Fire Safety Journal 71 (2015) 279–286
Contents lists available at ScienceDirect
Fire Safety Journal
journal homepage: www.elsevier.com/locate/firesaf
Self induced buoyant blow off in upward flame spread on thin solid
fuels
Michael C. Johnston a,n, James S. T'ien a, Derek E. Muff a, Xiaoyang Zhao a, Sandra L. Olson b,
Paul V. Ferkul c
a
Case Western Reserve University, Cleveland, OH, USA
NASA Glenn Research Center, Cleveland, OH, USA
c
National Center for Space Exploration Research, Cleveland, OH, USA
b
art ic l e i nf o
a b s t r a c t
Article history:
Received 7 May 2014
Received in revised form
15 October 2014
Accepted 23 November 2014
Upward flame spread experiments were conducted on long thin composite fabric fuels made of 75%
cotton and 25% fiberglass of various widths between 2 and 8.8 cm and lengths greater than 1.5 m.
Symmetric ignition at the bottom edge of the fuel resulted in two sided upward flame growth initially. As
flame grew to a critical length (15–30 cm depending on sample width) fluctuation or instability of the
flame base was observed. For samples 5 cm or less in width, this instability lead to flame blow off on one
side of the sample (can be either side in repeated tests). The remaining flame on the other side would
quickly shrink in length and spread all the way to the end of the sample with a constant limiting length
and steady spread rate. Flame blow off from the increased buoyancy induced air velocity (at the flame
base) with increasing flame length is proposed as the mechanism for this interesting phenomenon.
Experimental details and the proposed explanation, including sample width effect, are offered in the
paper.
& 2014 Elsevier Ltd. All rights reserved.
Keywords:
Buoyant blow off
Material flammability limits
Upward burning limit
One-sided extinction
Flame spread
SIBAL fuel
1. Introduction
The upward flame spread configuration is often used as a metric for quantifying the overall flammability of materials and
merits further in depth study of the characteristics and boundaries
of flammability. For example, NASA material flammability flight
qualification test NASA-STD-6001 Test #1 [15] and Underwriters
Laboratories test UL-94V [23] both utilize upward flame spread
geometries similar to the ones used in this work. The result of
NASA Test #1 is a simple pass/no-pass criteria based on whether
the flame damaged region propagates upwards further than 15 cm
on a 5 cm 30 cm sample. The results of UL-94V are categorized
based primarily on duration of burning. Neither of these tests take
into account detailed mechanisms of flame propagation or extinction and are assumed to be a worst case flammability configuration based on the fact that gravity tends to accelerate flame
spread in the upward direction.
It has been previously shown that sample width can have a
significant effect on the characteristics of upward flame spread,
including flame size, heat generation rate, and spread rate
n
Correspondence to: Glennan Bldg. MS 418, Case Western Reserve University,
10900 Euclid Avenue, Cleveland, OH 44106, USA.
E-mail address: michael.c.johnston@case.edu (M.C. Johnston).
http://dx.doi.org/10.1016/j.firesaf.2014.11.007
0379-7112/& 2014 Elsevier Ltd. All rights reserved.
[6,7,10,14,17,19,21]. It should be clear that sample width may also
affect the flame extinction limits despite the fixed width criteria in
standardized flammability testing methods. In this work, upward
flame spread tests were conducted in normal gravity using a
special composite fabric fuel. Several sample widths were used. An
unexpected but very interesting phenomenon, i.e. self-induced
flame extinction when the flame reached a certain length, was
observed in many of the tests. The observation and a proposed
interpretation are discussed below.
2. Material and methods
The experimental setup is shown schematically in Fig. 1. This
configuration mimics that of the NASA STD-6001 Test #1 and UL94V. The thin fuel is sandwiched between four parallel stainless
steel sample holders 0.035″ (0.889 mm) thick 2.5″ (6.35 cm)
wide with adjustable exposed sample width of 2-8.8 cm and
height up to 1.8 m. The fuel used in this experiment is unique. It is
made from a simple weave fabric consisting of thread spun with
75% cotton and 25% fiberglass strands with an area density of
0.01805 g/cm2 and is about 0.31 mm thick. As the cotton burns
away, the fiberglass component of the thread is left behind
maintaining the fuels structural integrity and shape. This inert
matrix simplifies the burning characteristics of the fuel by
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Fig. 2. (a) Unburned SIBAL fabric (left) and (b) inert fiberglass matrix after the
flame has passed (right). Ruler notches are 1/32″ (0.79 mm).
