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water droplets: Drop tower experiments and model predictions
Twenty-Sixth Symposium (International) on Combustion/The Combustion Institute, 1996/pp. 1209–1217
MICROGRAVITY COMBUSTION OF METHANOL AND METHANOL/WATER DROPLETS: DROP TOWER EXPERIMENTS AND MODEL PREDICTIONS A. J. MARCHESE and F. L. DRYER Dept. of Mechanical and Aerospace Engineering Princeton University Princeton, NJ 08544, USA R. O. COLANTONIO NASA Lewis Research Center Cleveland, OH 44135, USA V. NAYAGAM Analex Corporation Brook Park, OH 44142, USA
To experimentally validate single and bicomponent droplet combustion models, microgravity methanol and methanol/water droplet combustion experiments were conducted in the 2.2-s drop tower facility at NASA Lewis Research Center. The experiments were then simulated using a transient, bicomponent droplet combustion model developed earlier. Tests were performed in oxidizing environments of 18%– 35% O2/N2 with initial liquid water contents of 0–20%. Instantaneous droplet diameter measurements were made using back-lit, high-speed photography. The instantaneous flame position was determined by monitoring the chemiluminescence from electronically excited hydroxyl radicals (OH*). Analysis of the flame and droplet diameter data yielded burning rates and flame standoff ratios for a wide array of methanol and methanol/water droplet combustion conditions. For initially pure methanol droplets, the available burn time ('1.5 s) was not, in general, sufficient to observe extinction or significant nonlinearity in the regression of diameter squared with respect to time. For each oxygen content, the numerical model predicted the burning rate to within 10% and the flame position to within one normalized diameter without any independent parameter adjustment. In the case of 10% and 20% initial water content, substantial nonlinearity in diameter squared was observed. The numerical model, which accurately accounts for changes in liquid transport properties caused by variable liquid water content, did not predict the nonlinearity to the extent that it was observed. A possible explanation is that with the addition of initial water content to the droplet, the internal mass and thermal transport is enhanced as a result of increased internal mixing. The sources of this internal mixing are likely multifold but are not due to relative gas/liquid convection effects at the droplet surface.
Introduction To test the assumptions made in developing classical [1,2] and asymptotic [3–5] droplet combustion theories and experimentally validate numerical model predictions [6,7], it is of paramount importance to achieve spherically symmetric combustion of droplets large enough to permit accurate photographic analysis. Isolated, microgravity droplet combustion experiments performed using drop towers or space-based platforms represent the most ideal setting to satisfy these requirements. Accordingly, during the last decade, a substantial research effort has been directed toward refining experimental [8– 12] and data acquisition/analysis [13,14] techniques.
In these experiments, gravity levels on the order of 1015 g result in an environment virtually free of natural convection. Further, the effects of forced convection caused by residual velocity of the deployed droplet have been effectively minimized through the development of opposed-needle droplet growth/deployment [9,10] and symmetrical spark and hot-wire ignition techniques [15]. These refinements have been incorporated into experiments conducted in the NASA Lewis Research Center (LeRC) 2.2-s drop tower and 5.1-s Zero Gravity Facility, as well as the space-based Droplet Combustion Experiment (DCE) scheduled for flight aboard space shuttle mission MSL-1 in April 1997 [16]. The dramatically reduced natural and forced
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convection obtained in recent isolated, microgravity droplet combustion studies conducted at NASA LeRC have produced some unexpected results. In normal alkane droplet combustion experiments, these results appear to be predominantly a result of the production and thermophoretic collection of soot between the droplet surface and the flame. For example, Choi et al. [17] found that the presence of a ‘‘soot shell’’ resulted in a quiescent burning rate of n-heptane in air that was substantially lower than the value of 0.78 mm2/s that for many years had been presumed to be a benchmark [18]. This result has been reproduced by Jackson and Avedisian [19]. Shaw et al. [10] also observed disruptive burning in initially pure n-decane droplets and attributed this behavior to deposition of high molecular weight soot precursors into the liquid phase. The unexpected phenomena uncovered in the NASA LeRC n-alkane studies, while potentially valuable in terms of qualitatively studying the effects of soot formation, clearly present difficulties in quantitatively judging the success of numerical and asymptotic droplet combustion models. Moreover, even if sooting is suppressed (with reduced pressure and/or inert substitution) n-alkane oxidation kinetics are quite complicated and may require hundreds of species to accurately model the gas-phase chemistry [20,21]. Methanol, on the other hand, represents an attractive fuel candidate for comparison between microgravity droplet experiments and theory. The gas-phase oxidation kinetics are accurately modeled by considering only 19 species and 89 reactions [22,23]. Only trace amounts of CH3 are generated and, thus, no soot is present in the system. While the chemical kinetics are well understood and have been substantially validated elsewhere [22], methanol droplet combustion has the added complication that, during combustion, flame-generated water condenses at the droplet surface, dissolves into the droplet interior, and may revaporize during combustion [13,24,25]. Fortunately, unlike the problem of soot formation, the effects of water condensation, absorption, and revaporization are readily handled both numerically [12,7] and analytically [26,5]. In terms of multicomponent droplet combustion, initial mixtures of methanol/water represent perhaps the simplest and most ideal system for comparison with detailed numerical binary droplet combustion modeling [27]. No new species or reactions need to be added to the gas-phase oxidation mechanism because it already includes H2O as a major species. Also, substantial literature exists on the liquid density, liquid transport properties, and vapor/liquid equilibrium of the binary mixture. Moreover, Marchese and Dryer [7] have suggested that initial mixtures of methanol and water might be used to better characterize the liquid-phase transport in initially pure methanol droplets. The preceding arguments clearly suggest that the
combustion of methanol and methanol/water droplets in microgravity (conducted, for example, in a drop tower) represents the ideal experiment for validating existing single and bicomponent droplet combustion models. Thus, a major goal of this study is to generate microgravity methanol and methanol/ water droplet combustion data at a wide array of conditions for direct comparison with numerical and asymptotic models. Conducting experiments in a wide variety of oxygen indices, pressures, and inerts yields a broad range of flame temperatures, chemical times, and diffusive transport times, providing a stringent test for validation of numerical models and comparison with asymptotics. Currently, numerical and asymptotic model predictions are consistent in some areas but vary in others. For example, the recent asymptotic analysis of Zhang et al. [5] and the numerical modeling of Cho et al. [12] and Marchese and Dryer [7] all predict burning rates that agree well with drop tower experiments performed to date [12,28]. However, previous results [12,14] show that the numerical model accurately predicts the flame position, whereas the asymptotic analysis appears to overpredict the flame position by a factor of about 2. Finally, both the numerical and analytical models mentioned previously reproduce experimentally measured extinction diameters of Cho et al. [12] and Yang et al. [28] by considering detailed and reduced chemical kinetic mechanisms, respectively, but only if the internal liquid-phase transport is assumed to be enhanced by liquid-phase motion. In this study, new experiments have been conducted in the 2.2-s drop tower facility at NASA Lewis Research Center. Analysis of the flame and droplet diameter data yielded burning rates and flame standoff ratios for a wide array of methanol and methanol/water droplet combustion conditions. In general, the burn time available was not sufficient to observe extinction of the droplet flame. Later, the results of each experiment are presented and compared with the results of numerical simulations using a transient, spherically symmetric, finite-element model [2,7,14]. The experiments presented here are complementary to the recent FSDC-1 (Fiber-Supported Droplet Combustion Experiment) [29] droplet combustion experiments that were conducted aboard space shuttle mission USML-2 in November 1995. In FSDC-1, 3–5-mm droplets of several fuels including methanol/water were suspended on a quartz fiber and ignited using a hot wire. In the data presented in this study, initial diameters were smaller (1–1.5 mm), much more accurate measurements of flame position were made, and the experiments were conducted without the assistance of fiber suspension. Experiment The experiments were conducted at the 2.2-s drop tower facility at NASA Lewis Research Center [30]
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narrow band interference filter centered at 310 nm. Additional video data, acquired using a standard black and white video camera, are used to qualitatively judge the success of each experiment. Data from the video cameras are transported via fiber optic cables from the freely falling apparatus to the top of the drop tower where the data are stored at 30 frames per second on two Panasonic AG-7355 SVHS video cassette recorders. The video data are synchronized using Horita FP-50 time code generators. The data is analyzed using a PC-based image analysis system consisting of image tracking software developed at NASA Lewis, a frame grabber, and various input devices including VHS, film transports, and laser disk [31]. The frame grabber is a Matrox Image Series 1280, which is compatible with SVHS, NTSC, RGB, and digital input and can acquire a display at 1289 2 1024 pixels. The image tracking software automates the data analysis process by controlling the image digitization, enhancing the visibility of the object(s) in the image, determining and recording the position of the object(s), and automatically advancing the image input device. Fig. 1. Photograph of the droplet combustion apparatus used in the 2.2-s drop tower experiments.
