
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, Combust. Sci.
Technol., vol. 77, pp. 291-305, 1991.
[7] S. V. Patankar, Numerical Heat Transfer
and Fluid Flow, McGraw-Hill, New York,
USA, 1980.
[8] Nakamura, Y., Yamashita, H., and Takeno,
T., Combust. Flame 120:34 (2000).
[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).
y
Gravity
Flame
Entrained flow
Entrained flow
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.
Table 1
Gas Phase Governing Equations




   u   v               S
t
x
y
 x  x  y  y 
Equation

Continuity 1
x-Mom.
y-Mom.
Energy
u
v
T
Fuel
YF
Oxidizer
YO
Vapor
YH2O
2.5
2.0
YH 2 O =0
1.5

S

0


Gr

Pr Gr

Pr GrLe

Pr GrLe

Pr GrLe

 
p
 Sv  
y
   F
F
 q
YH 2 O =0.0
y
(cm)
1.0
0.5
0.0
p

 Su
x
Gr
YH 2 O =0.1
0.0
2.5
2.0
YH 2 O =0.2
YH 2 O =0.3
1.5
y
(cm)
1.0
0.5
0.0
-1.5
-1.0
-0.5
0.0
x (cm)
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 
1.0
1.5
235.8352282
F

F
f
-1.5 -1.0 -0.5 0.0
0.5
0.5
1.0
1.5
Reference Vectors (cm/s)
x (cm)
Fig. 2. Flames and flow velocity vector
distributions at various vapor concentration
after 2 s of ignition occur. The flame shapes
shown are the fuel reaction rate contour of
10-4 g/cm3/s.
2.5
YH 2 O =0.0
YH 2 O =0.1
2.0
0.6
1.5
Time = 4.70 s
y
(cm)
0.4
1.0
y
(cm)
0.5
0.0
2.5
0.2
YH 2 O =0.2
YH 2 O =0.3
0.0
-0.8
0.6
2.0
1.5
-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
y
(cm)
0.4
1.0
y
(cm)
0.5
0.2
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
x (cm)
Fig. 3. Temperature distributions at
various vapor concentration after 2 s of
ignition occur.
0.0
-0.8
0.6
0.4
0.4
0.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Time = 4.77 s
-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
-0.6
-0.4
-0.2
x (cm)
process at YH 2 O = 0.43. Shown are the
-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
0.0
0.2
0.4
0.6
0.8
Time = 5.06 s
y
(cm)
0.2
-4
-0.6
-0.4
-0.2
Time = 5.34 s
0.4
y
(cm)
0.2
0.0
-0.8
700
800
900
Fig. 5. Sequence for the extinction
0.2
0.0
-0.8
0.6
Time = 5.06 s
0.8
y
(cm)
0.4
0.0
0.2
0.2
0.0
-0.8
0.6
-0.2
y
(cm)
Time = 4.70 s
y
(cm)
0.4
-0.4
0.2
0.6
0.0
-0.8
0.6
-0.6
y
(cm)
0.0
-0.8
0.6
0.4
1400
1.5
-0.6
-0.4
-0.2
x (cm) Reference Vectors (cm/s)
80
Fig. 4. Sequence for the extinction
process at YH 2 O = 0.43. The contours shown
are the quantity of take log10.
temperature contours.