Suppression of Cellular Structure in Slot-Burner Flames

Transcription

1 Suppression of Cellular Structure in Slot-Burner Flames L. J. ROSEN 1 and R. L. AXELBAUM* Washington University, Department of Mechanical Engineering, St. Louis, MO 63130, USA The mechanisms responsible for suppression of corrugated (cellular) structure in premixed flames have been investigated for slot-burner flames. Employing a novel variable-width slot burner, the effects of rim temperature, aerodynamics at the rim, and slot width were isolated. The results reveal that the dominant mechanism responsible for suppression of corrugated structure with increasing flow rate or decreasing slot width is time along the flame front. The results also suggest that stretch-induced stability due to positive strain rate and curvature at the base of rim-stabilized flames is essential for suppression of corrugated structure. Additionally, the suppression process, previously thought to be abrupt, was identified to occur over a distinct range of velocities, and this range was found to increase with increasing slot width. This new regime, defined as the transition regime, was characterized by a smooth, two-dimensional structure in the lower region near the rim and a corrugated, multi-dimensional structure in the upper region near the tip. A critical slot width, defined as w c, was also identified beyond which the corrugated structure could not be suppressed throughout the entire flame with increasing velocity. By examining the time available for growth of the instability, a simple model was developed that qualitatively describes the experimental results. For the 1-butene/air/CO 2 mixture analyzed, particle-tracking measurements yielded a characteristic time for growth of 22 ms and a critical slot width of w c 0.7 cm, which agrees well with the model prediction of w c 0.75 cm by The Combustion Institute NOMENCLATURE dl L Le Le c S L v v n v t V V b V c w w c * differential length along flame overall length of flame Lewis number critical Lewis number laminar flame speed local velocity vector component of local velocity vector normal to flame surface component of local velocity vector tangent to flame surface free-stream velocity centerline velocity when corrugations are suppressed at the base of the flame centerline velocity when corrugations are suppressed throughout the flame slot width critical slot width beyond which corrugated structure can not be suppressed angle of flame relative to vertical angle of local velocity vector relative to flame surface total time along the flame front characteristic time for visual perception of corrugated structure * Corresponding author. rla@me.wustl.edu 1 Currently at AP Materials, St. Louis, MO INTRODUCTION Observations of wrinkled laminar flames, in the form of polyhedral flames, date back as early as 1892 [1]. These and later findings show that under appropriate conditions, a wrinkled flame front is attained for rim-stabilized flames. The wrinkled flame structure is recognized as being primarily a consequence of diffusional-thermal instability [2]. Although considerable progress has been made toward understanding diffusional-thermal instability, there are a number of features of these flames that as yet remain unexplained. For example, early flame-speed studies with slot burners showed that corrugations can be suppressed either by increasing flow rate or decreasing slot width [3]. Markstein and Schwartz [4], in their systematic study of flame stability, speculated that flow rate suppresses cellular structure by either changing conditions at the flame base where ridge formation is triggered, or by decreasing time for build-up of flame corrugations during upward flame propagation. However, no explanation for the slot width dependence on suppression could be given. To date, neither of these issues has been resolved. Herein we attempt to develop a greater understanding of these phenomena and to identify the dominant mechanisms responsi- COMBUSTION AND FLAME 126: (2001) 2001 by The Combustion Institute /01/$ see front matter Published by Elsevier Science Inc. PII S (01)

