Premixed edge-flames in spatially-varying straining flows

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1

Premixed edge
-
flames in spatially
-
varying straining flows


Jian
-
Bang Liu and Paul D. Ronney

Department of Aerospace and Mechanical Engineering

University of Southern California, Los Angeles, CA 90089
-
1453


Abstract



Premixed
-
gas flames subject to steady

spatially
-
varying straining flows were studied to
examine one aspect of premixed flames in strongly turbulent flows where strain rate gradients
are present and local strain rates may be high enough to cause local flame
-
front extinguishment.
The spatially
-
varying straining flows were created using a counterflow slot
-
jet burner with
slightly non
-
parallel jet exits. When the flow configuration was premixed combustible gas vs.
cold inert gas, so that only a single flame was produced, steady flame “edges” cou
ld be created
where the flame would exist in the low
-
strain region but would be extinguished in the high
-
strain
region. When the flow configuration was premixed gas vs. premixed gas, twin flames would
exist in the low
-
strain region that converged to a cor
ner
-
like tip in the high
-
strain region. For
both configurations the local strain at the location of the stationary flame edge was somewhat
lower than the strain required to extinguish flames in the same mixture subject to a spatially
uniform strain. The
difference was greater for the twin
-
flame configuration, particularly at high
Lewis number (Le). Due to diffusive
-
thermal instabilities, cellular flames were observed at low
Le and travelling
-
wave patterns were observed at high Le. Le effects also led to

the formation of
isolated “flame tubes” rather than continuous fronts at sufficiently low Le and high strain rates.
All of these results are consistent with recent theoretical predictions. These results indicate that
“laminar flamelet” models of premixe
d turbulent combustion may be reasonably accurate for
single flames over a wide range of Le and twin flames with Le close to unity, even at conditions
approaching those where local flame quenching occurs, but may not be accurate for twin
-
flames
except for
Le near unity. This finding is somewhat different from previous experimental and
theoretical results for
nonpremixed

edge
-
flames, where more substantial differences between
uniform flames and edge
-
flames were found for all Le.


Address for correspondence:

Paul D. Ronney

Department of Aerospace and Mechanical Engineering

University of Southern California

OHE 430

Los Angeles, CA 90089
-
1453

(213) 740
-
0496 (office); (213) 740
-
8071 (fax)

ronney@usc.edu


Revised version subm
itted to
Combustion Science and Technology
, November, 1998.

Introduction



Flames subject to temporally and spatially uniform hydrodynamic strain are frequently
used to model the local interactions of flame fronts with turbulent flow fields (Williams, 198
5;
Peters, 1986; Bradley, 1992). The "laminar flamelet" concept presumes that each surface element
of the flame front behaves as though it were a steady isolated front subject to uniform strain.
The applicability of laminar flamelet models in strongly tur
bulent flows have been questioned
recently (Shay and Ronney, 1998) because in turbulent flows the strain rate (

) changes at rates
comparable to


itself and the scale over which the flame front curvature and


changes is
comparable to the curvature scale
itself. Therefore quasi
-
static, local models of turbulent strain
and curvature effects on laminar flamelets may not be accurate under conditions where the strain
and curvature effects are most significant.

As a step towards more realistic quantification o
f strain effects in turbulent premixed
flames,
spatially uniform

premixed flames subject to
temporary varying

strain or curvature have
been studied theoretically (Saitoh and Otsuka, 1976; Huang
et al.
, 1998), computationally
(Egolfopoulos, 1994; Göttgens
e
t al.
, 1998) and experimentally (Saitoh and Otsuka, 1976).

In
this work we consider the opposite case of
steady

flames subject to
spatially
-
varying

strain and
in particular structures that may occur in the transition region between the extinguished and
bu
rning regions of the flame front. In regions of sufficiently large

, the flame is expected to be
extinguished, whereas at sufficiently low


the flame is expected to exist. We wish to determine
if steady flame “edges” separating burning from non
-
burning regions can exist and if so, how


at the edge
-
flame location (

edg
e
)
compares with the extinction strain of a uniform flame (

ext
).
If

ext

>

edge
,

local extinguishment in highly strained regions would be expected to spread into
regions of sub
-
critical strain, thus generating “holes” in the flame sheet that extend beyo
nd the
region expected based on laminar flamelet models. Conversely, if

edge

>

ext
, holes that develop
in the flame sheet would “heal” beyond the region expected based on flamelet models.

A recent experimental study of
nonpremixed

flames in spatially
-
va
rying strain (Shay and
Ronney, 1998) showed that stationary nonpremixed edge
-
flames could be produced.
In Shay
and Ronney,
edge
-
flames were found to be significantly weaker than uniformly strained flames,

i.e.
,

edge

was less than the

ext

in the same mix
ture, and some weak mixtures were capable of
supporting uniform flames but not edge
-
flames. Interferometer images indicated regions of
locally intense burning at
the flame edges and abrupt transitions from burning to non
-
burning
conditions. These results

were qualitatively consistent with theoretical models (Buckmaster,
1996; Buckmaster, 1997). It was also found that the edge location was practically independent
of the strain rate gradient, indicating that conventional uniformly strained nonpremixed flam
es
and edge
-
flames are distinct structures yet each has well
-
defined properties. These phenomena

2

were qualitatively independent of the Lewis numbers (Le, defined as the ratio of the mixture
thermal diffusivity to the reactant mass diffusivity) of both rea
ctants.