Fig. 1. (a) Experimental setup: video cameras image both front and back of the thin
fuel sample, a still image camera translates along the edge of the sample holder
with the flame. A remote camera strobe is located behind the sample pointed at an
upward angle (left). (b) Zoomed in front view shows the flame tip, pyrolysis tip, and
pyrolysis base. Smoldering of left over fuel can be seen below the pyrolysis base.
Thin black stainless steel sample holders can be seen to the left and right of the fuel
sample (right).
preventing tearing, ripping, and curling of the solids surface as
would happen with other burning materials such as paper. A detailed comparison of the burning characteristics of this fuel with
other materials is given in Ref. [8].
This custom-made fabric fuel (referred to as SIBAL), named
after the experiment for which it was originally designed Solid
Inflammability Boundary At Low-speed [4] has been studied in a
large number of careful laboratory scale experiments in a variety
of environmental conditions [4,8,11]. The pre-burned SIBAL fuel
can be seen in Fig. 2a, and after the flame front has passed the
remaining inert matrix is shown in Fig. 2b.
The leftover fiberglass matrix has been found to act as a flame
arrester since the gaps between the threads are large enough to
allow gas to pass through but smaller than the quenching diameter of the flame. This allows for the somewhat unique possibility of a one-sided flame existing on a thin fabric fuel [11]. Note
also that this fuel sample is sufficiently thin so that, in most experiments, it behaves as a thermally-thin specimen.
Fuel ignition was achieved using a 30 cm long 29 gage Kanthal
hot wire powered with 3.7 amps (about 62 W) bent into a sawtooth pattern alternating on the front and back of the fuel surface
at the free bottom edge of the fuel sample. Ignition power was
removed when a robust flame was observed.
The burning material is imaged at 30 frames per second with
two 1080p high-definition video cameras perpendicular to the
front and back surfaces of the fuel. A third high-resolution still
camera zoomed to the size of the flame views the fuel and sample
holder from the edge and moves along a track parallel to the flame
propagation. The still camera is capable of shooting an 8 frame
burst in approximately 1 s. A strobe light located on the opposite
side of the sample holder illuminates the unburned fuel vapor or
smoke and captures the instantaneous smoke field. The still
camera needs to integrate the light generated from the flame over
approximately 1/30–1/60th of a second in order to record the
image. However, the strobe illuminates the smoke field only for
about 1/1000th of a second to eliminate motion blur of the smoke.
The position of the pyrolysis front and pyrolysis base are
tracked with custom imaging software by searching for brightness
thresholds along the centerline of the fuel sample. The threshold
M.C. Johnston et al. / Fire Safety Journal 71 (2015) 279–286
281
value changes between tests depending on illumination from
flame brightness and can affect the tracked pyrolysis position by a
few pixels. However, this contributes to an uncertainty of only a
few millimeters in absolute pyrolysis position and has almost no
effect on measurement of propagation velocity.
3. Results
Fig. 1b shows the front view of an upward spreading flame over
the SIBAL fabric. Flame and solid images are recorded by the front
video camera. Pyrolysis tip and base are identified for further
computer processing. One notices that for this thin solid, the
pyrolysis base moves with the gas flame base when solid combustibles are mostly spent. A small amount of combustible residue
remains attached to the fiberglass fibers and undergoes smoldering. The percentage of fuel left for smoldering is small, less than
approximately 10% by mass (measured by microbalance in similar
tests).
