Experimental and numerical study of flame ball IR and UV emissions.

Experimental and numerical study of flame ball IR and UV emissions

M. Abid, M. S. Wu, J. B. Liu and P. D. Ronney

Department of Aerospace and Mechanical Engineering

University of Southern California, Los Angeles, CA 90089 USA

M. Ueki, K. Maruta, H. Kobayashi and T. Niioka

Institute of Fluid Sciences

Tohoku University, Sendai, Japan

D. M. VanZandt

ADF Corporation

Brookpark, OH 44142 USA

ABSTRACT

Near-infrared (IR) and ultraviolet (UV) emission profiles of flame balls at microgravity conditions in H2-O2-diluent mixtures were measured in the JAMIC 10-second drop-tower and compared to numerical simulations and supplemental experiments in KC135 aircraft µg experiments. Measured flame ball radii based on images obtained in the JAMIC, KC135 and recent space experiments (IR only) were quite consistent, indicating that radius is a rather robust property of flame balls. The predicted IR radii were always smaller than UV radii, whereas the experiments always showed the opposite behavior. Agreement between measured and predicted flame ball properties was closer for UV radii than IR radii in H2-air mixtures but closer for IR radii in H2-O2-CO2 mixtures. The large experimental IR radii in H2-air tests is particularly difficult to interpret even when uncertainties in chemical and radiation models are considered. Experimental radii would be consistent with a chemiluminescence reaction of the form HO2 + HO2 Æ H2O2 + O2 producing an excited state of H2O2, since HO2 is consumed at large radii through this reaction and its exothermicity is sufficient to create excited states that could emit at the observed wavelengths, however, no appropriate transition of H2O2* could be identified.

INTRODUCTION

Microgravity (µg) experiments in drop towers [1], aircraft [2] and orbiting spacecraft [3] have shown that stable, stationary spherical premixed flames ("flame balls") can exist near flammability limits in mixtures with low Lewis number (Le), defined as the ratio of the thermal diffusivity of the bulk mixture to mass diffusivity of the stoichiometrically limiting reactant. Flame balls are supported by diffusion of reactants to the ball surface and heat and product diffusion away from the ball. Convection plays no role in these steady, stable flame structures; the mass-averaged fluid velocity is zero everywhere at steady-state. While adiabatic flame balls are always predicted to be unstable [4, 5], as are flame balls in mixtures with Le close to or greater than unity [6], flame balls at low Le with significant volumetric heat loss (e.g. due to thermal radiation) are predicted to be stable [7, 8]. Consequently, flame balls in low-Le near-limit mixtures represent probably the simplest possible flame and thus are attractive for comparison to theoretical and computational models of premixed combustion, particularly at conditions near flammability or extinction limits.

Despite this simplicity, to date the agreement between model predictions and experimental observations, particularly with regard to the flame ball radius, has not been satisfactory [2, 9, 10]. One substantial problem is the uncertainty in the appropriate chemical model to employ for the very lean H2-O2-diluent mixtures in which most flame ball studies have been conducted; different published chemical mechanisms predict widely varying flame ball properties, even among models that predict the burning velocities of propagating planar H2-air flames quite well [10]. The flame ball calculations compare favorably with independent calculations [11] when the same chemical and radiation sub-models are employed, thus numerical accuracy issues are not considered a significant factor in these discrepancies.

The comparisons of model and experiment to date have only been made for flame ball radii based on images of the near-infrared and visible emissions of H2O because these emissions are readily detected by commercially available intensified video cameras. At the time of the early experiments using video cameras with sensitivity in the near-IR and visible region [2], unsuccessful attempts were made to image emissions from OH chemiluminescence using UV-sensitive intensified video cameras. Recent improvements in intensified video camera technology have now made OH imaging feasible, even in drop-tower and aircraft µg experiments. UV emissions from OH are more indicative of the location of heat release because they occur only where O, H and OH radicals are present, whereas the near-IR/visible emissions are more indicative of the locations where H2O and other stable radiating species are present at high temperature. The former may provide a more meaningful test of H2-O2 chemical kinetic models. Consequently, the purpose of this study is a comparison of predicted and measured UV emissions from excited-state OH molecules, and a comparison of the UV emissions to near-IR/visible emissions from H2O (and to a lesser extent CO2 and SF6 in mixtures containing these molecules).

