Measurements and Predictions of Flame/Stretch Interactions of Hydrogen-Fueled Laminar Premixed Flames

AOO-16444

AIAA 2000-0574

MEASUREMENTS AND PREDICTIONS OF FLAME/STRETCH INTERACTIONS OF HYDROGEN-FUELED LAMINAR PREMIXED FLAMES

0. C. Kwon and G. M. Faeth Department of Aerospace Engineering The University of Michigan Ann Arbor, MI

38th Aerospace Sciences Meeting & Exhibit IO-13January2000/Reno,NV

For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics 1801 Alexander Bell Drive, Suite 500, Reston, VA 20191 (c)2000 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization.

AIAA 2000-0574

MEASUREMENTS AND PREDICTIONS OF FLAME/STRETCH INTERACTIONS OF , HYDROGEN-FUELED LAMINAR PREMIXED FLAMES

O.C. Kwon’ G.M. Faeth’ . Departmentof AerospaceEngineering The University of Michigan Ann Arbor, Michigan 48 109-2140

Abstract D massdiffusivity E, activation energy Fundamental unstretched laminar burning (0 mole fraction of speciesi velocities, and flame response to stretch as k reaction coefficient characterizedby Markstein numbers, were considered K flame stretch or normalized increase both experimentally and computationally for premised of flame surfacearea, Eq. (3) laminar flames involving mixtures of hydrogen and Ka Karlovitz number,KDJSL2 oxygen with either nitrogen or argon as diluents. L M_ar&stellllength . Otittiardly-propagating spherical lam&a; premixed Ma Markstein number,L/FD flames were considered for fuel-equivalenceratios of MaH Markstein numberbased on (I&,=, 0.6-4.5, pressuresof 0.3-3.0 atm, and concentrationsof Eq. (4) O2 in the nonfuel gasesof 21% by volume at normal n power in reaction coefficient temperatures. The present flames were very sensitive expression to flame stretch, yielding ratios of stretched to P pressure

unstretched laminar burning velocities in the range rf flame radius 0.8-3.0 for levels of flame stretch well below R universal gasconstant

quenching conditions, e.g., for Karlovitz numbers less SL laminar burning velocity basedon than 0.5. The agreement between measured and unburnedgas properties

predicted unstretched laminar burning velocities and SL’ value of SLat the largest radius Markstein numbers was good using several observed

contemporary reaction mechanisms. The resulting t time structure predictions suggest that H-atom production T temperature

and transport is an important aspect of preferential- SD characteristicflame thickness, DdSL diffusion&retch interactions, reflecting the strong density correlation between laminar burning velocities and H- fuel-equivalenceratio atom concentrationsfor presenttest conditions. Subscripts b = burned gas Nomenclature max = maximum observedvalue

U = unburnedgas

A = pre-exponentialfactor co Ye? unstretchedflame condition

Introduction l GraduateStudent ResearchAssistant, Departmentof AerospaceEngineering. t Professor,Department of AerospaceEngineering, Recent studies’of the effects of flame stretch on Fellow AIAA. laminar premixed flames in this laboratory-’ were Copyright 0 2000 by G. M. Faeth. Publishedby the extended to consider hydrogen-tieled flames, seeking American Institute of Aeronauticsand Astronautics, to manipulatepreferential diffusion effects comparedto Inc., with permission. 1 American Institute of Aeronauticsand Astronautics (c)2000 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization.

past work by varying flame pressures and d&tents. where the dimensionlessKarlovitz, Ka, and Markstein, Experimental observations of outwardly-propagating Ma, numbers characterize flame stretch, and the spherical laminar premixed flames were used to find responseof the flame to stretch, respectively. The laminar burning velocities as a function of flame values of SL and Ka were found following Strehlow stretch (representedby the Karlovitz number), the and Savage,” basedon predicted burned gas properties sensitivity of the laminar burning velocities to flame found using the computer codes of McBride et al. 24 stretch (representedby the Markstein number), and the and Reynolds,*’ as describedlater. fundamental laminar burning velocities of unstretched Several other proposals have been made to (plane) flames. The measurementswere also used to representeffects of flame stretch on laminar burning evaluate recently proposed detailed HZ/O2 chemical velocities, seeRefs. 16-20 and referencescited therein; reaction rate mechanisms due to Mueller et al.,’ nevertheless,Eq. (1) is particularly convenientbecause Marinov et al.,9 and Frenklach et al.,” based on Ma has proven to be relatively constantfor wide ranges detailed numerical simulations of the same outwardly- of Ka. Thus, SL and Ma provide concise measuresof propagating spherical laminar premixed flames as the premixed flame propagation rates and response to experiments. stretch that will be used to summarize the findings of The fact that interactions betweenthe preferential the present investigation. The small stretch limit of diffusion of various speciesand heat and flame stretch Eq. (1) is also of interest, in order to connect present affect the structure, stability and speed of laminar results to classical asymptotic theories of laminar premixed flames has been recognizedfor sometime. “- premixed flame propagation; this expression can be ‘5 Recent studies have shown, however, that found from Eq. (1) as follows:4 preferential-diffusion/stretchinteractions are unusually strong, causing large variations of laminar burning SL/SLm=1-Ma&&,, KG<< 1 69 velocities even for modest levels of stretch well away from quenching conditons.‘~‘* ‘6-23 This provides where M&=Ma has been observedfor relatively wide strong motivation to study preferential-diffusion/stretch rangesof Ka as noted earlier. Other advantagesof the interactions, particularly for hydrogen-fueled flames present characterization of premixed-flame/stretch where the chemistry is relatively simple and reasonably interactions can be summarized as follows:4 data well known. Then detailed numerical simulations of reduction is direct and does not involve the use of stretchedflames are computationally tractable and can flame structure models that are diflicult to fully define help to provide insight about experimental results as and are likely to be revised in the future, the well as the mechanismsof premixed flame sensitivity characterization is concise which facilitates its use by to stretch. others, the positive and negative rangesof Ma provide The present experiments were analyzed to find a direct indication of stable and unstableflame surface preferential-diffusion/stretchinteractions similar to the conditions with respect to effects of preferential earlier studies of outwardly-propagating spherical diffusion, and the results can be readily transformedto laminar premixed flames described in Ref. l-7. As provide direct comparisons with other ways to before, problems of flame thickness variations, characterize premixed-flame/stretch interactions. It curvature and unsteadinesscaused by variations in should be noted, however, that the present approach laminar burning velocities with increasingflame radius has only been applied to outwardly-propagating were minimized during data reduction by only spherical laminar premixed flames when ?&jr’, effects considering conditions where so/r’ <