using a newly built droplet combustion apparatus of similar design to that which will be flown aboard the space shuttle in the upcoming DCE experiment [16]. The hardware is housed within a test chamber that can be evacuated and refilled to create various oxidizing environments at subatmospheric or superatmospheric pressures. Optical access to the test chamber is provided through three quartz windows. A photograph of the droplet combustion apparatus is shown in Fig. 1. All experimental functions and data acquisition are controlled via an on-board microprocessor. During the 2.2-s drop sequence, a droplet is grown and stretched between two hypodermic needles that, by simultaneous rapid retraction, deploy the droplet into the microgravity environment with very low residual velocity. The gas phase surrounding the droplet is then symmetrically ignited using dual, retractable hot-wire ignitors. After retraction of the hot-wire ignitors, approximately 1.5 s of isolated, microgravity droplet combustion is achieved in a successful experiment. Data are acquired using three separate imaging techniques. A 16-mm Milliken high-speed motion picture camera records black and white, back-lit droplet images onto Kodak RAR 2498 film at 200 frames per second. Ultraviolet emission caused by hydroxyl radical chemiluminescence occurring with the flame is acquired using a Xybion ISG-250 intensified-array CCD video camera fitted with a 50-mm, UV-transmissive lens (Hammamatsu A4869) and
Numerical Model The methanol and methanol/water droplet combustion experiments were numerically simulated using a detailed droplet combustion model described elsewhere [6,12,7]. The model simulates the transient, spherically symmetric combustion of a bicomponent liquid droplet in an infinite oxidizing medium. The computations consider multicomponent molecular transport and complex chemical kinetic mechanisms to solve the gas-phase conservation equations of mass, species, and energy. The governing equations are spatially discretized using a moving finite element method and temporally integrated using an implicit ODE solver. The gas-phase chemical kinetics are modeled using the comprehensive methanol oxidation mechanism of Held and Dryer (19 species, 89 forward chemical reactions) [22,23]. For comparison with measured UV flame emission, additional reactions describing the production, quenching, and emission of electronically excited hydroxyl radicals (OH*) were added to the original oxidation mechanism. The individual reactions and rate coefficients for the reaction mechanisms are available elsewhere [23,32] and will not be repeated here. In addition to the gasphase system, a semiempirical vapor-liquid equilibrium technique [7] is employed at the droplet surface and the conservation equations of energy and species are solved within the droplet interior. Recent studies [5,7] show that the extinction of a methanol droplet flame is highly dependent on the liquid-phase mass Peclet number defined as
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predicts both the average burning rate and quasisteady flame position regardless of the Peclet number chosen. Results
Fig. 2. (a) Standard video image and (b) ultraviolet flame emission image of a 1.5-mm methanol droplet burning in a 35% O2/65% N2 microgravity oxidizing environment at 0.6 s after ignition.
)drdt ) s
Pel,m 4
Dl rs
4
)
)
1 d 2 (d ) 8 dt s Dl
4
1Kb(t) 8dl
Two limits exist: Pel,m K 1 and Pel,m k 1. In the former (well-mixed) situation, a substantial quantity of water is dissolved into the droplet during combustion, thereby promoting droplet extinction. In the latter (diffusively controlled) situation, very little water dissolves into the droplet [26]. The value of liquid Peclet number as specified by known liquid properties is around 30, suggesting that very little water should dissolve into the droplet. But experiments [24,25] have measured significant water dissolution, suggesting increased liquid mass transport that has been attributed to internal circulation. Insufficient experimental evidence exists, however, to conclude that the interior is completely well-mixed (Pe K 1). Therefore, unless otherwise specified, calculations were performed with an intermediate Peclet number of approximately 5. For initially pure methanol droplets, the numerical model accurately
Fuel droplets have been ignited in various oxidizing environments of 18–35% O2/N2 and 40–70% O2/ He at pressures from 0.6 to 1.0 atm. To date, the most complete data sets were obtained for pure methanol in various O2/N2 oxidizing environments and methanol/water mixtures in 30% O2/70% N2. Figure 2a is a standard black and white video image of a burning methanol droplet (1.3-mm initial diameter) in a microgravity oxidizing environment of 35% O2/65% N2. The figure clearly shows the high degree of spherical symmetry obtainable in microgravity. Moreover, the methanol flame is sufficiently nonluminous that it is possible to observe the liquid droplet even in the absence of back lighting. In contrast, the flame surrounding a liquid alkane (e.g. nheptane or n-decane) droplet burning under the same conditions would appear as a bright yellow flame ball, completely obscuring the droplet. While it was possible to measure the droplet diameter directly from the video image of Fig. 2a, more accurate measurements of the instantaneous droplet diameter were obtained using a high-intensity backlight to capture silhouette images of the vaporizing droplet with the Milliken high-speed movie camera. Using the automated tracking system described previously, the left, right, top, and bottom edges of the silhouette droplet image were determined for each frame. The instantaneous droplet diameter was calculated by taking the average of the vertical and horizontal measurements. The instantaneous flame diameter was determined from hydroxyl radical chemiluminescence measurements using a technique outlined in another paper at this symposium [14]. This work showed that in methanol droplet flames, the location of maximum hydroxyl radical emission intensity coincides with the location of maximum flame temperature, the most logical choice for defining the flame position. Figure 2b shows a digitized image of the UV emission acquired by the Xybion camera for the combustion of a 1500-lm methanol droplet in 30% O2/ 70% N2 at 1 atm (t 4 0.60 s after ignition). To determine the maximum emission location, intensity profiles obtained from the Xybion camera images were deconvoluted using the inverse Abel transform. The procedure was repeated for each video frame yielding the flame position as a function of time after ignition. These results were then combined with the instantaneous droplet diameter measurements to calculate the instantaneous flame standoff ratio, df/ ds. Figure 3 is a plot of the experimentally measured
METHANOL/WATER DROPLET COMBUSTION
Fig. 3. Experimentally measured (symbols) and numerically predicted (lines) normalized diameter squared versus time for initially pure methanol droplets in various O2/N2 oxidizing environments at 1 atm.