2 1434 L. J. ROSEN AND R. L. AXELBAUM ble for suppression of instabilities with increasing flow rate or decreasing burner dimension. The cellular structure in rim-stabilized, premixed flames is commonly termed corrugated structure for slot-burner flames and polyhedral structure for axisymmetric flames. This structure manifests itself through imbalances in the rates of heat and mass diffusion, with diffusion of heat having a stabilizing effect and diffusion of mass having a destabilizing effect. Thus, stability is governed by the Lewis number, Le (ratio of thermal to mass diffusivities). Stability analysis shows that if the Le of the deficient reactant is less than a critical Lewis number, Le c, perturbations of the flame front grow to a characteristic wavelength, resulting in a steady, wrinkled flame front [2,5]. The Le Le c condition is attained for rich heavy-hydrocarbon or lean hydrogen flames. Several system parameters are known to affect the structure and stability limits of cellular flames. Experimental studies by Ishizuka et al. [6] and Ishizuka and Law [7] with propane/air mixtures, and theoretical studies by Sivashinsky et al. [8] showed that cellular instabilities are suppressed in the presence of positive stretch. Theoretical work by Joulin and Clavin [9] showed that stable adiabatic flames can be rendered unstable by an increase in heat loss. The experiments of Sohrab and Law [10] where heat loss was altered for rim-stabilized flames by changing the rim material, were consistent with this finding in that the limits of cellular instability increased with heat loss to the burner rim. As noted above, the earlier studies of slotburner flames [3, 4] demonstrated that cellular structure can be affected by altering not only mixture composition, but also flow rate and burner dimension. Isolating the effects of flow rate and burner dimension on stability limits is complicated by the coupling between relevant parameters. For example, changing flow rate or burner dimension can change the aerodynamics at the rim. Thus, stretch, heat loss, and entrainment at the base are varied, as is time for growth. Markstein and Schwartz [4] designed a novel burner to study the stability limits as functions of flow rate and burner dimension; however, their results did not identify the mechanisms responsible for suppression of cellular instabilities. Recent numerical simulations of corrugated flames stabilized on a slot burner, and polyhedral flames on a Bunsen burner, have successfully simulated experimentally observed flame shapes [5]. However, the simulations were unable to reproduce the suppression of corrugations with increasing free-stream velocity. Clearly, a better experimental understanding is needed. The present investigation aims at identifying the parameters affecting suppression of corrugated structure in rim stabilized flames and the mechanisms by which suppression occurs. EXPERIMENTAL APPARATUS Slot-burner flames were selected over axisymmetric flames for several reasons. First, the axisymmetric flame experiences concave curvature and, therefore, stretch in the bulk of the mixture, while the slot-burner flame does not. Both flames experience curvature and strain at the base and tip, this being an intrinsic characteristic of rim-stabilized flames. Second, the rectangular geometry is convenient to model. And third, the transition from smooth to corrugated structure can be more accurately identified by using a slot burner. The variable width slot burner constructed for this investigation is shown in Fig. 1. The burner consisted of two translatable walls onto which mm shim stock was attached. The lower (upstream) end of the shim stock was attached to a vertically translatable support so that the curvature of the converging nozzle could be adjusted until the desired velocity profile was achieved. Glass beads, honeycomb, and a 100-mesh screen acted as flow straighteners. The slot width could be varied continuously from 0 to 1.5 cm. The length of the slot was 6.0 cm and the rim thickness was 0.86 mm. A nitrogen shroud gas was introduced through a 0.70-cm-wide porous plate on the translatable walls to control the ambient composition near the base of the flame. The average velocity of the shroud gas was kept constant at 4.5 cm/s. The burner was sufficiently long such that the bulk of the flame did not suffer from curvature and could be considered two-dimensional when not corrugated.

3 CELLULAR STRUCTURE IN SLOT-BURNER FLAMES 1435 Fig. 1. Variable width slot burner: (a) schematic representation; and (b) view of burner with simple representation of corrugated flame. Drawing not to scale. The effect of burner-rim temperature was studied by varying the temperature with an electrically insulated Nichrome ribbon inserted between the rim and the porous plate. The voltage across the wire was varied by using a variable auto-transformer and measurements of the rim temperature were made by using a thermocouple attached flush to the burner rim. Gases were metered by using sonic nozzles and rotameters calibrated with soap-bubble meters. A bypass allowed the velocity of the mixture exiting the slot to be adjusted while maintaining a fixed mixture composition. Velocity measurements were obtained with a laser Doppler velocimeter. Measured turbulence levels were small (less than 1%) and thus, each velocity reported is the average of only five measurements. Velocity profiles for two different slot widths with the same free-stream velocity are shown in Fig. 2. Both profiles were obtained without a flame and exhibit top hat profiles with almost identical boundary layers. The boundary layer thickness is equivalent to that of flat-plate (Blasius) flow 1.1 cm from the leading edge [11]. Particle tracking measurements were performed by seeding the flow with Al 2 O 3 particles and illuminated by using a laser sheet from an argon-ion laser. The laser sheet was strobed at a frequency of 1750 Hz with an optical chopper. Fig. 2. Velocity profiles at the exit of the burner for two different slot widths with the same free-stream velocity. Results are for cold flow (no flame).

