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Extinction of near-limit premixed flames in microgravity
Proceedings of the Combustion Institute, Volume 28, 2000/pp. 1875–1882
EXTINCTION OF NEAR-LIMIT PREMIXED FLAMES IN MICROGRAVITY HAI ZHANG and FOKION N. EGOLFOPOULOS Department of Aerospace and Mechanical Engineering University of Southern California Los Angeles, CA 90089-1453, USA
The extinction characteristics of near-limit premixed flames were studied both experimentally and numerically under microgravity conditions in the opposed-jet counterflow configuration. The study assessed the synergistic effects of heat loss and strain rate on flame extinction and their implications on the existence of fundamental flammability limits. An experimental methodology was established appropriate for extinction studies of near-limit, weakly strained, premixed flames in microgravity. A novel approach was developed for the accurate determination of the mixture composition and the determination of extinction conditions. Experiments were conducted for CH4/air and C3H8/air mixtures, in order to assess Le number effects. Global extinction strain rates were determined for large nozzle separation distances, in order to minimize upstream heat losses. The numerical simulations of the experiments were conducted along the stagnation streamline and included the use of detailed description of chemical kinetics, molecular transport, and different models of thermal radiation. The original one-dimensional PREMIX and stagnation flow codes were modified to allow for one-point continuation, so that turning point, extinction behavior could be calculated. The numerical results showed that for Le ⬍ 1, near-limit mixtures exhibit a C-shape extinction response, while mixtures with Le ⬎ 1 exhibit a monotonic response, in agreement with previous studies. It was also found that as the nozzle separation distance is reduced, the extinction behavior is complicated by upstream heat losses, and the extinction diagram is of no fundamental value. Furthermore, when radiative heat reabsorption is included in the simulations, the structure of the postflame region is modified, and the maximum flame temperature is noticeably affected. However, the effect of reabsorption on the numerically determined flammability limits of CH4/air flames was found to be minor. The experimental data are also in good agreement with the simulations.
Introduction In early studies, the term flammability limit has been loosely used to describe the concentration limits beyond which flame propagation is not possible. Flammability limits are defined as the concentration limits beyond which the propagation of the ideal one-dimensional, steady, laminar, planar, nearly adiabatic flame configuration is not possible [1]; hereafter this model is referred to as the ideal onedimensional flame (IODF) model. Thus, if fundamental flammability limits exist, they must be intrinsic mixture properties, and, as such, they should not depend on any external loss mechanism, other than the inherently present radiative loss. Spalding [2] was the first to introduce a volumetric heat loss term in the IODF model by using one-step chemistry, and a turning point behavior was identified, as the heat loss parameter was increased. The confirmation of Spalding’s result was not possible over the years, as the IODF model can not be reproduced in the laboratory. Alternatively, flammability limits have been experimentally determined through the use of the standard flame tube (e.g., [3,4]) and/or the spherical bomb (e.g., [5]). Both approaches, however, include parameters such as heat
and radical losses, unsteadiness, strain rate, and ignition energy memory effect that are external to the mixture. Law et al. [6] proposed the use of stagnation-type flames to experimentally determine the true flammability limits, limit. The technique involves the determination of the extinction strain rates, Kext, by systematically varying the equivalence ratio, , of the mixture, and the determination of limit through linear extrapolation to Kext ⳱ 0. The effect of chemical kinetics on near-limit flames was addressed in Ref. [7] through a detailed numerical simulation of the IODF model for CH4/air mixtures. It was found that near-limit flames become particularly sensitive to chain mechanisms. Thus, a proper flammability exponent was formulated based on the kinetics. The flammability exponent was found to be of the order of one as the limits are approached. However, flame extinction was not observed because no heat loss was included. The effect of radiation on one-dimensional transient outwardly propagating and planar flames was first assessed in Refs. [8,9] by using one-step chemistry and allowing for radiation from CO2 and H2O. A limit concentration was identified beyond which propagation was not possible.
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Lakshmisha et al. [10] introduced for the first time the radiation term in detailed unsteady simulations of the IODF model. A limit concentration was identified beyond which a flame solution could not be found. The radiation was formulated based on Planck’s mean absorption coefficient and the assumption of the optically thin limit; hereafter, this model is referred to as the simple radiation model (SRM). Similarly to Ref. [10], Law and Egolfopoulos [11] introduced the SRM to the steady IODF model by invoking an arc-length continuation approach to describe singular points and detailed description of chemical kinetics and molecular transport. The simulations indeed captured a turning-point behavior by reducing . It was also found that the flammability exponent is of the order of unity at the vicinity of the turning point. The validity of the SRM in modeling flames was first addressed by Vranos and Hall [12] in strained non-premixed flames. The simulations included a detailed radiation model accounting for the wavelength dependence of the gas emissivity and absorptivity, as well as for reabsorption; hereafter, this model is referred to as the detailed radiation model (DRM). It was found that the SRM and DRM agree closely as long as the strain rate is not very low. Dixon-Lewis [13] and Egolfopoulos [14] first introduced the SRM in strained premixed flames. The results of Ref. [13] provided minimum information because limited calculations were performed on flame extinction. The study of Ref. [14] showed that, similarly to the unstrained flame simulations, the effect of radiation on extinction becomes profound as the limit concentrations are approached. The linear extrapolation to zero strain rate [6] was challenged by Maruta et al. [15] by introducing for the first time the counterflow configuration in microgravity. Thus, global extinction strain rates, Kglobal,ext, were determined for ultralow ’s; Kglobal ⬅ 2uexit/L, where uexit is the nozzle exit velocity and L is the nozzle separation distance. It was found that for flames with Le ⬍ 1, Kglobal,ext exhibits a turningpoint response to , while for Le ⬎ 1, Kglobal,ext decreases monotonically with . The C-shape behavior for flames with Le ⬍ 1 was attributed to the synergistic effect of the heat release reduction and the relative enhancement of radiation as the strain rate is reduced. The monotonic behavior for flames with Le ⬎ 1 was attributed to the relative enhancement of the heat release over radiation as the strain rate is reduced. The experimental data of Ref. [15] were numerically reproduced by Sung and Law [16] and Guo et al. [17], who also introduced the SRM to premixed strained flames, and by considering strain rates well below the ones of Ref. [14]. Both studies [16,17] confirmed the experimental findings of Ref. [15], and physical insight was provided.
