EFFECTS OF AMBIENT OXYGEN ON IGNITION OVER A
VERTICALLY THIN SOLID FUEL
By
TZUNG-HSIEN LIN
Associate Professor
Department of Mechanical Engineering,
Southern Taiwan University of Technology, Yung Kang, Tainan,
Taiwan 710
Full-length paper
Corresponding Author: Tzung-Hsien Lin
Department of Mechanical Engineering
Southern Taiwan University of Technology,
1 Nan Tai Road, Yung Kang City, Tainan County, Taiwan 710
Telephone : 886-6-2533131 Ext 3542
FAX
: 886-6-2425092
E-mail
: thlin@mail.stut.edu.tw
ABSTRACT
A numerical study on the spontaneous ignition process of a vertically
placed solid thin fuel heated by external radiation in normal gravity,
quiescent environment was made. The ambient oxygen mass fraction is
varied from 35 % down to the non-ignition limit. It was found that in the
non-ignition case, the maximum reaction rate and maximum temperature
in gas-phase were too weak to onset the combustion reaction. For the
ambient oxygen concentration greater than 17 % the ignition and
transition to flame spread all are achievable. The low ambient oxygen
concentration has larger and stronger ignited flame than the high ambient
oxygen concentration at the instant of ignition occurs. The flame grows
rate was found faster than the purely opposed and purely concurrent
spread flames. Although it has smaller ignited flame, the propagating
flame in high ambient oxygen concentration becomes longer and stronger
in structure than the low oxygen flame. The results reveal that, the flame
grows rate in transition increase with the increasing in ambient oxygen
concentration.
NOMENCLATURE
A s pre-exponential factor for fuel pyrolysis
B
frequency factor for gas-phase reaction
C p average specific heat for gas mixture
Cs
specific heat for solid fuel
D
species diffusivity
Da Damkohler number
E
activation energy for gas phase reaction
f
stoichiometric oxidizer/fuel mass ratio
g
gravitational acceleration
Gr Grashof number
k
thermal conductivity
Le Lewis number
m s fuel mass burning rate
P
pressure
Pr
Prandtl number
q
heat of combustion per unit mass of fuel
R
universal gas constant
S
surface radiant heat loss parameter
T
temperature
t
time
u
velocity parallel to the fuel surface
v
velocity normal to fuel surface
Vr reference velocity, g    f    * /  * 
1/ 3
x
distance along fuel surface
y
distance normal to fuel surface
Y
mass fraction

thermal diffusivity

*
thermal diffusion length,  / Vr

emissivity

dynamic viscosity

density of gas phase

Stefan-Boltzmann constant

fuel-bed half thickness
 F gas phase reaction rate

Overhead
dimensional quantities
Superscripts
*
reference state

flux
Subscripts
F
gaseous fuel
f
adiabatic flame temperature
O
oxidizer
s
solid phase
sf
burnout state
w
fuel wall

