NUMERICAL SIMULATION OF DILUENT EFFECTS ON FLAME BALLS

Ming-Shin Wu, Jian-Bang Liu and Paul D. Ronney

Department of Aerospace and Mechanical Engineering

University of Southern California, Los Angeles, CA 90089, USA

ABSTRACT

The effects of various diluent gases on steady, source-free spherical premixed flames ("flame balls") were modeled using a time-dependent numerical code with detailed chemical, transport, and radiation sub-models. The diluent gas affects the Lewis number (Le) and radiative properties of the flames. Numerical solutions for the steady properties and stability limits were obtained for lean H2-air, H2-O2, H2-O2-CO2 and H2-O2-SF6 mixtures. When results were non-dimensionalized by the properties at the dynamic stability limit, all results collapsed onto one of two curves depending only on whether the dominant source of radiative loss is from the product H2O, whose concentration decays to zero in the far-field, or diluent gas, whose concentration is constant in the far-field. No significant Le effect was found. Numerical predictions were compared to recent Space Shuttle experiments. For CO2 and SF6 diluents, experimental results lie between computational predictions obtained with diluent radiation included and with diluent radiation artificially suppressed, indicating that radiation models including reabsorption effects are needed in these cases. Significant influences of the chemical mechanism were found, even for mechanisms that properly predict the burning velocities of H2-air mixtures away from extinction limits. Sensitivity analysis showed that the discrepancies are due mainly to differences in the H + O2 + H2O Æ HO2 + H2O rate parameters for these mechanisms.

INTRODUCTION

Recent microgravity 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 bulk mixture thermal diffusivity to stoichiometrically limiting reactant mass diffusivity. 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; the mass-averaged fluid velocity is zero everywhere at steady-state. Since flame balls are one-dimensional, steady and convection-free, they are the simplest possible premixed flame structure and therefore provide a testbed for theoretical and numerical models of the interaction between chemical and transport processes in flames near extinction limits. Such models are crucial to fire safety assessment in mine shafts, oil refineries and chemical plants and the design of efficient, clean-burning combustion engines. Also, since flame balls can be observed in mixtures at g well outside conventional extinction limits, g can be more hazardous from the fire safety viewpoint. Flame balls may also be relevant to turbulent combustion of mixtures with low Le because flame balls are more robust than plane flames and may survive in mixtures where turbulent strain extinguishes planar flames. Hence, structures reminiscent of flame balls could occur in lean hydrogen-air mixtures proposed for cleaning-burning engines.

Theories [4-6] and numerical simulations [7-9] show that while equilibrium flame ball solutions exist for all combustible mixtures, Le and volumetric radiative heat loss effects play dominant roles in stability. Low Le is required so increasing curvature enhances flame temperature (T*), thus heat release rate. Radiative loss is required so increasing flame ball radius (r*) decreases temperature. This is because the temperature gradient at the ball surface decreases linearly with r* but the surface area increases with r*2, thus net heat release increases linearly with r*, while volumetric loss is proportional to r*3. Since the loss increases more rapidly with r* than does heat release, larger flames have lower temperature and thus lower reaction rates. Of course, losses must be small enough to avoid extinguishment. With these two features, stable solutions exist for a range of mixtures near extinction limits. (With radiative loss, two equilibrium radii exist for every mixture, but smaller, nearly adiabatic branch is always unstable [4-6,9].) Additionally, theory predicts qualitative differences in stability properties depending on where the loss occurs; only loss at r>>r*, where r is the radial coordinate, causes dynamic stability limits and oscillatory instabilities for mixtures richer than the classical turning-point limit. Also, the three-dimensional instability of flame balls [4,5], which causes breakup of flame balls in mixtures away from limits, is related to the magnitude of near-field loss, which must be sufficiently small for three-dimensional instability to occur.

Experiments [1-3] have been performed using varying diluent gases to study the aforementioned Le and radiation effects. Prior published numerical studies have only considered H2-air mixtures where Le0.28 and the diluent gas (N2) is radiatively inactive. In this study diluent effects are assessed numerically for comparison with theoretical predictions [4-6] and preliminary results of experiments performed on the MSL-1 Space Shuttle missions [3] (STS-83, April 1997 and STS-94, July 1997.)