Ju et al. [18] introduced the DRM in the IODF model. The effect of reabsorption on the response of near-limit flames was assessed. The microgravity extinction data presented in Ref. [15] were obtained for a nozzle separation distance L ⳱ 1.5 cm. Although the reported results have been qualitatively reproduced numerically [16,17], their fundamental validity is questioned because the flame thickness, d, can be of the order of 1.0 cm. Since d is of the order of L/2, it is apparent that upstream conductive heat loss to the (porous-type) burner was unavoidable. Furthermore, given that the experiments were conducted within a few seconds, the porous plates used could not be heated up noticeably because of their large thermal inertia. Thus, preheating of the mixture was not possible. Indeed, the numerical simulations of Ref. [16] have reproduced the C-shape behavior, but quantitative agreement with the microgravity data of Ref. [15] has been rather poor. In view of these considerations, the main objective of this work was to obtain experimental near-limit flame extinction data under microgravity conditions, free of any conductive loss. The study also aimed to numerically simulate the experiments by using detailed description of chemical kinetics, molecular transport, and various modes of heat losses.
Numerical Approach The PREMIX code [19] was used for the modeling of freely propagating flames. The counterflow configuration was simulated through the use of a stagnation flow code [20,21]. In both codes, a onepoint temperature continuation approach was implemented to allow for the calculation of turningpoint extinction behavior, as recommended in Ref. [22]. The codes were also modified to allow for radiative heat loss and were integrated with the CHEMKIN II [23] and TRANSPORT [24] subroutine packages. For the counterflow configuration, the SRM was adopted. For the freely propagating flame simulations, three radiation models were implemented to account for radiative loss from CO2, H2O, CO, and CH4. The SRM was used as in previous studies [11,14]. The DRM included the integration of the PREMIX code [19] with the RADCAL [25] radiation subroutine package. The semidetailed radiation model (SDRM) was derived from the DRM by removing the effect of reabsorption. The solutions of the counterflow were obtained in finite-domain configurations with various values of L in order to vary the magnitude of the upstream heat loss. Simulations were conducted for fuel-lean CH4/air (Le ⬍ 1) and C3H8/air (Le ⬎ 1) mixtures. The GRI 2.1 [26] kinetic scheme was used for the CH4/air
EXTINCTION OF FLAMES IN MICROGRAVITY
Fig. 1. (A) Microgravity experimental configuration. (B) Variation of with time.
flames. For the C3H8/air flames, a C3 [27] submechanism was added to the GRI 2.1. Experimental Approach Overview of the Microgravity Experimental System The extinction experiments on near-limit, laminar, premixed flames were conducted in the 2.2 s drop tower facility at NASA-Lewis Research Center. Two flames were established by impinging two identical mixtures on each other. L was large enough so that upstream heat loss was eliminated. The schematic of the microgravity apparatus is shown in Fig. 1a. It consists of several subsystems including power supply and distribution, mixture preparation, flow rate, and fuel concentration control through calibrated sonic nozzles, data acquisition, component action control, flame ignition, and flame visualization. All functions were automated through the use of a tattletale-based electronic circuit. Electronic pressure transducers were installed upstream of the sonic nozzles that controlled the air and fuel flow rates. A charge-coupled device (CCD) video camera was used to visualize the flame response. Experimental Procedures Lean premixed flames were ignited at normal gravity at a relatively high fuel concentration,
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through a combination of hot wire and a pilot-flame lighter. In these microgravity experiments, particular emphasis was given to the accurate determination of at the state of extinction, and an innovation was introduced. Fig. 1b depicts the variation of the fuel concentration during a typical duration of the experiment. Upon ignition at relatively high , the flames are separated by a relatively large distance. Subsequently, the fuel flow rate is reduced, the flames move toward the stagnation plane, and the experimental system is allowed to drop; the strain rate is largely determined by the airflow rate. Under microgravity conditions, stable and planar near-limit flames can be established [15]. Further lowering the fuel flow rate results in the reduction of to the point of extinction, as in Ref. [15]. In the present experiments and upon drop, the fuel flow rate was reduced to a lower level before the end of the 2.2 s period, and this level remained constant for the rest of the available microgravity time. The purpose of terminating the fuel reduction by reaching a constant fuel concentration level was to accurately determine ext. More specifically, if extinction did not occur, the experiment would be repeated by reducing the fuel flow rate to a lower level. The maximum at which the flame could be sustained was defined as ext at the corresponding Kglobal. The experimental uncertainty of this approach is of the order of the uncertainty of the calibration of sonic nozzles, that is, around 0.5%. The present approach requires a large number of drops. However, it is recommended as an improvement over that used in Ref. [15], in which is determined at the flame front by using a constant delay time. This approach was tested in our facilities, and it was found that the time delay depends not only on the total flow rate but also on the fuel concentration. At the same time, it should be realized that the approach used in Ref. [15] is still a meritorious one, given the overall complexity of the experimentation under microgravity conditions. Results and Discussion Comparisons of the Three Radiation Models: SRM, DRM, SDRM The effects of the three radiation models on the flame structure were compared for ⳱ 1.0, 0.7, and 0.51 CH4/air flames. Fig. 2 depicts the flame temperature profiles for these flames as predicted by using the three radiation models. For ⳱ 1.0, the temperature prediction of the two optically thin models (SRM and SDRM) are very close to each other. For the ⳱ 0.7 flame, SDRM predicts slightly higher temperatures compared to SRM, with a maximum difference of about 50 K. For ⳱ 0.51,
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Fig. 2. Numerically determined temperature profiles of CH4/air flames at p ⳱ 1 atm, using SRM, DRM, and SDRM.
Fig. 5. Numerically determined Tmax as function of Kglobal for ⳱ 0.48 and 0.50 CH4/air flames at p ⳱ 1 atm, using SRM and L ⳱ 100 mm.
the temperatures predicted by SDRM are noticeably higher compared to those predicted by SRM within the product zone, with a maximum difference of about 100 K. For all flames, the use of DRM results in higher temperatures, as expected. It is of interest to note that for both the ⳱ 1.0 and ⳱ 0.7 flames, the maximum flame temperature, Tmax, is minimally affected by reabsorption. For ⳱ 0.51, however, reabsorption has a noticeable effect. Figure 3 depicts the variation of Tmax versus for the IODF model, and a bifurcation behavior is seen. The results of Fig. 3 reveal that the lean flammability limits of CH4/air mixtures calculated by using the three radiation models are close to each other. SRM and SDRM predict lim ⬇ 0.51, while DRM predicts lim ⬇ 0.50. This observation is physically reasonable because ultralean CH4/air mixtures cannot effectively absorb heat in their unburned state. Fig. 3. Numerically determined flammability limits of CH4/air flames at p ⳱ 1 atm, using SRM, DRM, and SDRM.
Fig. 4. Numerically determined (dT/dx)nzl as function of and Kglobal for CH4/air flames at p ⳱ 1 atm, using SRM and L ⳱ 15 mm.