Fig. 4. Numerical prediction of the instantaneous burning rate plotted with the experimentally determined linear least-squares burning rate (bold lines) for initially pure methanol droplets in various O2/N2 oxidizing environments at 1 atm.
and numerically predicted droplet diameter squared versus time for initially pure methanol in various nitrogen/oxygen environments at 1 atm. The experimental data have been five-point averaged and both axes have been normalized by the initial diameter squared since initial diameter of the droplets varied between 1000 and 1500 lm. Initial droplet heating periods, during which droplet regression rate was
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minimal, were observed but generally lasted less than 5% of the total burn time. However, since the heating period varied between experiments, each experimental data set of Fig. 3 has been time shifted to the end of the droplet heating period. As expected, the measured burning rate increased substantially with rising oxygen content. Moreover, agreement between measured and calculated diameter history is excellent. The experiments did not show significant nonlinearity in the variation of diameter squared with respect to time, as had been observed previously by Choi et al. [13] and Cho et al. [12]. However, as indicated by the numerical predictions, the time available in the 2.2-s drop tower only allowed observation of approximately one-half of the total burn time. During this period, the numerical model predicts a net influx of water at the droplet surface resulting in less variation in the burning rate than during later stages when water begins to revaporize from the surface. Indeed, as the data suggest, any subtle nonlinearity in the plot of diameter squared during this period is not experimentally resolvable. Accordingly, a linear least-squares fit to the data was used to compare with the numerically calculated burning rates. The experimental burning rates are plotted along with the numerical modeling results, which predict an instantaneous droplet burning rate, |(d/dt)(d2s )|, that varies continuously during periods of ignition, vapor accumulation, droplet heating, quasi-steady combustion, and extinction. As shown in Fig. 4, although the subtle variation in instantaneous burning rate was not experimentally resolvable, the agreement in average burning rate is excellent. Over the comparison interval indicated in the figure, the measured burning rates were 0.56, 0.59, 0.65, and 0.82 mm2/s compared to average calculated values of 0.556, 0.632, 0.688, and 0.830 mm2/s for 18%, 21%, 24%, and 30% O2 in N2, respectively. Good agreement in average burning rate is obtained over the test interval regardless of the liquid Peclet number chosen. In the standard video camera (which is primarily sensitive to visible light), the ignition process and transient evolution of the flame position was obscured by the thermal radiation emitted from the resistively heated hot wire. Conversely, because only a fraction of the hot-wire thermal radiation is emitted in the UV, the transient evolution of OH* emission is clearly observed by the Xybion camera. Within the time resolution available using the video system (30 frames per s), the initial flame spread around the droplet and evolution to a spherically symmetric flame could not be resolved. Rather, from the first frame in which observations were made, the OH* emission appeared spherically symmetric with its maximum intensity generally occurring at less than 1 radii from the droplet surface. After the first
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Fig. 5. Comparison between numerically predicted (lines) and experimentally measured (symbols) normalized flame position, df/ds, for the combustion of initially pure methanol droplets in various O2/N2 oxidizing environments at 1 atm.
Fig. 6. Experimentally measured normalized diameter squared versus time for methanol/water mixtures in oxidizing environments of 30% O2/70% N2 at 1 atm.
frame, the flame grew in size, reaching a maximum diameter at about 0.1 s after ignition. Figure 5 shows the measured and predicted instantaneous flame position, df /ds, for methanol droplets in 21%, 30%, and 35% O2 with N2 inert. In methanol droplet combustion, the flame position is expected to decrease with time once the droplet begins to revaporize water that is absorbed into the liquid phase earlier in the combustion processes. The increased water within the flame zone decreases the flame temperature, which decreases the chemical reaction rate, causing the flame to move closer to the surface. In the experiments, the burn times
were not sufficient to observe regasification of condensed water. Thus, after the initial transient period, the flame position was very nearly constant for each initial oxygen content. As expected, the flame position decreases with increasing oxygen content because of stoichiometry considerations. After the initial transient period, average normalized flame positions of 4.1, 3.6, and 3.4 were measured for oxygen contents of 21%, 30%, and 35%, respectively. The numerical model predicts the quasi-steady flame position to within one normalized diameter at each condition. The slightly overpredicted flame position observed at each condition is most probably due to the neglect of gasphase radiative heat loss in the present calculations. Heat loss from the flame lowers the flame temperature, thereby requiring a smaller flame diameter to provide the required heat flux to the droplet surface. The effect of gas radiation is examined elsewhere [32]. Figure 6 is a plot of the experimentally measured diameter-squared history for methanol/water mixtures of 0%, 10%, and 20% water in an oxidizing environment of 30% O2/ 70% N2 at 1 atm. The figure shows that the addition of only small initial quantities of water results in substantial nonlinearity in the diameter-squared history, with several stages of burning evident. Initially, an abnormally long (with respect to the pure methanol data) droplet heating period is observed during which the droplet diameter is constant and may even increase slightly as a result of thermal swelling [33]. After the heating period is complete, the burning rate for the mixtures (as evidenced by the slope of the diameter-squared plot) actually increases to a higher value than that observed for the initially pure methanol. During the final observed stage, the burning rate decreases below the value observed for the initially pure methanol, apparently because of gasification of the condensed phase water. As noted previously, the latter stage was not observed for initially pure methanol droplet combustion here, although it has been observed by Choi et al. [13] and Cho et al. [12] in experiments with helium as the diluent. Previous numerical modeling results of Marchese and Dryer [7] predicted that addition of initial water content to methanol results in decreased burning rate, decreased flame standoff, and increased extinction diameter. The previous modeling results did not show substantial increases in the heating period or the second period of increased burning rate. In the previous study, comparisons were made between droplets of different initial water content assuming identical values of liquid mass and thermal Peclet number. This is not a bad assumption considering that the thermal and mass diffusivity of methanol/ water mixtures are relatively insensitive to the water content. A possible explanation for the experimental results
METHANOL/WATER DROPLET COMBUSTION
Fig. 7. Calculated instantaneous burning rate for methanol/water mixtures in oxidizing environments of 30% O2/ 70% N2 at 1 atm.
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and 20% actually increases above that of the initially pure methanol in agreement with observations. One possible reason for the increased circulation in the initial mixtures may be a solutal Marangoni instability wherein local differences in liquid concentration cause variations in surface tension that create secondary flows within the droplet [5,34]. There may also be an increase in the deployment-induced circulation in the methanol/water mixtures because of increased interfacial surface tension between the droplet and needles. Figure 8 shows the instantaneous flame position measurements and calculations for the same conditions as Fig. 6. Generally, the flame diameter decreased with increasing initial water content, although, as shown in Fig. 8, the measured flame position for 20% initial water was actually larger than the 10% case. This result may be due to uncertainty in the oxygen content and/or the effect of initial diameter. The numerical model was once again reasonably accurate, overpredicting the instantaneous flame position by about 1 normalized diameter. Summary
Fig. 8. Comparison between numerically predicted (lines) and experimentally measured (symbols) normalized flame position, df/ds, for the combustion of methanol/water droplets in oxidizing environments of 30% O2/70% N2 at 1 atm.
of Fig. 6 is that in the cases with 10% and 20% initial water content, the internal mass and thermal transport may have been enhanced compared to the initially pure methanol case, presumably because of increased internal convection. To reproduce this effect, the 0% initial water content was modeled with the actual thermal and mass diffusivities (Pel,h ' 1, Pel,m ' 20) and the 10% and 20% cases were modeled as well-mixed (Pel,h K 1, Pel,m K 1). As shown in Fig. 7, which is a plot of the calculated instantaneous burning rate for 0%, 10%, and 20% initial water content, the burning rate for the 10%
The experiments and associated modeling presented here have shown the predictive capabilities of time-dependent, spherically symmetric, bicomponent droplet combustion modeling when applied to mixtures of methanol and water. The results have also shown that the numerical model accurately reproduces both the measured burning rates and flame positions for a wide range of conditions. Good agreement in average burning rate and flame position is obtained over the test interval regardless of the liquid Peclet number chosen. Although the burn times available in the experiments presented here were not sufficient to observe droplet extinction, the comparisons made herein have further validated the numerical model such that it can be used with confidence to analyze the results of longer-burning experiments such as FSDC-1. Acknowledgments The authors wish to acknowledge the contributions of Charles Traylor Jr. for his assistance with the 2.2-s drop tower experiments and Arthur G. Birchenough in developing and troubleshooting the apparatus control system. Princeton contributions to this work were supported by the National Aeronautics and Space Administration through Grant No. NAG3-1231.