Fig. 3a shows a typical case of flame ignition, growth, and upward spread of a 5-cm wide sample of our thin fabric fuel. The
position of pyrolysis front and burn out front are plotted with
respect to time on the abscissa. In the very early stages, the pyrolysis tip can be seen to propagate downstream (upwards) at an
increasing rate (curve is concave upward). Due to the physically
thin nature of the fabric used, the amount of solid fuel available to
pyrolyze is limited and the flame base moves upward when most
of the combustible is consumed. Note that during the initial
growth stage, the flame tip will accelerate upwards while the
flame base lags behind, remaining at the ignition location until the
fuel begins to burn out. At some time, depending on conditions,
the burn out zone (and therefore the flame base) will propagate
upward. If the fuel burnout rate catches up with the pyrolysis front
propagation rate, a constant flame length is reached and a steady
spread with a constant spread rate results [22]. In many normal
gravity upward tests on wide samples, steady spread may not be
observed for the available fuel height. Steady spread with a limiting flame length is easier to find for narrow samples, in low
pressure environments, in partial gravity, and in concurrent purely
forced low-velocity flow in microgravity [1,2,3,5,22].
In the present, work one side of the flame is extinguished
(blown off) during the flame growth as indicated in Fig. 3a for the
5-cm wide sample. This happens at t 20 s when the pyrolysis
length is about 35 cm long. The flame remaining on the other side
continues burning but quickly shrinks in length. The flame
shrinking is due to the lack of flame heat input from the blown off
side. Conceptually, it is as if the fuel thickness doubled. Responding to this flame blow off and length shrinking event, the rate of
pyrolysis front propagation decreases followed by a decrease of
the fuel burnout rate as shown in Fig. 3a (with some time delay).
The one-sided flame then reaches a limiting length (approximately
20 cm) and spreads steadily all the way to the end of the sample.
The 2-cm wide sample test shown in Fig. 3b exhibits a qualitatively similar trend as in Fig. 3a for the 5-cm sample. However,
the critical pyrolysis length for the one-sided blow off to occur is
shorter ( 18 cm). Both the initial flame growth rate and the final
one-side steady spread rates are slower than the 5 cm case. Consistently, the steady pyrolysis length is also shorter (aproximately
12 cm).
For the 7.5-cm wide sample, Fig. 3c shows both the prolysis
front growth rate and the pyrolysis length increase with time
continuously over the entire sample. There is no one-sided extinction and steady spread rates are not observed. The flame
spread is in the growth phase for the entire duration of the test.
Flame tracking was terminated when the flame tip reached the top
of the sample. Tests with an 8.8 cm wide sample show a similar
Fig. 3. Pyrolysis positions and length vs. time for (a) 5-cm wide SIBAL fabric, (b) 2cm wide SIBAL fabric, and (c) 7.5-cm wide SIBAL fabric.
trend.
These upward tests have been repeated many times. Since the
one-side extinction was observed for the narrower samples (2–
5 cm widths), much care was taken to eliminate non-symmetries
in the experimental configuration and in the environment.
Nevertheless, repeated tests show that extinguishment can occur
on either side of the sample. After ignition, the initial flame
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growth is observed to be very symmetric on both sides of the
sample. One-sided extinction occurs only when the flame reaches
a critical length (e.g. 18 cm for the 2 cm wide sample and
35 cm for the 5 cm wide sample). As an example, the 5 cm wide
case was repeated over 30 times, about ten of which had extremely symmetric ignitions. Full two sided propagation was only
observed three times on this sample size. The flame extinction is
therefore not due to an ignition anomaly nor non-symmetry in the
experimental setup. We believe that the observed extinction is a
true physical phenomenon in buoyant flames. The next section is
devoted to the explanation.
4. Discussion
4.1. Proposed mechanism of self-induced flame extinction
Why does one side of the flame extinguish itself when it becomes too long? And why does the shorter and weaker flame on
the other side of the sample remain?
Before going into our interpretation, let us examine a detailed
sequence of photographs of the flame growth, extinction, spread
events. Fig. 4 shows the edge-view pictures of the 5 cm wide
sample case which was shown in Fig. 3a. The camera translates
with the flame in consecutive images to keep the region of interest
in view. The relative time stamps are shown at the top of each
photo.
In Fig. 4a, a well established two sided flame is already present.