Finite Domain and Upstream Heat Loss Effects The effect of upstream heat loss was addressed by varying L. Fig. 4 depicts the variation of the temperature gradient at the nozzle exit, (dT/dx)nzl, as a function of and Kglobal for L ⳱ 15 mm, which corresponds to the experimental conditions of Ref. [15]. It can be seen that for all values of Kglobal, (dT/ dx)nzl is reduced with , and eventually extinction is induced at a ext value beyond which convergence is not possible. The reduction of (dT/dx)nzl with is a result of the reduced flame temperature and the fact that the flame moves away from the burner. It is of interest to note that ext is initially reduced and subsequently increases as the (dT/dx)nzl increases. For Kglobal values greater than 5 sⳮ1, upstream heat loss is substantially reduced, the flames approach the stagnation plane, and the extinction is strain-rate induced. For lower Kglobal values, upstream heat loss is substantial. As Kglobal increases, the amount of conductive heat loss is reduced, and a leaner flame can be sustained.
EXTINCTION OF FLAMES IN MICROGRAVITY
Fig. 6. Numerically determined Tmax as function of Kglobal for a ⳱ 0.48 CH4/air flame at p ⳱ 1 atm, using SRM and L ⳱ 15 and 100 mm.
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⬎ 0. For L ⳱ 7 mm, the flames are affected by the upstream heat loss for the all Kglobal values, that is, (dT/dx)nzl ⬎ 0 everywhere. It should be noted that when upstream heat loss is present, the turningpoint extinction is not observed. The complete extinction Kglobal,ext versus diagram for CH4/air flames is shown in Fig. 7 for L ⳱ 100 and 15 mm. While the results obtained for L ⳱ 100 mm correspond to nearly adiabatic flames, the results obtained for L ⳱ 15 mm include the effect of upstream heat loss as Kglobal decreases. Adiabatic (i.e., no upstream heat loss) flames calculated for L ⳱ 100 mm exhibit the anticipated C-shape extinction behavior, as shown before in Ref. [16] by using L ⳱ 60 mm. For L ⳱ 15 mm, the extinction limits induced by strain rate at the same are lower compared to those for L ⳱ 100 mm because of the finite domain effect [14]. However, the lower branch for L ⳱ 15 mm is not shown because the notion of strain rate is meaningless given that a hydrodynamic zone cannot be defined when upstream heat loss is present. Microgravity Experiments and Comparisons with Numerical Simulations
Fig. 7. Numerically determined Kglobal,ext as function of for lean CH4/air flames at p ⳱ 1 atm, using SRM and L ⳱ 7, 12, and 100 mm.
Calculations were also conducted for L ⳱ 100 mm, which is large for any upstream heat loss to be present. Fig. 5 depicts the variation of Tmax with Kglobal, for ⳱ 0.48 and ⳱ 0.50 CH4/air flames. Similarly to the results of Refs. [16,17], a closed loop is formed, characterized by two extinction points. The one corresponding to the higher Kglobal,ext is caused by the strain rate, while the one corresponding to the lower Kglobal,ext is caused by the synergistic effects of thermal radiation, Lewis number, and strain rate. Additional simulations were conducted by reducing L in order to induce upstream heat loss. Fig. 6 depicts the variation of Tmax and (dT/dx)nzl with Kglobal for a ⳱ 0.48 CH4/air flame at different values of L. It can be seen that for the larger, L ⳱ 100 mm, the flame response is nearly adiabatic (i.e., no upstream heat loss). For the smaller, L ⳱ 12 mm, at high Kglobal values, the flames are adiabatic, that is, (dT/dx)nzl ⳱ 0, while at low Kglobal values, the upstream heat loss becomes finite, that is, (dT/dx)nzl
In normal gravity (1g), near-limit flames cannot be stabilized because of buoyancy-induced instabilities. In microgravity, steady near-limit planar flames can be stabilized. The extinction responses of near-limit CH4/air and C3H8/air mixtures were found to be consistent with the reported ones in Ref. [15]. As was decreased, extinction of CH4/air flames was observed after the flames merged at the stagnation plane, given that Le ⬍ 1 [28]. For the same L, , and Kglobal, C3H8/air flames were stabilized closer to the burner compared to CH4/air flames, as for the same , C3H8/air mixtures have higher flame speeds compared to CH4/air. It was observed that flame extinction occurred when the two C3H8/air flames were at a finite distance, given that Le ⬎ 1 [28]. Experimental microgravity data of Kglobal,ext versus for CH4/air and C3H8/air mixtures were obtained with L ⳱ 50 mm and are shown in Figs. 8 and 9 respectively, along with the microgravity data of Maruta et al. [15], and results from numerical simulations. The results in Fig. 8 exhibit a C-shape extinction response of Kglobal versus for CH4/air mixtures, which qualitatively agree with those reported in Ref. [15]. The results of the present numerical simulations obtained with L ⳱ 15 and 50 mm are also shown in Fig. 8. Compared to the experimental data of Ref. [15], the present data are shifted toward lower values and are in better agreement with the present simulations than the simulations of Ref. [16]. This was anticipated because in the present experiments, upstream heat losses were eliminated.
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Fig. 8. Experimentally and numerically determined Kglobal,ext as function of for lean CH4/air flames at p ⳱ 1 atm. Simulations were conducted using SRM.
Fig. 9. Experimentally and numerically determined Kglobal,ext as function of for lean C3H8/air flames at p ⳱ 1 atm. Simulations were conducted using SRM.
The results of Fig. 9 exhibit a monotonic extinction response of Kglobal versus for C3H8/air mixtures, similarly to Ref. [15]. The results of the present numerical simulations, obtained with L ⳱ 50 mm, are also shown. The discrepancies that are observed between experiments and simulations may be a result of inaccuracies associated with the C3 chemical scheme. At the same time, comparing with the data of Ref. [15], the present experimental data are shifted toward higher values of , which is the opposite to what was shown for CH4/air mixtures. This may be caused by finite-domain effects [14] given that different values of L were used. The present microgravity data are also compared with extinction data obtained in normal gravity for higher values, and the consistency between the two sets of data is apparent. Concluding Remarks A combined experimental and detailed numerical investigation was conducted on the extinction characteristics of near-limit laminar premixed flames.