REFERENCES 1. Godsave, G. A. E., Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1953, p. 818.
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2. Spalding, D. B., Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1953, p. 847. 3. Law, C. K., Combust. Flame 24:89 (1975). 4. Card, J. M. and Williams, F. A., Combust. Sci. Technol. 84:91–119 (1992). 5. Zhang, B. L., Card, J., and Williams, F. A., Combust. Flame 105:267–290 (1996). 6. Cho, S. Y., Yetter, R. A., and Dryer, F. L., J. Comp. Phys. 102:160–179 (1992). 7. Marchese, A. J. and Dryer, F. L., Combust. Flame 105:104–122 (1996). 8. Knight, B. and Williams, F. A., Combust. Flame 38:111 (1980). 9. Haggard, J. B. and Kropp, J., AIAA paper no. 87-0576 (1987). 10. Shaw, B. D, Dryer, F. L., Williams, F. A., and Haggard, J. B., Jr., Acta Astronautica 17(11/12):1195–1202 (1988). 11. Avedisian, C. T., Yang, J. C., and Wang, C. H., Proc. R. Soc. London A 420:183–200 (1988). 12. Cho, S. Y., Choi, M. Y., and Dryer, F. L., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, p. 1611. 13. Choi, M. Y., Dryer, F. L., Haggard, J. B., and Brace, M. H., Am. Inst. Phys. Conf. Proc. 197:338–359 (1989). 14. Marchese, A. J., Dryer, F. L., Nayagam, V., and Colantonio, R., Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996, pp. 1219–1226. 15. Shaw, B. D., Dryer, F. L., Williams, F. A., and Gat, N., Combust. Flame 74:233 (1988). 16. Williams, F. A. and Dryer, F. L., Science Requirements Document for the Droplet Combustion Experiment, NASA Lewis Research Center, Cleveland, 1994. 17. Choi, M. Y., Dryer, F. L., and Haggard, J. B., Jr., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, p. 1611. 18. Kumagai, S., Sakai, T., and Okajima, S., Thirteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1971, p. 779.
19. Jackson, G. and Avedisian, C., 31st Aerospace Sciences Meeting and Exhibit, Reno, AIAA-93-0130 (1993). 20. Westbrook, C. K., Warnatz, J., and Pitz, W., TwentySecond Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, p. 893. 21. Held, T. J., Marchese, A. J., and Dryer, F. L., Central States, Western States, and Mexican National Sectional Meeting of the Combustion Institute, ESS/WSS/MNS/ CI, San Antonio, TX, 1995, p. 251. 22. Held, T. J. and Dryer, F. L., Twenty-Fifth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1994, p. 908. 23. Held, T. J. Ph. D. Thesis, Princeton University, Dept. of M.A.E., 1993. 24. Choi, M. Y., Cho, S. Y., Stein, Y. S., and Dryer, F. L., Fall Eastern States Meeting of the Combustion Institute, ESS/CI, Orlando, FL, 1990. 25. Lee, A. and Law, C. K., Combust. Sci. and Technol. 86:253–265 (1992). 26. Shaw, B. D., Combust. Flame 81:277–288 (1990). 27. Marchese, A. J. and Dryer, F. L., Eastern States Sectional Meeting of the Combustion Institute, ESS/CI, Clearwater, Fl, 1994, p. 355. 28. Yang, J. C., Jackson, G. S., and Avedisian, C. T., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, p. 1619. 29. Dietrich, D. L., Dryer, F. L, Haggard, J. B., Jr., Nayagam, V., Shaw, B. D., and Williams, F. A., TwentySixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996, pp. 000–000. 30. The Microgravity Combustion Group, Microgravity Combustion Science: A Program Overview, NASA TM-101424 (1989). 31. Klimeck, R. B., Wright, T. W., and Sielken, R. S., NASA TM-107144 (1996). 32. Marchese, A. J., Ph. D. Thesis, Princeton University, Dept. of M.A.E., 1996. 33. Megaridis, C. M., Combust. Sci. Technol. 92:291–311 (1993). 34. Aharon, I., and Shaw, B. D., 1995, submitted.
COMMENTS W. A. Sirignano, University of California, Irvine, USA. The large initial droplet size chosen for experimental convenience gives an unusually long characteristic diffusion time. The more practical range of initial droplet size would result in a diffusion time that is two to four orders of magnitude less. In that case, the chemical time becomes relatively larger. The emergence of this other (chemical) characteristic raises concern about the ability to scale these experimental results into the practical range. Author’s Reply. One need not consider droplets of the
practical (i.e. spray) size range in order to produce diffusion times of the same order of the chemical time. For example, by performing methanol experiments in He/O2 environments, Cho and co-workers [1] have measured flame extinction for 350 micron droplets. Similarly, by conducting methanol droplet combustion experiments with very large initial droplet diameters (3–5 mm), Dietrich and co-workers [2] have measured flame extinction in 1 to 2 mm droplets. In the former case, the presence of the inert helium resulted in decreased characteristic diffusion times; in the latter case, re-vaporization of condensed phase water
METHANOL/WATER DROPLET COMBUSTION lowered the flame temperature, thereby increasing the characteristic reaction time. In the experiments described in the present work, flame extinction would also have been observed had an additional 0.5 seconds of microgravity test time been available.
REFERENCES 1. Cho, S. Y., Choi, M. Y., and Dryer, F. L., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, p. 1611. 2. Dietrich, D. L., Dryer, F. L., Haggard, J. B., Jr., Nayagam, V., Shaw B. D., and Williams, F. A., Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996. ● I. Go¨kalp, CNRS, France. Could you explain why it was difficult to obtain the instantaneous burning rate from your experiments? Author’s Reply. As shown in Figure 3, the measured
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droplet diameter-squared vs. time contains a low-level, high frequency noise component. As frequently encountered in data analysis, the experimental noise is greatly amplified when one attempts to take the derivative of this data with respect to time. In some cases, it is possible to filter out the high frequency noise component prior to differentiation. For example, further analysis of the space-based droplet combustion experiments of Dietrich and co-workers [1] has allowed the calculation of the instantaneous burning rate [2,3]. The latter calculation is possible because of the large length and time scales available in space-based experiments.
REFERENCES 1. Dietrich, D. L., Dryer, F. L., Haggard, J. B., Jr., Nayagam, V., Shaw, B. D., and Williams, F. A., Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996. 2. Nayagam, V., personal communication, 1996. 3. Marchese, A. J. and Dryer, F. L., 1996 Fall Technical Meeting, Eastern States Section, The Combustion Institute, Hilton Head, SC.