dilution on flame/stretch interactions and also Data Reduction complete numerical simulations of these flames finding reasonably good agreement between measurements and Present measurements were limited to flames predictions based on the mechanisms of Frenklach ct having diameters larger than 10 mm to avoid ignition al..” Kim et al.,‘” and Wang and Rogg.” Thus. the disturbances and smaller than 60 mm to limit pressure specific objectives of the present investigation were to increases during the measuring period to values less consider further effects of pressure variations and than 0.4% of the initial pressure. No results were dilution with argon and nitrogen in order to modify the considered where the flame surface was distorted or transport environment of the flames compared to past wrinkled due to effects of buoyancy or flame instability. work and to provide a new perspective for gaining a Similar to earlier work, Refs. l-7> measurements were better understanding of premixed-flame/stretch limited to KD/rf < 2% so that effects of curvature and interactions. In addition, while continuing evaluation transient phenomena associated with large flame of the mechanism of Frenklach et al.,” more recent thicknesses were small. Finally. radiative heat losses mechanisms of Mueller et a1.,8 and Marinov et al.’ were small due to the large flame speeds of hydrogen- were also considered during numerical simulations of fueled flames and &re ignored similar to past work. flame properties. For these conditions, the laminar burning velocity and The present discussion begins with descriptions of flame stretch arc given as follows: experimental and computational methods. Results are then considered. treating flame evolution and stability, SL = (ph/p,)dr$dt, K = (Yrf)drddt. (3) flame response to-stretch. tihstretched-laniinar burning. velocities. Markstein numbers. flame structure and The density ratio appearing in Eq. (3) was found from effects of H-atom concentrations on flame behavior, in McBride et al.24 and Reynolds2’ (both yielding the turn. same results) which assumes adiabatic constant- pressure combustion with the same concentrations of Experimental Methods elements in the unburned and burned gases. This is a convention that follows past practice which ignores Apparatus preferential diffusion effects that modify local mixture fractions and energy transport and cause (pdpf) to Experimental methods were similar to past work differ from plane flame conditions. The convention is and will only be discussed briefly, see Refs. l-7 for convenient, however, because a single density ratio more details. The experiments were conducted in a relates all flame speeds and the approach retrieves the spherical windowed chamber having an inside correct flame displacement velocity, drddt, for given diameter of 360mm. The reactant mixture was unburned mixture conditions and Ka. Given reliable prepared in the chamber by adding gases at appropriate flame structure predictions, however, density ratios can partial pressures to reach the specified final pressure. be found as a function of Ka so that actual laminar The gases were mixed using a small metal fan located burning velocities and mass burning rates can be within the chamber with motion allowed to decay prior found; this work will be considered in the future to ignition (10 minutes for both mixing and decay). pending successful evaluation of flame property The combustible mixture was spark-ignited at the predictions. center of the chamber using minimum spark ignition Final results were obtained by averaging energies to control ignition disturbances. The flames measurements of 4-6 tests at each condition. The were observed using high speed (up to 7000 pictures resulting experimental uncertainties (95% confidence) per second) motion picture shadowgraphy. Once are as follows: Si less than lo%, Ka less than 20%, combustion was complete, the chamber was vented and and IMal less than 25% for (Ma1 >l and less than then flushed with air to remove condensed water vapor 25/IMal% for [MaI ~1. and cool the system to the allowable initial temperature range of the experiments (298+3K). Test Conditions

Experimental conditions involved reactant significantly by the criterion used to define the flame mixtures at normal temperature with fuel-equivalence positions. ratios of 0.6-4.5, pressures of 0.3-3.0 atm, Separate calculations were completed for concentrationsof oxygen in the nonfuel gasesof 21% unstretched (plane) flames using the steady one- by volume, Karlovitz numbers of O-0.5, ratios of dimensional laminar premixed flame code, PREMIX, stretchedto unstretched laminar burning velocities of of Kee and coworkers.33This code allowed evaluation 0.8-3.0 and values of unstretched laminar burning of effects of the use of the mixture-averagedmuhi- velocities of 820-3500mm/s. component diffusion approximation; similar to the findings of Aung et a1.3V4use of the mixture-averaged Computational Methods multicomponent mass diffusion approximation while including effects of thermal diffusion yielded errors of Numerical Simulations predicted flame properties much smaller than experimentaluncertainties and this procedurewas used Computational methods for the present flames for the RUN-IDL calculations. were similar to those used by Aung et a1.3.4 The outwardly-propagatingspherical flames were simulated Chemical Reaction Mechanism using the unsteady, one-dimensional laminar flame computer code RUN-IDL developedby Rogg.*’ This Three relatively recent I-I/O reaction mechanisms algorithm allows for mixture-averaged multi- were considered,as follows: Mueller et al.,’ Marinov component diffusion, thermal diffusion, variable et al.,’ and Frenklach et al.” C/H/O and N/O thermochemical properties, and variable transport chemistry were not important for present conditions, properties. The CHEMKIN packagezgM3was’ usedas a similar to the findings of Aung et al., 3,4and were preprocessorto find the thermochemical and transport deleted from the mechanisms. Finally, an updated properties for RUN-IDL. Transport properties were version of the mechanismof Marinov et al.’ was used, found following Hirschfelder and Curtiss3* using the seeTable 1 for a summary of the specific changesfrom transport property data base of Kee et a1.;3’ the original source. thermochemical properties were found from the The final reduced chemical reaction mechanisms, thermodynamic data base of Kee et a1.,2gexcept for after incorporating the simplifications just discussed, HO2 where the recommendationsof Kim et a1.26were involved 10 speciesand 19 reversiblereactions for the used. Prior to computing flame properties, all approachof Mueller et al.,* 20 reversible reactionsfor transport and thermochemical properties computed the approach of Marinov et al.,’ and 25 reversible using the results of Refs. 29, 30 and 31 were checked reactionsfor the approachof GRI-Mech 2.1 developed against original sources. Effects of radiation were by Frenklach et al.,” not counting the range of third small due to the large flame velocities of hydrogen- body collision efficiencies that were used. The fueled flames and were ignored. Flame propagation backward rates for all the mechanisms were found was allowed to proceedsufficiently far so that effects of from chemical equilibrium requirements using the initial conditions were small, similar to the CHEMKIN package.30 measurements. Other limitations used to control experimental uncertainties, e.g., 8&+2%, etc., were Results and Discussion also applied to the predictions. Finally, the computational grid in space and time was varied to Flame Stability and Evolution ensure numerical accuracy within l%, estimated by Richardson extrapolation of SL. The numerical Three kinds of flame surface instabilities were simulations were analyzed similar to the observed:preferential-diffusion instability (when Ma < measurements,taking the flame position at the point 0), hydrodynamic instability and buoyant instability. where gastemperatures were the averageof the hot and Shadowgraph photographs of flame surface after cold boundaries. Due to stringent flame thickness distortion by these instabilities for outwardly- limitations, however, the results were not affected propagating spherical flames appear in Kwon et al.’ and references cited therein. The presence of

