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

To appear in Combustion Science and Technology, 1999

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.

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 (s) changes at rates comparable to s itself and the scale over which the flame front curvature and s change 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 s, the flame is expected to be extinguished, whereas at sufficiently low s 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 s at the edge-flame location (s_edge) compares with the extinction strain of a uniform flame (s_ext). If s_ext > s_edge, local extinguishment in highly strained regions of a turbulent flame sheet 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 s_edge > s_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 indeed stationary nonpremixed edge-flames could be produced. Edge-flames were found to be significantly weaker than uniformly strained flames, i.e., s_edge was less than the s_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 s € s_edge that advance into the unburned region for s < s_edge or retreat into the burned region for s > s_edge. Triple flames are rapidly advancing edge-flames that exist under conditions of sufficiently low s (or scalar gradient) that lean and rich premixed flame branches emanate from the leading edge of the nonpremixed flame and curve toward the direction opposite the propagation, forming an arrow-shaped flame structure. At higher s, close to s_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 where the reactant fluxes are in stoichiometric proportion. 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 flames 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 s the flame edge would advance at a steady rate into the non-burning region whereas for sufficiently high values of s the flame edge would retreat into the burning region. The edge speed was predicted to increase monotonically as s decreases. The ratio of s_edge to s_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-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 s_edge/s_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 is predicted to increase 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 undesirable 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 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 s(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)

(1)

where s(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, r_upper and r_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

(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, 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-flames (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 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 at the flame front for a conventional one-dimensional 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 V_upper > V_lower to move the flame farther from the upper nozzle and thus reduce heat losses (see Results).

Figure 1. Edge-flame experimental apparatus

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). 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, the uncertainty in the edge-flame location led to less than 2% uncertainty in the value of s(x) at the flame edge.

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 s(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 Ronney, 1998) because the flame position is at the location of stoichiometric ratio of reactant fluxes, 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 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 S_L is practically zero at the corner, nonetheless reaction is strengthened for CH₄/O₂/CO₂ mixtures (Le š 0.6) (Fig. 2, middle) and weakened to the point of having an open edge in C₃H₈/O₂/He mixtures (Le š 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.

Interferograms of some edge-flames were 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. Figure 3 shows that 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. This implies a sudden temperature drop on the non-burning side of the flame edge, which is consistent with the corresponding visual flame images (Fig. 2).

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 direct video images (Fig. 2, upper) and interferometer images (Fig. 3, upper and middle). For both single and twin-flames in Le < 1 mixtures, along the flame as the edge is approached, the flame front position first shifts toward the nozzle exit due to higher S_L before hooking toward the stagnation plane due to lower S_L. Consistent with this hypothesis, no similar behavior was observed for Le > 1 mixtures 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.

Ideally, the response of premixed flames to strain depends only on s 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 s_ext than under adiabatic conditions. To ensure that only near-adiabatic conditions were employed, the effects of V_upper and V_lower on s_ext were examined for uniformly-strained flames (Fig. 4). At low V, an increase in s_ext with increasing V is seen, implying a decreasing impact of heat loss. At larger V, s_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.

Figure 4. Example of effect of nozzle exit velocity (V = V_upper = V_lower) on extinction strain rate (s_ext) of twin uniform flames for CH₄-air mixtures.

Comparison of uniformly strained flames and edge-flames

Figures 5a - d show comparisons of s_ext for uniformly strained twin flames and s_edge for twin edge-flames. For uniform flames, s_ext was determined for fixed V_upper and V_lower by decreasing d until extinction occurred. For edge-flames, s_ext 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 s_ext is lower for the edge-flame, with the difference being much greater for mixtures with higher Le. For CH₄-air mixtures (Le š 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, s_ext/s_edge is close to unity for Le š 0.6, whereas Daou and Liñán predict s_ext/s_edge š 0.7 for this case. Otherwise, the results are very consistent with experiments in that s_ext/s_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 s_edge/s_ext is relatively minor in view of how 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 edge flames in mixtures with Le < 1 to exhibit positive propagation speeds that are larger than S_L when s is significantly less than s_edge, but of course for s > s_edge the edge speed is negative. Since stationary edges occur for s close to s_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 s_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 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-strained flames; each type of flame exhibits consistent but different response to strain. For the single flame configuration (Figs. 6a - d), s_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 s_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 our experiments indicate that twin-flame 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 this 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 s (Fig. 7, upper) whereas at higher s (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 structure for this case since s is close to s_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 s, 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 (š 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 s 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 occurs 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 s(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 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 (Le_fuel š Le_O2 š 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).

Motivated by these theoretical predictions, a set of experiments was performed using H₂-O₂-N₂ mixtures (Le_fuel š 0.3; Le_O2 š 1.0). In both premixed and nonpremixed cases, flame tubes were in fact observed. Examples of isolated premixed and nonpremixed flame tubes, at values of s 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) confirmed that these structures are tube-like rather than ball-like. The cross-section of the tubes is not round but is generally somewhat 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 s_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 s, 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 š 1.7). Somewhat surprisingly, the travelling-wave patterns were observed even in CH₄-air flames (Le š 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 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 behavior 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 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 may also increase 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 (s_edge) was nearly always lower than the extinction strain rates of uniformly strained flames in the same mixture (s_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 s_edge and s_ext for these mixtures. For the single-flame configuration s_edge was only very slightly lower than s_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 between s_edge and s_ext. For both single and twin flames the strain rate gradient had no significant effect on s_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 s, 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 that of the local quenching, 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 these 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 edge-flames by Daou and Liñán (1998b), who predicted that for Le = 3/8, 1 and 13/8, the corresponding values of s_edge/s_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 those of the fuel.) 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 s_edge/s_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, the range of applicability of laminar flamelet models, especially for high-Le mixtures, might 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 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 s < s_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 laser-induced 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, s(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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