The comparisons are conducted as follows. Numerical predictions of UV and near-IR/visible emissions from flame balls were obtained from computations employing detailed chemical, transport, thermal radiation and UV emission sub-models. Images of UV emissions from flame balls were obtained in the Japan Microgravity Facility (JAMIC) in Kamisunagawa, Hokkaido, Japan. This facility provides 10 seconds of fairly high-quality µg (< 10-5 go, where go denotes earth gravity). Supplemental tests were conducted in NASA’s KC135 low-gravity aircraft which enable more tests to be conducted with slightly longer durations (typically 15 s) at the expense of much poorer quality of µg (typically 0.02 go). These results are also compared to calculated near-IR/visible emissions and corresponding experimental data obtained in JAMIC and KC135 tests. Preliminary data on near-IR/visible radii obtained from space experiments conducted using the Combustion Module-1 (CM-1) facility on the STS-83 and STS-94 Space Shuttle missions [3] are also presented.

NUMERICAL STUDY

As in our previous numerical studies of flame balls [9, 10], a one dimensional, time-dependent flame code with detailed chemical and transport sub-models [12, 13], was employed. The usual nonsteady equations for energy and species conservation were solved in spherical geometry at constant pressure. The compositions studied were H2-air, H2-O2-CO2 and H2-O2-SF6 mixtures. For the latter two mixture families a fixed H2:O2 ratio of 0.5, corresponding to equivalence ratio of 0.25 was employed, as opposed to the H2-air mixtures where the O2:N2 ratio is fixed at 0.21.

The choice of H2-O2 chemical mechanism presents some difficulty. Previous studies [9,10] have shown that different published chemical mechanisms predict widely varying flame ball properties (e.g., radius and total heat release), even though all predict the laminar burning velocities of propagating H2-air flames quite well. All of these mechanisms yield predicted flame ball sizes that are much smaller than the experimental observations. In particular, flame ball properties are very sensitive to the rate of the recombination step H + O2 + H2O Æ HO2 + H2O, whose rate varies widely between published mechanisms. (Flame ball properties are almost equally sensitive to the branching step H + O2 Æ OH + O, but there is much less variability among literature values of this rate). Because the H2-O2 sub-mechanism extracted from the GRI methane oxidation mechanism [14] was found to yield flame ball radii predictions that are intermediate between those of other mechanisms we tested in [9, 10], and because it is a widely-used standard, we chose to employ GRIMech 2.1 for the chemical kinetics. In H2-O2-CO2 mixtures, wet CO chemistry was included though its influence on flame ball properties was found to be negligible. N2 and SF6 were assumed inert. Gas chromatography confirmed that very little SF6 decomposition occurred in the KC135 and space experiments, which is expected since the rate of radical attack on SF6 at combustion temperatures is much lower than the rate of radical attack on H2 or O2 [15, 16]. No third-body recombination efficiencies could be found for SF6, so they were assumed equal to N2. Optically-thin thermal radiation was assumed with loss per unit volume 4sap(T4-To4), where s, ap, T and To are the Stefan-Boltzman constant, Planck mean absorption coefficient, local temperature and ambient temperature (300K), respectively. Data on ap were taken from Hubbard and Tn [17] for H2O, CO2 and CO and Dunn et al. [18] for SF6.

Boundary conditions were ambient temperature and composition at the outer boundary (r = 100 cm) and zero-gradient at r = 0. 151 to 191 grid points were employed with dynamically-adaptive re-gridding and time-stepping. Once a steady solution for one mixture was obtained, the outer boundary composition was modified slightly and the calculation re-started to obtain solutions for other compositions. Near the lean and rich dynamic stability limits, the H2 mole fraction was changed in increments of 0.0001 to ensure accurate limit determination. Prior work [9] showed that these limits are physical, not numerical, in nature because at these limits small positive (negative) radial perturbations from the steady solution led to expanding (shrinking) flames and eventually extinguishment, whereas farther from these limits, perturbations were damped and convergence to the steady solution was observed. Hence, our computed limits are dynamic stability limits, analogous to those determined by linear stability analyses [4 - 8], rather than static turning-point limits, and thus may be more readily compared to experiments.