preferential-diffusion instability could be identified by measurementssupporting a linear variation of SL.JSL irregular (chaotic) distortions of the flame surface with increasing.Ka and similar values of 4 for unstable relatively early in the flame propagation process. (Ma < 0) and stable (Ma > 0) preferential-diffusion Hydrodynamic instability could be identified by the behavior. development of a somewhat regular cellular disturbancepattern on the flame surface, rather late in UnstretchedLaminar Burning Velocities the flame propagation process, similar to the observationsof Groff.34 Finally, buoyant instabilities In the following, measured values of laminar were readily detectedby distortion of the flame surface burning velocities will be limited to results that have from a spherical shape,as well as by upward motion of been corrected to provide SLm. Measurements and the centroid of the flame image. As noted earlier, no predictions of SLmas a function of fuel-equivalence measurements were made when any of these ratio for hydrogen/airflames at NTF are plotted in Fig. instabilities were observed. 2. Measurementsshown on the figure include results of Taylor,16 Karpov et al.,” Egolfopoulos and Law,” Flame Responseto Stretch Vagelopoulos et a1.,22Aung et a1.3and the present investigation. Predictions shown on the plot included Results for finite flame radii involve finite values results of Sun et a1.23for unstretchedflames using an of flame stretch; therefore,values of SLmwere found by integral method and the mechanismof Kim et al.26as extrapolating the measurementsto Ka = 0 similar to well as presentpredictions for the reaction.mechanisms past work.“’ Then given &,.& plots- of S&S, as a of- Refs. S-10 found by extrapolating results for function of Ka can be constructedfor various values of simulations of outwardly-propagatingspherical flames I#as suggestedby Eq. (1). A sample of such results for similar to the measurements. It should be noted that H,/21% Oz/Ar flames (i.e., oxygen concentrations of the mechanism of Kim et al.26was used by Aung et 21% by volume in the nonfuel gases) at normal a1.3.4and is an earlier version of Mueller et al.’ used temperatureand pressure(NTP) with 4 = 0.60, 0.90, during the present investigation. The measurements 1.50 and 3.75 is illustrated in Fig. 1. Results at all generally agree within experimental uncertainties other test conditions are qualitatively similar. whereas measurementsand all the predictions are in Results of both measurements and predictions good agreementfor tiel-lean conditions. At fuel-rich illustrated in Fig. 1 exhibit the linear relationships conditions, the predictions of Frenklach et al. (GRI- betweenSLJSL and Ka that was exploited to find SLm; MECH-2.1)” and Sun et al.23 are somewhat larger similar linear behavior was observed during earlier than the measurements;nevertheless, the GRJ-MECH work, seeRefs. 1-7. The slope of these plots is equal to predictions are still surprisingly good even though this Ma according to Eq. (1) which already is independent mechanismwas not particularly tailored for hydrogen- of Ka over the range of the measurements.Similar fueled flames. The predictions of Sun et al.23are very behavior was observed over the present test range, similar to the earlier predictions of Aung et a1.3.4using which involves Ka < 0.5, however, quenching effects the same mechanism in conjunction with a numerical as extinction conditions are approached (where Ka simulation of the propagatingflame. would be on the order of unity, see Law”) would Measurementsof laminar burning velocities were probably yield a more complex response to stretch. carried out replacing the nitrogen in air with argon. Even for the present modest range of Ka, however, The specific heats of argon are smaller than nitrogen effects of flame stretch on SL were significant, e.g., which provide a way to consider effects of larger flame over the entire test range, SLdSL varied in the range temperatures on flame/stretch interactions. The 0.8-3.0 for Ka < 0.5. correspondingmeasurements and predictions of SLmas The predictions illustrated in Fig. 1 were basedon a function of fuel-equivalenceratio are plotted in Fig. the mechanismof Mueller et al.* but results using the 3. In this case,only results from the present study are Marinov et al.’ and Frenklach et al.” mechanisms available with the three predictions obtained from the were similar. The results of the numerical simulations mechanismsof Refs. S-10, as before. Comparing Figs. are shown to be qualitatively similar to the 2 and 3 shows that replacing nitrogen with argon yields roughly a 25% increase of the maximum