The study aimed to provide insight into phenomena of relevance to the experimental and numerical determination of extinction and flammability limits. Experiments included the use of the counterflow configuration in microgravity, and an improved approach was introduced for the accurate determination of the mixture composition at extinction. Furthermore, special care was taken to avoid upstream heat losses, which could be present in near-limit experiments. The numerical simulations included the use of the CHEMKIN-based freely propagating and stagnation-flow flame codes, which were modified by introducing a one-point continuation approach to capture turning-point behavior around extinction conditions. Furthermore, three thermal radiation models were used. In these models, the gas emissivity was calculated by either using Planck’s mean absorption coefficient (SRM) or by accounting for the wavelength dependence of the gas emission/absorption characteristics (DRM). The DRM model was also used at the optically thin limit (SDRM). For vigorously burning flames, it was found that both SRM and SDRM similarly predict the thermal radiation. However, for near-limit flames, the SRM was found to significantly overpredict the radiation loss. It was also found that radiation noticeably affects the maximum flame temperature, only for nearlimit flames. Flammability limits calculated by using the different radiation models differ slightly, although the rates of downstream radiative transfer are significantly different. This suggests that the extent of the downstream heat loss plays a minor role. Mixtures with Le ⬍ 1 were found both experimentally and numerically to exhibit a C-chape nearlimit extinction response, which is caused by the synergistic effects of strain rate and radiation. Mixtures with Le ⬎ 1 were found to exhibit a monotonic nearlimit extinction response. Both these findings are consistent with previous studies. The microgravity experimental data presented in this paper, however, appear to be in better agreement with numerical predictions than previous data in which upstream heat loss may have been present. Simulations were conducted for a wide range of nozzle separation distances, and it was found that as the nozzle separation distance is reduced, upstream heat loss becomes important, and the extinction diagram is not of fundamental value. Furthermore, when upstream heat loss is present, the characterization of the fluid mechanics by referencing to strain rate is incorrect, because no hydrodynamic zone can be identified. Acknowledgments This study was funded by NASA, grant no. NAG3-1615, under the technical supervision of Dr. Fletcher Miller. The
EXTINCTION OF FLAMES IN MICROGRAVITY assistance of Mr. J.-Y. Ren in the preparation of the final manuscript is greatly appreciated.
REFERENCES 1. Williams, F. A., Combustion Theory, 2nd ed., Benjamin-Cummings, Menlo Park, CA, 1985. 2. Spalding, D. B., Proc. R. Soc. London A 240:83–100 (1957). 3. Coward, H. F., and Jones, G. W., Limits of Flammability of Gases and Vapors, Bureau of Mines Bulletin 503, 1952. 4. Strehlow, R. A., Noe, K. A., and Wherley, B. L., Proc. Combust. Inst. 21:1899–1908 (1986). 5. Ronney, P. D., and Wachman, H. Y., Combust. Flame 62:107–119 (1985). 6. Law, C. K., Zhu, D. L., and Yu, G., Proc. Combust. Inst. 21:1419–1426 (1986). 7. Law, C. K., and Egolfopoulos, F. N., Proc. Combust. Inst. 23:413–421 (1990). 8. Sibulkin, M., and Frendi, A., Combust. Flame 82:334– 345 (1990). 9. Frendi, A., and Sibulkin, M., Combust. Flame 86:185– 186 (1991). 10. Lakshmisha, K. N., Paul, P. J., and Mukunda, H. S., Proc. Combust. Inst. 23:433–440 (1990). 11. Law, C. K., and Egolfopoulos, F. N., Proc. Combust. Inst. 24:137–144 (1992). 12. Vranos, A., and Hall, R. J., Combust. Flame 93:230– 238 (1993).
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13. Dixon-Lewis, G., Proc. Combust. Inst. 25:1325–1332 (1994). 14. Egolfopoulos, F. N., Proc. Combust. Inst. 25:1375– 1381 (1994). 15. Maruta, K., Yoshida, M., Ju, Y., and Niioka, T., Proc. Combust. Inst. 26:1283–1289 (1996). 16. Sung, C. J., and Law, C. K., Proc. Combust. Inst. 26:865–873 (1996). 17. Guo, H., Ju, Y., Maruta, K., Niioka, T., and Liu, F., Combust. Flame 109:639–651 (1997). 18. Ju, Y., Masuya, G., and Ronney, P. D., Proc. Combust. Inst. 27:2619–2626 (1998). 19. Kee, R. J., Grcar, J. F., Smooke, M. D., and Miller, J. A., Sandia report SAND85-8240. 20. Egolfopoulos, F. N., Proc. Combust. Inst. 25:1365– 1373 (1994). 21. Egolfopoulos, F. N., and Campbell, C. S., J. Fluid Mech. 318:1–27 (1996). 22. Nishioka, M., Law, C. K., and Takeno, T., Combust. Flame 104:328–342 (1996). 23. Kee, R. J., Rupley, F. M., and Miller, J. A., Sandia report SAND89-8009. 24. Kee, R. J., Warnatz, J., and Miller, J. A., Sandia report SAND83-8209. 25. Grosshandler, W. L., RADCAL: A Narrow-Band Model for Radiation Calculations in a Combustion Environment, NIST Technical Note 1402, 1993. 26. Bowman, C. T., Frenklack, M., Gardiner, W., and Smith, G., The GRI 2.1 Mechanism, 1995. 27. Pitz, W. A., and Westbrook, C. K., Combust. Flame 63:113–133 (1986). 28. Law, C. K., Proc. Combust. Inst. 22:1381–1402 (1988).
COMMENTS Kaoru Maruta, Akita Prefectural University, Japan. A possible source of discrepancy between one-dimensional modeling and the experimental results might be boundary effects such as diffusion toward radial direction. May I have your opinion on this?
Author’s Reply. Indeed, the observed discrepancies may be attributed to a number of effects. In addition to the one that you mentioned, it may be that near-limit flames may be sensitive to effects of curvature that may develop in the absence of coflow. Furthermore, mixture dilution by the ambient air at the outer edges of the reacting jets may also affect the overall extinction response. Such effects can only be captured through an exact, axisymmetric, numerical simulation of the experiments. It must also be kept in mind that the reliability of existing detailed chemical kinetic mechanisms in closely describing near-limit flames could be a potential error factor as detailed experimental data for
such flames that would be appropriate for validation do not exist. ● K. N. Lakshmisha, Indian Institute of Science, Banglore, India. We know that on either side of the unity equivalence ratio the instability mechanisms and the kinetic mechanisms are very different. For instance, fuel-rich flammability limits of H2-air mixtures are likely to have pulsating instabilities. There could be cellular instabilities for other near-limit mixtures, influencing the flammability limit. Do you think one could eventually develop a unified explanation for these different situations? If so, what possible effects do you suggest would be required in numerical situations? Author’s Reply. A number of recent experimental and detailed numerical studies have indeed revealed the exis-
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tence of the mentioned behavior for near-limit mixtures. Even though the observed phenomena may differ between fuels as well as between lean and rich limits, it is true that in all cases the mixtures become particularly sensitive to heat-loss mechanisms as the limit concentrations are approached. Past studies have also shown that at the vicinity of the experimentally observed limits, the sensitivity between the controlling branching and termination reactions is heightened, and that an appropriately normalized value
of this sensitivity assumes values of the order of orders. It is the authors’ opinion that if a unified explanation is to be derived, the response of the kinetics must be considered. While one-dimensional simulations reveal the basis behavior of ideal reacting fronts, the interpretation of actual experiments for near-limit concentration through numerical simulations must ideally include the use of multidimensional codes that can account for every detail of the experiment.