CO2 and SF6 have mean absorption lengths (ap-1) of 2.8 and 0.26 cm, respectively, at ambient conditions, which are much smaller than the chamber radius in the JAMIC, KC135 and CM-1 facilities. Consequently, reabsorption of emitted radiation cannot be neglected. Detailed quantification of reabsorption effects is beyond the scope of this study, however, as discussed in our previous study [10] an upper bound on reabsorption effects (aP,diluentÆ∞) can be obtained by neglecting diluent radiation entirely because as aP,diluentÆ∞ there is no radiative loss from the diluent and furthermore the "radiative conductivity" ∫ 16sT3/3aP approaches zero, thus there is no additional heat transport due to radiative transfer. In all cases H2O radiation is optically thin (no reabsorption) because ap,H2O-1 is much larger than the chamber radius and the major H2O emission/absorption bands do not overlap significantly with CO2 and SF6 bands. In future work, flame ball properties will be computed using detailed radiative emission and absorption modeling. Initial results for steady planar flames [19] indicate that net heat loss still occurs even in strongly absorbing gases due to differences in emission/absorption spectra of the reactant and product molecules as well as temperature broadening of these spectra.

It should be noted that the near-IR/visible and UV emissions imaged using intensified video cameras correspond to emission/absorption bands that are extremely weak (absorption lengths much larger than the system dimension) and thus can be considered optically thin. Reabsorption effects are only important for the thermal radiation emitted by H2O, CO2 and SF6 at much longer wavelengths (where practically all of the heat loss due to radiation occurs) that are not detected by the cameras we employed.

OH chemiluminescence from flame balls was modeled as follows. In hydrogen-oxygen-diluent flames without hydrocarbons, electronically excited hydroxyl radical (OH*) is produced primarily from the reaction H + O + M Æ OH* + M [20], which produces OH* in the first electronically excited state. Emission resulting from the transition 2S+ Æ 2P may be observed at 305.4 nm. The OH* may disappear by the quenching step OH* + M Æ OH + M or by emission OH* Æ OH + hn. The rate constants for these steps were taken from [21, 22]. Note that the rate constants for the quenching step depend on the collision partner M [21], which has been included in the calculations. The OH* chemiluminescence was calculated via post-processing the flame calculations using the steady profiles for temperature and species concentrations. It was not necessary to incorporate the OH* chemiluminescence reactions into the flame ball calculations because they have negligible influence on the concentrations of O, H and OH. The predicted emissions (in photons per unit volume per unit time) were transformed into emission intensity vs. position predictions (Figs. 1a and 1b) using line of sight integrations (Abel inversions). In this way a valid comparison between the predictions and experiments can be made, since the camera images are line of sight integrations of the flame ball emission along rays from the camera to the flame ball. The volumetric OH* emission intensity profile usually shows a maximum near the location of maximum heat release, whereas the Abel-transformed profile may or may not show such a peak. The flame radius based on the Abel-transformed OH* emission intensity profile (r*OH*) was arbitrarily defined as the profile half-width at one-third of the peak intensity (see Figs. 1a and 1b).

Near-IR/visible emission from flame balls was modeled as follows. The H2O, CO2, CO and SF6 emissions were calculated at each radial location from our computed temperature and species mole fraction profiles using Planck’s law and spectral line-strength data taken from the HITRAN database [23] for the 5000 strongest lines in the 400-900 nm range that the near-IR/visible intensified video camera can detect. These emissions (the most intense of which is from H2O near 823 nm) were weighted by the camera sensitivity vs. wavelength (l) (manufacturer’s published data) and, as with the UV emissions, were transformed into emission intensity vs. position predictions (Fig. 2) using Abel inversions. Intensity drops sharply as the temperature (T) decreases because for the relevant T and wavelengths the intensity per unit wavenumber exhibits an Arrhenius-like dependence on T (Wien’s limit of Planck’s law) with an effective "activation energy" nAhc/l = 34.7 kcal/mole at l = 823 nm, where nA, h and c are Avogadro’s number, Planck’s constant and light speed, respectively. As with UV emissions, the flame radius based on near-IR/visible wavelength emissions (r*VIS) was arbitrarily defined as the intensity profile half-width at one-third of the peak intensity.