unstretched laminar burning velocity but with little slowly between $ * 2 and 5 even though present changein the value of the fuel-equivalenceratio where experimentsdid not approachflammability limits. It is the maximum is observed, e.g., + = 1.8. All the encouraging that the numerical simulations based on predictions reproducethis trend but the mechanismof detailed chemical mechanisms can reproduce these Mueller et al.’ is seen to provide the best quantitative trends, even though Markstein numberswere not used predictions over the entire test range of Figs. 2 and 3. during past efforts to optimize the chemical kinetic parametersof thesemechanisms. An attempt to exploit Markstein Numbers the predictions in order to obtain a better fundamental understanding of the behavior of Markstein numbers As discussed earlier, Markstein numbers are for hydrogen-fueledflames will be discussedlater. independent of Karloviti numbers for present Corresponding measurementsand predictions of conditions and can be plotted as a function of reactant Markstein numbers for hydrogen-fueledflames when conditions only. Measured and predicted values of nitrogen is replacedby argon at NTP are illustrated in Markstein numbersfor hydrogen/airflames at NTP are Fig. 5. As before, only measurementsand predictions plotted as a function of fuel-equivalenceratio in Fig. 4. from the present study are available for these Measurementsshown on the figure include the results conditions. Comparing Figs. 4 and 5 shows that of Taylor,’ 6 Karpov et al.,” Aung et a1.3 and the replacing nitrogen with argon has remarkably little present investigation. Predictions shown on the plot effect on either the trends or magnitudes of the include results of Sun et al.23 and the present Markstein numbers. Computations using all three investigation. Over the range of conditions where 8&r mechanismsreproduce this behavior very well, which < 2%, the various measurements agree within is encouraging. experimentaluncertainties. Outside this range for very Effects of pressure on Markstein numbers were lean $I < 0.60 and very rich $I > 5.0 flames, also investigated.Aung et al4 presentextensive results discrepancies among the various measurements for variations of Markstein numberswith pressureand become relatively large, reflecting the larger fuel-equivalence ratios for hydrogen/air flames at experimental uncertainties and the intrusion of other pressuresof 0.35-4.00 atm and normal temperature. effects (e.g., transient phenomena)on measuredvalues These results suggest reasonably good agreement of Markstein numbers. Similar to the results for between measurementsand predictions and relatively unstretchedlaminar burning velocities in Fig. 2, all the small effects of pressureon the magnitude and trends measurementsand predictions are in reasonablygood of Markstein numbers. Present predictions using the agreement for fuel-lean conditions. Discrepancies newer mechanismsof Refs. 8 and 9, indicated similar amongthe predictions are somewhatlarger at fuel-rich behavior. Present measurementsand predictions of conditions with present predictions using all three Markstein numbers as a function of pressure for mechanismsbeing somewhat smaller than that of Sun hydrogen-fueled flames where nitrogen has been et alz3 Earlier predictions of Aung et al.’ using the replaced by argon are illustrated in Fig. 6. These Kim et a1.26mechanism used by Sun et a1.23are also results are very similar to the hydrogen/air results of similar to the present results so the reason for these Aung et al.:4 measurementsand predictions agreed differences remain unknown. The general reasonablywell and pressurevariations do not have a characteristicsof unstable behavior (Ma < 0) at fuel- large effect on Markstein number values for pressures lean conditions and stable behavior (Ma > 0) at fuel- of 0.3-3.0 atm. rich conditions are consistent with conventional explanations based on preferential diffusion of the Flame Structure deficient reactant, see Refs. 1 and 3 and references therein. Behavior at intermediateconditions (between4 Measurementsand predictions of SLYand Ma are = 1 where Ma = 0 and I$ N 1.8 where SLmreaches a in reasonably good agreement over the present test maximum) is more complex, however, and must range; therefore,the predictions were exploited to seek involve preferential diffusion of both heat and mass. improved understanding about flame/stretch Another interesting feature of the results illustrated in interactions, Results of this type for flames where Fig. 4 is the extended plateau region where Ma varies nitrogen has been replaced by argon are discussedin

