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” could 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 corner-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 premixed 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 submitted to Combustion Science and Technology, November, 1998.
1
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, 1985;
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 turbulent 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 of 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 et 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
burning 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 (edge) 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 beyond 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-varying 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 mixture, 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 flames
and edge-flames are distinct structures yet each has well-defined properties. These phenomena
were qualitatively independent of the Lewis numbers (Le, defined as the ratio of the mixture
thermal diffusivity to the reactant mass diffusivity) of both reactants.
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-flames 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 and rich premixed flame branches emanate from the leading edge of
the nonpremixed flame and curve in the direction opposite the propagation, forming an arrowshaped flame structure. At higher , close to edge, these premixed branches merge with the
nonpremixed 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
relevant 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 burning 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 rising 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 the 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 twinflames. 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 edge2
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 activation 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 predictions, 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 same
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, 1986; 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 intentionally 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-flames 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,
thus 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 one 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 strain 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 strain 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
3
representative of the conditions 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 edge velocity should
be a stable equilibrium point.
The global strain rate for counterflowing slot-jet streams is given by (Seshadri and
Williams, 1978)
 (x) 
2Vupper  Vlower
1 
d(x)  Vupper
lower 

 upper 

(1)
where (x) is the strain rate at the location x along the length of the slot, Vupper and Vlower 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, thus the simplified relation 
 (x) 
Vupper  Vlower
 
d(x)
(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 strain
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, constantdensity 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-flames (Buckmaster, 1996; Buckmaster, 1997; Vedarajan and
Buckmaster, 1997; Vedarajan et al., 1998; Daou and Liñán, 1998a, b) have used the constantdensity assumption, thereby sidestepping the issue of flow-field modification near the flame edge
due to thermal 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-dimensional
4
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/translation 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 inside 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 mass-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 maintain symmetry. For single-flames, the upper nozzle contained the
reactive flow and the lower non-combustible flow was the same inert gas (He, N2 or CO2) as
used in the upper flow. In some single-flame cases, we employed Vupper > Vlower to move the
flame farther from the upper nozzle and thus reduce heat losses (see Results).
To obtain a wide range of Lewis numbers, CH4/air, C3H8/air, CH4/O2/CO2 and
C3H8/O2/He mixtures were employed, providing estimated Lewis numbers of 0.9, 1.7, 0.6 and
3.0, respectively. In the CH4/O2/CO2 and C3H8/O2/He mixtures, the fuel:O2 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 scarce 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 image signal-to-noise ratio. The images were then digitized by a
video processing system (Global Lab Image software with a DT3851 frame grabber). Edgeflame 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% uncertainty in the
value of (x) at the flame edge.
5
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 exhibit 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 (SL) decreases and the equilibrium location
of the flame (where SL 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 edgeflames (Shay and Ronney, 1998) because the flame position is at the location of stoichiometric
mixture fraction, rather than being determined by the balance between SL and local flow
velocity. For the twin premixed flame configuration, the two mirror-image flame hooks join
together 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 SL is practically zero at the corner, nonetheless reaction is strengthened for
CH4/O2/CO2 mixtures (Le ≈ 0.6) (Fig. 2, middle) and weakened to the point of having an open
edge in C3H8/O2/He mixtures (Le ≈ 3.0) (Fig. 2, lower). These observations are also consistent
with the well-known (e.g., Williams, 1985) characteristic 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 SL, 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 direct 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, rather 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 SL before hooking toward the stagnation flame due to
lower SL. Consistent with this hypothesis, no similar behavior was observed for Le > 1 mixtures
6
and in fact a region of weak burning exists near the edge (Fig. 3, lower), which is consistent 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.