Predicted flame ball radii are shown in Figs. 3a, 3b and 3c for H2-air, H2-O2-CO2 and H2-O2-SF6 mixtures, respectively. In most cases the flame radius based on the OH* emission profile as defined above (r*OH*) is virtually identical to the radial location of the peak of the heat release (r*HRR), though this close correspondence is apparently completely coincidental. The radial location of peak OH molecule concentration (r*OH) is slightly smaller, and the radius of the near-IR/visible emission as defined above (r*VIS) smaller still. Note that the predicted near-IR/visible and UV radii can be different by as much as a factor of 1.5. The reason r*VIS is the smallest is that, as described above, the near-IR/visible emissions are very sensitive to temperature, thus r*VIS is essentially the width of the high-temperature plateau seen in Figs. 1 and 2, whereas r*OH* occurs where H and O radicals are present, which is mainly near the location of maximum heat release rate. Heat release causes a change in the slope of the temperature profile and thus the majority of heat release must lie at a temperature slightly less than the maximum value, corresponding to a larger radius than the location where the temperature plateau ends.

EXPERIMENTAL STUDY

Experimental apparatus and procedures

A total of 30 drop tests were conducted in the JAMIC facility. The experimental apparatus consisted of a combustion chamber, spark generator, and video imaging system. The entire experimental apparatus described below was mounted in a 0.92 m x 0.87 m x 0.43 m frame that was installed in the JAMIC drop capsule. The combustion chamber was a cylindrical vessel with inside diameter 200 mm and length 250 mm. Quartz windows on the side and on top of the vessel enabled observation of the flames by the intensified video cameras described below. The combustible gas mixtures tested in this chamber were prepared by filling a mixing chamber via the partial pressure method, then transferring this mixture to the combustion chamber. Except where noted otherwise, all tests were conducted at an initial pressure of 1 atm. The estimated accuracy of the mixtures is ±1% of each component, e.g., 5.00 ± 0.05% H2. This accuracy level was verified by gas chromatography. The spark generator, which was functionally identical to that used in previous µg experiments [1, 2, 24], provided about 5 J of energy in 25 ms to ignite the very weak mixtures of interest in this study. The spark gap was located at the center of the chamber.

Two types of intensified video cameras were used in the JAMIC experiments. One camera, used for all tests, detected near-IR/visible emissions from 400 to 900 nm. A 12 mm focal length lens transmitted these emissions practically without attenuation. No filter was used on this camera/lens system. The other camera used in some tests was of similar design but with a different intensifier capable of detecting UV and visible emissions from 300 to 600 nm. A 50 mm focal length lens with quartz optical elements was used in order to transmit and focus these emissions. A bandpass filter centered at 310 nm with 10 nm width at 50% of the peak transmission blocked essentially all emission except that from OH*. Both video signals were recorded by on-board 8 mm VCRs.

The apparatus for the supplemental KC135 aircraft µg experiments was the same as that described above with the following exceptions. The combustion chamber was somewhat larger (322 mm diameter x 320 mm length). The combustible mixtures were created by filling gas bottles by the gravimetric method, rolling the bottles for at least 12 h to ensure mixture uniformity, then transferring the mixtures to separate smaller bottles that were loaded onto the aircraft. The combustion chamber was filled from these smaller bottles during flight. The spark generator produced up to 700 mJ of ignition energy in about 500 µs. A different near-IR/visible video camera and a 10 mm focal length lens was employed, but this camera uses the same type of intensifier as that in the JAMIC experiments and thus has the same spectral response. The UV camera, lens and filter arrangement was identical to that used in the JAMIC experiments.

The STS-83 and STS-94 space flight experiments employed the CM-1 facility that was functionally identical to the KC135 flight experiments in all aspects relevant to the current study, including gas mixing and filling. In fact, the KC135 apparatus served as an engineering test facility for the space flight hardware. The acceleration level during the space experiments, when smoothed with a 1 Hz low-pass filter, was generally less than 1 µg (vector sum of all three components) and in some cases averaged only 0.4 µg for an entire 500 s test!