We note that nonpremixed edge
-
flames are essentially a superset of so
-
called “triple
flames” (Ruetch
et al
., 1995; Plessing
et al.
, 1998; Kioni
et al
., 1999). Buckmaster (1996, 1997)
and Daou and Liñán (1998b) showed that non
-
stationary edge
-
fla
mes exist for




edge

that
advance into the unburned region for


<

edge

or retreat into the burned region for


>

edge
.
Triple flames are rapidly advancing edge
-
flames that exist under conditions of sufficiently low


(or scalar gradient) that lean a
nd rich premixed flame branches emanate from the leading edge of
the nonpremixed flame and curve in the direction opposite the propagation, forming an arrow
-
shaped flame structure. At higher

, close to

edge
, these premixed branches merge with the
nonpre
mixed flame and the triple
-
flame structure vanishes.

In non
-
premixed edge
-
flames, only one counterflow configuration is possible, namely
fuel + inert vs. oxygen + inert, which exhibits a single flame at the location of stoichiometric
mixture fraction. For

premixed flames, two configurations are possible: premixed combustible
gas vs. inert gas, where a single flame is produced, and premixed gas vs. premixed gas, where
twin flames are produced on either side of the stagnation plane. The former may be more
r
elevant to turbulent flames since one side of the flame front has fresh reactants whereas the
other side has burned products, however, the twin
-
flame configuration is considered here also
because it is frequently employed in studies of strained laminar bur
ning velocities and may be
relevant to highly strongly wrinkled flames at high turbulence levels where back
-
to
-
back flames
may exist. It has also been suggested that single premixed edge
-
flame studies are relevant to
laminar flame quenching,
e.g
., of risi
ng flames in tubes (Vedarajan and Buckmaster, 1997).

To our knowledge, no experimental studies of premixed flames in spatially varying
straining flows or premixed edge
-
flames have been performed to date. Theoretically, Vedarajan
and Buckmaster (1997) and
Vedarajan
et al
. (1998) have analyzed single and twin premixed
edge
-
flames, respectively, using two
-
dimensional numerical models. Unity Lewis numbers
(defined for premixed flames as the ratio of the mixture thermal diffusivity to the mass
diffusivity of t
he
stoichiometrically limiting

reactant) were assumed in both studies. Steady
solutions were sought in the configuration of a flame a uniform strain which is initially burning
on one side and initially quenched in the other. In both single and twin
-
flame

cases, it was
predicted that for sufficiently low values of


the flame edge would advance at a steady rate into
the non
-
burning region whereas for sufficiently high values of


the flame edge would retreat
into the burning region. The edge speed was predicted to increase monotonically as


decreases.
The ratio of


edge

to

ext

was predicted to be 0.93 and 0.49, respectively, for single
-

and twin
-
flames. This indicates that, as with nonpremixed flames, premixed edge
-
flames are weaker than
uniform flames in the same mixture. Recently Daou and Liñán (1998a) studied

premixed edge
-

3

flames analytically and computationally in the twin
-
flame configuration for general Lewis
numbers. For Le = 1/2, 5/8, 1 and 11/8 the predicted values of

edge
/

ext

were 0.82, 0.70, 0.50
and 0.48, respectively, assuming a non
-
dimensional act
ivation energy of 8. Thus, the difference
between uniform flames and edge
-
flames increases as Le increases. The value for unity Lewis
number of 0.50 is very close to the corresponding prediction of 0.49 by Vedarajan
et al
. (1998).

In light of these predi
ctions, the goal of this study is to search for the existence of
premixed edge
-
flames in strain rate gradients for single
-
flame and twin
-
flame configurations, to
compare the strain rate at the flame edge to the extinction strain of uniform flames in the sa
me
mixture, and to compare these results to theoretical predictions (Vedarajan and Buckmaster,
1997; Vedarajan
et al.
, 1998, Daou and Liñán, 1998a). Since both strained premixed flames and
edge
-
flames are strongly affected by Le (Williams, 1985; Peters, 1
986; Bradley, 1992; Daou and
Liñán, 1998a), mixtures providing a wide range of Le are examined.



Experimental approach


As in previous work (Shay and Ronney, 1998), edge
-
flames were created using a
counterflow slot
-
jet burner with the jet exits
intentiona
lly misaligned

slightly to produce small
strain rate gradients. While counterflowing round
-
jets are more commonly employed than
counterflowing slot
-
jets for strained flame experiments, angled round
-
jet experiments are less
desirable for studying edge
-
flam
es because angled round
-
jets would produce ellipse
-
shaped
flame zone(s) (one or two for single or twin flames, respectively) with continually varying strain
all along the perimeter of the flame edge. This configuration is inherently three
-
dimensional,
thu
s it would be difficult to interpret results obtained in this geometry. The slot jets produce
plane strain, which, like axisymmetric strain, can be reduced to a one
-
dimensional system. Thus,
our slightly angled slot
-
jet configuration provides a quasi
-
one
-
dimensional system that is slowly
varying along the length of the slot. This is ideal for comparison with theoretical works
described above. Another reason for our preference for the slot
-
jet configuration is that
extensional strain occurs along only on
e coordinate direction in the plane of the flame, whereas
for round jets the flame is equally strained in both directions. Computations by Ashurst
et al
.
(1987) have shown that highly strained regions of turbulent flows exhibit a most probable ratio
of st
rain along the three principal axes in the ratio 0.75:0.25:
-
1, where positive values denote
extensional strain. Thus, highly strained regions, where flame stretch effects are most important,
do not typically exhibit nearly equal rates of extensional strai
n along two of the principal axes.
The slot
-
jet configuration provides strain rates in the ratio 1:0:
-
1 whereas round jets provide
0.5:0.5:
-
1. Thus, the slot
-
jet configuration provides straining characteristics that are more

4

representative of the conditi
ons of flames in strongly turbulent flows than axisymmetric jets can
provide.