MICROGRAVITY COMBUSTION OF METHANOL AND METHANOL/WATER DROPLETS: DROP TOWER EXPERIMENTS AND MODEL PREDICTIONS A. J. MARCHESE and F. L. DRYER Dept. of Mechanical and Aerospace Engineering Princeton University Princeton, NJ 08544, USA R. O. COLANTONIO NASA Lewis Research Center Cleveland, OH 44135, USA V. NAYAGAM Analex Corporation Brook Park, OH 44142, USA
To experimentally validate single and bicomponent droplet combustion models, microgravity methanol and methanol/water droplet combustion experiments were conducted in the 2.2-s drop tower facility at NASA Lewis Research Center. The experiments were then simulated using a transient, bicomponent droplet combustion model developed earlier. Tests were performed in oxidizing environments of 18%– 35% O2/N2 with initial liquid water contents of 0–20%. Instantaneous droplet diameter measurements were made using back-lit, high-speed photography. The instantaneous flame position was determined by monitoring the chemiluminescence from electronically excited hydroxyl radicals (OH*). Analysis of the flame and droplet diameter data yielded burning rates and flame standoff ratios for a wide array of methanol and methanol/water droplet combustion conditions. For initially pure methanol droplets, the available burn time ('1.5 s) was not, in general, sufficient to observe extinction or significant nonlinearity in the regression of diameter squared with respect to time. For each oxygen content, the numerical model predicted the burning rate to within 10% and the flame position to within one normalized diameter without any independent parameter adjustment. In the case of 10% and 20% initial water content, substantial nonlinearity in diameter squared was observed. The numerical model, which accurately accounts for changes in liquid transport properties caused by variable liquid water content, did not predict the nonlinearity to the extent that it was observed. A possible explanation is that with the addition of initial water content to the droplet, the internal mass and thermal transport is enhanced as a result of increased internal mixing. The sources of this internal mixing are likely multifold but are not due to relative gas/liquid convection effects at the droplet surface.
Introduction To test the assumptions made in developing classical [1,2] and asymptotic [3–5] droplet combustion theories and experimentally validate numerical model predictions [6,7], it is of paramount importance to achieve spherically symmetric combustion of droplets large enough to permit accurate photographic analysis. Isolated, microgravity droplet combustion experiments performed using drop towers or space-based platforms represent the most ideal setting to satisfy these requirements. Accordingly, during the last decade, a substantial research effort has been directed toward refining experimental [8– 12] and data acquisition/analysis [13,14] techniques.
In these experiments, gravity levels on the order of 1015 g result in an environment virtually free of natural convection. Further, the effects of forced convection caused by residual velocity of the deployed droplet have been effectively minimized through the development of opposed-needle droplet growth/deployment [9,10] and symmetrical spark and hot-wire ignition techniques [15]. These refinements have been incorporated into experiments conducted in the NASA Lewis Research Center (LeRC) 2.2-s drop tower and 5.1-s Zero Gravity Facility, as well as the space-based Droplet Combustion Experiment (DCE) scheduled for flight aboard space shuttle mission MSL-1 in April 1997 [16]. The dramatically reduced natural and forced
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convection obtained in recent isolated, microgravity droplet combustion studies conducted at NASA LeRC have produced some unexpected results. In normal alkane droplet combustion experiments, these results appear to be predominantly a result of the production and thermophoretic collection of soot between the droplet surface and the flame. For example, Choi et al. [17] found that the presence of a ‘‘soot shell’’ resulted in a quiescent burning rate of n-heptane in air that was substantially lower than the value of 0.78 mm2/s that for many years had been presumed to be a benchmark [18]. This result has been reproduced by Jackson and Avedisian [19]. Shaw et al. [10] also observed disruptive burning in initially pure n-decane droplets and attributed this behavior to deposition of high molecular weight soot precursors into the liquid phase. The unexpected phenomena uncovered in the NASA LeRC n-alkane studies, while potentially valuable in terms of qualitatively studying the effects of soot formation, clearly present difficulties in quantitatively judging the success of numerical and asymptotic droplet combustion models. Moreover, even if sooting is suppressed (with reduced pressure and/or inert substitution) n-alkane oxidation kinetics are quite complicated and may require hundreds of species to accurately model the gas-phase chemistry [20,21]. Methanol, on the other hand, represents an attractive fuel candidate for comparison between microgravity droplet experiments and theory. The gas-phase oxidation kinetics are accurately modeled by considering only 19 species and 89 reactions [22,23]. Only trace amounts of CH3 are generated and, thus, no soot is present in the system. While the chemical kinetics are well understood and have been substantially validated elsewhere [22], methanol droplet combustion has the added complication that, during combustion, flame-generated water condenses at the droplet surface, dissolves into the droplet interior, and may revaporize during combustion [13,24,25]. Fortunately, unlike the problem of soot formation, the effects of water condensation, absorption, and revaporization are readily handled both numerically [12,7] and analytically [26,5]. In terms of multicomponent droplet combustion, initial mixtures of methanol/water represent perhaps the simplest and most ideal system for comparison with detailed numerical binary droplet combustion modeling [27]. No new species or reactions need to be added to the gas-phase oxidation mechanism because it already includes H2O as a major species. Also, substantial literature exists on the liquid density, liquid transport properties, and vapor/liquid equilibrium of the binary mixture. Moreover, Marchese and Dryer [7] have suggested that initial mixtures of methanol and water might be used to better characterize the liquid-phase transport in initially pure methanol droplets. The preceding arguments clearly suggest that the
combustion of methanol and methanol/water droplets in microgravity (conducted, for example, in a drop tower) represents the ideal experiment for validating existing single and bicomponent droplet combustion models. Thus, a major goal of this study is to generate microgravity methanol and methanol/ water droplet combustion data at a wide array of conditions for direct comparison with numerical and asymptotic models. Conducting experiments in a wide variety of oxygen indices, pressures, and inerts yields a broad range of flame temperatures, chemical times, and diffusive transport times, providing a stringent test for validation of numerical models and comparison with asymptotics. Currently, numerical and asymptotic model predictions are consistent in some areas but vary in others. For example, the recent asymptotic analysis of Zhang et al. [5] and the numerical modeling of Cho et al. [12] and Marchese and Dryer [7] all predict burning rates that agree well with drop tower experiments performed to date [12,28]. However, previous results [12,14] show that the numerical model accurately predicts the flame position, whereas the asymptotic analysis appears to overpredict the flame position by a factor of about 2. Finally, both the numerical and analytical models mentioned previously reproduce experimentally measured extinction diameters of Cho et al. [12] and Yang et al. [28] by considering detailed and reduced chemical kinetic mechanisms, respectively, but only if the internal liquid-phase transport is assumed to be enhanced by liquid-phase motion. In this study, new experiments have been conducted in the 2.2-s drop tower facility at NASA Lewis Research Center. Analysis of the flame and droplet diameter data yielded burning rates and flame standoff ratios for a wide array of methanol and methanol/water droplet combustion conditions. In general, the burn time available was not sufficient to observe extinction of the droplet flame. Later, the results of each experiment are presented and compared with the results of numerical simulations using a transient, spherically symmetric, finite-element model [2,7,14]. The experiments presented here are complementary to the recent FSDC-1 (Fiber-Supported Droplet Combustion Experiment) [29] droplet combustion experiments that were conducted aboard space shuttle mission USML-2 in November 1995. In FSDC-1, 3–5-mm droplets of several fuels including methanol/water were suspended on a quartz fiber and ignited using a hot wire. In the data presented in this study, initial diameters were smaller (1–1.5 mm), much more accurate measurements of flame position were made, and the experiments were conducted without the assistance of fiber suspension. Experiment The experiments were conducted at the 2.2-s drop tower facility at NASA Lewis Research Center [30]
METHANOL/WATER DROPLET COMBUSTION
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narrow band interference filter centered at 310 nm. Additional video data, acquired using a standard black and white video camera, are used to qualitatively judge the success of each experiment. Data from the video cameras are transported via fiber optic cables from the freely falling apparatus to the top of the drop tower where the data are stored at 30 frames per second on two Panasonic AG-7355 SVHS video cassette recorders. The video data are synchronized using Horita FP-50 time code generators. The data is analyzed using a PC-based image analysis system consisting of image tracking software developed at NASA Lewis, a frame grabber, and various input devices including VHS, film transports, and laser disk [31]. The frame grabber is a Matrox Image Series 1280, which is compatible with SVHS, NTSC, RGB, and digital input and can acquire a display at 1289 2 1024 pixels. The image tracking software automates the data analysis process by controlling the image digitization, enhancing the visibility of the object(s) in the image, determining and recording the position of the object(s), and automatically advancing the image input device. Fig. 1. Photograph of the droplet combustion apparatus used in the 2.2-s drop tower experiments.