the following based on the Mueller et al.’ mechanism. flame): this causes a corresponding reduction of flame Corresponding results based on the mechanisms of tcmperaturcs of the stretched flame compared to the Marinov et aL9 and Frenklach et al.‘O were similar. unstretched flame. The reduced temperature Similar results for hydrogen/air flames can be found in (somewhat opposed by increased hydrogen atom Aung et al.3 The approach involved numerical concentrations) causes radical concentrations in the simulations of outwardly-propagating spherical flames reaction zone of the stretched flame to decrease for unstable (4 = 0.6) and stable ($ = 4.5) prcferential- compared to the unstretched flame (cg., the maximum diffusion conditions. Flame-structure/stretch mole fractions of H in the stretched and unstretched interactions were observed by comparing results for a flames are roughly 0.026 and 0.033. respectively) moderate level of .stretch (Ka = 0.07) with decreasing reaction rates and thus laminar burning corresponding predictions for unstretched (plane) velocities for the stretched flames. flames. Similar to the behavior of hydrogctiair flames. Typical predicted structures’ of stretched and discussed by Aung et al.,3 effects of flame structure on unstretched laminar premixed H2/2 1% O,/Ar flames at H,/21% Oz/Ar flames at NTP arc more complex at NTP arc illustrated in Figs. 7 and 8 for unstable and intermediate fuel-equivalence ratios near the maximum stable conditions, respectively. Results illustrated in the laminar burning velocity condition (where effects of figures include distributions of temperature and species fuel-equivalence ratio on the laminar burning velocity concentrations as a function of distance though the are weaker than for more fuel-lean and fuel-rich flame. (Note that the origins of the length scales for conditions). In this intermediate regime, cffec@ of unstretched and stretched- flame% are arbitrary and- do prkfer&&l diffusion of heat and mass, ai- well as the not correspond to the central ignition point.) tendency of increased hydrogen concentrations in the Considering the results for the unstable flame in reaction zone to increase radical concentrations there, Fig. 7, finite levels of stretch cause flame temperatures become factors in addition to effects of preferential to increase. This occurs because the faster diffusing diffusion that were just discussed. Consideration of hydrogen compared to oxygen causes the flame to effects of radicals on laminar burning velocities helps become more nearly stoichiomctric. (note the reduced provide insight about this behavior that will be concentrations of oxygen and increased concentrations considered next. of water vapor at the hot boundary of the stretched flame compared to the unstretched flame); this causes a H-Atom Behavior corresponding increase of flame temperatures of the stretched flame compared to the unstretched flame. The results of Figs. 7 and 8 indicate that H-atom The increased temperature (and possibly increased has the largest concentrations of all radicals in the hydrogen atom concentrations) causes radical reaction zone of the present flames, even for lean concentrations in the reaction zone of the stretched flames with fuel-equivalence ratios as small as $ = 0.6, flame to increase compared to the unstretched flame the smallest value considered during the present study. (c.g., the maximum mole fraction of H in the stretched In addition, Padley and Sugden3’ established a strong and unstretched flames are roughly 0.020 and 0.017, correlation between laminar burning velocities and H- respectively), increasing reaction rates and thus atom concentrations for H2/02/N2 flames based 011 their laminar burning velocities for the stretched flame. direct measurements of radial concentrations and the The effect of stretch on flame structure for stable laminar burning velocity measurements of Jahn.36 conditions is just opposite to the behavior just Combining these observations with the fact that H- discussed for unstable condilions (compare Figs. 7 and atom has significantly larger diffusivities than those of 8). For stable conditions, finite levels of stretch cause other species and heat in the present Hz/02/diluent flame temperatures to decrease. This occurs because flames tends to implicate this radical as an important the faster-diffusing hydrogen compared to oxygen factor in the relatively strong flame/stretch interactions causes the flame to become even richer (note the observed for present test conditions. The following increased concentrations of H2 and decreased discussion seeks to quantify this H-atom preferential concentrations of water vapor at the hot boundary of diffusion mechanism. the stretched flame compared to the unstretched

Present computations were used to study the These results suggest,however, that other factors are correlation between laminar burning velocities and involved, e.g.. the correlation is not linear and maximum H-atom concentrations. These results are conditions where Ma and MaH = 0 do not coincide. illustrated in Fig. 9. Presentpredictions shown on the Thus. additional study is neededto better understand plot involve all fuel-equivalenceratios and pressures the mechanism of flame/stretch interactions, even in for flames using both nitrogen and argon as diluents, relatively simple HJOz/diluent flames. and includes results for both stretchedand unstretched flames. This large range of conditions yields a Conclusions somewhat scatteredbut still quite strong correlation between laminar burning velocities and maximum H Efiects of positive flame stretch on the laminar mole fractions. The present correlation is qualitatively burning velocities of flames involving H2/0& or Ar similar to the correlation reported by Padley and mixtures were studied experimentally and Sugden,35which is also shown on the plot. computationally. The experimentsinvolved outwardly- The behavior observed in Fig. 9 suggests that propagating laminar spherical flames similar to past maximum H-atom concentrations could serve as a work in this laboratory,see Refs. 1-7; the computations surrogate for the laminar burning velocity when involved numerical simulations of the same flame considering flame/stretch interactions.This behavior is configuration considering detailed reaction explored in Fig. 10 where the ratios of the unstretched- mechanismsdue to Mueller et al.,* Ma.rinov et al.,’ and to-stretchedmaximum H mole fractions are plotted as Frenklach et al.‘” The reactant mixtures were at a function of Karlovitz numbers,analogous to the plot normal temperaturewith fuel-equivalenceratios of 0.6- of SLdSL as a function of Karlovitz number in Fig. 1. 4.5, pressuresof 0.3-3.0 atm, concentrationsof oxygen Effects of diluent are also shown on the plot, with in nonfuel gasesof 2 1% by volume, Karlovitz numbers results for Hz/air flames shown at the top and results of O-O.5 and ratios of unstretched&retched laminar for H,/21% OZ/Ar flames shown at the bottom, both for burning velocities of 0.8-3.0. The major conclusionsof reactants at NTP. Three sets of results are shown for the study are as follows: each diluent, spanning the present range of fuel- equivalence ratios; results for other conditions are 1. Effects of flame/stretch inteiactions for both similar. Remarkably, these plots are linear, similar to measurementsand predictions could be correlated the laminar burning velocity results of Fig. -1, and basedon the local conditions hypothesisaccording numerous other measurementsof laminar burning to SLdSI, = 1 + MaKa to obtain a linear velocities reportedin Refs. 1-7. This behavior suggests relationship between SL&, and Ka, yielding defining an expression for the effects of stretch on Markstein numbers that were constants for given maximum H-atom concentrations, analogous to Eq. reactantconditions. (l), as follows: 2. Effects of flame stretch on laminar burning velocities were substantial, yielding Markstein @hmxao/OI)max= 1+ Ma&a (4) numbersin the range-2 to 5. 3. Predicted and measured unstretched laminar The behavior of MaH was studied by plotting the burning velocities and Markstein numberswere in correlation betweenMaH and Ma as illustrated in Fig. good agreementusing reaction mechanismsdue to 11. Results shownon the plot considerthe full range of Mueller et al.,’ Marinov et al.’ and Frenklach et present test conditions at normal temperature (NT). al..“’ Based on the results illustrated in Fig. 10, the 4. Predictions show that stretched and unstretched correlation of Fig. 11 includes stretched flames, flames exhibit a strong correlation between extending up to the maximum stretch values Iaminar burning velocities and H-atom consideredduring the presentinvestigation. The strong concentrations similar to the measurementsof correlation betweenMa and MaH is evident, supporting Padleyand Sugden35in similar flames. the importance of H-atom concentrations for the 5. The local conditions hypothesisprovides a simple preferential diffusion effects causing the flame/stretch correlation between unstretched/stretched interactions observedduring the present investigation. maximum H-atom concentrations and the