4 1436 L. J. ROSEN AND R. L. AXELBAUM Fig. 3. Stability map for 1-butene/air/CO 2 mixture with 8% CO 2 and slot width of 0.66 cm. Velocities are measured at the exit of the burner along the centerline. The magnitude and direction of the velocity vector were determined by photographing the flame and measuring the length of the particle streaks. RESULTS Stability maps in velocity-equivalence ratio space were obtained for a number of n-butane and 1-butene mixtures. The results for a 1-butene/air/CO 2 mixture are shown in Fig. 3. Results were obtained by maintaining a fixed composition and varying the flow rate of the mixture. Four distinct flame-types were identified over the range of equivalence ratios and centerline velocities studied: 1) smooth flames; 2) steady corrugated flames; 3) unsteady corrugated flames; and 4) oscillatory flames, being either corrugated or smooth. Steady corrugated flames are defined as flames with cells that are either stationary or whose motion can be stopped by inserting a small wire at the base of the flame [4]. Over a narrow range of equivalence ratios and velocities the motion of the cells could not be stopped with the wire. These flames are defined as unsteady corrugated flames [4], with the transition from steady to unsteady denoted by open triangles. The motion of these unsteady cells appeared random and persisted to the flashback limit, shown by open circles. Above the curve defined by the filled circles is a region in which the flames were observed to oscillate at frequencies and amplitudes that could be audibly detected. This oscillatory behavior persisted to the maximum velocity attainable with the existing flow system, 300 cm/s. The basic characteristics of the stability maps are similar to those reported by Gutman et al. [5] for lean H 2 /air flames. The effect of slot width on the critical velocity for suppression of corrugations was initially considered for a butane/air flame with an equivalence ratio of For small slot widths the findings of this study were similar to those of Markstein and Schwartz [4] and Gutman et al. [5] in that there was a well-defined velocity where the cellular structure was suppressed throughout the flame. However, at intermediate slot widths a narrow range of velocities was identified over which the corrugations grew from the tip to the base as velocity was decreased. This finding, that the transition from corrugated to smooth structure was not abrupt, but instead was a gradual process, necessitated defining a third regime, the transition regime. Thus, three distinct regimes could be distinguished during the transition from corrugated to smooth structure: 1) a corrugated regime in

5 CELLULAR STRUCTURE IN SLOT-BURNER FLAMES 1437 Fig. 4. Slot width dependence for 1-butene/air/CO 2 mixture with 8% CO 2 and an equivalence ratio of Circles denote limit conditions at which the corrugated structure appeared at the base (V b ), and triangles denote limit conditions at which the corrugated structure was suppressed throughout the entire flame (V c ). Insets schematically identify flame appearance. Velocities were measured at the exit of the burner along the centerline. which the entire flame was corrugated (steady or unsteady); 2) a transition regime in which the tip had a corrugated structure while the base appeared smooth; and 3) a smooth regime in which the entire flame appeared smooth. The identification of the transition regime, which apparently has not been previously reported for slot burners, will be shown to be crucial to our understanding of the mechanism responsible for suppression of the corrugated structure. The burner employed, with its continuously variable slot width, was essential for studying the transition process. To facilitate the study of the transition regime, CO 2 was added as a diluent to the butane/ air flame. Adding CO 2 allowed the Lewis number to be decreased in a controlled manner, and a lower Lewis number made the flame less stable and more prone to corrugated structure. However, the addition of CO 2 also weakened the butane/air flame, making it excessively sensitive to ambient air currents. Alternatively, mixtures of 1-butene/air/CO 2 were found to yield strong flames that were insensitive to ambient air currents, while retaining cellular instability, and thus this mixture was used instead of butane/air mixtures. The equivalence ratio and amount of CO 2 were chosen to yield a mixture that allowed clear observation of the transition behavior. The limit velocities for the three regimes described above are shown in Fig. 4 for a mixture of 1-butene/air/CO 2 with an equivalence ratio of 1.45 and 8% CO 2 by volume. The insets schematically represent the appearance of the flame in each regime. The data were obtained by varying flow rate for a given mixture composition and slot width, and visually monitoring the behavior of the flame. Because the burner is rectangular, with a minimum aspect ratio of 10:1, the flame could be viewed from a direction nearly tangent to the long dimension of the slot. This allowed minor perturbations in flame flatness to be detected. The circles in Fig. 4 correspond to the limit velocities where the corrugated structure first appeared at the base when velocity was decreased. Equivalently, this is the limit velocity where the corrugations were first suppressed at the base when velocity was increased. No hysteresis was observed. The triangles represent limit velocities where the cor-