NUMERICAL MODEL

A one dimensional, time dependent flame code employing detailed chemical and transport sub-models [10,11], was employed. The usual nonsteady equations for energy and species conservation were solved in spherical geometry at constant pressure. As in the space experiments [3], H2-air mixtures were examined along with H2-O2-CO2 and H2-O2-SF6 mixtures with a fixed H2:O2 ratio of 0.5, corresponding to equivalence ratio (f)=0.25, and diluted with CO2 or SF6 to near extinction limits. The H2-O2 chemical kinetics were extracted from the GRI methane oxidation mechanism [12]. In H2-O2-CO2 mixtures, wet CO chemistry was included though its influence was negligible. N2 and SF6 were assumed inert. Gas chromatography confirmed that very little SF6 decomposition occurred in the space experiments, which was 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 [13,14]. No third-body recombination efficiencies could be found for SF6, so they were assumed equal to N2. Optically-thin radiation was assumed with loss per unit volume (L)=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 [15] for H2O, CO2 and CO and [16] 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 (XH2) 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 [4-6], 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 space experiments (16 cm). Consequently, reabsorption of emitted radiation cannot be neglected entirely. Detailed quantification of reabsorption effects is beyond the scope of this study because this requires a spectrally-resolved radiation model, however, 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 no additional heat transport occurs 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.

The space experiments employed intensified video cameras (Xybion ISG-450) which detect emissions in the 400-900 nm wavelength range. To compare computed values of r* with video images, 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 [17] for the 5000 strongest lines in the 400-900 nm range. These emissions were weighted by the camera sensitivity vs. wavelength (manufacturer’s published data) and transformed into emission intensity vs. position predictions (Fig. 1) using Abel inversions. Intensity drops sharply as T decreases because for the relevant T and wavelengths the intensity per unit wavenumber increases exponentially with T (Wien’s limit of Planck’s law). For both computations and experiments, r* was arbitrarily defined as the intensity profile half-width at one-third of the peak intensity. The computed intensity-based radii (r*VIS) were always slightly smaller than the computed radius at the maximum volumetric heat release rate (r*HRR). For brevity in the results reported below, r*HRR is shown for all conditions, but r*VIS is shown only for conditions where experimental data are available for comparison.

RESULTS

Radial profiles

Figure 2a shows non-dimensional radial profiles of temperature, integrated heat release (QR) and integrated radiative heat loss (QL) for H2-air, H2-O2-CO2 and H2-O2-SF6 mixtures at the dynamic stability limit. Temperature and QR profiles are fairly similar for all mixtures, which is expected since the radial coordinate is non-dimensionalized with r*HRR. Because heat release rates increase rapidly with temperature, heat release occurs at small r where T is highest; half of QR occurs at r/r*HRR1.7 for all cases. QR rises slightly more rapidly for H2-air than H2-O2-CO2 or H2-O2-SF6 mixtures because T(r) drops more rapidly for H2-air, thus more reaction occurs at smaller r/r*HRR.

QL profiles are less similar because aP,SF6>>aP,CO2 and because for H2-air the only radiator is the product H2O, whose concentration decays to zero in the far-field, whereas for H2-O2-CO2 and H2-O2-SF6 the primary radiator is the diluent, whose concentration is constant in the far-field. Consequently the QL profile rises fastest (slowest), and far-field radiation is least (most) important, for H2-O2-SF6 (H2-air) mixtures. In all cases less than 1% of QL occurs at r/r*HRR1 because radiative loss is far less sensitive to temperature than heat release is. Despite this fact, simple estimates [9] for H2-air mixtures suggest near-field and far-field radiation have roughly equal influences on stability properties. Consequently, for H2-O2-CO2 and H2-O2-SF6 mixtures, near-field radiation is probably far more influential. Further evidence of near-field loss impact for these cases is presented later. This may explain why oscillating flame balls predicted by theory when far-field losses are important (particularly when Le<<1, as in H2-O2-SF6 mixtures) have never been observed experimentally nor predicted by computations using detailed chemical and transport models, and why three-dimensional breakup of flame balls, which is related to near-field losses [4,5], is always observed for mixtures not far removed from the limits.

In contrast, when diluent radiation is artificially suppressed, the non-dimensional profiles of temperature, QR and QL (Fig. 2b) are nearly identical for all three diluents since in this case only the product H2O radiates.