Analogous to non
-
premixed edge
-
flames (Shay and Ronney, 1998), stable premixed
edge
-
flames are anticipated in our premixed
-
flame experimental configuration because,
according to
theory (Vedarajan and Buckmaster, 1997; Vedarajan
et al
., 1998; Daou and Liñán,
1998a), the edge velocity is negative (retreating) in high
-
strain regions and positive (advancing)
in low
-
strain regions, and thus the location where

(x) corresponds to zero e
dge velocity should
be a stable equilibrium point.

The global strain rate for counterflowing slot
-
jet streams is given by (Seshadri and
Williams, 1978)









(1)


where

(x) is the strain rate at the location x along the length of
the slot, V
upper

and V
lower

are the
upper and lower jet exit velocities,

upper

and

lower

the corresponding densities of the streams,
d(x) the nozzle separation at location x. In all of our experiments the two streams have very
nearly equal densities, t
hus the simplified relation











(2)


is appropriate. The
local

strain will vary in the streamwise direction due to thermal expansion
effects, however, for
comparison

of uniformly strained flames and edge
-
flames, the
global

st
rain
is considered to be the more appropriate parameter, especially considering that correlations of
strain effects for turbulent flames (
e.g
. Bradley, 1992) employ global strain rate estimates based
on the cold
-
gas conditions. Moreover
, far ahead of the
flame front, in the cold
-
gas, constant
-
density region, Eq. (2) is certainly valid. Furthermore, most early experiments on uniformly
strained flames,
e.g
., Ishizuka and Tsuji (1981), reported only global strain rates, and most
theoretical works on edge
-
fla
mes (
Buckmaster, 1996; Buckmaster, 1997; Vedarajan and
Buckmaster, 1997; Vedarajan
et al.
, 1998; Daou and Liñán, 1998a, b) have used the constant
-
density assumption, thereby sidestepping the issue of flow
-
field modification near the flame edge
due to therm
al expansion.
Indeed, it is unclear whether a unique “local” strain rate can be
defined for a two
-
dimensional structure such as an edge
-
flame, considering how difficult it has
been to determine a proper definition of strain rate in a conventional one
-
dime
nsional

5

counterflow flame and how to extrapolate these data to zero strain rate to determine the
unstretched laminar burning velocity (Vagelopoulos
et al.
, 1994).

The experimental apparatus we employed (Fig. 1) consisted of two 7.6 cm x 1.0 cm
rectangular
nozzles configured as a counterflow burner. Steel wool and honeycomb inside the
nozzles ensured uniform exit flow. The nozzles (and thus reactants) were maintained at room
temperature by water cooling. The lower nozzle was mounted on a rotation/translat
ion stage
with micrometers for adjusting the nozzle separation and wedge angle between the slot exits.
Steel mesh screens were placed above and below the test section to minimize external
disturbances and buoyancy effects. This apparatus was placed insid
e a steel box to isolate the
flames from laboratory drafts and facilitate ventilation. Commercial mass flow controllers with
accuracy ±1% of full scale (verified by calibration with wet
-
test meters) delivered the
combustible gases to the nozzles. The mas
s
-
flow controllers were commanded by a PC
-
based
digital
-
to
-
analog converter board and custom software that enabled independent control of gas
composition and V for each nozzle. For twin
-
flames, the two nozzles always had identical
composition and V to mai
ntain symmetry. For single
-
flames, the upper nozzle contained the
reactive flow and the lower non
-
combustible flow was the same inert gas (He, N
2

or CO
2
) as
used in the upper flow. In some single
-
flame cases, we employed V
upper

> V
lower

to move the
flame

farther from the upper nozzle and thus reduce heat losses (see Results).


To obtain a wide range of Lewis numbers, CH
4
/air, C
3
H
8
/air, CH
4
/O
2
/CO
2

and
C
3
H
8
/O
2
/He mixtures were employed, providing estimated Lewis numbers of 0.9, 1.7, 0.6 and
3.0, respectivel
y. In the CH
4
/O
2
/CO
2

and C
3
H
8
/O
2
/He mixtures, the fuel:O
2

mole ratios were
usually 1:4 and 1:10, respectively, to provide equivalence ratios of 0.5. In all cases only lean
mixtures were tested to avoid soot formation and to ensure that fuel was the scarc
e reactant for
the purpose of determining Le.


The flames were recorded by a video camera (framing rate 30 Hz, shutter speed 1/60
sec). Faster shutter speeds (1/1000 sec) were sometimes used to observe flame instabilities at
high Le, at the expense of imag
e signal
-
to
-
noise ratio. The images were then digitized by a
video processing system (Global Lab Image software with a DT3851 frame grabber). Edge
-
flame locations were measured from these digitized flame images and averaged over 10
measurements. Strain
rates at the flame edge were then computed from Eq. (2) using d(x) at the
measured edge location. Since the wedge angles were always less than 7 degrees, and thus d is a
weak function of x, uncertainty in the edge
-
flame location led to less than 2% uncert
ainty in the
value of

(x) at the flame edge.