The strobe light can be seen in the bottom of the frame, but as the
camera translates upward it will leave the field of view. In frame b,
the flame base on the right hand side of the fuel sample is beginning to retreat downstream. Frame c shows the right hand side
flame base continuing to retreat but unburned fuel pyrolyzate
(visible as white smoke) continues to leave the fuel surface. Frame
d shows the right hand side flame nearing extinction, the flame is
propagating into a region where the fuel surface is not adequately
preheated, and the retreating flame has blown off.
The extinguished side of the fuel sample will not reignite due to
the inert mesh left behind which acts as a flame arrester. The blue
colored smoke seen near the bottom of the photos are the products of smoldering fuel residue. It is unknown whether the actual
smoke is blue (different compositions compared to the white
smoke) or if it is artificial color cast created by the strobe light
( 5200 K color temperature). Frame e shows the large amount of
fuel vapor which continues to enter the gas phase, but remains
unburned. The absence of flame heat feedback from the extinguished side shortens the flame on the remaining side. One may
regard this as equivalent to an increase of sample thickness (since
the flame is only on one side). The shortened flame shows good
stability with no indication of being near a blow-off limit and is
able to spread upward all the way to the end of the sample. So
again, why does the longer (seemingly more robust) flame extinguish, but the shorter (weaker) flame remain?
To answer this question, we first examine the extinction mechanism of a diffusion flame, specifically for a spreading solid
diffusion flame in concurrent flow. Fig. 5(a) illustrates several
hypothetical flammability boundaries using ambient oxygen percentage as the ordinate and flow velocity at the flame base (the
flame stabilization zone) as the abscissa. Different flammability
boundaries represent different sample widths and it is expected
that narrower samples will have a smaller flammability domain
due to three dimensional aerodynamics effects such as lateral heat
loss, lateral fuel vapor escape (due to diffusion) [17], and lateral
cold air entrainment [16,17,21]. Each boundary consists of two
branches: a high velocity blow off branch and a low-velocity
quenching branch [3]. In a fixed ambient oxygen environment,
quenching occurs when the oxygen supply rate becomes too low
and the weak low-intensity flame loses a large percentage of energy due to radiation and conduction. This is an active area of
research interest in microgravity combustion. On the other end,
high-velocity extinction is a flame stabilization problem. When the
air velocity near the flame stabilization zone becomes too large,
the flow residence time in the reaction initiation zone becomes
too small (or in nondimensional terms, the Damkohler number
based on the stabilization zone size is too small) and the flame
cannot be stabilized. The reaction zone is therefore blown off
Fig. 4. One sided extinguishment from the edge view is shown. Gravity is oriented parallel to the sample length. (a) A two sided flame is established, (b) the right hand side
(RHS) flame begins retreating downstream, (c) RHS flame is continuing to retreat while pyrolysis is maintained, (d) RHS flame blows off, (e) unburned fuel vapor on the right
hand side continues to escape, (f) the left hand side flame shrinks due to the reduced heat flux to the solid, and (g) the left hand side flame reaches a steady length and will
propagate to the end of the sample. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
M.C. Johnston et al. / Fire Safety Journal 71 (2015) 279–286
Fig. 5. (a) Qualitative flammability map bounded by quenching and blow off limits
for the 5 cm wide sample. Qualitative blow off branches are drawn for 2 cm and
7.5 cm wide samples (left). (b) Qualitative curve of the characteristic entrained air
velocity in the flame stabilization zone plotted with respect to time (right).
downstream. In this extinction mode, the near limit flame has a
high intensity since the air velocity and oxygen supply rate are
high. Note that the relevant air velocity used to characterize extinction is at the flame stabilization zone where fuel vapor first
meets the upstream oxygen. In the upward spreading flame configuration, this occurs at the flame base. In upward flame spread,
the velocity at the base is induced by gravity acting upon the entire
flame and thermal plume and thus the buoyant velocity magnitude at the base is affected by the size of the flame. Within certain
limits, it is expected that a longer flame will induce a larger
average velocity at the base (see Appendix for computations to
support this argument). A purely forced system, in contrast, has
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the velocity magnitude at the stabilization zone which is controlled by the upstream condition and will not change with the
flame length. In normal earth gravity, the buoyant induced flow
velocity at the flame base may become large enough so the blow
off extinction conditions are reached. To make sure that flame
extinction mode in normal gravity is indeed from blow off and not
from quenching, the following analysis is made. By balancing
gravity acceleration and fluid inertia, gravity induced velocity u is
(gL)1/2, where g is gravitational level and L is the pertinent
length. Choosing L as the length of the flame stabilization zone,
L α/u, where α is the thermal diffusivity of air, this yields u (αg)1/3.