Effects of mixture strength and equivalence ratio

Figures 3a-c show the effects of XH2 on r*HRR and QL for H2-air, H2-O2-CO2, and H2-O2-SF6 mixtures, with and without diluent radiation for the latter two cases. Consistent with theory [4,5,7], for this stable solution branch r*HRR increases with XH2, and as r*HRR increases, QL~L(r*HRR)3 follows. Figures 3b-c show that at the same XH2, r*HRR is much larger without diluent radiation. This is because eliminating diluent radiation decreases L, thus r*HRR must increase to cause sufficient radiative loss to balance heat release. However, the heat release increases in proportion to r*HRR (see Introduction), and at steady state QR and QL are nearly equal [9], thus r*HRR~L-1/2 and QL~L-1/2. This last relation illustrates the unusual property that the total radiative loss (QL) increases when the loss per unit volume decreases!

The dotted vertical line in Figs. 3a-c corresponds to transition from O2 to H2 leakage to r=0. Even though all ambient mixtures studied are very lean, in these cases chemical reaction occurs at rich conditions (O2 deficient), thus the relevant Le is LeO2 rather than LeH2. Joulin [18] predicted this transition occurs at f=fcLeH2/LeO2. For H2-air mixtures, fc0.30, close to the transition f we found numerically (0.255). Corroborating experimental evidence of this transition is reported in [2]. However, Figs. 3b-c shows that transitions also occur for H2-O2-CO2 (LeH20.19, LeO20.85, fc0.22) and H2-O2-SF6 mixtures (LeH20.06, LeO20.29, fc0.23) with fixed f=0.25 but varying XH2. In these cases LeO2 is low enough that stable flame balls can exist for rich-burning conditions. Additional computations for H2-O2-CO2 mixtures (Fig. 3d) show that mixtures with f=0.2 are always lean-burning whereas f=0.3 mixtures are always rich-burning. Thus, theory, computation and experiment all concur on this unusual property of flame balls, except for the computed transition from lean to rich burning in H2-O2-CO2 and H2-O2-SF6 mixtures with fixed f close to fc.

For H2-air mixtures (LeH20.28, LeO20.94) slightly richer than fc, flame balls are unstable (Fig. 3a). This is consistent with theory [6] which predicts that all flame balls are unstable at Le1 or larger. However, Figs. 3b-c show that rich stability limits exist even when LeO2 is low. This limit occurs because at large XH2 the most abundant species at the flame front is product H2O, not diluent (note the maximum possible XH2 is 0.333 for f=0.25), and in pure H2O LeO21.1. The combination of the shift to rich-burning, coupled with the shift in LeO2, causes dynamic stability limits for large XH2 analogous to those seen in Fig. 3a for H2-air mixtures.

Correlation of numerical results

Figure 4 shows the predictions of Figs. 3a-c non-dimensionalized by the values of XH2, r*HRR, and QL at the dynamic stability limit. These predictions are well correlated in this manner, following one nearly universal curve for cases with diluent radiation and another without diluent radiation. Note that the effective Le varies from about 0.06 to 0.85 for these data, thus no systematic Le effect is found. In neither case are turning-point limits reached where r*HRR/XH2=. Significantly, non-dimensional values of r*HRR/XH2 at the dynamic stability limit (at the origin in Fig. 4) are much larger, by a factor of about 5, for cases with diluent radiation. This indicates that cases with diluent radiation are closer to the turning-point limit. According to theory [5], dynamic stability limits are closer to turning points when far-field loss effects are weaker. This is consistent with the discussion of Fig. 2a concerning effects of diluent radiation on near-field vs. far-field losses.

Comparison with experiment

Figures 3a-c show comparisons between numerical predictions and preliminary experimental results from MSL-1. (Space experiments were conducted for narrow ranges of XH2 because only near extinction limits are flame balls stable to three-dimensional disturbances [4,5].) For H2-air mixtures, agreement for radiative emission is reasonable, but poor for r*VIS. For H2-O2-CO2 and H2-O2-SF6 mixtures the experimental r*VIS and QL are bracketed by numerical results with and without diluent radiation, which represent lower and upper bounds for reabsorption effects (see Numerical Model). For H2-O2-CO2 mixtures the experimental flammability limit is also bracketed by the numerical predictions with/without diluent radiation (though not for H2-O2-SF6 mixtures). These observations strongly suggest that radiative reabsorption effects are needed for accurate numerical simulation in these cases.