ambient conditions
max maximum boundary
min minimum boundary
ex
external
e
Earth
INTRODUCTION
There are many environmental factors that can affect the
spontaneous ignition behavior of a solid material heated by external
radiant flux. These factors including the intensity or/and distribution of
incident radiant source, magnitude of force or/and natural convective
flow velocity, orientation of solid fuel surface, strength of ambient
pressure and concentration of ambient oxygen. To understand the effects
of these factors are important for fire protection because ignition is an
initiation of fire.
Literatures investigated the ignition of a solid fuel in normal gravity
can be brief review as follows: In the study of Alvares and Martin (1971)
and of Ohlemiller and Summerfield (1971), the effects of atmospheres,
oxygen concentration, incident flux and inert diluents on ignition delay
time were investigated. The results indicated that the ignition delay time
decreases monotonically as the total pressure, incident flux and oxygen
concentration increase. Kashiwagi (1979a, 1979b, 1981) experimentally
studied the radiative ignition mechanism of both horizontally and
vertically placed materials. The investigation indicated that the absorption
of external radiation by the vaporized fuel in gas phase will raise its
temperature above the fuel surface and can cause ignition. Kashiwagi
(1982) further indicated that under the same external radiant flux, the
ignition delay time was shorter for the horizontal fuel than that of the
vertical fuel; the effect of sample orientation on ignition was reported.
Mutoh, et al. (1978) and Yoshizawa and Kubota (1982) experimentally
observed the radiative ignition of a horizontal sample. The ignition
location and ignition delay time were examined under various radiant
fluxes. Both experiments shown the ignition occurred at the axis
symmetric line in gas phase above the sample surface.
On the other hand, many theoretical analyses limited in the
one-dimensional model such as Kashiwagi (1974), Kindelan and
Williams (1977), Gandhi and Kanury (1988), Amos and Fernandez-Pello
(1988), Tzeng et al. (1990), and Park and Tien (1994). Whereas, Kushida
et al. (1992) take the advantage of neglect the natural convection effect to
simplify
the
formulation,
an
two-dimensional
axisymmetric,
time-dependent model but with potential flow assumption, were used to
investigate the ignition in microgravity environment. In the work of
Nakabe et al. (1994) and of Mcgrattan et al. (1996), extend that work to
investigate the effects of ambient oxygen, external radiant flux
distribution, and slow forced flow on ignition delay time and subsequent
transition to flame spread. The results indicated that the ignition delay
time decreases with the increasing in peak flux of external radiation. A
three dimensional model used by Kashiwagi et al. (1996) to study the
effects of slow forced wind on ignition and transition to flame spread in
microgravity. The results were compared with the experiments obtained
in drop tower, and indicated that there are no significant effects of slow
wind on ignition delay time. Nakamura et al. (2000) investigated the
effects of gravity and ambient oxygen on ignition of a horizontally placed
solid fuel. Two ignition types were identified over the whole range of
ambient oxygen and gravity level. Lin and Chen (1999), and Lin and
Chen (2000) developed time-dependent models to investigate the ignition
of thin and thick solid fuel in normal gravity, respectively. The ignition
processes were described. Lin (2001) extends the former model to study
the buoyant flow effect on ignition delay time and flame spreads behavior
in elevated gravity. The model results described the flame blowoff
extinction process and indicated that the ignition delay time increases
with the buoyant flow brought by the gravity level.
In light of the above literature review, it is revealed that the effect of
ambient oxygen on the ignition behavior of a vertical sample in normal
gravity has not been exploded. When a horizontally placed sample is
heated, the pyrolysis fuel vapor eject into the oxygen atmosphere and
start to mixed with the ambient oxygen by means of the mass difussion
and convection. Since the fuel vapor eject direction is coincide with that
of the buoyant flow, the mixture rise as a vertical plume. The ignition
point could either at the tip or inside of the plume (Nakamura et al., 2000).
Whereas, for a vertically placed sample, the eject fuel vapor is in
transverse direction of the buoyant flow. In this situation a hot boundary
layer of mixture adjacent to the surface is formed instead of a hot plume.
Under this circumstance the ignition behavior is quite different from the
former. The main purpose of this study is to investigate numerically the
effects of ambient oxygen on the ignition behavior of a vertically oriented
thin solid fuel in normal gravity. The gas phase model including the
time-dependent, two-dimensional mass, momentum, energy and species
conservation equations with second order reaction kinetics describe the
combustion of the fuel gases. The solid phase consists of time-dependent
mass and energy balance equations with Arrhenius equation describe the
solid pyrolysis. The physical problem will be described as follows.
MATHEMATICAL MODEL
Figure 1 shows a schematic illustration for the ignition of a vertical
thin fuel sample heated by an external radiant heat source in normal
gravity. At time zero, a Gaussian distribution radiant heat flux with peak
value 5 W/cm2 and half width 0.5 cm is applied in the middle of the
sample with the center aimed at the original of the coordinate. The
thermal degradation of the solid begins as the surface temperature reaches
its pyrolysis value through the absorption the external radiant heat. The
evolved fuel vapors mix with the ambient oxidizer to form a combustible
mixture of boundary layer due to the buoyancy. If the local temperature in
the boundary layer is high enough to onset the runaway chemical reaction,
ignition occurs. This transient process is analyzed by solving the time
dependent conservation equations in the solid and the gas phases
simultaneously. The numerical model used in this study is basically the
same as previous (Lin and Chen, 1999), but here we have somewhat
modified to suit the configuration of ignition in the middle of an infinite
vertical sample and also account for the solid surface radiative heat loss.
This model solves the system of governing equations in
dimensionless form. For the choice of scaling parameters and
non-dimensionalized procedures, refer to Lin and Chen (1999). The
dimensionless
gas
phase
governing
conservation
equations
are
summarized in Table 1. The dimensionless solid phase governing
equations can be expressed as follows:
Mass Conservation
ms  
s
E
 A s s  exp( s ) .
t
Ts
(1)
Energy Conservation
Ts
 2 Ts

T







s
 s

m

L

1

C
T

1


s
s
t
x 2
 Pr Gr y w
 qex 
S
1  Ts4 .