6

Results


Characterization of edge
-
flames



Edge
-
flames were observed for both single
-

and twin
-
flame configurations for all mixture
families studied. For the single
-
flame configuration, the edge
-
flames exhi
bit a hook
-
like
structure (Fig. 2, upper) with the tip bending downward toward the inert flow. This bending is
expected since as

(x) increases, the burning velocity (S
L
) decreases and the equilibrium location
of the flame (where S
L

equals the local flow
velocity) is pushed toward the stagnation plane
where the local velocity is lower. This hook
-
like structure is also predicted theoretically
(Vedarajan and Buckmaster, 1997). No similar structures were observed for non
-
premixed edge
-
flames (Shay and Ronne
y, 1998) because the flame position is at the location of stoichiometric
mixture fraction, rather than being determined by the balance between S
L

and local flow
velocity. For the twin premixed flame configuration, the two mirror
-
image flame hooks join
tog
ether at a corner
-
like edge (Fig. 2, middle and lower).


It is well known (Williams, 1985) that sharp curvature such as that at the corner of twin
edge
-
flames increases (decreases) the local chemical reaction rate relative to a flat flame in
mixtures with
Le < 1 (Le > 1). While the classical models of curvature effects do not strictly
apply to the corners of twin edge
-
flames because the flow at the corner is parallel to the flame
front and S
L

is practically zero at the corner, nonetheless reaction is stren
gthened for
CH
4
/O
2
/CO
2

mixtures (Le ≈ 0.6) (Fig. 2, middle) and weakened to the point of having an open
edge in C
3
H
8
/O
2
/He mixtures (Le ≈ 3.0) (Fig. 2, lower). These observations are also consistent
with the well
-
known (
e.g.
, Williams, 1985) characteristi
c of strained twin premixed flames that
for Le < 1, the flames will merge before extinguishing, whereas for Le > 1 extinguishment
occurs before merging.


Theory (Buckmaster and Mikolaitis, 1982) predicts that sufficiently strong strain always
decreases S
L
,

but for mixtures with Le < 1, weak strain increases S
L

to a value greater than that
of the unstrained flame. Thus, the strain rate gradient in premixed edge
-
flames should lead to
non
-
monotonic flame shapes in Le < 1 mixtures. This was confirmed by direc
t video images
(Fig. 2, upper) and images (Fig. 3, upper and middle) taken using a common
-
path shearing
interferometer system (Liu and Ronney, 1997). The shearing interferometer produces fringes
whose spacing is proportional to the density gradient, rathe
r than the density difference between
the test section and a reference path as in most other types of interferometers. For both single
and twin
-
flames in Le < 1 mixtures, along the flame as the edge is approached, the flame first
shifts toward the nozzle
exit due to higher S
L

before hooking toward the stagnation flame due to
lower S
L
. Consistent with this hypothesis, no similar behavior was observed for Le > 1 mixtures

7

and in fact a region of weak burning exists near the edge (Fig. 3, lower), which is con
sistent with
the inference from the visible images (Fig. 2, lower). Moreover, these observed Le effects are
entirely consistent with the numerical results presented by Daou and Liñán (1998a), in terms of
both the flame shapes and burning intensities.


Int
erferograms of twin flames (Fig. 3, middle and lower) show that there are fringes
passing through the corner of the twin flame. This indicates the presence of a vertical
temperature gradient there,
i.e
., the flame temperature at the corner is different fr
om the other
parts of the flame, but does not necessary indicate that the flame is extinguished there. The
fringe density at the high strain rate side of the hook tip (for the single flame, Fig. 3, upper) or
corner (for the twin flames, Fig. 3, middle and

lower) changes rapidly, implying a sudden
temperature drop on the non
-
burning side of the flame edge, which is consistent with the visual
flame images (Fig. 2).


Ideally, the response of premixed flames to strain depends only on


itself,
i.e
., only on
(V
upper
+V
lower
)/d and not V
upper
, V
lower

or d individually. However, if V
upper
or V
lower

is too low,
i.e
., comparable to S
L
, the flame position is close to the nozzle exit, which weakens it by heat
loss, leading to lower

ext

than under adiabatic condition
s. To ensure that only near
-
adiabatic
conditions were employed, the effects of V
upper

and V
lower
on

ext

were examined for uniformly
-
strained flames (Fig. 4). At low V, an increase in

ext

with increasing V is seen, implying a
decreasing impact of heat l
oss. At larger V,

ext

is practically constant, indicating negligible
impact of heat loss. All of the quantitative results reported below were conducted in the flat
region of these curves at sufficiently high V.


Comparison of uniformly strained flames a
nd edge
-
flames



Figures 5a
-

d show comparisons of

ext

for uniformly strained twin flames and

edge

for
twin edge
-
flames. For uniform flames,

ext

was determined for fixed V
upper

and V
lower

by
decreasing d until extinction occurred. For edge
-
flames,

e
xt

was determined for the same V
upper

and V
lower

by Eq. 2 with d(x) corresponding to the value at the flame edge. For practically all
cases

ext

is lower for the edge
-
flame, with the difference being much greater for higher Le. For
CH
4
-
air mixtures (Le ≈

0.9), the difference does not seem to be nearly a factor of two as
predicted for Le = 1 (Vedarajan
et al
., 1998; Daou and Liñán, 1998a). Also,

ext
/

edge

is close to
unity for Le ≈ 0.6, whereas Daou and Liñán predict

ext
/

edge

≈ 0.7 for this case. Othe
rwise, the
results are very consistent with experiments in that

ext
/

edge

decreases with increasing Le and
reaches a nearly constant value of about 0.5 for sufficiently high Le. These Le effects might be
expected considering the effect Le has on the burn
ing intensity at the corner (Fig. 2); indeed, it is
somewhat surprising that the effect of Le on

edge
/

ext

is relatively minor considering how

8

different the visible appearances of the twin edge
-
flame images are for Le < 1 and Le > 1 (Fig. 2,
middle and lo
wer).