The video images from both camera systems were digitized and analyzed in the following way. The images were thresholded at varying intensity levels and the number of pixels at each threshold level were counted. For each threshold level the number of pixels was transformed into an area and converted into an equivalent radius. The experimental intensity profiles shown in Figs. 4a - e are plots of this equivalent radius vs. threshold level. In this way intensity information from the entire flame ball image, instead of only along a line or averaged over several lines, is used. With this technique it is possible to obtain meaningful profiles only when the intensity is a monotonically decreasing function of radius. Line intensity profiles showed that this was the case for all mixtures tested even though in some cases the predicted UV profiles do show non-monotonic behavior (e.g., Fig. 1a).

The near-IR/visible imaging system resolution was tested using simulated flame ball targets of varying radii. It was found that target and image radii defined in the manner outlined above matched to within ±20% for targets with radii larger than 2.5 mm, which is smaller than any of the near-IR/visible flame radii reported below. The UV imaging system resolution is considerably better than this because its field of view is much narrower (about 37 mm x 50 mm at the center of the chamber) than the near-IR/visible system. Thus, imaging system resolution is not considered to be a significant cause of the discrepancies between model and experiment reported below. The disadvantage of the narrower field of view of the UV camera is that often flame balls would drift out of its field of view within a few seconds after the test began, especially in the KC135 tests were the acceleration levels (thus drift speeds) were much higher than in JAMIC. The narrow-angle UV lens used was chosen because it is the only commercially available UV lens compatible with our video cameras. It was not possible to move the UV camera further from the chamber to obtain a larger field of view because of the limited space in the drop package, the window dimensions and the decreased collection f-number at larger distances from the chamber.

For the JAMIC tests the data reported were taken just before the end of the drop test. The KC135 data were taken at least 5 s after ignition, during times when the instantaneous µg level was less than 0.01 go. The preliminary results from the STS-83 and STS-94 space flight experiments were taken when steady behavior of all properties including temperature profiles and radiative emission was observed, which was generally at times over 100 s. In some cases noted below, data from the space experiments taken 9 s after ignition is shown for comparison with the JAMIC tests.

Flame ball properties are affected by the presence of buoyant convection [2, 25], flow non-uniformities [26] and neighboring flame balls [27]. In contrast, the computational predictions reported in the previous section apply to isolated flame balls in quiescent atmospheres. The convection and flow-non-uniformity issue is most severe in the aircraft experiments because of the poorer quality of µg, hence, in these tests results are reported under conditions where the flame balls were most nearly stationary, corresponding to low instantaneous acceleration levels (< 0.005 go). Because the flame balls drift apart over time, the impact of neighboring flame balls is most severe in the shorter-duration JAMIC tests, consequently, except where noted otherwise the JAMIC test results are reported near just before the end of the drop period.

Results

Figures 4a and 4b show comparisons of predicted and measured flame ball near-IR/visible and UV intensity profiles, respectively, for a 3.44% H2-air mixture. The predicted near-IR/visible radius is smaller than the predicted UV radius, whereas the measured near-IR/visible radius is larger than the measured UV radius. This behavior was observed for all mixtures tested in all three facilities employed. For the H2-air mixtures, the predicted UV radius is larger than the measured value, whereas the predicted near-IR/visible radius is smaller than the measured value. The discrepancy between model and experiment is less for the UV radii. Note also that the measured UV intensity decreases monotonically with increasing radial distance from the center of the ball whereas the predicted UV intensity exhibits a peak at non-zero radial distance.

This 3.44% H2-air mixture is at the computational lean stability limit and thus is the leanest mixture for which comparisons between model and experiment can be made. The prediction of 3.44% H2 compares reasonably well with the experimental results 3.35 ± 0.05% H2 from earlier KC135 experiments [2] and 3.2 ± 0.1% H2 inferred from the JAMIC tests. (Lean limits were not measured in the STS-83 and STS-94 space experiments but are planned for a proposed reflight on STS-108 in the fall of 2000.)