Depending on what temperature α is evaluated, u can be estimated
between 8 and 18 cm/s. Since this flow speed estimate is based on
the smallest pertinent length in the flame, it is the minimum buoyant
induced velocity in the flame and occurs at the flame base. The
computed flow velocity at the lowest oxygen point (the dividing
point between blow off and quenching branches, the bottom of the
U-shaped curve in Fig. 5) is about 5 cm/s [3]. Therefore, flame extinction mechanism in this free convection upward burning configuration is by blowoff. Although, the extinction mode is blowoff, the
extinction limit is close to the lowest oxygen point along the
flammability boundary, i.e. near the bottom of the the U-shaped in
Fig. 5a. Note that the lowest oxygen point (referred to as the fundamental oxygen limit in Ref. [18], is the merging point between the
quenching and the blowoff branch. At this point, the extinction
mechanisms of residence time and heat loss are of comparable importance. So even when the extinction is on the blowoff side, there is
effect of heat loss as qualitatively illustrated in Fig. 5a for the different
sample widths. We expect that a narrower sample will have a
smaller flammable range as supported by related experimental evidence on flammable limits in variable ambient pressure for upward
flame spread [9] and downward flame spread [6]. Coupled with the
previous statement that a longer flame will induce a larger flow
velocity at the flame base is sufficient to explain the observed selfinduced extinction phenomena in upward spread, to be detailed
next.
For 21% oxygen, the flame blowoff velocity boundaries for three
sample widths are illustrated in Fig. 5(b) with time as the ordinate.
The burning history of three samples are qualitatively traced. For
the 5 cm wide sample, trace A starts with a small induced velocity
at the flame base. As the flame lengthens, the buoyant velocity
increases and eventually exceeds the critical blowoff velocity, at
which time the flame on one side is blown off (marked by an “x” in
the graph). The absence of the flame on one side leads to a shorter
flame on the remaining side (roughly half the length). The buoyant
induced velocity on this remaining side reduces at the base just
enough to stave off blowoff and the one-sided flame can persist
(the fact that a shorter flame induces a lower flow velocity at the
flame base will be discussed in Appendix). The shorter one-sided
flame reaches a limiting length for steady upward spread.
Trace B for the 2 cm case in Fig. 5(b) is similar to trace A with a
smaller critical blowoff velocity and shorterflame. For the 7.5-cm
sample, trace C shows that the blowoff velocity limit is larger and
the buoyant induced velocity at the base does not cross over the
limit. The flame continues to grow until reaching the end of the
sample.
4.2. Comments on the statistical nature of flame extincion processes
Why does the flame blows off on one side of the sample but not
on both sides simultaneously? We believe this has to do with the
stability of near-limit flames. As many experimenters investigating
extinction can attest, flames close to the extinction limits are very
sensitive to disturbances. The closer the flame is to the limit, the
smaller the disturbace needed to trigger an extinction. Theoretically, extinction limits are neutral stable points in stability analysis
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Fig. 6. A 5-cm wide sample which does not extinguish. Despite the constant flame size on the reverse side (not shown), the front side flame nearly blows off but is able to
recover.
Fig. 7. The flame base (highlighted with a solid yellow line) changes shape significantly during propagation just before blowff occurs. (For interpretation of the references to
color in this figure legend, the reader is referred to the web version of this article.)
(e.g.turning point in a response curve) which explains their sensitivity to disturbances [20]. This sensitivity leads to a band of
environmental conditions that define the limit. Within the band,
there is a probability distribution of the likelyhood of an extinction
event. This probablistic nature also applies spatially. A seemingly
symmetric flame can see the disappearance of symmetry as the
‘limit’ is approached. A well-known example case is the blowoff
experiment of a premixed bunsen burner flame from a circular
tube. As the mixture feeding velocity is gradually increased near
blowoff, it is often observed that a portion of the flame base is
lifted first (i.e. local blowoff) before the entire flame blows off.