We propose the following interpretation of this behavior. According to
Daou and Liñán, Le effects cause edges in mixtures with Le < 1 to exhibit positive propagation
speeds that are larger than S
L

when


is significantly less than

edge
, but of cou
rse for



edge

the edge speed is negative. Since stationary edges occur for


close to

ext
, Le effects might be
expected to be more nearly aligned with the behavior of uniformly strained flames near
extinction than flames far from extinction.

Figures
5a
-
d show that there is no significant dependence of

ext

on the wedge angle
between the nozzles. This indicates that the strain rate gradient does not significantly affect
edge
-
flame properties. The angle
-
independence also indicates that flow parallel t
o the slots (in
the x
-
direction) induced by angling the slots is insignificant, otherwise the flame edge would
move to different x locations having different d(x) to balance the edge
-
flame propagation
velocity with the flow velocity in the x direction. Th
e same conclusion was reached in our non
-
premixed edge
-
flame study (Shay and Ronney, 1998). There is no gradual transition from edge
-
flame to uniform
-
strain behavior as the divergence angle decreases. Thus, edge
-
flames are
distinct from uniformly
-
straine
d flames; each type of flame exhibits consistent but different
response to strain.


For the single flame configuration (Figs. 6a
-

d),

ext

is practically the same for edge
-
flames and uniformly
-
strained flames, with the edge
-
flame probably slightly weaker.

This is
consistent with Vedarajan and Buckmaster (1997), who predicted

ext

is only 7% lower for single
edge
-
flames in Le = 1 mixtures. Again, the wedge angle has almost no effect on these results
and in this case Le has no significant effect either. U
nfortunately, no predictions of the
properties of single edge
-
flames with Le ≠ 1 are available for comparison with our observations.
It is interesting to note that twin
-
flames properties are moderately dependent on Le and exhibit
significant differences f
rom uniform flames, whereas single flames apparently exhibit practically
no Le dependence and have characteristics that are more similar to uniform flames.


Flame instabilities



For the low
-
Le CH
4
/O
2
/CO
2

mixtures, cellular structures were observed for bot
h
uniformly strained flames and edge
-
flames. Since these structures were observed only for the
low
-
Le mixture, we attribute them to the well
-
known diffusive
-
thermal instability of premixed
flames (Sivashinsky, 1977; Joulin and Clavin, 1979; Williams, 1985
). In the twin
-
flame
configuration, cellular structures were observed at low


(Fig. 7, upper) whereas at higher


(not
shown) the flames were nearly flat. The effect of strain on the cellular instability can also be
seen for the CH
4
/O
2
/CO
2

twin edge
-
fla
me in Fig. 2 (middle); there is no evidence of cellular

9

structure for this case since


is close to

ext

for the entire flame. These observations are
consistent with the analysis of Buckmaster and Ludford (1983), who showed that for the plane
-
strain (slot
-
jet counterflow) symmetric twin
-
flame configuration, sufficiently strong strain
suppresses cell formation. Similar behavior was also shown for axisymmetric twin flames by
Sivashinsky
et al
. (1982). Very recently, Buckmaster and Short (1998) showed that
at very high
stretch rates, close to extinction, the cellular structure may reappear in the plane
-
strain
configuration. This phenomenon was not observed for either uniform flames or edge
-
flames in
CH
4
/O
2
/CO
2

mixtures, perhaps because (as discussed further

below) Buckmaster and Short’s
calculations were performed only for Le = 0.3 whereas Le is significantly higher (≈ 0.6) for the
CH
4
/O
2
/CO
2

flames.

In contrast, for the single
-
flame case cellular structures were observed in CH
4
/O
2
/CO
2

mixtures at all


up t
o and including the extinction value. An example of this is shown in Fig. 7
(middle) for an edge
-
flame. Thus, the experiments indicate that the single
-
flame configuration is
more susceptible to diffusive
-
thermal instability than the twin flame configurat
ion, though
apparently there are no corresponding theoretical predictions available for comparison. It is
plausible that the cold inert stream acts as a downstream conductive heat loss mechanism that
increases the tendency for diffusive
-
thermal instabilit
y in a manner qualitatively similar to that
described by Joulin and Clavin (1979), who showed that for volumetric heat losses the maximum
Le for which the cellular instability can occur increases as the impact of heat losses increases.
This loss mechanism

is not present in the twin flame configuration because the two back
-
to
-
back
flames suppress each other’s downstream loss.

For both the single and twin
-
flame configurations, for uniformly strained flames the
cellular structures were steady and the cell spa
cing was nearly constant. For edge
-
flames, the
cells were steady only at a specific location (x) along the length of the slot, whereas at higher or
lower x, and thus different

(x), the cells traveled away from this location.

Very recent theoretical work
on premixed (Daou and Liñán, 1998a; Buckmaster and
Short, 1998) and nonpremixed (Thatcher
et al
., 1998) edge
-
flames indicate that at sufficiently
low Le, a transition in edge
-
flame structure from smooth or moderately wrinkled flames to
“flame tubes”
*

may o
ccur near extinction, which enables the flame to survive in the presence of
strain that would cause it to extinguish were it forced to remain planar and continuous. In
essence, the behavior seen for the low
-
Le flame in Fig. 2 (middle) is taken to an extre
me
condition for which the region behind the leading edge cannot survive without the intensification
seen at the leading edge, thus the trailing part of the flame quenches. This behavior is somewhat



*

While Buckmaste
r and Short (1998) use the term “flame strings” and Daou and Liñán (1998a) use the term
“spots,” we prefer the term “flame tubes” to emphasize that chemical reaction occurs primarily on the surface of the
structure.