Prior numerical investigations [9, 10] have shown that the lean limit and the flame radii near the limit are strongly affected by the chemical mechanism and in particular the rate constants for the H + O2 + H2O Æ HO2 + H2O recombination step, which are quite different for different published H2-O2 oxidation mechanisms. Improved agreement between model and experiment for both the UV and near-IR/visible radii can be obtained with a smaller rate for this reaction than that given in the GRI mechanism, though this would not change the prediction that (contrary to experiment) the UV radius is larger than the near-IR/visible radius. Of course, changes in the Planck mean absorption coefficient will also affect the predictions. Recently the accuracy of the radiation data for H2O from Hubbard and Tien [17] has been challenged by Bedir et al [28] and Ju et al. [29] because Hubbard and Tien used older (pre-1965) integrated band absorption coefficient data whereas high-resolution spectral data are now available [23]. Slightly better agreement between model and experiment is obtained with the Ju et al. [29] radiation data; the lean limit is shifted from 3.44% to 3.34% H2 while r*OH* and r*VIS for the 3.44% H2 mixture are shifted from 2.12 and 1.27 mm, respectively, with Hubbard and Tien radiation to 2.81 and 1.68 mm, respectively, with Ju et al. radiation.

For H2-O2-CO2 mixtures (Figs. 4c and 4d), as shown previously [10] the experimental results lie much closer to the predictions obtained neglecting CO2 radiation (optically thick limit of CO2 radiation), thus only optically-thick predictions are shown. In this case the agreement between model and experiment is much better than for H2-air mixtures in terms of the flame ball near-IR/visible and UV radii, though worse in terms of the lean limit (3.97% H2 predicted vs. 4.6 ± 0.1% H2 in early KC135 experiments [2] and 4.5 ± 0.2% H2 in JAMIC experiments.) In contrast to the H2-air mixtures, for H2-O2-CO2 mixtures the discrepancy between prediction and measurement is less for the near-IR/visible radius than the UV radius. As with the H2-air mixture (Fig. 4a) the measured UV intensity profile is monotonic whereas the predicted intensity exhibits a peak at non-zero radial distance.

Figure 4d also shows that near-IR/visible profiles obtained from JAMIC and space experiments are fairly similar, indicating that even within 9 s the flame ball radius is not too far from steady state even though some flame ball properties, e.g., total radiative loss and far-field temperature profiles, require much more time to reach quasi-steady state [3]. Such long evolution times for temperature and radiation are expected since the response time of flame balls is on the order of the time for thermal diffusion of energy from the near-field region of the flame ball to the far-field region. Theory [4-8] shows that the former region is characterized by radii of the order of the flame radius r* and the latter region is characterized by radii of the order of qr*, where q is the non-dimensional activation energy, estimated to be typically 12 for the mixtures employed here [9]. Consequently, the far-field time scale for the case shown in Fig. 4d is of the order (qr*)2/a ≈ 120 s where a is the ambient mixture thermal diffusivity. This evolution time scale is confirmed by numerical simulations [9]. Of course the flame ball radius can reach state-state only when its far-field has reached steady state, but the effect of H2O produced at the flame front diffusing to the far-field, which increases radiative loss and acts to decrease the flame radius, is nearly balanced by the effect of thermal energy diffusing to the far-field, which decreases the temperature gradient and conductive loss at the flame front and acts to increase the flame radius. That these effects should nearly cancel might be expected since the Lewis number of H2O in these mixtures is close to unity. The net result of all this is that the flame radius (and probably flame temperature, though we are not able to measure this directly) tends to stay more constant over time than the net radiative loss and far-field temperature profiles. This point is illustrated further in Fig. 4e, which shows that even only 1 s after ignition, UV and near-IR/visible profiles are not markedly different from those at the end of the test.

Figures 5a - d show comparisons of predicted and measured flame ball UV and near-IR/visible radii as a function of fuel concentration. The differences between these radii discussed above in relation to Figs. 4a - d are seen in all these data, with no effect of fuel concentration on these trends. Note that the number of UV points is sometimes lower than the number of near-IR/visible points because of the much smaller field of view for the UV camera discussed earlier. Figs. 5a - d show that data obtained in all three facilities, JAMIC, KC135 and space experiments, are quite consistent. The agreement between JAMIC and space experiments might be expected based on the earlier discussion of the time scale for development of the steady radius but it is somewhat surprising that the KC135 flame balls, which suffer from much higher acceleration levels than the JAMIC or space experiments, would exhibit nearly identical radii. Thus, UV and near-IR/visible radii are rather robust properties of flame balls.