Interferograms 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 from 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
(Vupper+Vlower)/d and not Vupper, Vlower or d individually. However, if Vupper or Vlower is too low,
i.e., comparable to SL, the flame position is close to the nozzle exit, which weakens it by heat
loss, leading to lower ext than under adiabatic conditions. To ensure that only near-adiabatic
conditions were employed, the effects of Vupper and Vlower on ext were examined for uniformlystrained flames (Fig. 4). At low V, an increase in ext with increasing V is seen, implying a
decreasing impact of heat loss. 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 and 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 Vupper and Vlower by
decreasing d until extinction occurred. For edge-flames, ext was determined for the same Vupper
and Vlower 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
CH4-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. Otherwise, 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 burning intensity at the corner (Fig. 2); indeed, it is
somewhat surprising that the effect of Le on edge/ext is relatively minor considering how
7
different the visible appearances of the twin edge-flame images are for Le < 1 and Le > 1 (Fig. 2,
middle and lower). 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 SL when  is significantly less than edge, but of course 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 to 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. The same conclusion was reached in our nonpremixed edge-flame study (Shay and Ronney, 1998). There is no gradual transition from edgeflame to uniform-strain behavior as the divergence angle decreases. Thus, edge-flames are
distinct from uniformly-strained 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 edgeflames 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. Unfortunately, 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 from 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 CH4/O2/CO2 mixtures, cellular structures were observed for both
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 CH4/O2/CO2 twin edge-flame in Fig. 2 (middle); there is no evidence of cellular
8
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 planestrain (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
CH4/O2/CO2 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
CH4/O2/CO2 flames.
In contrast, for the single-flame case cellular structures were observed in CH4/O2/CO2
mixtures at all  up to 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 configuration, 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 instability 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 spacing 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 occur 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 extreme
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 Buckmaster 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.
9
analogous to spherically-symmetric “flame balls” observed 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 survive 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 isolated
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
CH4-O2-CO2 mixtures (Lefuel ≈ LeO2 ≈ 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 H2-O2-N2
mixtures (Lefuel ≈ 0.3; LeO2 ≈ 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 nonpropagating, it was not necessary to employ angled slot jets to stabilize the flames. Images of
these flames in the orthogonal view (not shown) confirmed 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 direction (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 C3H8/O2/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 C3H8/air mixtures (Le ≈ 1.7).
Somewhat surprisingly, the travelling-wave patterns were observed even in CH4-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 typical frequencies around 200
10
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 chamber 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 edgeflame 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 observe 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 curvature-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 regions 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 (Vedarajan 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 influence on the comparison. For both cases the strain rate
11
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-flames 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, especially 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 as 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 H2-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 uniformly-strained flames was greater in that case and was
observed for all Le. This is consistent with a recent numerical study of nonpremixed edgeflames by Daou and Liñán (1998b), who predicted that for Le = 3/8, 1 and 13/8, the
corresponding values of edge/ext were 0.52, 0.41 and 0.28, respectively, assuming a nondimensional 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 with 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 well-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
12
parameter in edge-flame libraries. Of course, rules for merging edge-flames and locally-uniform
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 properties 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 or
plane measurements of temperature or species concentrations, e.g., via Raman scattering or laserinduced fluorescence, will be made to obtain more detailed quantitative information about the
edge-flame structure for comparison with theoretical models. Also, laser Doppler velocimetry
will be used examine the estimation for the local strain rate, (x) = (Vupper+Vlower)/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
T o ventilation
Insulation
Nozzle
Screen
Cooling
Pipe
Flame
Enclosure
Micrometer
Figure 1. Edge-flame experimental apparatus
16
Figure 2. Video images of edge-flames. Upper: single flame, 9.0% CH4 in air, Vupper = Vlower =
63 cm/sec, wedge angle 6.8˚; middle: twin-flame, 9.0% CH4 / 31.7% O2 / 56.3% CO2 (low Le),
Vupper = Vlower = 40 cm/sec, wedge angle 6.8˚; lower: twin-flame, 2.1% C3H8 / 23.0% O2 / 74.9%
He (high Le), Vupper = Vlower = 30 cm/sec, wedge angle 6.8˚. In these 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 view is 2.9 cm x 8.1 cm for each image.
17
Figure 3. Interferograms of edge-flames. Upper: single flame, 7.5% CH4 in air, Vupper = Vlower =
40 cm/sec; middle: twin-flame, 7.4% CH4 / 29.6% O2 / 63.0% CO2 (low Le), Vupper = Vlower = 45
cm/sec; lower: twin-flame, 2.85% C3H8 in air (high Le), Vupper = Vlower = 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.
18
400
Extinction strain rate (1/s)
350
300
7.0% CH
6.5% CH
250
4
4
200
150
100
20
40
60
Flow velocity (cm/s)
80
100
Figure 4. Example of effect of nozzle exit velocity (V = Vupper = Vlower) on extinction strain rate
(ext) of twin uniform flames for CH4-air mixtures.