Symmetry is often broken at the premixed flame flashback limit
where one side of the flame enters into the tube first [12]. In this
experiment, before blowoff we observe that the flame base first
becomes unstable. This is manifested as the unsteady retreat and
flashback of a portion of the base. This motion is both spatial and
time varying (i.e. irregular) before the entire flame blows off on
one side. Figs. 6 and 7 illustrate the flame base fluctuations in two
sperate tests: one leads to blowoff and the other does not. Fig. 6
shows the front view at various times for a 5 cm wide case which
did not extinguish. It can be seen that the flame on the front goes
through the sequence of blowing downstream and shrinking until
around the 1.6 s mark. In this particular case, due to the smaller
size of the flame generating less entrained air velocity, the flame is
able to recover. The flame base propagates back upstream to the
pyrolysis base where fuel is still being vaporized from the flame on
the backside. Fig. 7 shows a similar test under identical conditions
where blow off does occur. The flame bases before blowoff are
highlighted over a short duration (the actual images are very faint
near the flame base and therefore colored in yellow). One sees that
both the shape and the position of the flame base fluctuate indicative of the closeness to the blowoff stability limit. Because of
this random feature of the flame base, symmetry on two sides of
the sample do not exist as blowoff is approached despite the very
symmetric experimental conditions. In all the tests we conducted
for this fuel, one side of the flame will go out first (with no preferred side). When one side of the flame is blown off, the remaining flame immediately benefits by a reduction in buoyant
flow. It is no longer near the blow off boundary and can be
stabilized.
The probabilistic nature of the events also manifests in two
other ways. First, the limiting sample width for flame blowoff in
this experiment is not an exact number. The 5-cm case has been
conducted many times, mostly exhibiting one sided blow off. Of
the 10 most symmetric ignition and growth phases, 7 of these
have one-sided blowoff, for the other three cases the flames propagate all the way to the top of the sample. The location where
blowoffs first occur also vary. This makes us conclude that the
5 cm wide sample (in air and in earth gravity) is a near limit case.
Twelve 2 cm wide and four 3.5 cm wide samples tested all show
one-sided blowoff. Although the test number is small, one sided
blow off occurs early indicating the narrow samples are away from
the probablistic range. There are two 7.5 cm and 8.8 cm samples
tested which all show a strong growing flame until reaching the
end of the sample. The flame base in the wider samples tend to
oscillate upstream and downstream, but do not show an indication
that they will blow off.
5. Conclusions
A very interesting flame extinction mode has been found in
upward spread over a solid fuel. One side of the upward spreading
flame blows off when it becomes too large. An explanation is offerred based on increased buoyant induced velocity at the flame
base stabilization zone. Although we report the experimental
findings only in one special type of solid sample in this paper, we
believe it may be a more general near-limit phenomenon which
could occur on other sample materials.
Based on our present understanding of flame stability and
M.C. Johnston et al. / Fire Safety Journal 71 (2015) 279–286
extinction as a function of flow velocity, it is proposed that a larger
buoyant induced velocity near the flame stabilization zone (at the
base of the flame) may cause blowoff as the flame length increases.
To test this hypothesis, numerical simulations have been performed (see Appendix). The simulations verify that in a gravitational field, a longer flame induces a larger average velocity near
the flame base region. However, the velocity increase due to the
longer flame is modest. Therefore, the observed blow off phenomenon may be most readily observed in near limit conditions
where the flame is especially sensitive to small flow changes. On
the other hand, assuming the proposed mechanism is valid, this
self-induced bouyant blowoff is not limited to thin samples. We
expect thick solids could behave in a similar manner with complete flame extinguishment. However, this case is more difficult to
detect and distinguish from other extinguishment modes since a
285
two-sided to one-sided flame transition is not possible with a
thermally thick solid.