10

analogous to spherically
-
symmetric “flame balls” observe
d in microgravity experiments (Ronney
et al.
, 1998) where in that case radiative transfer rather than extensional strain is the prevailing
loss mechanism, but in both cases the Lewis number enhancement of flame temperature causes
the curved flame to surviv
e where a plane flame could not. These tubes are elongated along the
direction of extensional strain (out of the plane of the images shown in Figs. 2, 3, 7, and 8). An
infinite chain of tubes is predicted for moderately high strain whereas two then one i
solated
tube(s) are predicted at progressively higher strain (Buckmaster and Short, 1998). Yet higher
strain causes complete flame extinguishment. In Daou and Liñán’s work, tube
-
like flames were
predicted for Le = 1/2 but not Le = 5/8. In Thatcher
et al
., for equal Lewis numbers of fuel and
oxidant, this behavior required Le less than about 0.5. (Buckmaster and Short studied only Le =
0.3, thus no transition Le was identified.) Thus such behavior might not be expected for our
CH
4
-
O
2
-
CO
2

mixtures (Le
fue
l

≈ Le
O2

≈ 0.6) in either the premixed or nonpremixed configuration,
and in fact it was not seen in this work nor in non
-
premixed edge
-
flames (Shay and Ronney,
1998).

In light of these predictions, a set of experiments were performed using H
2
-
O
2
-
N
2

mixtures

(Le
fuel

≈ 0.3; Le
O2

≈ 1.0) to test the theoretical predictions. In both premixed and
nonpremixed cases, flame tubes were in fact observed. Examples of isolated premixed and
nonpremixed flame tubes, at values of


just below the value for complete flame
extinguishment,
are shown in Fig. 8. Since this special type of edge
-
flame structure is inherently non
-
propagating, it was not necessary to employ angled slot jets to stabilize the flames. Images of
these flames in the orthogonal view (not shown) confirm
ed that these structures are tube
-
like
rather than ball
-
like. The cross
-
section of the tubes is not round but is generally longer
dimension in the unstrained direction (the horizontal direction in Figs. 2, 3, 7, and 8) than in the
compressional strain dir
ection (the vertical direction in these figures). This is consistent with
theoretical predictions of flame tubes (Daou and Liñán, 1998a; Buckmaster and Short, 1998). It
is noteworthy that the premixed and nonpremixed tubes are similar. This is probably
because in
the nonpremixed case the strain rate is well above

ext

for the planar flame and thus the reactant
streams mix without burning initially, causing the flame to assume a somewhat premixed
-
like
character.


For the high
-
Le C
3
H
8
/O
2
/He mixtures, especially at large

, video images revealed
striped traveling
-
wave

patterns on the flames. These stripes were found for both edge
-
flames
and uniform flames and for both single and twin flames. An example image is shown in Fig. 7
(lower). The same phenomena was also seen to a lesser extent in C
3
H
8
/air mixtures (Le ≈ 1.
7).
Somewhat surprisingly, the travelling
-
wave patterns were observed even in CH
4
-
air flames (Le ≈
0.9) mixtures, but only for stoichiometric mixtures very close to extinction. The flames
exhibiting travelling waves emitted a loud screeching noise with t
ypical frequencies around 200

11

Hz. This frequency corresponds to an acoustic wavelength of 1.5 m, which is much longer than
the longest dimension of the apparatus. To verify that the phenomenon was not due to an
acoustic resonance, the walls of the test c
hamber were removed and it was found that the sound
emission did not change. As would be expected, to observe the travelling
-
wave patterns, a high
camera shutter speed (typically 1/1000 s) was required. In fact, the image of the high
-
Le edge
-
flame shown
in Fig. 2 (lower) was taken under the same conditions as Fig. 7 (lower) except for
the shutter speed (1/60 sec vs. 1/1000 sec).

Traveling
-
wave instabilities on freely
-
propagating premixed flames having high Le are
predicted by the diffusive
-
thermal theory
(Joulin and Clavin, 1979) and have been observed
experimentally (Pearlman and Ronney, 1994), but to our knowledge they have not been reported
previously in counterflow flames. This may result from the high Le and high camera shutter
speeds required to obs
erve them. It is possible that high
-
Le diffusive
-
thermal instabilities would
occur more readily in stretched counterflow flames than freely
-
propagating flames because it has
been shown for spherically expanding flames (Farmer and Ronney, 1989) that curvat
ure
-
induced
flame stretch increases the tendency for diffusive
-
thermal instability to occur in high
-
Le
mixtures. Additionally, in the single
-
flame configuration, the downstream heat loss probably
also increases the tendency for this instability to occur (
Joulin and Clavin, 1979).



Discussion and conclusions



Experiments were conducted to observe the effect of strain rate gradients on steady
strained premixed flames. It was found that in these strain rate gradients, edge
-
flames occur for
both single and
twin premixed
-
flame configurations. Hook
-
like structures were observed for the
single
-
flame configuration and corner
-
like structures were observed for twin
-
flames. Video
images and interferograms indicated a sharp transition from non
-
burning to burning r
egions at
the flame edge.


For the twin
-
flame configuration, the strain rate at the edge of stationary edge
-
flames
(

edge
) was nearly always lower than the extinction strain rates of uniformly strained flames in
the same mixture (

ext
), though theory (Veda
rajan
et al
., 1998; Daou and Liñán, 1998a) predicts
a factor of about two difference for Le = 1 whereas experimentally a difference of this magnitude
was observed only at somewhat higher Le. Low
-
Le mixtures received some benefit of curvature
at the flame
edge, but only in sense that there was less disparity between

edge

and

ext

in these
cases. For the single
-
flame configuration

edge

was only very slightly lower than

ext
, which is
also consistent with the theoretical predictions for Le = 1 (Vedarajan and Buckmaster, 1997). In
this case, Le had practically no inf
luence on the comparison. For both cases the strain rate

12

gradient had no significant effect on

edge

and there was no gradual transition from edge
-
flame to
uniformly strained flame behavior as the wedge angle was decreased, indicating that premixed
edge
-
f
lames are distinctly different flame structures from uniformly strained flames.