Effects of chemical and transport models

The agreement between computed and measured r*VIS is unfavorable, even for H2-air mixtures (Fig. 3a) where reabsorption effects are negligible. Previously [8,9] the importance of chemical mechanisms on r* was noted. Figure 5a shows that three widely-accepted H2-O2 oxidation mechanisms [12,21,22] yield similar predictions for the burning velocities (SL) of planar flames far from extinction limits that agree well with experiments, yet Fig. 5b shows that these models yield widely varying predictions for r*HRR. Also, agreement of these mechanisms with each other and with experiments is poor near the lean planar flammability limit (Fig. 5a).

These observations motivate simple sensitivity analyses on elementary reaction rates. The results (Table 1) show that sensitivity coefficients are highest by far for the chain-branching step H+O2ÆOH+O and inhibiting step H+O2+H2OÆHO2+H2O. Similar behavior was found for near-limit propagating H2-air flames [19,20]. The ratios of the rates at 1075K (a typical value at the location of maximum heat release rate) for the Yetter et al. [21], GRI [12] and Peters [22] mechanisms are 0.782:1.00:0.883 for the chain-branching step and 0.497:1.000:1.205 for the inhibiting step. Thus, most of the differences seen in Fig. 5b are attributed to differences in the inhibition step rate. Uncertainties in this rate in this temperature range has been noted previously [20]. (Note that the sensitivity to H+O2+N2ÆHO2+N2 is considerably lower because, depending on the chemical model, the efficacy of N2 can be 20 times lower than H2O; similarly, the efficacy of SF6 had only minor effects on H2-O2-SF6 flame ball properties.) Decreasing inhibition rates would improve the agreement between model and experiment seen in Fig. 3a, and would improve agreement in SL for lean H2-air mixtures (Fig. 5a). In contrast, changing the branching rate would hurt the favorable comparison between predicted and measured SL away from the limits, since these SL are much more affected by branching than termination rates [19,20].

With this motivation, calculations were performed with varying H+O2+H2OÆHO2+H2O rates. It was found that the rate must be decreased five-fold to match the experimental r*VIS (Fig. 3a). This decrease also yields similar improvements in the match with SL experiments (Fig. 5a). Still, such large changes cannot readily be reconciled with other experimental data upon which the mechanisms [12,21,22] are based, thus further assessment of appropriate rates for near-limit flames is required. Potentially the third-body efficiency relative to N2 might be temperature-dependent [23].

Sensitivity to the diffusivity (D) of H atoms and H2 molecules and the thermal conductivity (l) of N2 is also shown in Table 1. The sensitivity to D(H2) and l(N2) is much higher than that of any chemical step. This is because increasing D(H2) or decreasing l(N2) decreases Le, which increases the adiabatic T*, which is similar to increasing XH2. (Of course, for plane propagating flames the adiabatic temperature is independent of Le). In contrast, D(H) has practically no impact since H atoms only appear near the reaction zone, whose thickness is much smaller than r*. Thus, increasing D(H) spreads out the reaction zone without changing the total heat release rate significantly. Thermal diffusion (the Soret effect) for H atoms and H2 molecules was found to increase r* by 30%, mainly because this increases the effective D(H2). Thus, while the diffusion coefficients of these species are commonly thought to be well known, flame ball properties are sensitive to small changes in these coefficients.

CONCLUSIONS

Numerical studies of flame balls in lean H2-air, H2-O2, H2-O2-CO2 and H2-O2-SF6 mixtures were conducted to examine the effects of varying diluents on size, radiant emission and stability properties and compare these predictions with theoretical results and space experiments. These properties were readily correlated by one of two nearly universal trends depending solely on whether the dominant source of radiative loss were from the product H2O or diluent gas. Poor agreement between numerical predictions and experimental results on flame ball size for optically-thick mixtures (CO2 or SF6) suggest that better radiation models, including spectrally-resolved emission and absorption, are needed for accurate numerical simulation in these cases. Improved chemical reaction mechanisms for near-limit H2-O2 oxidation may also be required, particularly for the 3-body H+O2+H2OÆHO2+H2O reaction.

ACKNOWLEDGMENTS

This work was supported by NASA-Lewis under Grant NAG3-1523. We thank Mr. Quin Blackburn for assistance with data analysis.

