ON THE BLOW OFF EXTINCTION OF A DIFFUSION FLAME
OVER A THIN SOLID SHEET
Effects of elevated gravity on propagating flame over a thin solid fuel sheet
By
TZUNG-HSIEN LIN
Associate Professor
Department of Mechanical Engineering,
Southern Taiwan University of Technology, Yung Kang, Tainan 710,
Taiwan
Full-length paper
Corresponding Author: Tzung-Hsien Lin
Department of Mechanical Engineering
Southern Taiwan University of Technology,
1 Nan Tai Street, Yung Kang, Tainan 710, Taiwan
Telephone : 886-6-2533131 Ext 3542
FAX
: 886-6-2425092
E-mail
: thlin@mail.stut.edu.tw
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 increasing
gravity within the computational range. 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 after
few stagnant time. The greater the gravity the weaker the flame structure
as well as the rate of flame spread. Because of the short fuel vapor
resident time in high gravity environment, the fuel reaction rate reduced
cause the flame shrike and temperature drops even to reach extinction.
INTRODUCTION
Intense theoretical and experimental investigations have recently been
conducted 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 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 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 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 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 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 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 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 buoyancy on both the ignition delay
time and the flame spread behavior over a horizontal thin solid fuel. 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 blowoff 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.
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 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 varied above the normal
gravity. The ignition and subsequent flame spread behaviors in elevated
gravitational field were examined.
The mathematical model of the physical problem described proceed
include unsteady gas-phase and solid-phase governing equations which
coupled each other. The governing equations are described as follows:
Governing Equations
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
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  
s
E
 A s s  exp( s ) .
t
Ts
(1)
and for energy conservation:
Ts
 2 Ts

T




s
 s

m

L

(
1

C
)(
T

1
)


 qex
s
s
t
x 2

y
 Pr Gr
w
(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:
u  0, T  Ts , mw   w v w
mw  mw YFw 
mw YOw 
Y

 F
Pr Le Gr y
Y

 O
Pr Le Gr y
w
w
.
(4)
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 .
II. Initial conditions in dimensionless form are, for the gas phase:
(7)
At t0:
u  0, v  0, T  1, YF  0, YO  YO , P  P
(9)
and for the solid phase:
At t0:
 s  1, Ts  1 .
(10)
Computational Grid
The strong coupling between pressure and velocity in the full
unsteady Navier-Stokes equations in gas phase are solved using the
SIMPLE algorithm [7](Patankar, 1980). The detail computational
procedure can be referred to Ref [5](Lin and Chen 1999). 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
dimensional
computational
computational
domain
area
was
was
445.36363.21,
61.2450.16
cm2.
and
The
nondimensional time step for computation was 13 corresponding 0.0712 s
of the physical time.
RESULTS AND DISCUSSION
The ignition delay time as a function of gravity level was shown in
Figure 2. The ignition delay time was defined as the time elapse from the
external radiation applied to the instance of local maximum fuel reaction
rate exceeds 110-4 g/cm3/s. The choice of this ignition criterion is
because of we defined this value of contour in fuel reaction rate
distribution as a visible 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 (2000)[8] for
gravity near normal gravity.
Figure 3 shows the time histories of both right and 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 model the rate of flame spread can obtain from the slope of the loci
of flames propagate. As shown in the figure, the rate of flame spread in
1g environment is about 0.29 cm/s but it decrease with the increasing in
gravity due to the Damkohler number effects (Fernandz-Pello and Hirano
1983)[9]. Comparing to the downward flame spread (Altenkirch et al
1980[4], Duh and Chen 1991[6], Lin 2001[10]), the rate of flame spread
in this horizontal direction is faster then that in downward. This result
coincides with the experimental observations in the work of Hirano et al.
(1974)[11]. Also, the rate of flame spread in horizontal direction obtained
from this present unsteady flame model is near that obtained from the
steady flame model (Chen and Chan 1992)[12], which using the
integration of mass blowing rate from the solid surface to calculate the
rate of flame spread. The case of 4-g in Figure 3 shows that the rate of
flame spread was decelerated and eventually reaches zero after 4 s; the
flame fronts almost no further advance, in other words, flame was
stagnated. This is because of that, in this buoyancy level, the gas
residence time becomes too small for the completion of the exothermic
chemical reaction to maintain the flame spread process at a constant rate,
the blow off extinction may occurs 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 Figure 7 at 4.70 s. Finally, the flat
flame shrinks and the temperature drops continuously to become a point
flame and disappear eventually, as shown at 5.06 s and 5.34 s in Figure 6
and Figure 7, respectively.
CONCLUSIONS
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 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 flame
and disappear eventually.
ACKNOWLEDGMENTS
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.
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.
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, 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).
Table 1
Gas Phase Governing Equations




   u   v               S
t
x
y
 x  x  y  y 
Equation
Continuity

1
x-Momentum
u
y-Momentum
v
Energy
T
Fuel
YF
Oxidizer
YO


S
0
p

 Su
x

Gr

Gr


 
p
 Sv  
y
  F
F
q
Pr Gr

F

Pr Gr  Le

F
f 
Pr Gr  Le
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 