Cellular structures resulting from diffusive
-
thermal instabilities were observed for low
-
Le
mixtures in both edge
-
flames and uniformly strained flames. For the twin flame but

not the
single flame, sufficiently high strain suppressed the cell formation. At sufficiently low Le and
high

, the planar nature of the flame sheets was lost and the flames assumed tube
-
like
characteristics with the axis of the tube parallel to the axis of extensional strain. Moving striped
patterns and sound emissions were observed in high
-
Le mixtures, especia
lly near extinction
conditions. All of these results are consistent with theoretical predictions, where such
predictions are available.


The extinction strain rates of edge
-
flames and uniform flames are similar for twin flames
with Le near unity as well a
s single flames of all Le tested. Consequently, for such conditions
laminar flamelet models of premixed turbulent combustion may be approximately valid up to
conditions near the local quenching condition, a position advocated in a recent review (Bradley,
1992),

when the global strain rate is properly characterized
. Of course, these conclusions might
not apply in large strain rate gradients or in combined spatially
-

and temporally
-
varying flows.
Furthermore, twin flames with low Le,
e.g.
, lean H
2
-
air, or
high Le,
e.g
., lean gasoline
-
air, do not
conform to laminar flamelet model assumptions. It is interesting that a somewhat different
conclusion was reached for non
-
premixed flames (Shay and Ronney, 1998) because the
differences between edge
-
flames and unif
ormly
-
strained flames was greater in that case and was
observed for all Le. This is consistent with a recent numerical study of
nonpremixed

edge
-
flames by Daou and Liñán (1998b), who predicted that for Le = 3/8, 1 and 13/8, the
corresponding values of

ed
ge
/

ext

were 0.52, 0.41 and 0.28, respectively, assuming a non
-
dimensional activation energy of 8. (In these calculations the Lewis number of oxygen was fixed
at unity and these values of Le are based on the fuel Lewis number.) Thus a comparison of Daou
and Liñán’s work for nonpremixed (1998b) and premixed (1998a) edge
-
flames shows that the
distinction between edge
-
flames and uniform flames in terms of

edge
/

ext

is greater for
nonpremixed flames and extends across all Le, which is entirely consistent wit
h our experimental
observations for premixed flames (this work) and nonpremixed flames (Shay and Ronney, 1998).


Since turbulent premixed flames are frequently modeled using “laminar flamelet
libraries,” and since edge
-
flames, like uniform flames, have we
ll
-
defined responses to strain, we
propose that the range of applicability of laminar flamelet models, especially for high
-
Le
mixtures, could be extended by adding “edge
-
flame libraries” to existing laminar flamelet
libraries. This addition is facilitated

by the apparent independence of edge
-
flame properties on
strain rate gradients, thus, at least at the first stage, the strain rate gradient does not need to be a

13

parameter in edge
-
flame libraries. Of course, rules for merging edge
-
flames and locally
-
unif
orm
flames need to be developed, since one needs to determine whether a particular strain rate
gradient (and perhaps strain rate history) would cause the flame to exhibit uniform
-
flame or
edge
-
flame characteristics.


In future work, the dynamical propertie
s of edge
-
flames,
i.e
., the rate of advancement or
retreat of non
-
steady edges will be measured for both premixed and nonpremixed edge
-
flames;
this is an important prediction of the theoretical models. Preliminary experiments, examples of
which are shown
in Fig. 9, show that the visible structure of advancing edge
-
flames,
corresponding to


<

edge
, are somewhat different from stationary edge
-
flames. These
differences have also been noted computationally (Vedarajan and Buckmaster, 1997; Daou and
Liñán, 1998a). Besides study of the dynamical properties of edge
-
flames, non
-
intrusive point o
r
plane measurements of temperature or species concentrations,
e.g
., via Raman scattering or laser
-
induced fluorescence, will be made to obtain more detailed quantitative information about the
edge
-
flame structure for comparison with theoretical models. A
lso, laser Doppler velocimetry
will be used examine the estimation for the local strain rate,

(x) = (V
upper
+V
lower
)/d(x).
Furthermore, theoretical models of single edge
-
flames having non
-
unity Lewis numbers are
needed for comparison with the observations reported here.



Acknowledgments



This work was supported by the NASA Lewis Research Center
under grant NAG3
-
1523.
The authors thank Profs. John Buckmaster and Amable Liñán for helpful discussions.



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15

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16



Figure 1. Edge
-
flame experimental apparatus



17








Figure 2. Video images of edge
-
flames. Upper: single flame, 9.0% CH
4

in air, V
upper

= V
lower

=
63 cm/sec, wedge angle 6.8˚; middle: twin
-
flame, 9.0% CH
4
/ 31.7% O
2
/ 56.3% CO
2

(low Le),
V
upper

= V
lower

= 40 cm/sec, wedge angle 6.8˚; lower: twin
-
flame, 2.1% C
3
H
8
/ 23.0% O
2
/ 74.9%
He (high Le), V
upper

= V
lower

= 30 cm/sec, wedge angle 6.8˚. In th
ese views the axis of
extensional strain (and the short dimension of the slot jets) is in/out of the plane of the image, the
long dimension of the slot jets in the horizontal direction and the flow out of the jets is in the
vertical direction. Field of v
iew is 2.9 cm x 8.1 cm for each image.