6 1438 L. J. ROSEN AND R. L. AXELBAUM Fig. 5. Slot width dependence for H 2 /air/he/co 2 mixture with 30% He, 2.5% CO 2, and an equivalence ratio of Circles denote limit conditions at which the corrugated structure appeared at the base (V b ), and triangles denote limit conditions at which the corrugated structure was suppressed throughout the entire flame (V c ). Insets schematically identify flame appearance. Velocities were measured at the exit of the burner along the centerline. rugated structure was completely suppressed throughout the entire flame. Because this corrugated structure is a result of diffusional-thermal instability [5], we expect to find the same behavior with lean H 2 /air flames because, once again, the Lewis number for the deficient reactant is much less than unity, or more precisely Le Le c [2]. Therefore, similar tests were performed with H 2 /air mixtures. However, as Gutman et al. [5] reported, the velocities required to suppress instabilities in pure H 2 /air flames are quite high. To obtain a more manageable system, He was added to the mixture to weaken the flame while increasing the thermal diffusivity, thereby suppressing cellular instabilities. A small amount of CO 2 was also added to increase flame luminosity. The limit velocities for the H 2 /air/he/co 2 mixture with equivalence ratio of 0.54, 30% He and 2.5% CO 2 are shown in Fig. 5. Indeed the behavior was similar to that of the 1-butene/air/ CO 2 mixture described above. Singer [3] found that the cellular structure could always be suppressed by increasing velocity or decreasing slot width. It should be noted, however, that this study was confined to small slot widths ( cm) where, as seen from Figs. 4 and 5, the transition from smooth to cellular structure occurs over a narrow range of velocities. Gutman et al. [5] reported similar findings for small slot widths. Figures 4 and 5 reveal a number of interesting trends for corrugated flames. First, for slot widths greater than 0.6 cm, the velocity at which the corrugations appear at the base is nearly independent of slot width. Second, the velocity required to suppress the corrugated structure throughout the entire flame increases as slot width increases. Third, beyond a critical slot width, defined as w c, the instabilities can not be suppressed in the upper portion of the flames. Beyond the critical slot width, increasing velocity only results in an increase in flame height the upper portion remains corrugated. Figure 6a c show direct photographs of a 1-butene/air/CO 2 flame with an equivalence ratio of 1.45, 8% CO 2, and slot width of 0.60 cm for three different free-stream velocities. The flame is rich so in the absence of an inert shroud gas, a diffusion flame would exist downstream of

7 CELLULAR STRUCTURE IN SLOT-BURNER FLAMES 1439 Fig. 6. Direct photographs of 1-butene/air/CO 2 flames with 8% CO 2 and equivalence ratio of (a) Corrugated regime in which corrugated structure is evident throughout the flame; (b) transition regime in which corrugated structure is evident in upper regions but not at base; (c) smooth regime; (d) transition regime at slot width greater than the critical slot width. The diffusion flame seen on the short sides exists because there is no inert shroud gas on these sides (see Fig. 1). the premixed flame. The nitrogen shroud gas shown in Fig. 1 eliminates the diffusion flame along the length of the flame, but because the shroud gas is not present for the short ends (see Fig. 1), a diffusion flame is visible on either side in Fig. 6. Being confined to the short ends, the diffusion flames do not affect the characteristics in the bulk of the flame. Figure 6a shows the corrugated regime in which the entire flame appears corrugated, V 80 cm/s. Figure 6b shows the transition regime in which the upper portion of the flame appears corrugated while the base appears smooth, V 110 cm/s. Figure 6c shows the smooth regime in which the corrugated structure is completely suppressed, V 140 cm/s. Figure 6d shows a flame with the same composition as Figs. 6a c but at a slot width of 0.85 cm with velocity, V