EXTINCTION OF NEAR-LIMIT PREMIXED FLAMES IN MICROGRAVITY HAI ZHANG and FOKION N. EGOLFOPOULOS Department of Aerospace and Mechanical Engineering University of Southern California Los Angeles, CA 90089-1453, USA
The extinction characteristics of near-limit premixed flames were studied both experimentally and numerically under microgravity conditions in the opposed-jet counterflow configuration. The study assessed the synergistic effects of heat loss and strain rate on flame extinction and their implications on the existence of fundamental flammability limits. An experimental methodology was established appropriate for extinction studies of near-limit, weakly strained, premixed flames in microgravity. A novel approach was developed for the accurate determination of the mixture composition and the determination of extinction conditions. Experiments were conducted for CH4/air and C3H8/air mixtures, in order to assess Le number effects. Global extinction strain rates were determined for large nozzle separation distances, in order to minimize upstream heat losses. The numerical simulations of the experiments were conducted along the stagnation streamline and included the use of detailed description of chemical kinetics, molecular transport, and different models of thermal radiation. The original one-dimensional PREMIX and stagnation flow codes were modified to allow for one-point continuation, so that turning point, extinction behavior could be calculated. The numerical results showed that for Le ⬍ 1, near-limit mixtures exhibit a C-shape extinction response, while mixtures with Le ⬎ 1 exhibit a monotonic response, in agreement with previous studies. It was also found that as the nozzle separation distance is reduced, the extinction behavior is complicated by upstream heat losses, and the extinction diagram is of no fundamental value. Furthermore, when radiative heat reabsorption is included in the simulations, the structure of the postflame region is modified, and the maximum flame temperature is noticeably affected. However, the effect of reabsorption on the numerically determined flammability limits of CH4/air flames was found to be minor. The experimental data are also in good agreement with the simulations.
Introduction In early studies, the term flammability limit has been loosely used to describe the concentration limits beyond which flame propagation is not possible. Flammability limits are defined as the concentration limits beyond which the propagation of the ideal one-dimensional, steady, laminar, planar, nearly adiabatic flame configuration is not possible [1]; hereafter this model is referred to as the ideal onedimensional flame (IODF) model. Thus, if fundamental flammability limits exist, they must be intrinsic mixture properties, and, as such, they should not depend on any external loss mechanism, other than the inherently present radiative loss. Spalding [2] was the first to introduce a volumetric heat loss term in the IODF model by using one-step chemistry, and a turning point behavior was identified, as the heat loss parameter was increased. The confirmation of Spalding’s result was not possible over the years, as the IODF model can not be reproduced in the laboratory. Alternatively, flammability limits have been experimentally determined through the use of the standard flame tube (e.g., [3,4]) and/or the spherical bomb (e.g., [5]). Both approaches, however, include parameters such as heat
and radical losses, unsteadiness, strain rate, and ignition energy memory effect that are external to the mixture. Law et al. [6] proposed the use of stagnation-type flames to experimentally determine the true flammability limits, limit. The technique involves the determination of the extinction strain rates, Kext, by systematically varying the equivalence ratio, , of the mixture, and the determination of limit through linear extrapolation to Kext ⳱ 0. The effect of chemical kinetics on near-limit flames was addressed in Ref. [7] through a detailed numerical simulation of the IODF model for CH4/air mixtures. It was found that near-limit flames become particularly sensitive to chain mechanisms. Thus, a proper flammability exponent was formulated based on the kinetics. The flammability exponent was found to be of the order of one as the limits are approached. However, flame extinction was not observed because no heat loss was included. The effect of radiation on one-dimensional transient outwardly propagating and planar flames was first assessed in Refs. [8,9] by using one-step chemistry and allowing for radiation from CO2 and H2O. A limit concentration was identified beyond which propagation was not possible.
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Lakshmisha et al. [10] introduced for the first time the radiation term in detailed unsteady simulations of the IODF model. A limit concentration was identified beyond which a flame solution could not be found. The radiation was formulated based on Planck’s mean absorption coefficient and the assumption of the optically thin limit; hereafter, this model is referred to as the simple radiation model (SRM). Similarly to Ref. [10], Law and Egolfopoulos [11] introduced the SRM to the steady IODF model by invoking an arc-length continuation approach to describe singular points and detailed description of chemical kinetics and molecular transport. The simulations indeed captured a turning-point behavior by reducing . It was also found that the flammability exponent is of the order of unity at the vicinity of the turning point. The validity of the SRM in modeling flames was first addressed by Vranos and Hall [12] in strained non-premixed flames. The simulations included a detailed radiation model accounting for the wavelength dependence of the gas emissivity and absorptivity, as well as for reabsorption; hereafter, this model is referred to as the detailed radiation model (DRM). It was found that the SRM and DRM agree closely as long as the strain rate is not very low. Dixon-Lewis [13] and Egolfopoulos [14] first introduced the SRM in strained premixed flames. The results of Ref. [13] provided minimum information because limited calculations were performed on flame extinction. The study of Ref. [14] showed that, similarly to the unstrained flame simulations, the effect of radiation on extinction becomes profound as the limit concentrations are approached. The linear extrapolation to zero strain rate [6] was challenged by Maruta et al. [15] by introducing for the first time the counterflow configuration in microgravity. Thus, global extinction strain rates, Kglobal,ext, were determined for ultralow ’s; Kglobal ⬅ 2uexit/L, where uexit is the nozzle exit velocity and L is the nozzle separation distance. It was found that for flames with Le ⬍ 1, Kglobal,ext exhibits a turningpoint response to , while for Le ⬎ 1, Kglobal,ext decreases monotonically with . The C-shape behavior for flames with Le ⬍ 1 was attributed to the synergistic effect of the heat release reduction and the relative enhancement of radiation as the strain rate is reduced. The monotonic behavior for flames with Le ⬎ 1 was attributed to the relative enhancement of the heat release over radiation as the strain rate is reduced. The experimental data of Ref. [15] were numerically reproduced by Sung and Law [16] and Guo et al. [17], who also introduced the SRM to premixed strained flames, and by considering strain rates well below the ones of Ref. [14]. Both studies [16,17] confirmed the experimental findings of Ref. [15], and physical insight was provided.