using a newly built droplet combustion apparatus of similar design to that which will be flown aboard the space shuttle in the upcoming DCE experiment [16]. The hardware is housed within a test chamber that can be evacuated and refilled to create various oxidizing environments at subatmospheric or superatmospheric pressures. Optical access to the test chamber is provided through three quartz windows. A photograph of the droplet combustion apparatus is shown in Fig. 1. All experimental functions and data acquisition are controlled via an on-board microprocessor. During the 2.2-s drop sequence, a droplet is grown and stretched between two hypodermic needles that, by simultaneous rapid retraction, deploy the droplet into the microgravity environment with very low residual velocity. The gas phase surrounding the droplet is then symmetrically ignited using dual, retractable hot-wire ignitors. After retraction of the hot-wire ignitors, approximately 1.5 s of isolated, microgravity droplet combustion is achieved in a successful experiment. Data are acquired using three separate imaging techniques. A 16-mm Milliken high-speed motion picture camera records black and white, back-lit droplet images onto Kodak RAR 2498 film at 200 frames per second. Ultraviolet emission caused by hydroxyl radical chemiluminescence occurring with the flame is acquired using a Xybion ISG-250 intensified-array CCD video camera fitted with a 50-mm, UV-transmissive lens (Hammamatsu A4869) and
Numerical Model The methanol and methanol/water droplet combustion experiments were numerically simulated using a detailed droplet combustion model described elsewhere [6,12,7]. The model simulates the transient, spherically symmetric combustion of a bicomponent liquid droplet in an infinite oxidizing medium. The computations consider multicomponent molecular transport and complex chemical kinetic mechanisms to solve the gas-phase conservation equations of mass, species, and energy. The governing equations are spatially discretized using a moving finite element method and temporally integrated using an implicit ODE solver. The gas-phase chemical kinetics are modeled using the comprehensive methanol oxidation mechanism of Held and Dryer (19 species, 89 forward chemical reactions) [22,23]. For comparison with measured UV flame emission, additional reactions describing the production, quenching, and emission of electronically excited hydroxyl radicals (OH*) were added to the original oxidation mechanism. The individual reactions and rate coefficients for the reaction mechanisms are available elsewhere [23,32] and will not be repeated here. In addition to the gasphase system, a semiempirical vapor-liquid equilibrium technique [7] is employed at the droplet surface and the conservation equations of energy and species are solved within the droplet interior. Recent studies [5,7] show that the extinction of a methanol droplet flame is highly dependent on the liquid-phase mass Peclet number defined as
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predicts both the average burning rate and quasisteady flame position regardless of the Peclet number chosen. Results
Fig. 2. (a) Standard video image and (b) ultraviolet flame emission image of a 1.5-mm methanol droplet burning in a 35% O2/65% N2 microgravity oxidizing environment at 0.6 s after ignition.
)drdt ) s
Pel,m 4
Dl rs
4
)
)
1 d 2 (d ) 8 dt s Dl
4
1Kb(t) 8dl
Two limits exist: Pel,m K 1 and Pel,m k 1. In the former (well-mixed) situation, a substantial quantity of water is dissolved into the droplet during combustion, thereby promoting droplet extinction. In the latter (diffusively controlled) situation, very little water dissolves into the droplet [26]. The value of liquid Peclet number as specified by known liquid properties is around 30, suggesting that very little water should dissolve into the droplet. But experiments [24,25] have measured significant water dissolution, suggesting increased liquid mass transport that has been attributed to internal circulation. Insufficient experimental evidence exists, however, to conclude that the interior is completely well-mixed (Pe K 1). Therefore, unless otherwise specified, calculations were performed with an intermediate Peclet number of approximately 5. For initially pure methanol droplets, the numerical model accurately
Fuel droplets have been ignited in various oxidizing environments of 18–35% O2/N2 and 40–70% O2/ He at pressures from 0.6 to 1.0 atm. To date, the most complete data sets were obtained for pure methanol in various O2/N2 oxidizing environments and methanol/water mixtures in 30% O2/70% N2. Figure 2a is a standard black and white video image of a burning methanol droplet (1.3-mm initial diameter) in a microgravity oxidizing environment of 35% O2/65% N2. The figure clearly shows the high degree of spherical symmetry obtainable in microgravity. Moreover, the methanol flame is sufficiently nonluminous that it is possible to observe the liquid droplet even in the absence of back lighting. In contrast, the flame surrounding a liquid alkane (e.g. nheptane or n-decane) droplet burning under the same conditions would appear as a bright yellow flame ball, completely obscuring the droplet. While it was possible to measure the droplet diameter directly from the video image of Fig. 2a, more accurate measurements of the instantaneous droplet diameter were obtained using a high-intensity backlight to capture silhouette images of the vaporizing droplet with the Milliken high-speed movie camera. Using the automated tracking system described previously, the left, right, top, and bottom edges of the silhouette droplet image were determined for each frame. The instantaneous droplet diameter was calculated by taking the average of the vertical and horizontal measurements. The instantaneous flame diameter was determined from hydroxyl radical chemiluminescence measurements using a technique outlined in another paper at this symposium [14]. This work showed that in methanol droplet flames, the location of maximum hydroxyl radical emission intensity coincides with the location of maximum flame temperature, the most logical choice for defining the flame position. Figure 2b shows a digitized image of the UV emission acquired by the Xybion camera for the combustion of a 1500-lm methanol droplet in 30% O2/ 70% N2 at 1 atm (t 4 0.60 s after ignition). To determine the maximum emission location, intensity profiles obtained from the Xybion camera images were deconvoluted using the inverse Abel transform. The procedure was repeated for each video frame yielding the flame position as a function of time after ignition. These results were then combined with the instantaneous droplet diameter measurements to calculate the instantaneous flame standoff ratio, df/ ds. Figure 3 is a plot of the experimentally measured
METHANOL/WATER DROPLET COMBUSTION
Fig. 3. Experimentally measured (symbols) and numerically predicted (lines) normalized diameter squared versus time for initially pure methanol droplets in various O2/N2 oxidizing environments at 1 atm.