Karlovitz number similar to the behavior of ‘Kwon, O.C.. Hassan, M.I., and G.M. Faeth, laminar burning velocities, yielding constant H- “Flame/Stretch Interactions of Premixed Fuel- Markstein numbers for particular reactant Vapor/02/N: Flames,” J. Prop. Power, in press. conditions. 8Mueller. M.A.. Kim, T.J., Yetter, R.A., and Dryer, 6. The corresponding strong correlation between H- F.L., “Flow Reactor Studies and Kinetic Modeling of Markstein numbers suggests that H-atom the HZ/O2Reaction, ” Int. J. Chem. Kinetics, Vol. 31, production and transport is an important aspectof No. 2, 1999,pp. 113-125. preferential diffusion/stretch interactions which is ‘Marinov, N.M., Westbrook, C.K., and Pitz, W.J., not surprising in view of the unusually large “Detailed and Global Chemical Kinetics Model for ditisivity and strong effect on laminar burning Hydrogen,” Trnnsport Phenomena in Combustion (S.H. velocities of this light radical. Chan, ed.), Vol. I. Taylor & Francis, Washington, DC, 1996, pp. 118-129. Acknowledgments ‘?reuklach. M.. Wang, H., Bowman, C.T., Hanson, R.K., Smith, G.P.. Goldin, D.M., Gardiner, W.C., and This researchwas supportedin part by NSF Grant Lissianski V.. “An Optimized Kinetics Model for CTS-9321959under the Technical Managementof F. Natural Gas Combustion,” World Wide Web, Fisher. Support from the Rackham Fellowship http://www.gri.org/Basic ResearchiGRI-Mech,Version Program of the University of Michigan for O.C. Kwon 2.1, 1995. is also gratefully acknowledged. “Manton, J.. van Elbe, G., and Lewis, B., “NonisoCropic Prbptigation of Combustion-Waves in References Explosive Gas Mixtures and Development of Cellular Flames.” J. Chem. Phvs. Vol. 20, 1952,pp. 153-158. ‘Kwon, S., Tseng, L.-K., and Faeth, G.M., “Laminar ‘*Markstein. G.H., Non-Steady Flame Propagation, Burning Velocities and Transition to Unstable Flames Pergamon,New York, 1964,p. 22. in H2/02/N2 and C3Hs/O2/N2 Mixtures,” Combust. ‘3Strelilow, R.A.. and Savage,L.D., “The Concept of Flame, Vol. 90, No. 3, 1992,pp. 230-246. Flame Strclch.” Combust.Flame, Vol. 31, No. 2. 1978, 2Tseng, L.-K., Ismail, M.A., and Faeth, G.M., pp. 209-211. “Laminar Burning Velocities and Markstein Numbers 14Clavin,P., “Dynamic Behavior of Premixed Flame of Hydrocarbon/Air Flames,” Combust. Flame, Vol. Fronts in Laminar and Turbulent Flows,” Prog. Enerm 95, No. 4, 1993,pp. 410-426. Combust. Sci.. Vol. 11, No. 1, 1985 , pp. l-59. 3Aung, K.T., Hassan, M.I., and Faeth, G.M., “Law. C.K.. “Dynamics of Stretched Flames,” “Flame/Stretch Interactions of Laminar Premixed Twentv-Second 6Symposiun~ (International) on Hydrogen/Air Flames at Normal Temperature and Combustion. The Combustion Institute, Pittsburgh. Pressure,” Combust. Flame, Vol. 109, No. l/2, 1997, 1988, pp. 1381-1402. pp. l-24. 16Taylor, S.C.. “Burning Velocity and Influence of 4Aung, K.T., Hassan, M.I., and Faeth, G.M., Flame Strelch.” Ph.D. Thesis, University of Leeds, “Effects of Pressure and Nitrogen Dilution on England, UK. 190I. Flame/Stretch Interactions of Laminar Premixed “Dowdy, D.R.. Smith, D.B., Taylor, S.C., and H2/02/N2Flames, ” Combust.Flame, Vol. 112,No. l/2, Williams, A.. “The Use of Expanding Spherical 1998pp. 1-15. Flames to Determine Burning Velocities and Stretch ‘Hassan, M.I., Aung, K.T., and Faeth, G.M., Effects on Hydrogen/Air Mixtures,” Twenty-Third “Measured and Predicted Properties of Laminar Sympo.Gum (International) on Combustion, The Premixed Methane/Air Flames at Various Pressures,” Combustion Institute, Pittsburgh, 1990,pp. 325-333. Combust.Flame, Vol. 115, No. 4, 1998,pp. 539-550. “Brown, M.J.. McLean, I.C.. Smith, D.B., and 6Hassan,M.I., Aung, K.T., Kwon, O.C., and Faeth, Taylor, S.C., “Markstein Lengths of CO/Hz/Air G.M., “Properties of Laminar Premixed Flames. Using Expanding Spherical Flames,” Twencv- Hydrocarbon/Air Flames at Various Pressures,” J. Sixth ~~~vmposiurn(International) on Combustion, The Prou. Power,Vol. 14, No. 4, 1998,pp. 479-488. Combustion Institute. Pittsburgh, 1996,pp. 875-882.