8 1440 L. J. ROSEN AND R. L. AXELBAUM 134 cm/s. As can be seen from Fig. 4, this slot width is greater than the critical slot width, w c 0.75 cm, for this mixture, and thus the instabilities could not be completely suppressed at any velocity. Typical of flames in this regime, the flame is corrugated near the tip and smooth near the base. The number of cells is the same in Figs. 6a, b, and d even though the velocity varied from 80 to 140 cm/s. Thus, it is unlikely that a change in the characteristic wavelength of the cells is responsible for the suppression at the base. The effect of rim temperature on the transition from corrugated to smooth flames was also considered. With the experimental results discussed above as a baseline, the rim was heated to 260 C, which was 100 C above the steady state temperature without heating. The velocities required for complete suppression were identified and found to remain essentially unchanged. DISCUSSION The following summarizes our observations of the effects of slot width and freestream velocity on the corrugated structure: 1) The limit velocity for complete suppression of corrugations, V c, increased with slot width; 2) the corrugations were visibly suppressed first at the base and last at the tip with the cell size remaining essentially unchanged throughout the transition; 3) for small slot widths the transition from smooth structure (complete suppression) to corrugated structure was abrupt, occurring at a specific velocity; however, for larger slot widths the transition occurred over a distinct velocity interval V and V increased with slot width; 4) beyond a critical slot width, w c, the instabilities near the tip could not be suppressed by increasing velocity; 5) the limit velocity for suppression at the base, V b, was nearly constant for slot widths greater than 0.6 cm but decreased with decreasing slot width below 0.5 cm, particularly for 1-butene mixtures; and 6) increasing the rim temperature 100 C had a negligible effect on the limit velocities. Observation (1), that V c increased with slot width, suggests that flame stretch in the shear layer at the rim is not the only mechanism Fig. 7. Coordinate system to identify time along the flame front. responsible for suppression because the velocity gradients in the shear layer are constant for a given centerline velocity, as is evident from the velocity profiles in Fig. 1. Thus, one would expect that suppression would not be a function of slot width if flame stretch triggered suppression. This is not to say that flame stretch is not important to suppression, and we will see that it is, but clearly an additional mechanism is needed to explain the observations. It is possible that the changes in rim temperature, and subsequently heat transfer, are affecting suppression. However, as reasoned above, this cannot explain why V c increased with slot width, because just as the shear layer is constant for a given velocity, the rim temperature is constant. Furthermore, the change in rim temperature with velocity is not expected to be greater that 100 C over the range of velocities where transition is observed and thus, observation (6) suggests that rim temperature is not a dominant mechanism for the observed behavior. To explain all of the above observations, the time available for growth of the instability was considered. If we assume that the instability is initiated at the base and grows as it is convected along the flame front, then the time available for growth can be characterized by the time along the flame front. To characterize this time we define a coordinate system as shown in Fig. 7, where w is the slot width, L the overall length of the flame, v the local velocity, v t the component of v in the direction tangent to the flame,

9 CELLULAR STRUCTURE IN SLOT-BURNER FLAMES 1441 v n the component of v normal to the flame, the angle the flame surface makes with the vertical, the angle the velocity vector makes with the flame surface, and dl a differential length along the flame. The appearance of the flame in Fig. 7 was obtained from a direct photograph of a 1-butene/air/CO 2 flame. Figure 7 depicts the flame tip as open, which is a consequence of the Lewis number being less than unity. The total time along the flame front (i.e., the time available for growth of the instability) can then be characterized by: L 0 dl v t (1) The characteristic time for cell growth, *, will be defined as the time required for the disturbance to grow to an amplitude that can be visually detected. Physically this means that if the time available for growth,, is less than *, the flame will appear smooth because the disturbance has not had sufficient time to grow to a perceptible amplitude. For * the disturbance has had sufficient time to grow, and the flame will appear corrugated beyond the location where *. The characteristic time for cell growth can be evaluated by analyzing particle tracking images. Particle tracking measurements were performed on two flames of Fig. 4 where the conditions were such that a corrugated structure was barely perceptible at the flame tip (triangles in Fig. 4). The angle of the flame surface relative to the velocity vector at the flame surface,, was determined from the photographs as well. The velocity vector and angle of the flame surface were measured at various points along the flame in the vicinity of the luminous zone to allow v t to be determined. Curves were then fit to the experimental data to allow for smoothing and interpolation. The magnitude of the time along the flame front was determined by numerically integrating Eq. 1 from the tip of the flame to the base. With this approach, the magnitude of the integral increases nearly linearly until the integration approaches the region of high curvature at the base where the time abruptly goes to infinity because v t goes to zero. Neglecting this region, we found that the characteristic time for growth of the corrugated structure was 22 ms. The justification for neglecting this region will be discussed later. To simplify the subsequent discussion, the flame is assumed to be a flame sheet and the case of uniform velocity profile and constant density will be considered (i.e., v V and ). The flame sheet assumption implies that v t is invariant across the infinitely thin flame zone. To explain the observed behavior, it is necessary to consider the effect of free-stream velocity on the total time along the flame front. To do so, we write the expression for as a function of free-stream velocity, flame speed, and slot width, where we have assumed that S L v n at the upstream edge of the flame and that S L is constant along the flame. Thus, w 2S L 1 S L V 2. (2) Equation 2 can now be used to evaluate the total time along the flame front as a function of free-stream velocity, slot width, and flame speed. This has been done and is shown in Fig. 8. The flame speed used in Eq. 2 was the measured flame speed of 16 cm/s as determined from the particle tracking measurements in the bulk of the flame. Additionally, a value of * 22 ms, as measured above, is shown by the dashed line. We see from this figure that for small slot widths (w 0.70 cm), as velocity is increased the time along the flame front decreases to a value less than *. Thus, at these slot widths, corrugations can be suppressed throughout the entire flame by increasing velocity. Furthermore, as slot width increases, the velocity required to completely suppress the instabilities increases as well. These conclusions are consistent with observations (1) and (2) above. The effects of slot width and velocity are purely geometric; the flame height, and thus L, scales with slot width, requiring that the velocity be increased to suppress the corrugations. Increasing velocity reduces the time available for growth, not only because the velocity is higher