Ju et al. [18] introduced the DRM in the IODF model. The effect of reabsorption on the response of near-limit flames was assessed. The microgravity extinction data presented in Ref. [15] were obtained for a nozzle separation distance L ⳱ 1.5 cm. Although the reported results have been qualitatively reproduced numerically [16,17], their fundamental validity is questioned because the flame thickness, d, can be of the order of 1.0 cm. Since d is of the order of L/2, it is apparent that upstream conductive heat loss to the (porous-type) burner was unavoidable. Furthermore, given that the experiments were conducted within a few seconds, the porous plates used could not be heated up noticeably because of their large thermal inertia. Thus, preheating of the mixture was not possible. Indeed, the numerical simulations of Ref. [16] have reproduced the C-shape behavior, but quantitative agreement with the microgravity data of Ref. [15] has been rather poor. In view of these considerations, the main objective of this work was to obtain experimental near-limit flame extinction data under microgravity conditions, free of any conductive loss. The study also aimed to numerically simulate the experiments by using detailed description of chemical kinetics, molecular transport, and various modes of heat losses.
Numerical Approach The PREMIX code [19] was used for the modeling of freely propagating flames. The counterflow configuration was simulated through the use of a stagnation flow code [20,21]. In both codes, a onepoint temperature continuation approach was implemented to allow for the calculation of turningpoint extinction behavior, as recommended in Ref. [22]. The codes were also modified to allow for radiative heat loss and were integrated with the CHEMKIN II [23] and TRANSPORT [24] subroutine packages. For the counterflow configuration, the SRM was adopted. For the freely propagating flame simulations, three radiation models were implemented to account for radiative loss from CO2, H2O, CO, and CH4. The SRM was used as in previous studies [11,14]. The DRM included the integration of the PREMIX code [19] with the RADCAL [25] radiation subroutine package. The semidetailed radiation model (SDRM) was derived from the DRM by removing the effect of reabsorption. The solutions of the counterflow were obtained in finite-domain configurations with various values of L in order to vary the magnitude of the upstream heat loss. Simulations were conducted for fuel-lean CH4/air (Le ⬍ 1) and C3H8/air (Le ⬎ 1) mixtures. The GRI 2.1 [26] kinetic scheme was used for the CH4/air
EXTINCTION OF FLAMES IN MICROGRAVITY
Fig. 1. (A) Microgravity experimental configuration. (B) Variation of with time.
flames. For the C3H8/air flames, a C3 [27] submechanism was added to the GRI 2.1. Experimental Approach Overview of the Microgravity Experimental System The extinction experiments on near-limit, laminar, premixed flames were conducted in the 2.2 s drop tower facility at NASA-Lewis Research Center. Two flames were established by impinging two identical mixtures on each other. L was large enough so that upstream heat loss was eliminated. The schematic of the microgravity apparatus is shown in Fig. 1a. It consists of several subsystems including power supply and distribution, mixture preparation, flow rate, and fuel concentration control through calibrated sonic nozzles, data acquisition, component action control, flame ignition, and flame visualization. All functions were automated through the use of a tattletale-based electronic circuit. Electronic pressure transducers were installed upstream of the sonic nozzles that controlled the air and fuel flow rates. A charge-coupled device (CCD) video camera was used to visualize the flame response. Experimental Procedures Lean premixed flames were ignited at normal gravity at a relatively high fuel concentration,
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through a combination of hot wire and a pilot-flame lighter. In these microgravity experiments, particular emphasis was given to the accurate determination of at the state of extinction, and an innovation was introduced. Fig. 1b depicts the variation of the fuel concentration during a typical duration of the experiment. Upon ignition at relatively high , the flames are separated by a relatively large distance. Subsequently, the fuel flow rate is reduced, the flames move toward the stagnation plane, and the experimental system is allowed to drop; the strain rate is largely determined by the airflow rate. Under microgravity conditions, stable and planar near-limit flames can be established [15]. Further lowering the fuel flow rate results in the reduction of to the point of extinction, as in Ref. [15]. In the present experiments and upon drop, the fuel flow rate was reduced to a lower level before the end of the 2.2 s period, and this level remained constant for the rest of the available microgravity time. The purpose of terminating the fuel reduction by reaching a constant fuel concentration level was to accurately determine ext. More specifically, if extinction did not occur, the experiment would be repeated by reducing the fuel flow rate to a lower level. The maximum at which the flame could be sustained was defined as ext at the corresponding Kglobal. The experimental uncertainty of this approach is of the order of the uncertainty of the calibration of sonic nozzles, that is, around 0.5%. The present approach requires a large number of drops. However, it is recommended as an improvement over that used in Ref. [15], in which is determined at the flame front by using a constant delay time. This approach was tested in our facilities, and it was found that the time delay depends not only on the total flow rate but also on the fuel concentration. At the same time, it should be realized that the approach used in Ref. [15] is still a meritorious one, given the overall complexity of the experimentation under microgravity conditions. Results and Discussion Comparisons of the Three Radiation Models: SRM, DRM, SDRM The effects of the three radiation models on the flame structure were compared for ⳱ 1.0, 0.7, and 0.51 CH4/air flames. Fig. 2 depicts the flame temperature profiles for these flames as predicted by using the three radiation models. For ⳱ 1.0, the temperature prediction of the two optically thin models (SRM and SDRM) are very close to each other. For the ⳱ 0.7 flame, SDRM predicts slightly higher temperatures compared to SRM, with a maximum difference of about 50 K. For ⳱ 0.51,
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Fig. 2. Numerically determined temperature profiles of CH4/air flames at p ⳱ 1 atm, using SRM, DRM, and SDRM.
Fig. 5. Numerically determined Tmax as function of Kglobal for ⳱ 0.48 and 0.50 CH4/air flames at p ⳱ 1 atm, using SRM and L ⳱ 100 mm.
the temperatures predicted by SDRM are noticeably higher compared to those predicted by SRM within the product zone, with a maximum difference of about 100 K. For all flames, the use of DRM results in higher temperatures, as expected. It is of interest to note that for both the ⳱ 1.0 and ⳱ 0.7 flames, the maximum flame temperature, Tmax, is minimally affected by reabsorption. For ⳱ 0.51, however, reabsorption has a noticeable effect. Figure 3 depicts the variation of Tmax versus for the IODF model, and a bifurcation behavior is seen. The results of Fig. 3 reveal that the lean flammability limits of CH4/air mixtures calculated by using the three radiation models are close to each other. SRM and SDRM predict lim ⬇ 0.51, while DRM predicts lim ⬇ 0.50. This observation is physically reasonable because ultralean CH4/air mixtures cannot effectively absorb heat in their unburned state. Fig. 3. Numerically determined flammability limits of CH4/air flames at p ⳱ 1 atm, using SRM, DRM, and SDRM.
Fig. 4. Numerically determined (dT/dx)nzl as function of and Kglobal for CH4/air flames at p ⳱ 1 atm, using SRM and L ⳱ 15 mm.