The end result of a large seemingly robust flame extinguishing
itself in the upward configuration could have wider implications
when considering material qualification from a flammability
standpoint. Although flame spread may be unstable in the upward
mode, the material may still be very flammable in other
configurations.
Acknowledgments
This research was initially funded by a grant from NASA (Dr.
Gary Ruff, technical monitor) and concluded with a grant from the
Underwriters Laboratories (Dr. Pravinray Gandhi, technical
monitor).
Appendix. : Supporting results of induced flow field by combustion model
Fig. A1. streamline plot for visible flame length of 9.57 cm (at 2.88 s) vs. 39.7 cm
(at 5.14 s). Visible flame is defined using the fuel reaction rate contour value of
10 4 g/cm3/s.
One of the key elements in the interpretation of the observed
flame extinction event on one side of the fuel sample is that the
(average) flow velocity just upstream of the flame base becomes
too large for the flame to be stabilized. Although flame blow off is
a well-known phenomenon, self-induced blow off when the flame
length grows too long has not been reported as far as we know. It
is important to verify that a longer flame in a gravitational field
indeed induces a larger velocity at the flame base. The most direct
method for verification is through experiment. However, measuring the detailed buoyant flow field in the flame stabilization
zone is very challenging. A neutrally-buoyant seeding and a nonintrusive method to introduce the seeding are required. So instead,
a numerical simulation is used to support our argument.
In the numerical simulation, an upward spreading flame over a
2-cm wide sample is solved. The numerical model is modified
from a three-dimensional transient combustion code previously
used for solid ignition [13]. With the sole purpose of studying the
flow field, the rate constants of the gas-phase reaction kinetics are
specified to be large enough so that no flame extinction is
expected.
Fig. A2. Close up view of the flame stabilization zone for the two flame lengths. Shown on the plots are streamlines, velocity vectors, grid cells, and reaction rate contours. An
imaginary control volume with the upstream face y1 y2 is shown here and explained in the text.
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lengths. The qualitative trend is the same as the above flame simulation, i.e. longer heated section produces a larger induced flow
rate at the lower edge of the heated section.
References
y2
Fig. A3. Air mass flux per unit depth (defined as m′ = ∫ ρudy [g /cm/s], y1¼0,
y1
y2¼ 2 mm, integrated for center-cut plane, at 2 mm upstream of maximum reaction location) vs. flame length.
Fig. A1 shows the flow streamlines along the center symmetry
plane for a growing flame at two time steps. At 2.88 s, the flame
length (defined by the fuel vapor reaction rate¼10 4 g/cm3/s) is
9.57 cm and at 5.14 s, it is 39.4 cm. One sees that there are substantial differences of the flow patterns near the bottom parts of
the flames. The longer flame draws more flow from a wider upstream area at the bottom region. This is intuitively correct and
shows that a substantial part of the buoyant flame cannot be
treated by boundary layer type of analyses. Fig. A2 is the close up
of the flow vectors near the flame base for the two flame sizes.
One sees a larger velocity profile just upstream of the flame stabilization zone for the longer flame. To make it more quantitative,
a control volume face is drawn upstream of the flame-base stabilization zone. The face is labeled y1 y2 and is located 2 mm
upstream of the maximum reaction point and 2 mm in height
(about the size of the flame stabilization zone). The air mass flux
(per unit depth) entering into the control volume through y1 y2
is computed and presented in Fig. A3 as a function of flame length.
Qualitatively, one can think about the flame stabilization zone as a
reactor and the mass flux as being proportional to the average
incoming flow velocity. Fig. A3 shows that as flame length increases, the incoming mass flux increases. The percentage of increase (over the 9.57 cm flame case) is also shown on the right
hand side of Fig. A3. Although the percentage increase is modest,
for near-limit situations the blow off boundary can be crossed.
The above simulation is not to compare the experimental results quantitatively as only one sample width is used and with uncalibrated reaction kinetics.The computational results presented
above is merely to check and verify our postulate that a longer
flame indeed induces a greater buoyant velocity at the flame base.
It should be noted that this trend is purely based on considerations
from fluid mechanics and heat transfer. For example, we have
tested this on a vertical plate heated with two different section
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