10 1442 L. J. ROSEN AND R. L. AXELBAUM Fig. 8. Total time available along the flame front as a function of freestream velocity for several slot widths as given by Eq. 2, and using the measured value of flame speed, S L 16 cm/s. but, more importantly because the angle (cf. Fig. 7) is reduced. Figure 8 is also consistent with observation (3) in that for small slot widths the transition from corrugated to smooth structure is abrupt, occurring over a narrow velocity interval V because at * d /dv is large. As slot width increases * d /dv decreases, implying that the velocity interval for transition increases. Taking the limit of Eq. 2 as V 3, results in 3 w/2s L. Thus, the critical slot width corresponds to the curve that asymptotes to *, and we can write: w c 2S L *. (3) This result is consistent with observation (4) in that there exists a critical slot width beyond which instabilities can not be suppressed by increasing velocity. This asymptote occurs because for V S L, 3 0 and cos 1 (S L /V) Thus, an increase in velocity is accompanied by a corresponding increase in flame length, and the total time along the flame can no longer be reduced. Time for growth can also explain observation (5). Unlike V c, only the velocity field near the rim affects V b ; the length and shape of the bulk of the flame are not important near the base. As seen in Fig. 2, the boundary layers in this burner were similar for a given free-stream velocity, implying that suppression at the base should not be a function of slot width. This is what was observed for large w. Nonetheless, for w 0.5 cm, V b decreased with decreasing w. This falloff in V b is reasonable because the velocity profile was not a perfect plug flow. As seen in Fig. 2, the boundary layer almost engulfed the velocity field for w 0.38 cm. Therefore, for small w the velocity profile in the boundary layer must steepen to obtain the same centerline velocity. Consequently, the mean velocity in the boundary layer will be greater for the same centerline velocity as w decreases. Thus, as observed, we expect V b to decrease with w when the boundary layer reaches the centerline. Although this model is effective at qualitatively explaining the observed trends, Eq. 2 cannot be used in a quantitative sense because of the many simplifications in its derivation. It might be expected that if the flow field were more accurately modeled then * could be accurately determined and the onset of wrinkles could be predicted. In principle this is true, but there are uncertainties, particularly associated with conditions near the rim, that complicate this approach. First, the flame speed varies near