Finite Domain and Upstream Heat Loss Effects The effect of upstream heat loss was addressed by varying L. Fig. 4 depicts the variation of the temperature gradient at the nozzle exit, (dT/dx)nzl, as a function of and Kglobal for L ⳱ 15 mm, which corresponds to the experimental conditions of Ref. [15]. It can be seen that for all values of Kglobal, (dT/ dx)nzl is reduced with , and eventually extinction is induced at a ext value beyond which convergence is not possible. The reduction of (dT/dx)nzl with is a result of the reduced flame temperature and the fact that the flame moves away from the burner. It is of interest to note that ext is initially reduced and subsequently increases as the (dT/dx)nzl increases. For Kglobal values greater than 5 sⳮ1, upstream heat loss is substantially reduced, the flames approach the stagnation plane, and the extinction is strain-rate induced. For lower Kglobal values, upstream heat loss is substantial. As Kglobal increases, the amount of conductive heat loss is reduced, and a leaner flame can be sustained.
EXTINCTION OF FLAMES IN MICROGRAVITY
Fig. 6. Numerically determined Tmax as function of Kglobal for a ⳱ 0.48 CH4/air flame at p ⳱ 1 atm, using SRM and L ⳱ 15 and 100 mm.
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⬎ 0. For L ⳱ 7 mm, the flames are affected by the upstream heat loss for the all Kglobal values, that is, (dT/dx)nzl ⬎ 0 everywhere. It should be noted that when upstream heat loss is present, the turningpoint extinction is not observed. The complete extinction Kglobal,ext versus diagram for CH4/air flames is shown in Fig. 7 for L ⳱ 100 and 15 mm. While the results obtained for L ⳱ 100 mm correspond to nearly adiabatic flames, the results obtained for L ⳱ 15 mm include the effect of upstream heat loss as Kglobal decreases. Adiabatic (i.e., no upstream heat loss) flames calculated for L ⳱ 100 mm exhibit the anticipated C-shape extinction behavior, as shown before in Ref. [16] by using L ⳱ 60 mm. For L ⳱ 15 mm, the extinction limits induced by strain rate at the same are lower compared to those for L ⳱ 100 mm because of the finite domain effect [14]. However, the lower branch for L ⳱ 15 mm is not shown because the notion of strain rate is meaningless given that a hydrodynamic zone cannot be defined when upstream heat loss is present. Microgravity Experiments and Comparisons with Numerical Simulations
Fig. 7. Numerically determined Kglobal,ext as function of for lean CH4/air flames at p ⳱ 1 atm, using SRM and L ⳱ 7, 12, and 100 mm.
Calculations were also conducted for L ⳱ 100 mm, which is large for any upstream heat loss to be present. Fig. 5 depicts the variation of Tmax with Kglobal, for ⳱ 0.48 and ⳱ 0.50 CH4/air flames. Similarly to the results of Refs. [16,17], a closed loop is formed, characterized by two extinction points. The one corresponding to the higher Kglobal,ext is caused by the strain rate, while the one corresponding to the lower Kglobal,ext is caused by the synergistic effects of thermal radiation, Lewis number, and strain rate. Additional simulations were conducted by reducing L in order to induce upstream heat loss. Fig. 6 depicts the variation of Tmax and (dT/dx)nzl with Kglobal for a ⳱ 0.48 CH4/air flame at different values of L. It can be seen that for the larger, L ⳱ 100 mm, the flame response is nearly adiabatic (i.e., no upstream heat loss). For the smaller, L ⳱ 12 mm, at high Kglobal values, the flames are adiabatic, that is, (dT/dx)nzl ⳱ 0, while at low Kglobal values, the upstream heat loss becomes finite, that is, (dT/dx)nzl
In normal gravity (1g), near-limit flames cannot be stabilized because of buoyancy-induced instabilities. In microgravity, steady near-limit planar flames can be stabilized. The extinction responses of near-limit CH4/air and C3H8/air mixtures were found to be consistent with the reported ones in Ref. [15]. As was decreased, extinction of CH4/air flames was observed after the flames merged at the stagnation plane, given that Le ⬍ 1 [28]. For the same L, , and Kglobal, C3H8/air flames were stabilized closer to the burner compared to CH4/air flames, as for the same , C3H8/air mixtures have higher flame speeds compared to CH4/air. It was observed that flame extinction occurred when the two C3H8/air flames were at a finite distance, given that Le ⬎ 1 [28]. Experimental microgravity data of Kglobal,ext versus for CH4/air and C3H8/air mixtures were obtained with L ⳱ 50 mm and are shown in Figs. 8 and 9 respectively, along with the microgravity data of Maruta et al. [15], and results from numerical simulations. The results in Fig. 8 exhibit a C-shape extinction response of Kglobal versus for CH4/air mixtures, which qualitatively agree with those reported in Ref. [15]. The results of the present numerical simulations obtained with L ⳱ 15 and 50 mm are also shown in Fig. 8. Compared to the experimental data of Ref. [15], the present data are shifted toward lower values and are in better agreement with the present simulations than the simulations of Ref. [16]. This was anticipated because in the present experiments, upstream heat losses were eliminated.
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Fig. 8. Experimentally and numerically determined Kglobal,ext as function of for lean CH4/air flames at p ⳱ 1 atm. Simulations were conducted using SRM.
Fig. 9. Experimentally and numerically determined Kglobal,ext as function of for lean C3H8/air flames at p ⳱ 1 atm. Simulations were conducted using SRM.
The results of Fig. 9 exhibit a monotonic extinction response of Kglobal versus for C3H8/air mixtures, similarly to Ref. [15]. The results of the present numerical simulations, obtained with L ⳱ 50 mm, are also shown. The discrepancies that are observed between experiments and simulations may be a result of inaccuracies associated with the C3 chemical scheme. At the same time, comparing with the data of Ref. [15], the present experimental data are shifted toward higher values of , which is the opposite to what was shown for CH4/air mixtures. This may be caused by finite-domain effects [14] given that different values of L were used. The present microgravity data are also compared with extinction data obtained in normal gravity for higher values, and the consistency between the two sets of data is apparent. Concluding Remarks A combined experimental and detailed numerical investigation was conducted on the extinction characteristics of near-limit laminar premixed flames.