lgKarpov, V.P., Lipatnikov, A.N., and Wolanski, P., 27Wang, W.. and Rogg, B., “Reduced Kinetic “Finding the Markstein Number Using the Mechanisms and Their Numerical Treatment I: Wet Measurements of Expanding Spherical Laminar CO Flames,” Combust.Flame, Vol. 94, 1993,pp. 271- Flames,” Combust. Flame, Vol. 109, No. 3, 1996, pp. 292. 436-448. 28Rogg.B.. “RUN- 1DL: The Cambridge Universal ‘%adley, D., Hicks, R.A., Lawes, M., Sheppard, Laminar F1a1w Code,” Technical Report CUED/A- C.G.W., and Woolley, R., “The Measurement of THERMO/TR3 9. Department of Engineering, Laminar Burning Velocities and Markstein Numbers University of Cambridge,England, UK, 1991. for lso-Octane-Air and lso-Octane-n-Heptanein Air 29Kee.R.J.. Rupley, F.M., and Miller, J.A., “The Mixtures at ElevatedTemperatures and Pressuresin an CHEMKIN Thermodynamic Data Base,” Report No. Explosion Bomb,” Combust.Flame, Vol. 115, No. l/2, SAND8782 15B. Sandia National Laboratories, 1998,pp. 126-144. Albuquerque.NM. 1992. “Egolfopoulos, F.N., and Law, C.K., “An 30Kee. R.J.. Rupley, F.M.. and Miller, J.A., Experimental and Computational Study of the Burning “CHEMKIN 11: A Fortran Chemical Kinetics Package Rates of Ultra-Lean to Moderately-Rich H2/02/N2 for the Analysis of Gas Phase Chemical Kinetics,” Laminar Flames with Pressure Variations,” Twenty- Report No. SAND89-8009B, Sandia National Third Symposium (International) on Combustion, The Laboratories.Albuquerque, NM, 1993. CombustionInstitute, Pittsburgh, 1990,pp. 333-340. 3’Kee, R.J., Dixon-Lewis, G., Warnatz, J., Coltrin, 22Vage10poulos,C.M., Egolfopoulos, F.N., and Law, M.E., and Miller, J.A., “A FORTRAN Computer Code C.K.,“Further Considerationson the Determination of Package for the Evaluation of Gas-Phase, Multi- Laminar Flame Speeds with the Counterflow Twin- component Transport Properties,” Report No. Flame Technique,” Twenty-Fifth Symposium SANDSG-8246. Sandia National Laboratories, (International) on Combustion, The Combustion Albuquerque,NM, 1992. Institute, Pittsburgh, 1994, pp. 1341-1347. 32Hirsc1ifelder,J.O., and Curtiss, CF., “Theory of 23Sun, C.J., Sung, C.J., He, L., and Law, C.K., Propagation of Flames. Part I: General Equations,” “Dynamics of Weakly Stretched Flames: Quantitative Third .\:vmposiurn on Combustion and Flame and Description and Extraction of Global Flame Explosion Phenomena, The Combustion Institute, Parameters,”Combust. Flame, Vol. 118,No. l/2, 1999, Pittsburgh, 1948.pp. 121-127. pp. 108-128. 33Kee,R.J., Grcar, J.F., Smooke, M.D., and Miller, 24McBride, B.J., Reno, M.A., and Gordon, S., J.A., “A FORTRAN Program for Modeling Steady “CET93 and CETPC: An Interim Updated Version of Laminar One-Dimensional Premixed Flames,” Report the NASA Lewis Computer Program for Calculating No. SAND85-8240. Sandia National Laboratories, Complex Chemical Equilibrium with Applications,” Albuquerque.NM. 1993. NASA Technical Memorandum4557, 1994. 34Groff. E.G.. “The Cellular Nature of Confined “Reynolds, W.C., “The Element Potential Method Spherical Propane-Air Flames,” Combust.Flame, Vol. for Chemical Equilibrium Analysis: Implementation in 48, 1982. pp. 5 l-62. the Interactive Program STANJAN,” Department of 35Padley. P.J., and Sugden, T.M., Mechanical Engineering Report, Stanford University, “Chemilumincscence and Radical Recombination in Stanford,CA, 1986. Hydrogen Fla~nes.” Seventh Symposium (International) 26Kim, T.J., Yetter, R.A., and Dryer, F.L., “New on (‘01?tbl(.Ff10/7.The Combustion Institute, Pittsburgh, Results on Moist CO Oxidation: High Pressure,High PA, 1958,pp. 235-244. TemperatureExperiments and ComprehensiveKinetic 3hJahn.G.. cited in Lewis, B., and von Elbe, G., Modeling,” Twenty-Fifth Symposium (International) on Combust/on, I~lames and Explosions of Gases, 3rd ed., Combustion, The Combustion Institute, Pittsburgh, Academic Press.New York, 1987,pp. 395-402. 1994,pp. 759-766.

Table 1. Correctionsof Marinov et al.’ Mechanism”

No. Reaction A n EL3 5b H+H+H1 = H,+H, 9.20E+16 -0.6 0.0 7 H+O+M = OH+Mh 4.71E+18 -1.0 0.0 8 H+OH+M = H20+Mh 2.21E+22 -2.0 0.0 10 H+HOz = H2+02 6.63E+13 0.0 2.126 14 OH+HO,?= H,O+O,” 2.13E+28 -4.827 3.500 OH+H02 = H,0+02” 9.10E+14 0.0 10.964 aH2/O~reaction mechanismwith equationsnumbered same as original source;all other equationsunchanged from original source.Units are cm3/gmol/s/‘kcal/K and the reaction coefficient is taken as k = AT” exp(-E,/RT). bEfficiency factors for the collision partnersof this reaction are 6.4 for H20, all other specieshave efficiency factors of unity. “This reaction is expressedas the sum of the two rate espressions.

SIMULATIONS: MUELLER ETAL. MECHANISM

SUN ET AL. (1999)

H2/02/AR FLAMES Q NTP: 02/(02+AR) = 21% HYDROGEN-AIR FLAMES

1.0 ----•------. i STRETCHED FLAMES UNSTABLE 0.6 ’ J “““-.-.--....-.--.TICS LINE . .LER ET AL (1999) - 0.5 MARINOV ET AL. (1996) - - - - MEASUREMENTS LI . j GRI-MECH-2.1 (1995) -.-

I I I I I I I 0.01 I I I I 0 1 2 3 4 5 6 7 0.00 0.05 0.10 FUEL-EQUIVALENCE RATIO

UARLOWTZ NUMBER

Fig. 1. Measured and predicted laminar burning Fig. 2. Measured and predicted unstretched laminar velocities as a function of Karlovitz number and burning velocities as a function of fuel-equivalenceratio fuel-equivalenceratio for H2/21% OJAr flames at for hydrogen/air flames at NTP. Measurements of NTP. Karpov et al..“’ Aung et a1.,3 Vagelopoulos et a1.,22 Taylor, ” Egolfopoulos and Law2’ and the present investigation: predictions of Sun et aLs3and the present investigation.