(2)
The non-dimensional form of external radiant heat flux, q ex , can be
expressed as
q ex  Q ex exp(-x2).
(3)
where Q ex is the non-dimensional peak value of the external radiant
heat flux, x and  are the non-dimensional half width, and the shape
constant of the Gaussian distribution, respectively. All of these quantities
are various in different oxygen concentration due to the variation in
thermal length brought by the change of ambient oxygen concentration.
The expression of Q ex can be found in the non-dimensional parameters
list in Table 2.
The governing equations are subjected to the following boundary
and initial conditions.
I. Boundary conditions in dimensionless form are:
Gas phase
At x=xmin:
u  0, v  0, T  1, YF  0, YO  YO .
(4)
At x=xmax:
u v T YF YO




 0 , P  P .
x x x
x
x
(5)
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
.
(6)
At y=ymax:
u  0,
v
 0, T  1, YF  0, YO  YO , P  P .
y
(7)
Solid phase
At x=xmin:
 s  1, Ts  1 .
(8)
At x=xmax:
 s  1, Ts  1 .
(9)
II. Initial conditions in dimensionless form are:
Gas phase
At t0:
u  0, v  0, T  1, YF  0, YO  YO , P  P .
(10)
Solid phase
At t0:
 s  1, Ts  1 .
(11)
The strong coupling between pressure and velocity in the full
unsteady Navier-Stokes equations are solved using the SIMPLE
algorithm (Patankar, 1980). In each time step, iteration of both the
gas-phase and solid-phase equations are calculated separately, and the
solid phase is coupled with the gas phase through the linkage of the
conductive heat feed back from the gas phase to the solid phase; as can
been seen in the solid phase energy balance equation, Equation (2). The
numerical calculations began when the external radiant heat flux applied
on the sample at time zero. The solid phase calculation was carried out
first to obtain the pyrolysis mass flux, the fuel wall blowing velocity, and
the surface temperature which to be used as the boundary conditions in
the gas phase calculation. After the convergence of the solid phase
calculation, the gas phase calculations were carried out with the updated
interfacial boundary conditions that were the previous values of the
pyrolysis mass flux and the surface temperature. When the gas phase
calculations were completed, the solid phase variables were also updated
then went into the next time step to start with the solid phase calculation.
A non-uniform grid of exponential distribution in the gas phase was
used with the highest concentration of grid point near the gas-solid
interface, where the ignition will possible occurred, to capture the
dramatically change in the temperature and flow field. The grid sizes are
chosen according to the optimization between the solution resolution and
the requirements for computational time and memory space. The selected
non-dimensional
computational
domain
is
143.859.7, and
the
corresponding grid points is 19640. The non-dimensional time step in
each computed oxygen concentration case is chosen such that the
corresponding physical time step are equal in all cases, that is 0.137 s.
RESULTS AND DISCUSSION
Table 3 lists the properties for both gas and solid phase used in this
study together with the reference they are adopted from. The gas-phase
specific heat C p , density  * , thermal diffusivity  * , thermal
conductivity k * , and viscosity  * are evaluated at the reference
temperature T * , i.e., T *  ( Tf  T ) / 2 . These gas-phase thermal
properties vary with the ambient oxygen concentration, because the
varying in the adiabatic flame temperature Tf . Numerical computations
were conducted for range of the ambient oxygen percentages from 15 %
to 35 % with an increase increment of 2 %. The lower limit was a case
that the ignition does not occur, while the upper limit was chosen that the
ignition delay time no longer significant change as the oxygen percentage
increase. To illustrate the trend of ambient oxygen concentration effects
on the ignition behaviors, we demonstrate five different oxygen
concentrations computation results, that is, 15 %, 17 %, 21 %, 27 %, and
35 %.
Non-ignition case
The distributions of gas-phase temperature and gas-phase fuel
reaction rate at four different times for 15 % ambient oxygen
concentration are shown in figure 2 and figure 3, respectively. As shown
in figure 2, the maximum gas-phase temperature region moves upward
due to the consumption of the solid fuel and remains at a constant value
about 660 K as time increases. Figure 3 shows corresponding reaction
rate at four different times. It can be seen that the maximum reaction rates
also remains at a constant value of about 0.30910-4 g/cm3/s in all times.
In this study we defined, as in the previous studies (Ferkul and T’ien
(1994), Nakabe et al. (1994)), the gas phase reaction rate of 10-4 g/cm3/s
contour as a visible flame boundary. Thus the maximum temperature and
maximum reaction rate are relatively weak, and the vigorous chemical
reaction and rapid heat release, which characterize the ignition, do not
occur in all times. There is no flame appears, therefore, this is a
non-ignition case due to a low oxidizer concentration which can not
supply the fuel vapor to react to reach the combustion reaction.
Effects of ambient oxygen
The premixed mixture distributions at the instant before ignition
occur of four different ambient oxygen concentrations are shown in figure
4. It can be seen that, low ambient oxygen percentage has larger amount
of pre-ignition premixed mixture than that of high ambient oxygen. This
is because of the lower ambient oxygen concentration duration a larger
ignition delay time, which needs for the mixture to react to reach the
required temperature and reaction rate that can on set the ignition. As a