The study aimed to provide insight into phenomena of relevance to the experimental and numerical determination of extinction and flammability limits. Experiments included the use of the counterflow configuration in microgravity, and an improved approach was introduced for the accurate determination of the mixture composition at extinction. Furthermore, special care was taken to avoid upstream heat losses, which could be present in near-limit experiments. The numerical simulations included the use of the CHEMKIN-based freely propagating and stagnation-flow flame codes, which were modified by introducing a one-point continuation approach to capture turning-point behavior around extinction conditions. Furthermore, three thermal radiation models were used. In these models, the gas emissivity was calculated by either using Planck’s mean absorption coefficient (SRM) or by accounting for the wavelength dependence of the gas emission/absorption characteristics (DRM). The DRM model was also used at the optically thin limit (SDRM). For vigorously burning flames, it was found that both SRM and SDRM similarly predict the thermal radiation. However, for near-limit flames, the SRM was found to significantly overpredict the radiation loss. It was also found that radiation noticeably affects the maximum flame temperature, only for nearlimit flames. Flammability limits calculated by using the different radiation models differ slightly, although the rates of downstream radiative transfer are significantly different. This suggests that the extent of the downstream heat loss plays a minor role. Mixtures with Le ⬍ 1 were found both experimentally and numerically to exhibit a C-chape nearlimit extinction response, which is caused by the synergistic effects of strain rate and radiation. Mixtures with Le ⬎ 1 were found to exhibit a monotonic nearlimit extinction response. Both these findings are consistent with previous studies. The microgravity experimental data presented in this paper, however, appear to be in better agreement with numerical predictions than previous data in which upstream heat loss may have been present. Simulations were conducted for a wide range of nozzle separation distances, and it was found that as the nozzle separation distance is reduced, upstream heat loss becomes important, and the extinction diagram is not of fundamental value. Furthermore, when upstream heat loss is present, the characterization of the fluid mechanics by referencing to strain rate is incorrect, because no hydrodynamic zone can be identified. Acknowledgments This study was funded by NASA, grant no. NAG3-1615, under the technical supervision of Dr. Fletcher Miller. The
EXTINCTION OF FLAMES IN MICROGRAVITY assistance of Mr. J.-Y. Ren in the preparation of the final manuscript is greatly appreciated.
REFERENCES 1. Williams, F. A., Combustion Theory, 2nd ed., Benjamin-Cummings, Menlo Park, CA, 1985. 2. Spalding, D. B., Proc. R. Soc. London A 240:83–100 (1957). 3. Coward, H. F., and Jones, G. W., Limits of Flammability of Gases and Vapors, Bureau of Mines Bulletin 503, 1952. 4. Strehlow, R. A., Noe, K. A., and Wherley, B. L., Proc. Combust. Inst. 21:1899–1908 (1986). 5. Ronney, P. D., and Wachman, H. Y., Combust. Flame 62:107–119 (1985). 6. Law, C. K., Zhu, D. L., and Yu, G., Proc. Combust. Inst. 21:1419–1426 (1986). 7. Law, C. K., and Egolfopoulos, F. N., Proc. Combust. Inst. 23:413–421 (1990). 8. Sibulkin, M., and Frendi, A., Combust. Flame 82:334– 345 (1990). 9. Frendi, A., and Sibulkin, M., Combust. Flame 86:185– 186 (1991). 10. Lakshmisha, K. N., Paul, P. J., and Mukunda, H. S., Proc. Combust. Inst. 23:433–440 (1990). 11. Law, C. K., and Egolfopoulos, F. N., Proc. Combust. Inst. 24:137–144 (1992). 12. Vranos, A., and Hall, R. J., Combust. Flame 93:230– 238 (1993).
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13. Dixon-Lewis, G., Proc. Combust. Inst. 25:1325–1332 (1994). 14. Egolfopoulos, F. N., Proc. Combust. Inst. 25:1375– 1381 (1994). 15. Maruta, K., Yoshida, M., Ju, Y., and Niioka, T., Proc. Combust. Inst. 26:1283–1289 (1996). 16. Sung, C. J., and Law, C. K., Proc. Combust. Inst. 26:865–873 (1996). 17. Guo, H., Ju, Y., Maruta, K., Niioka, T., and Liu, F., Combust. Flame 109:639–651 (1997). 18. Ju, Y., Masuya, G., and Ronney, P. D., Proc. Combust. Inst. 27:2619–2626 (1998). 19. Kee, R. J., Grcar, J. F., Smooke, M. D., and Miller, J. A., Sandia report SAND85-8240. 20. Egolfopoulos, F. N., Proc. Combust. Inst. 25:1365– 1373 (1994). 21. Egolfopoulos, F. N., and Campbell, C. S., J. Fluid Mech. 318:1–27 (1996). 22. Nishioka, M., Law, C. K., and Takeno, T., Combust. Flame 104:328–342 (1996). 23. Kee, R. J., Rupley, F. M., and Miller, J. A., Sandia report SAND89-8009. 24. Kee, R. J., Warnatz, J., and Miller, J. A., Sandia report SAND83-8209. 25. Grosshandler, W. L., RADCAL: A Narrow-Band Model for Radiation Calculations in a Combustion Environment, NIST Technical Note 1402, 1993. 26. Bowman, C. T., Frenklack, M., Gardiner, W., and Smith, G., The GRI 2.1 Mechanism, 1995. 27. Pitz, W. A., and Westbrook, C. K., Combust. Flame 63:113–133 (1986). 28. Law, C. K., Proc. Combust. Inst. 22:1381–1402 (1988).
COMMENTS Kaoru Maruta, Akita Prefectural University, Japan. A possible source of discrepancy between one-dimensional modeling and the experimental results might be boundary effects such as diffusion toward radial direction. May I have your opinion on this?
Author’s Reply. Indeed, the observed discrepancies may be attributed to a number of effects. In addition to the one that you mentioned, it may be that near-limit flames may be sensitive to effects of curvature that may develop in the absence of coflow. Furthermore, mixture dilution by the ambient air at the outer edges of the reacting jets may also affect the overall extinction response. Such effects can only be captured through an exact, axisymmetric, numerical simulation of the experiments. It must also be kept in mind that the reliability of existing detailed chemical kinetic mechanisms in closely describing near-limit flames could be a potential error factor as detailed experimental data for
such flames that would be appropriate for validation do not exist. ● K. N. Lakshmisha, Indian Institute of Science, Banglore, India. We know that on either side of the unity equivalence ratio the instability mechanisms and the kinetic mechanisms are very different. For instance, fuel-rich flammability limits of H2-air mixtures are likely to have pulsating instabilities. There could be cellular instabilities for other near-limit mixtures, influencing the flammability limit. Do you think one could eventually develop a unified explanation for these different situations? If so, what possible effects do you suggest would be required in numerical situations? Author’s Reply. A number of recent experimental and detailed numerical studies have indeed revealed the exis-
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tence of the mentioned behavior for near-limit mixtures. Even though the observed phenomena may differ between fuels as well as between lean and rich limits, it is true that in all cases the mixtures become particularly sensitive to heat-loss mechanisms as the limit concentrations are approached. Past studies have also shown that at the vicinity of the experimentally observed limits, the sensitivity between the controlling branching and termination reactions is heightened, and that an appropriately normalized value
of this sensitivity assumes values of the order of orders. It is the authors’ opinion that if a unified explanation is to be derived, the response of the kinetics must be considered. While one-dimensional simulations reveal the basis behavior of ideal reacting fronts, the interpretation of actual experiments for near-limit concentration through numerical simulations must ideally include the use of multidimensional codes that can account for every detail of the experiment.