11 CELLULAR STRUCTURE IN SLOT-BURNER FLAMES 1443 the rim, and this variation must be accounted for to determine time for growth. More importantly, however, the flame in the base region experiences positive flame stretch due to the strained flow field and positive curvature. Because positive strain rate [6,7] and positive curvature [8,12] suppress cellular instabilities, the positive stretch at the base of these slotburner flames results in local suppression of instabilities. Thus the characteristic rate of cell growth near the rim is reduced if not eliminated and it would be necessary to know the dependence of cellular growth rate on stretch to accurately predict the onset of wrinkles. That the instabilities are suppressed by positive stretch at the base appears to be essential for suppression of cellular growth in rim stabilized flames. This fact can be appreciated by noting that in rim stabilized flames a location near the rim exists where the velocity vector of the approaching flow is normal to the flame [13]. Thus, the tangential component of velocity in the vicinity of this point is exceedingly small and our observations as to the importance of time for growth would suggest that it would not be possible to suppress instabilities with flow rate because in this region there would always be sufficient time for growth. Nonetheless, the flame in this region is inherently experiencing positive stretch. The fact that suppression is at all possible implies that the flame stretch in this region is sufficient to suppress the growth of instabilities. It is only at locations away from the rim, where flame stretch is small, (or even negative for axisymmetric flames), that the instabilities grow and lead to a wrinkled structure. This may explain why the simulations in Ref. 5 were unable to show cellular suppression with increasing flow rate. The model employed in Ref. 5 did not include suppression at the base. Thus, there was always infinite time for cellular growth at the base. If we can assume that the instabilities are suppressed near the rim then the assumption made in the particle tracking analysis above, i.e., to neglect this region when calculating *, is valid. As noted earlier, the results of this analysis yielded * 22 ms and S L 16 cm/s. Substituting these values into Eq. 3, the model predicts that w c 0.7 cm. This finding is consistent with the observation in Fig. 4 that V 3 as w cm, (i.e., w c 0.75) and thus it supports the simple model and the assumption that instabilities are suppressed near the rim due to positive stretch. CONCLUDING REMARKS The mechanisms responsible for the suppression of corrugated structure due to increases in flow rate or changes in slot width in rim stabilized flames of a slot burner were considered. Changing rim temperature 100 C, proved to have little effect on the suppression of the corrugated structure for the flames studied, suggesting that changes in rim temperature due to increasing flow rate are not responsible for suppression. Slot width studies identified a transition regime in which the flame transforms from corrugated to smooth structure. This transition was not sharp, but rather occurred over a finite velocity interval. The interval was quite small at small slot widths, and grew as the slot width increased. Beyond a critical slot width, however, the instabilities could not be suppressed by increasing velocity. By identifying time along the flame front as the variable responsible for suppression, a model was developed that qualitatively described the stability diagrams for velocity and slot width. Suppression of instabilities at the base due to positive flame stretch appears to be essential to suppression of wrinkled structure in rim-stabilized flames. The authors are grateful to Professor C.K. Law for helpful discussions. L.J.R. was partially supported by the Lowy Fellowship and gratefully acknowledges this support. REFERENCES 1. Smithels, S., and Ingle, K., J. Chem. Soc. 61:204 (1892). 2. Sivashinsky, G. I., Combust. Sci. Tech. 15:137 (1977). 3. Singer, J. M., Proceedings of the Fourth International Symposium on Combustion. The Combustion Institute, Pittsburgh, 1953, p Markstein, G. H., and Schwartz, D., Proceedings of the Gas Dynamics Symposium on Aerothermochemistry. Northwestern University, Evanston, IL, 1956, p Gutman, S., Axelbaum, R. L., and Sivashinsky, G. I., Combust. Sci. Tech. 98:57 (1994).

12 1444 L. J. ROSEN AND R. L. AXELBAUM 6. Ishizuka, S., Miyasaka, K., and Law, C. K., Combust. Flame 45:293 (1982). 7. Ishizuka, S., and Law, C. K., Proceedings of the Nineteenth (International) Symposium on Combustion. The Combustion Institute, Pittsburgh, 1982, p Sivashinsky, G. I., Law, C. K., and Joulin, G., Combust. Sci. Tech. 28:155 (1982). 9. Joulin, G., and Clavin, P., Combust. Flame 35:139 (1979). 10. Sohrab, S. H., and Law, C. K., Combust. Flame 62:243 (1985). 11. Panton, R. L., Incompressible Flow. Wiley, New York, Bechtold, J. K., and Matalon, M., Combust. Flame 67:77 (1987). 13. Lewis, B., and von Elbe, G., Combustion, Flames and Explosions of Gases. Academic Press, New York, Received 20 September 1999; revised 24 March 2001; accepted 19 April 2001