Fig. 4. Numerical prediction of the instantaneous burning rate plotted with the experimentally determined linear least-squares burning rate (bold lines) for initially pure methanol droplets in various O2/N2 oxidizing environments at 1 atm.
and numerically predicted droplet diameter squared versus time for initially pure methanol in various nitrogen/oxygen environments at 1 atm. The experimental data have been five-point averaged and both axes have been normalized by the initial diameter squared since initial diameter of the droplets varied between 1000 and 1500 lm. Initial droplet heating periods, during which droplet regression rate was
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minimal, were observed but generally lasted less than 5% of the total burn time. However, since the heating period varied between experiments, each experimental data set of Fig. 3 has been time shifted to the end of the droplet heating period. As expected, the measured burning rate increased substantially with rising oxygen content. Moreover, agreement between measured and calculated diameter history is excellent. The experiments did not show significant nonlinearity in the variation of diameter squared with respect to time, as had been observed previously by Choi et al. [13] and Cho et al. [12]. However, as indicated by the numerical predictions, the time available in the 2.2-s drop tower only allowed observation of approximately one-half of the total burn time. During this period, the numerical model predicts a net influx of water at the droplet surface resulting in less variation in the burning rate than during later stages when water begins to revaporize from the surface. Indeed, as the data suggest, any subtle nonlinearity in the plot of diameter squared during this period is not experimentally resolvable. Accordingly, a linear least-squares fit to the data was used to compare with the numerically calculated burning rates. The experimental burning rates are plotted along with the numerical modeling results, which predict an instantaneous droplet burning rate, |(d/dt)(d2s )|, that varies continuously during periods of ignition, vapor accumulation, droplet heating, quasi-steady combustion, and extinction. As shown in Fig. 4, although the subtle variation in instantaneous burning rate was not experimentally resolvable, the agreement in average burning rate is excellent. Over the comparison interval indicated in the figure, the measured burning rates were 0.56, 0.59, 0.65, and 0.82 mm2/s compared to average calculated values of 0.556, 0.632, 0.688, and 0.830 mm2/s for 18%, 21%, 24%, and 30% O2 in N2, respectively. Good agreement in average burning rate is obtained over the test interval regardless of the liquid Peclet number chosen. In the standard video camera (which is primarily sensitive to visible light), the ignition process and transient evolution of the flame position was obscured by the thermal radiation emitted from the resistively heated hot wire. Conversely, because only a fraction of the hot-wire thermal radiation is emitted in the UV, the transient evolution of OH* emission is clearly observed by the Xybion camera. Within the time resolution available using the video system (30 frames per s), the initial flame spread around the droplet and evolution to a spherically symmetric flame could not be resolved. Rather, from the first frame in which observations were made, the OH* emission appeared spherically symmetric with its maximum intensity generally occurring at less than 1 radii from the droplet surface. After the first
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Fig. 5. Comparison between numerically predicted (lines) and experimentally measured (symbols) normalized flame position, df/ds, for the combustion of initially pure methanol droplets in various O2/N2 oxidizing environments at 1 atm.
Fig. 6. Experimentally measured normalized diameter squared versus time for methanol/water mixtures in oxidizing environments of 30% O2/70% N2 at 1 atm.
frame, the flame grew in size, reaching a maximum diameter at about 0.1 s after ignition. Figure 5 shows the measured and predicted instantaneous flame position, df /ds, for methanol droplets in 21%, 30%, and 35% O2 with N2 inert. In methanol droplet combustion, the flame position is expected to decrease with time once the droplet begins to revaporize water that is absorbed into the liquid phase earlier in the combustion processes. The increased water within the flame zone decreases the flame temperature, which decreases the chemical reaction rate, causing the flame to move closer to the surface. In the experiments, the burn times
were not sufficient to observe regasification of condensed water. Thus, after the initial transient period, the flame position was very nearly constant for each initial oxygen content. As expected, the flame position decreases with increasing oxygen content because of stoichiometry considerations. After the initial transient period, average normalized flame positions of 4.1, 3.6, and 3.4 were measured for oxygen contents of 21%, 30%, and 35%, respectively. The numerical model predicts the quasi-steady flame position to within one normalized diameter at each condition. The slightly overpredicted flame position observed at each condition is most probably due to the neglect of gasphase radiative heat loss in the present calculations. Heat loss from the flame lowers the flame temperature, thereby requiring a smaller flame diameter to provide the required heat flux to the droplet surface. The effect of gas radiation is examined elsewhere [32]. Figure 6 is a plot of the experimentally measured diameter-squared history for methanol/water mixtures of 0%, 10%, and 20% water in an oxidizing environment of 30% O2/ 70% N2 at 1 atm. The figure shows that the addition of only small initial quantities of water results in substantial nonlinearity in the diameter-squared history, with several stages of burning evident. Initially, an abnormally long (with respect to the pure methanol data) droplet heating period is observed during which the droplet diameter is constant and may even increase slightly as a result of thermal swelling [33]. After the heating period is complete, the burning rate for the mixtures (as evidenced by the slope of the diameter-squared plot) actually increases to a higher value than that observed for the initially pure methanol. During the final observed stage, the burning rate decreases below the value observed for the initially pure methanol, apparently because of gasification of the condensed phase water. As noted previously, the latter stage was not observed for initially pure methanol droplet combustion here, although it has been observed by Choi et al. [13] and Cho et al. [12] in experiments with helium as the diluent. Previous numerical modeling results of Marchese and Dryer [7] predicted that addition of initial water content to methanol results in decreased burning rate, decreased flame standoff, and increased extinction diameter. The previous modeling results did not show substantial increases in the heating period or the second period of increased burning rate. In the previous study, comparisons were made between droplets of different initial water content assuming identical values of liquid mass and thermal Peclet number. This is not a bad assumption considering that the thermal and mass diffusivity of methanol/ water mixtures are relatively insensitive to the water content. A possible explanation for the experimental results
METHANOL/WATER DROPLET COMBUSTION
Fig. 7. Calculated instantaneous burning rate for methanol/water mixtures in oxidizing environments of 30% O2/ 70% N2 at 1 atm.
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and 20% actually increases above that of the initially pure methanol in agreement with observations. One possible reason for the increased circulation in the initial mixtures may be a solutal Marangoni instability wherein local differences in liquid concentration cause variations in surface tension that create secondary flows within the droplet [5,34]. There may also be an increase in the deployment-induced circulation in the methanol/water mixtures because of increased interfacial surface tension between the droplet and needles. Figure 8 shows the instantaneous flame position measurements and calculations for the same conditions as Fig. 6. Generally, the flame diameter decreased with increasing initial water content, although, as shown in Fig. 8, the measured flame position for 20% initial water was actually larger than the 10% case. This result may be due to uncertainty in the oxygen content and/or the effect of initial diameter. The numerical model was once again reasonably accurate, overpredicting the instantaneous flame position by about 1 normalized diameter. Summary
Fig. 8. Comparison between numerically predicted (lines) and experimentally measured (symbols) normalized flame position, df/ds, for the combustion of methanol/water droplets in oxidizing environments of 30% O2/70% N2 at 1 atm.
of Fig. 6 is that in the cases with 10% and 20% initial water content, the internal mass and thermal transport may have been enhanced compared to the initially pure methanol case, presumably because of increased internal convection. To reproduce this effect, the 0% initial water content was modeled with the actual thermal and mass diffusivities (Pel,h ' 1, Pel,m ' 20) and the 10% and 20% cases were modeled as well-mixed (Pel,h K 1, Pel,m K 1). As shown in Fig. 7, which is a plot of the calculated instantaneous burning rate for 0%, 10%, and 20% initial water content, the burning rate for the 10%
The experiments and associated modeling presented here have shown the predictive capabilities of time-dependent, spherically symmetric, bicomponent droplet combustion modeling when applied to mixtures of methanol and water. The results have also shown that the numerical model accurately reproduces both the measured burning rates and flame positions for a wide range of conditions. Good agreement in average burning rate and flame position is obtained over the test interval regardless of the liquid Peclet number chosen. Although the burn times available in the experiments presented here were not sufficient to observe droplet extinction, the comparisons made herein have further validated the numerical model such that it can be used with confidence to analyze the results of longer-burning experiments such as FSDC-1. Acknowledgments The authors wish to acknowledge the contributions of Charles Traylor Jr. for his assistance with the 2.2-s drop tower experiments and Arthur G. Birchenough in developing and troubleshooting the apparatus control system. Princeton contributions to this work were supported by the National Aeronautics and Space Administration through Grant No. NAG3-1231.