REFERENCES

1. Ronney, P.D., Combust. Flame 82:1-14 (1990).

2. Ronney, P.D., Whaling, K.N., Abbud-Madrid, A., Gatto, J.L., Pisowicz, V.L., AIAA J. 32:569-577 (1994).

3. Ronney, P.D., Wu, M.-S., Pearlman, H.G., Weiland, K.J., AIAA Journal, to appear (1998).

4. Buckmaster, J.D., Joulin, G., Ronney, P.D., Combust. Flame, 79:381-392 (1990).

5. Buckmaster, J.D., Joulin, G., Ronney, P.D., Combust. Flame 84:411-422 (1991).

6. Lee, C., Buckmaster, J.D., SIAM J. Appl. Math. 51:1315-1326 (1991)

7. Buckmaster, J.D., Smooke, M.D., Giovangigli, V., Combust. Flame 94:113-124 (1993).

8. Smooke, M.D., Ern, A. NASA Conference Publication 10174, pp. 445-450 (1995).

9. Wu, M.-S., Ronney, P.D., Combust. Flame , to appear (1998).

10. Rogg, B., in: Reduced Kinetic Mechanisms for Applications in Combustion Systems, Appendix C, Springer-Verlag, Berlin-Heidelberg, 1993.

11. Rogg, B., "RUN-1DL: The Cambridge Universal Flamelet Computer Code," User Manual, 1993.

12. Frenklach, M., et al., "An Optimized Kinetics Model for Natural Gas Combustion," 25th Symposium (International) on Combustion, Poster 26, 1994.

13. Fenimore, C., Jones, G., Combust. Flame 8:231-234 (1964).

14. Wray, K. L., Feldman, E. V., Fourteenth Symposium (International) on Combustion, Combustion Institute, Pittsburgh, 1972, pp. 229-238.

15. Hubbard, G.L., Tien, C.L., J. Heat Trans. 100:235-239 (1978).

16. Dunn, D.S., Scanlon, K., Overend, J., Spectrochimica Acta 38A:841-847 (1982).

17. Rothman, L.S., et al., J. Quant. Spectros. Radiat. Trans. 48:469-507 (1992).

18. Joulin, G., SIAM J. Appl. Math 47:998-1016 (1987).

19. Coffee, T.P. and Heimerl, J.M., Combust. Flame 50:323-340 (1983).

20. Egolfopoulos, F.N. and Law, C.K., Twenty-Third Symposium (International) on Combustion, Combustion Institute, Pittsburgh, 1990, pp. 413-421.

21. Yetter, R.A., Dryer, F.L., Rabitz, H., Combust. Sci. Tech. 79:97-128 (1991).

22. Peters, N., in: Reduced Kinetic Mechanisms for Applications in Combustion Systems, Chapters 1 and 5, Springer-Verlag, Berlin-Heidelberg, 1993.

23. Lindstedt, R. P., this Symposium.

24. Mauss, F., Peters, N., Rogg, B., Williams, F.A., in: Reduced Kinetic Mechanisms for Applications in Combustion Systems, Chapter 3, Springer-Verlag, Berlin-Heidelberg, 1993.

 

 

Elementary step

Sr*

SHR

H + O2 + H2O Æ HO2 + H2O

-0.394

-0.316

H + O2 Æ OH + O

0.324

0.251

H2 + OH Æ H2O + H

0.154

0.137

H + HO2 Æ OH + OH

0.118

0.089

H + O2 + N2 Æ HO2 + N2

-0.115

-0.092

OH + HO2 Æ O2 + H2O

-0.088

-0.067

H2 + O Æ OH + H

0.072

0.054

OH + OH Æ H2O + O

0.025

0.027

H + O2 + O2 Æ HO2 + O2

-0.016

-0.013

H + HO2 Æ O2 + H2

-0.014

-0.011

O + HO2 Æ OH + O2

-0.012

-0.009

D(H)

-0.0118

-0.0047

D(H2)

2.34

3.17

l(N2)

-2.07

-1.90

Table 1. Sensitivity coefficients Sr* ln(rHRR*)/ln(Ai) and SHR ln(QR)/ln(Ai) where Ai is the pre-exponential factor for reaction i, for a flame ball in a 4.03 H2-air mixture. For brevity, only sensitivity coefficients with absolute values greater than 0.01 are shown. Sensitivity coefficients for the diffusivity (D) of H atoms and H2 molecules and thermal conductivity (l) of N2 are also listed. Sensitivity to several other flame ball properties was studied; all exhibited very similar trends.

 

Figure 1. Predicted flame ball emissive power per unit volume profile (weighted by camera sensitivity) and Abel-transformed intensity profile for a 4.03% H2-air mixture. For reference, the predicted temperature and H2O mole fraction profiles are also shown.