18









Figure 3. Interferograms of edge
-
flames. Upper: single flame, 7.5% CH
4

in air, V
upper

= V
lower

=
40 cm/sec; middle: twin
-
flame, 7.4% CH
4
/ 29.6% O
2
/ 63.0% CO
2

(low Le), V
upper

= V
lower

= 45
cm/sec; lower
: twin
-
flame, 2.85% C
3
H
8

in air (high Le), V
upper

= V
lower

= 40 cm/sec. Orientation
of images is the same as in Fig. 2. Field of view is 1.3 cm x 4.0 cm for each image.


19



Figure 4. Example of effect of nozzle exit velocity (V = V
upper

= V
lower
) on ext
inction strain rate
(

ext
) of twin uniform flames for CH
4
-
air mixtures.


20



Figure 5. Extinction strain rate vs. fuel mole fraction for twin
-
flames at various wedge angles
and exit flow velocities. Zero wedge angle corresponds to uniformly strained flam
es.

(a) CH
4
/O
2
/CO
2

mixtures


21


Figure 5. Extinction strain rate vs. fuel mole fraction for twin
-
flames at various wedge angles
and exit flow velocities. Zero wedge angle corresponds to uniformly strained flames.


(b) CH
4
/air mixtures


22


Figure 5. Ex
tinction strain rate vs. fuel mole fraction for twin
-
flames at various wedge angles
and exit flow velocities. Zero wedge angle corresponds to uniformly strained flames.


(c) C
3
H
8
/air mixtures


23


Figure 5. Extinction strain rate vs. fuel mole fraction f
or twin
-
flames at various wedge angles
and exit flow velocities. Zero wedge angle corresponds to uniformly strained flames.


(d) C
3
H
8
/O
2
/He mixtures


24



Figure 6. Extinction strain rate vs. fuel mole fraction for single flames at various wedge angles
a
nd exit flow velocities. Where two velocities are shown, these correspond to the upper and
lower nozzle exit velocities, respectively. Zero wedge angle corresponds to uniformly strained
flames.

(a) CH
4
/O
2
/CO
2

mixtures


25


Figure 6. Extinction strain ra
te vs. fuel mole fraction for single flames at various wedge angles
and exit flow velocities. Where two velocities are shown, these correspond to the upper and
lower nozzle exit velocities, respectively. Zero wedge angle corresponds to uniformly strained

flames.

(b) CH
4
/air mixtures


26


Figure 6. Extinction strain rate vs. fuel mole fraction for single flames at various wedge angles
and exit flow velocities. Where two velocities are shown, these correspond to the upper and
lower nozzle exit velocities,

respectively. Zero wedge angle corresponds to uniformly strained
flames.

(c) C
3
H
8
/air mixtures


27


Figure 6. Extinction strain rate vs. fuel mole fraction for single flames at various wedge angles
and exit flow velocities. Where two velocities are sho
wn, these correspond to the upper and
lower nozzle exit velocities, respectively. Zero wedge angle corresponds to uniformly strained
flames.

(d) C
3
H
8
/O
2
/He mixtures


28







Figure 7. Video images of diffusive
-
thermal instabilities. Upper: single edge
flame, 10.4 % CH
4
/ 34.4% O
2
/ 55.2% CO
2

(low Le), V
upper

= V
lower

= 56 cm/sec; middle: twin flame, uniformly
strained, 11.6 % CH
4
/ 30.7% O
2
/ 57.7% CO
2

(low Le), jet spacing 1.6 cm, V
upper

= V
lower

= 22
cm/sec; lower: twin
-
flame, 2.1% C
3
H
8
/ 23.0% O
2
/
74.9% He (high Le), V
upper

= V
lower

= 30
cm/sec, wedge angle 6.8˚, shutter speed 1/1000 sec. Orientation of images is the same as in Fig.
2. Field of view is 2.3 cm x 7.4 cm for each image.


29







Figure 8. Shadowgraph images of uniformly strained, near
-
extinction H
2
-
O
2
-
N
2

flames. Upp
er:
premixed twin
-
flame configuration, 5.4% H
2
/ 94.6% air, V
upper

= V
lower

= 100 cm/s, nozzle
spacing (d) = 1.27 cm (


= 157 s
-
1
). Lower: nonpremixed
-
flame configuration, upper nozzle
10.5% H
2

/ 89.5% N
2
, lower nozzle 21.0% O
2

/ 79.0% N
2
, V
upper

= V
low
er

= 40 cm/s, d = 1.27 cm,


= 63 s
-
1
. Field of view 1.3 cm x 2.6 cm in each image. Orientation of images is the same as in
Fig. 2. Both flame configurations are temporally stable.


30





Figure 9. Direct images of uniformly strained, propagating (from

left to right) edge
-
flames.
Upper: single flame, upper nozzle 6.1% CH
4

/ 93.9% air, lower nozzle 100% air, V
upper

= V
lower

= 25 cm/s, d = 1.5 cm,


= 33 s
-
1
, edge propagation rate is 37 cm/s, laminar burning velocity 12
cm/s (Vagelopoulos
et al
, 1994).

Lower: twin flame, both nozzles 6.8% CH
4

/ 93.2% air, V =
20 cm/s, d = 1.22 cm,


= 33 s
-
1
, edge propagation rate is 44 cm/s, laminar burning velocity 15
cm/s (Vagelopoulos
et al
, 1994). Orientation of images is the same as in Fig. 2.