19
Extinction strain rate (1/s)
500
400
300
6.79 deg., 55 cm/sec
4.54 deg., 55 cm/sec
3.40 deg., 55 cm/sec
0 deg., 55 cm/sec
3.40 deg., 45 cm/sec
4.54 deg., 45 cm/sec
6.79 deg., 45 cm/sec
0 deg., 45 cm/sec
200
100
0
7.6
8
8.4
8.8
9.2
CH mole fraction (%)
4
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.
(a) CH4/O2/CO2 mixtures
20
700
Extinction strain rate (1/s)
600
500
6.79 deg., 60 cm/sec
4.54 deg., 60 cm/sec
3.40 deg., 60 cm/sec
0 deg., 60 cm/sec
3.40 deg., 80 cm/sec
4.54 deg., 80 cm/sec
6.79 deg., 80 cm/sec
0 deg., 80 cm/sec
400
300
200
100
6.25
6.5
6.75
7
7.25
CH mole fraction (%)
7.5
7.75
4
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) CH4/air mixtures
21
500
6.79 deg., 60 cm/sec
4.54 deg., 60 cm/sec
3.40 deg., 60 cm/sec
0 deg., 60 cm/sec
Extinction strain rate (1/s)
450
400
350
300
250
200
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
C H mole fraction (%)
3
8
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.
(c) C3H8/air mixtures
22
500
Extinction strain rate (1/s)
400
300
200
6.79 deg., 40 cm/sec
4.54 deg., 40 cm/sec
3.40 deg., 40 cm/sec
0 deg., 40 cm/sec
100
0
2.2
2.4
2.6
2.8
3
3.2
C H mole fraction (%)
3
8
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.
(d) C3H8/O2/He mixtures
23
130
3.40 deg., 60 cm/sec
4.54 deg., 60 cm/sec
6.79 deg., 60 cm/sec
0 deg., 60 cm/sec
Extinction strain rate (1/s)
120
110
100
90
80
70
9.2
9.4
9.6
9.8
CH mole fraction (%)
10
10.2
4
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.
(a) CH4/O2/CO2 mixtures
24
400
4.54 deg., 60/20 cm/sec
3.40 deg., 60/20 cm/sec
2.27 deg., 60/20 cm/sec
0 deg., 60/20 cm/sec
Extinction strain rate (1/s)
350
300
250
200
150
100
50
7
7.5
8
8.5
9
CH4 mole fraction (%)
9.5
10
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.
(b) CH4/air mixtures
25
6.79 deg., 60/20 cm/sec
4.54 deg., 60/20 cm/sec
3.40 deg., 60/20 cm/sec
0 deg., 60/20 cm/sec
Extinction strain rate (1/s)
400
300
200
100
3
3.2
3.4
3.6
3.8
C H mole fraction (%)
3
4
4.2
8
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) C3H8/air mixtures
26
250
6.79 deg., 60 cm/sec
4.54 deg., 60 cm/sec
3.40 deg., 60 cm/sec
0 deg., 60 cm/sec
Extinction strain rate (1/s)
200
150
100
50
2
2.5
3
3.5
C H mole fraction (%)
3
8
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.
(d) C3H8/O2/He mixtures
27
Figure 7. Video images of diffusive-thermal instabilities. Upper: single edge flame, 10.4 % CH4
/ 34.4% O2 / 55.2% CO2 (low Le), Vupper = Vlower = 56 cm/sec; middle: twin flame, uniformly
strained, 11.6 % CH4 / 30.7% O2 / 57.7% CO2 (low Le), jet spacing 1.6 cm, Vupper = Vlower = 22
cm/sec; lower: twin-flame, 2.1% C3H8 / 23.0% O2 / 74.9% He (high Le), Vupper = Vlower = 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.
28
Figure 8. Shadowgraph images of uniformly strained, near-extinction H2-O2-N2 flames. Upper:
premixed twin-flame configuration, 5.4% H2 / 94.6% air, Vupper = Vlower = 100 cm/s, nozzle
spacing (d) = 1.27 cm ( = 157 s-1). Lower: nonpremixed-flame configuration, upper nozzle
10.5% H2 / 89.5% N2, lower nozzle 21.0% O2 / 79.0% N2, Vupper = Vlower = 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.
29
Figure 9. Direct images of uniformly strained, propagating (from left to right) edge-flames.
Upper: single flame, upper nozzle 6.1% CH4 / 93.9% air, lower nozzle 100% air, Vupper = Vlower
= 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% CH4 / 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.
30