Predicted radii for the H2-O2-SF6 mixtures are not shown in Figs. 5c and 5d because the experimental results lie nearly mid-way between the predictions obtained assuming optically-thin and optically-thick SF6 radiation. This is in contrast to the H2-O2-CO2 experimental results, which lie close to the optically-thick limit. Although SF6 has a much larger Planck mean absorption coefficient than CO2, this is mostly due to the extraordinarily strong but narrow n3 absorption band of SF6 centered near 10.5 µm. Because of net radiative loss due to temperature broadening of the absorption spectrum, more net loss would be expected from SF6-diluted mixtures than from mixtures diluted with CO2, which has broader and more numerous (though somewhat weaker) absorption bands. As a consequence, CO2 would be expected to exhibit more nearly optically-thick behavior than SF6 even though CO2 has a smaller Planck mean absorption coefficient.

DISCUSSION

The results show significant differences between model and experiments, even for H2-air mixtures where reabsorption effects are negligible [10], especially for near-IR/visible radii. Particularly surprising is that the relative sizes of UV and near-IR/visible radii are different in model predictions and experimental observations. The data obtained in all three experimental facilities are quite consistent, indicating that variations in acceleration level and experiment duration cannot account for the differences. Alternative chemical mechanisms and radiation models can account for some but seemingly not all of the discrepancy, nor can it account for the observation that the relative sizes of UV and near-IR/visible radii are different in model predictions and experimental observations. Decreasing the H + O2 + H2O Æ HO2 + H2O rate by a factor of 5 would provide favorable comparisons between measured and predicted near-IR/visible radii in H2-air mixtures [10], but such a large change cannot readily be reconciled with other kinetic data, would lead to a predicted lean stability limit much leaner than the experimental limit, and would adversely affect the moderate agreement between measured and predicted r*OH* radii shown in Fig. 5a. Also, agreement between predicted total radiative emissions in H2-air mixtures and measurements obtained in long-duration space experiments is favorable [10] and would be adversely affected by any change in the model that would increase the size of the thermal field and thus the total radiative loss.

As a result of these considerations, it is instructive to seek an alternative source of near-IR/visible emission that is prevalent at larger radii. This would change the experimental r*VIS without affecting other flame ball properties. Figure 1a shows that for the 3.44% H2-air mixture, at 5 mm (the minimum value of r*VIS that might be compatible with the experimental results shown in Fig. 5a) the predicted T has dropped to 59% of the peak temperature, or 682K. Clearly, at 682K the spontaneous emissions of H2O, CO, CO2 and SF6 at the wavelengths imaged in this study will be orders of magnitude smaller than at temperatures closer to r*VIS because these emissions are in Wien’s limit of Planck’s law. This motivates a search for a minor species that might exhibit a chemiluminescence emission. Figure 6 shows the calculated minor species concentration profiles for the 3.44% H2-air mixture (predictions for all other mixtures in all diluents are qualitatively identical.) As expected, the H, OH and O mass fractions peak at r ≈ 2 mm, which is close to r*HRR, indicating a relatively thin shell were heat release occurs, with little chemical activity outside this shell. Outside this zone, at larger radii and thus lower temperatures, the recombination reaction H + O2 + M Æ HO2 + M dominates the branching step H + O2 Æ OH + O. Significant concentrations of HO2, peaking near 3 mm, are found in this region. The HO2 is subsequently converted to H2O2 at still larger radii and lower temperatures, almost entirely through HO2 + HO2 Æ H2O2 + O2. When the r3 volume factor is considered, it is apparent that significant amounts of HO2 are being consumed and H2O2 produced out to radii of about 5 mm. As Fig. 6 shows, H2O2 produced in this region diffuses to the far-field without further reaction in the same manner as other stable species such as H2O. Consequently, a chemiluminescent reaction of the form HO2 + HO2 Æ H2O2* + O2 followed by H2O2* Æ H2O2 + hn would lead to an observed r*VIS that is much larger than that based on spontaneous emission of H2O and other stable species. (The concentration of H2O2 is about 1000 times lower than H2O, hence, spontaneous emission from H2O2 can be neglected). The exothermicity of HO2 + HO2 Æ H2O2 + O2 in the ground state is 33.5 kcal/mole, which corresponds to photons of wavelength 852 nm and is therefore in the range of wavelengths we would be able to detect if this energy were used to produce an excited state of H2O2 that subsequently returned to a ground state and emitted a photon. (Similarly, the H + O + M Æ OH + M that generates the OH* we detected has an exothermicity of 102.3 kcal/mole, corresponding to a wavelength of 279 nm, which is close to the wavelength of the observed emissions). However, no transition of H2O2 in this energy range could be identified. Images obtained with 710 nm and 780 nm long-pass filters were practically the same as those obtained with no filter, indicating that near-IR rather than visible emissions dominate. This would be consistent with either a near-IR chemiluminescence or the 823 nm spontaneous emission of H2O. Attempts to obtain more precise information on the emission spectra of flame balls in the near-IR were made, but tests with spectrometers compatible with the KC135 flight experiments have been unsuccessful due to the weakness of these emissions. In future work these emissions will be quantified further using a series of bandpass filters to identify the dominant wavelengths.