consequence, a larger amount of fuel gas evolved to accumulate to form a
larger amount of premixed mixture.
Figure 5 shows the effect of ambient oxygen concentration on
ignition delay time. The ignition delay time decreases exponentially with
a increasing in the ambient oxygen concentration. The same trend has
been found in one-dimensional model of nature convective ignition (Park
and Tien (1994)), as well as in zero-gravity ignition over a horizontal thin
fuel (Nakamura et al. (2000)). The ignition delay time remains almost
constant as the ambient oxygen concentrations higher than 35 %. The
existence of this minimum ignition delay time is mainly attributed to the
time required for the solid to absorb the external radiation to reach the
pyrolysis temperature.
The distributions of gas-phase fuel reaction rate and flow velocity
vector, temperature, and fuel and oxygen mass fraction at the instant of
ignition are shown in figure 6-8, respectively. Each figure consists of four
plots in different ambient oxygen concentration. At this instant, the rapid
increase in reaction rate release a large amount of heat result in a sudden
gas expansion and sudden temperature increase in gas phase. According
 F =110-4
to the visible flame definition mentioned above (reaction rate 
g/cm3/s), the flame shape at the instant of ignition of various ambient
oxygen concentrations are shown in figure 6. As show in figure 6, lower
ambient oxygen concentration has longer ignited flame length because of
larger amount of premixed mixture has been reacted which accumulated
before the ignition occur (see figure 4). For the same reason, the lower
ambient oxygen concentration has bigger and stronger ignited
temperature distribution because of a larger amount of mixture has been
reacted and a larger amount of heat has been released, as can be seen in
figure 7. Because of the ignition delay time does not change significant
for the ambient oxygen concentration higher than 35 %. The ignite flame
temperature and flame size does not change significant for the ambient
oxygen concentration higher than 35 %.
The distributions of fuel and oxygen mass fraction at the instant of
ignition in figure 8 are quite different from those of the pre-ignition in
figure 4. In figure 4, before ignition occurs, the fuel gas and the oxidizer
are mixed as a mixture whereas in figure 8, at the instant of ignition, we
can distinguish the fuel gas side from the oxidizer side.
Propagating flame
Figure 9 and 10 show the reaction rate and temperature contours of
propagating flame in four different ambient oxygen concentrations at
time of 2.055 s after the ignition occurs. All flame fronts propagate
beyond the width of the external radiation heat source (0.5 cm) at this
moment. These indicate that the transition from ignition to flame spread
are achievable for all cases. Compare to the concurrent flame (Chen and
Hou, 1991) and opposed flame (Duh and Chen, 1991), it is found that the
flame structure are longer and stronger. This is because of the flames are
initiated at the middle of fuel sample, and then spread not only in opposed
but also in concurrent direction with the buoyancy flow which result in a
longer pyrolysis length. Moreover, the flame grows faster than those in
the purely opposed or concurrent flame when in the transition process
because of the larger amount of evolved fuel gas.
On the other hand, high oxygen concentration flame has longer and
stronger flame structure than that in low oxygen concentration although it
has weaker and smaller ignited flame. This can be seen in figure 6 and
figure 9, in case of 35 % oxygen, the flame length reaches about 11 cm,
and the flame temperature reaches a value of 2600 K within 2.055 s of
flame grows times. It also indicates that, the flame grows rate increases
with the increasing in ambient oxygen concentration. Flame grows much
faster in high oxygen concentration than in low oxygen concentration.
CONCLUTIONS
Ignition and subsequent transition to flame spread over a vertical
solid thin fuel heated by external radiation has been investigated
numerically. The external radiant heat flux is Gaussian distribution to
model the ignition heat source in laboratory, and applied at the middle
of the longitude of the fuel sample at time=0 s.
By varying the ambient oxygen concentration as study parameter, a
non-ignition case, 15 %, was found. In this case, the ambient oxidizer
was too dilute to react the fuel gas to reach the combustion reaction rate,
thus the sudden gas expansion and rapid heat release, which
characterize the ignition were not occur. For the ambient oxygen
concentration greater than 17 % the ignition and transition to flame
spread all are achievable. It was shown that, because of the greater
ignition delay time, the low ambient oxygen concentration has larger
amount of pre-ignition mixture accumulate near the fuel surface before
ignition occur, which result in a larger and stronger ignited flame than
the high ambient oxygen concentration at the instant of ignition occur.
The flame grows rate was found faster than the purely opposed and
purely concurrent flames. After 2.055 s grow times, the propagating
flame in high ambient oxygen concentration becomes longer and
stronger in structure than the low oxygen flame although it has smaller
ignited flame. The results reveal that, the flame grows rate in transition
increase with the increasing in ambient oxygen concentration.
ACKNOWLEDGMENTS
The author thanks the National Science Council of Taiwan for
financially
supporting
this
research
under
contract
no.
NSC
90-2212-E-218-006.
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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