REFERENCES 1. Godsave, G. A. E., Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1953, p. 818.
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2. Spalding, D. B., Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1953, p. 847. 3. Law, C. K., Combust. Flame 24:89 (1975). 4. Card, J. M. and Williams, F. A., Combust. Sci. Technol. 84:91–119 (1992). 5. Zhang, B. L., Card, J., and Williams, F. A., Combust. Flame 105:267–290 (1996). 6. Cho, S. Y., Yetter, R. A., and Dryer, F. L., J. Comp. Phys. 102:160–179 (1992). 7. Marchese, A. J. and Dryer, F. L., Combust. Flame 105:104–122 (1996). 8. Knight, B. and Williams, F. A., Combust. Flame 38:111 (1980). 9. Haggard, J. B. and Kropp, J., AIAA paper no. 87-0576 (1987). 10. Shaw, B. D, Dryer, F. L., Williams, F. A., and Haggard, J. B., Jr., Acta Astronautica 17(11/12):1195–1202 (1988). 11. Avedisian, C. T., Yang, J. C., and Wang, C. H., Proc. R. Soc. London A 420:183–200 (1988). 12. Cho, S. Y., Choi, M. Y., and Dryer, F. L., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, p. 1611. 13. Choi, M. Y., Dryer, F. L., Haggard, J. B., and Brace, M. H., Am. Inst. Phys. Conf. Proc. 197:338–359 (1989). 14. Marchese, A. J., Dryer, F. L., Nayagam, V., and Colantonio, R., Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996, pp. 1219–1226. 15. Shaw, B. D., Dryer, F. L., Williams, F. A., and Gat, N., Combust. Flame 74:233 (1988). 16. Williams, F. A. and Dryer, F. L., Science Requirements Document for the Droplet Combustion Experiment, NASA Lewis Research Center, Cleveland, 1994. 17. Choi, M. Y., Dryer, F. L., and Haggard, J. B., Jr., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, p. 1611. 18. Kumagai, S., Sakai, T., and Okajima, S., Thirteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1971, p. 779.
19. Jackson, G. and Avedisian, C., 31st Aerospace Sciences Meeting and Exhibit, Reno, AIAA-93-0130 (1993). 20. Westbrook, C. K., Warnatz, J., and Pitz, W., TwentySecond Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, p. 893. 21. Held, T. J., Marchese, A. J., and Dryer, F. L., Central States, Western States, and Mexican National Sectional Meeting of the Combustion Institute, ESS/WSS/MNS/ CI, San Antonio, TX, 1995, p. 251. 22. Held, T. J. and Dryer, F. L., Twenty-Fifth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1994, p. 908. 23. Held, T. J. Ph. D. Thesis, Princeton University, Dept. of M.A.E., 1993. 24. Choi, M. Y., Cho, S. Y., Stein, Y. S., and Dryer, F. L., Fall Eastern States Meeting of the Combustion Institute, ESS/CI, Orlando, FL, 1990. 25. Lee, A. and Law, C. K., Combust. Sci. and Technol. 86:253–265 (1992). 26. Shaw, B. D., Combust. Flame 81:277–288 (1990). 27. Marchese, A. J. and Dryer, F. L., Eastern States Sectional Meeting of the Combustion Institute, ESS/CI, Clearwater, Fl, 1994, p. 355. 28. Yang, J. C., Jackson, G. S., and Avedisian, C. T., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, p. 1619. 29. Dietrich, D. L., Dryer, F. L, Haggard, J. B., Jr., Nayagam, V., Shaw, B. D., and Williams, F. A., TwentySixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996, pp. 000–000. 30. The Microgravity Combustion Group, Microgravity Combustion Science: A Program Overview, NASA TM-101424 (1989). 31. Klimeck, R. B., Wright, T. W., and Sielken, R. S., NASA TM-107144 (1996). 32. Marchese, A. J., Ph. D. Thesis, Princeton University, Dept. of M.A.E., 1996. 33. Megaridis, C. M., Combust. Sci. Technol. 92:291–311 (1993). 34. Aharon, I., and Shaw, B. D., 1995, submitted.
COMMENTS W. A. Sirignano, University of California, Irvine, USA. The large initial droplet size chosen for experimental convenience gives an unusually long characteristic diffusion time. The more practical range of initial droplet size would result in a diffusion time that is two to four orders of magnitude less. In that case, the chemical time becomes relatively larger. The emergence of this other (chemical) characteristic raises concern about the ability to scale these experimental results into the practical range. Author’s Reply. One need not consider droplets of the
practical (i.e. spray) size range in order to produce diffusion times of the same order of the chemical time. For example, by performing methanol experiments in He/O2 environments, Cho and co-workers [1] have measured flame extinction for 350 micron droplets. Similarly, by conducting methanol droplet combustion experiments with very large initial droplet diameters (3–5 mm), Dietrich and co-workers [2] have measured flame extinction in 1 to 2 mm droplets. In the former case, the presence of the inert helium resulted in decreased characteristic diffusion times; in the latter case, re-vaporization of condensed phase water
METHANOL/WATER DROPLET COMBUSTION lowered the flame temperature, thereby increasing the characteristic reaction time. In the experiments described in the present work, flame extinction would also have been observed had an additional 0.5 seconds of microgravity test time been available.
REFERENCES 1. Cho, S. Y., Choi, M. Y., and Dryer, F. L., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1990, p. 1611. 2. Dietrich, D. L., Dryer, F. L., Haggard, J. B., Jr., Nayagam, V., Shaw B. D., and Williams, F. A., Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996. ● I. Go¨kalp, CNRS, France. Could you explain why it was difficult to obtain the instantaneous burning rate from your experiments? Author’s Reply. As shown in Figure 3, the measured
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droplet diameter-squared vs. time contains a low-level, high frequency noise component. As frequently encountered in data analysis, the experimental noise is greatly amplified when one attempts to take the derivative of this data with respect to time. In some cases, it is possible to filter out the high frequency noise component prior to differentiation. For example, further analysis of the space-based droplet combustion experiments of Dietrich and co-workers [1] has allowed the calculation of the instantaneous burning rate [2,3]. The latter calculation is possible because of the large length and time scales available in space-based experiments.
REFERENCES 1. Dietrich, D. L., Dryer, F. L., Haggard, J. B., Jr., Nayagam, V., Shaw, B. D., and Williams, F. A., Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1996. 2. Nayagam, V., personal communication, 1996. 3. Marchese, A. J. and Dryer, F. L., 1996 Fall Technical Meeting, Eastern States Section, The Combustion Institute, Hilton Head, SC.