SUMMARY AND CONCLUSIONS

Near-IR/visible and UV emission profiles of flame balls in H2-O2-diluent mixtures were obtained in µg experiments employing drop tower, aircraft and space-based facilities. Data for both types of emissions obtained in all three facilities were quite consistent, indicating that radius is a rather robust property of flame balls. In marked contrast to experiments, the predicted near-IR/visible flame radii were always smaller than UV radii. The magnitude of discrepancy between measured and predicted flame ball properties was lower for UV radii than near-IR/visible radii in H2-air mixtures but higher for near-IR/visible radii in H2-O2-CO2 mixtures.

The most puzzling aspect of the observations is the remarkably large size of the experimental IR radii in H2-air mixtures compared to theoretical predictions. The magnitude of the adjustment in chemical or transport coefficients required to change the predicted temperature profiles enough to obtain agreement between model and experiment seems unjustifiable and would adversely affect the more favorable agreement with UV radii, flammability limits, and total radiative heat loss. A search for alternative sources of emissions suggested that experimental radii would be consistent with a chemiluminescence reaction of the form HO2 + HO2 Æ H2O2 + O2 producing an excited state of H2O2, however, no appropriate transition of H2O2* could be identified. These findings indicate that while a stationary flame ball is perhaps the simplest combustion system, quantitative agreement between computation and experiment has been elusive, even when using detailed chemical, transport and radiation sub-models, and thus represents a continuing modeling challenge.

ACKNOWLEDGMENTS

The USC portion of this work was supported by NASA under grants NAG3-1816 and NAG3-2124. We are grateful to Dr. S. Vosen for helpful discussions concerning OH emissions.

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Figure 1. Predicted flame ball OH chemiluminescence emissive power per unit volume profile and Abel-transformed emission intensity profile. For reference, the predicted temperature profile is also shown.

(a) 3.44% H2 in air

b) 3.97% H2 - 7.94% O2 - 87.91% CO2 (radiative heat loss due to CO2 radiation excluded).

Figure 2. Predicted flame ball near-IR/visible emissive power per unit volume profile (weighted by camera sensitivity) and Abel-transformed emission intensity profile for a 4.03% H2-air mixture. For reference, the predicted temperature and H2O mole fraction profiles are also shown.

Figure 3. Predicted flame ball radii based on the OH chemiluminescence profile (r*OH*), maximum heat release (r*HRR), maximum OH molecule concentration (r*OH) and near-IR/visible emission profile (r*VIS). For clarity, only a few predictions of r*OH* are shown because this was found to correspond almost exactly with r*HRR.

a) H2-air mixtures

b) H2-O2-CO2 mixtures, with and without heat loss due to CO2 radiation included.