Figure 2. Profiles of temperature, integrated (starting from r=0) heat release and integrated heat loss profiles for steady flame balls in H2-air, H2-O2-CO2 and H2-O2-SF6 mixtures at the dynamic stability limit. The radial coordinate is non-dimensionalized by r*HRR for each mixture. Temperature profiles are non-dimensionalized by the maximum temperature. Integrated heat release and heat loss profiles are non-dimensionalized by the total heat release (QR) and heat loss (QL).

a) H2-air (3.44% H2, r*HRR=0.197 cm), H2-O2-CO2 (5.85% H2, r*HRR=0.054 cm) and H2-O2-SF6 (5.27% H2, r*HRR=0.035 cm) mixtures, with diluent radiation for CO2 and SF6.

 

Figure 2. Profiles of temperature, integrated (starting from r=0) heat release and integrated heat loss profiles for steady flame balls in H2-air, H2-O2-CO2 and H2-O2-SF6 mixtures at the dynamic stability limit. The radial coordinate is non-dimensionalized by r*HRR for each mixture. Temperature profiles are non-dimensionalized by the maximum temperature. Integrated heat release and heat loss profiles are non-dimensionalized by the total heat release (QR) and heat loss (QL).

b) H2-air, H2-O2-CO2 (3.97% H2, r*HRR=0.197) and H2-O2-SF6 (2.45% H2, r*HRR=0.172 cm) mixtures, without diluent radiation for CO2 and SF6.

 

Figure 3. Computed flame ball radius at the location of maximum volumetric heat release (r*HRR ) and total radiation heat loss (QL) as a function of the H2 mole fraction (XH2) for steady flame balls. Preliminary experimental results from MSL-1 are also shown (filled circles), along with computed radii based on visible emission radius (r*VIS) (dashed line). (The number of data points on the two plots are different because each experiment yields one or more flame balls but only one averaged value of QL for all balls.) Transitions from lean to rich burning at the flame front are also shown.

a) H2-air mixtures

 

Figure 3. Computed flame ball radius at the location of maximum volumetric heat release (r*HRR ) and total radiation heat loss (QL) as a function of the H2 mole fraction (XH2) for steady flame balls. Preliminary experimental results from MSL-1 are also shown (filled circles), along with computed radii based on visible emission radius (r*VIS) (dashed line). (The number of data points on the two plots are different because each experiment yields one or more flame balls but only one averaged value of QL for all balls.) Transitions from lean to rich burning at the flame front are also shown.

b) H2-O2-CO2 mixtures, f=0.25

 

Figure 3. Computed flame ball radius at the location of maximum volumetric heat release (r*HRR ) and total radiation heat loss (QL) as a function of the H2 mole fraction (XH2) for steady flame balls. Preliminary experimental results from MSL-1 are also shown (filled circles), along with computed radii based on visible emission radius (r*VIS) (dashed line). (The number of data points on the two plots are different because each experiment yields one or more flame balls but only one averaged value of QL for all balls.) Transitions from lean to rich burning at the flame front are also shown.

c) H2-O2-SF6 mixtures, f=0.25

 

Figure 3. Computed flame ball radius at the location of maximum volumetric heat release (r*HRR ) and total radiation heat loss (QL) as a function of the H2 mole fraction (XH2) for steady flame balls. Preliminary experimental results from MSL-1 are also shown (filled circles), along with computed radii based on visible emission radius (r*VIS) (dashed line). (The number of data points on the two plots are different because each experiment yields one or more flame balls but only one averaged value of QL for all balls.) Transitions from lean to rich burning at the flame front are also shown.

d) H2-O2-CO2 mixtures, f=0.20, 0.25, and 0.30

 

 

Figure 4. Data from Figs. 3a-c non-dimensionalized by values of r*HRR and XH2 at the lean dynamic stability limit. Also shown are results for H2-O2 mixtures with no diluent (limit condition 3.25% H2, r*HRR=0.189 cm).

 

Figure 5. Comparison of computed flame properties for 3 different H2-O2 chemical mechanisms [12,21,22].

a) Burning velocity (SL) as a function of f in H2-air mixtures. A compilation of experimental results from several sources is also shown [24].

 

Figure 5. Comparison of computed flame properties for 3 different H2-O2 chemical mechanisms [12,21,22].

b) r*HRR as a function of XH2 for steady flame balls in H2-air mixtures.