I I I I I I HYDROGEN/AIR FLAMES Q NTP

H2/02/AR FLAMES @ NTP: 02/(02+AR) q 21% SIMULATIONS: KINETICS LINE cJ----j MUELLER ET AL. (1999) - MARINOV ET AL. (1996) - - - - GRI-MECH-2.1 (1995) -.- l

SYMBOL MEASUREMENTS: PRESENT a SIMULATIONS: KARPOV ETAL. (1997) n AUNG ET AL. (1997) ETAL (iB99) - TAYLOR (1991) : MARINOVETAL:(i996) ---- PREDICTIONS: GRIMECH-2.1 (1995) -.- SUN ET AL. (1999) + I I I I I I -0 1 2 3 4 5 6 I I I I I I FUEL-EQUIVALENCE RATIO 0 1 2 3 4 5 6 7 FUEL-EQUIVALENCE RATIO

Fig. 3. Measuredand predicted unstretchedlaminar Fig. 4. Measuredand predicted Markstein numbersas a burning velocities as a function of fuel-equivalence function of fileI-equivalenceratio for hydrogen/airflames ratio for Hz/21% O*/Ar flames at NTP. at NTF’. Measurementsof Karpov et a.l.,19Aung et al.,3 Taylor,’ ’ and the presentinvestigation.

10 I I I I I I

I I I I I I . HYDROGEN/AIR FLAMES @ NTP SIMULATIONS: KINETIC LINE - MUELLESRET AL. (1999) - MARINOV ET AL. (1996) - - - - “I GRI-MEW-2.1 (1995) -.- l MEASUREMENTS: SOUERCE SYMBOL PRESENT .

MEASUREMENTS: 7 PRESENT . n . KARPOV ET AL. (1997) . . AUNG ETAL. (1997) A TAYLOR (1991) l PREDICTIONS: SUN ET AL. (1999) +

I I I I I I $=0.6 0 1 2 3 4 5 6 7 -5 FUEL-EQUIVALENCE RATIO I I I I I I I I 0.0 1.0 2.0 3.0 PRESSURE (ATM)

Fig. 5. Measuredand predicted Markstein numbers Fig. 6. Measuredand predicted Markstein numbersas a as a function of fuel-equivalenceratio for H2/21% function of pressurefor HJ21% OJAr flames at fuel- O,/Ar flamesat NTP. equivalenceratios of 0.6 and 4.5 and a temperatureof 298 K.

0.30 2500 0.30 2500 H2/21%02/AR FLAME STRUCTURE @ NTP

2000 2000

0.20 0.20 1500 1500 02

+ =0.60 k 1000 1000 0.10

500 500

n “l-l l-l 0 “.“” 0 1 2 3 4 0 1 2 3 4” DlSTANCE(mm) _ DISTANCE (mm) _ -. -

0.025 0.025

H2R1%02/AR FLAME STRUCTURE @ NTP H2R1%02/AR FLAME STRUCTURE Q NTP

0.020 q 0.60 H Ka = 0.07 + q 0.60 0.015 -

- H02x25

0 1 2 3 4 0 1 2 3 4 DISTANCE (mm) DISTANCE (mm)

Fig. 7. Predicted flame structure for an unstable condition (HJ21% O?/Ar at a hel-equivalence ratio of 0.6 and NTP).

0.80 I11111114 I I I I I I 4 H2R1%02/AR FLAME STRUCTURE @ NTP H2R1%02/AR FLAME STRUCTURE Q NTP

T -,I500 = 0.60 P L 2 - IWO !! 0.40 0.40 - % + =4.50 8 Ka = 0.00 Ka = 0.07 G L - 500 IJ 0.20 0.20 - Ii20

0.00 0 0 1 2 3 4- 0 1 2 3 4 DISTANCE (mm) DISTANCE (mm)

0.040) , , , , , , I H2/21%02!AR FLAME STRUCTURE @ NTP H2Rl%02/AR FLAME STRUCTURE @ NTP

5 00.030 r--c ’040l * =4.50 - I= Ka=O.OO -

0 1 2 3 0 1 2 3 4 DISTANCE (mm) DISTANCE (mm)

Fig. 8. Predictedflame structure for a stable condition (H2/21%OJAr flame at a fuel-equivalenceratio of 4.5 and NTP)

4000 I I I H210210lL. FLAMES@ NT: 021(02+OIL.) = 218 z 1.0 P = 0.3 - 3.0 ATM Fl P UNSTABLE

H2/AIR FLAMES @ NTP

SIMULATIONS: MUELLER ET AL. (1999) MECHANISM

I- STABLE

0 C' I I I I H21021AR FLAMES @NTP: OZ/(OZ+AR) = 21% 0.000 0.025 0.050 0.075 0.100

MAXIMUM H MOLE FRACTION 0.00 0.05 0.10 0.1

KARLOVITZ NUMBER Fig. 9. Laminar burning velocities as a function of Fig. 10. Predictions of maximum H-atom mole maximum H-atom mole fraction for Hz/OZ/diluent fraction as a function of Karlovitz number and fuel- flames. Measurements of Padley and Sugden3’ equivalenceratio for Hz/Oz/diluentflames at NTP. predictions of the presentinvestigation.

-2 0 2 4

Fig. 11. Correlation between Ma and Mau for HJOddiluent flames at a temperatureof 298 K.

15 American Institute of Aeronauticsand Astronautics