Gr

Gr

S
0

 
p
 Su  
x
  f

p
 Sv
y
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 
Table 2
Nondimensional Parameters
Symbol
Parameter group
Value
As
A s  * / Vr2
variable
C
Cp / Cs
0.798
E
E / R T
35.196
Es
E s / R T
Gr
g (    f )  3 /  * 
ks
ks / k*
0.781
L
L / Cs T
-2.005
Le
/D
1.000
Pr
/
0.705
Q ex
  * / s T Vr2 Cs 
Q ex
variable
q
q / Cp T
45.349
S
  * T3 / k * Vr
variable
t
tVr / 
variable

T * / T
5.235

Cs s Vr / k *
Variable
*
50.685
*2
Variable
Table 3
Gas and solid properties values
Symbol
Units
Value
Reference
As
cm/s
1.001010
Frey and T’ien (1979)
B
cm3/mols
1.001012
Duh and Chen (1991)
Cp
J/gK
f (T*)
Natl. Bur. Stan. (1955)
Cs
J/gK
1.260
Altenkirch et al. (1980)
E
J/mol
8.720104
Duh and Chen (1991)
Es
J/mol
1.255105
Frey and T’ien (1979)
f

1.185
Altenkirch et al. (1980)
k*
W/cmK
f( T * )
Natl. Bur. Stan. (1955)
ks
W/cmK
1.25510-3
Frey and T’ien (1979)
L
J/g
753.0
Altenkirch et al. (1980)
q
J/g
1.674104
Altenkirch et al. (1980)
R
J/molK
8.314
Natl. Bur. Stan. (1955)
T
K
298
Altenkirch et al. (1980)
*
cm2/s
f( T * )
Natl. Bur. Stan. (1955)


0.92
Hottel, Sarofim (1967)
*
g/cms
f( T * )
Natl. Bur. Stan. (1955)
*
g/cm3
f( T * )
Natl. Bur. Stan. (1955)
 s
g/cm3
0.750
Altenkirch et al. (1980)

cm
9.810-3
Altenkirch et al. (1980)