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N2 diffusion flames
Twenty-first Symposium (International) on Combustion/The Combustion Institute, 1986/pp. 1579-1589
S T R E T C H E D L A M I N A R FLAMELET ANALYSIS OF T U R B U L E N T H2 A N D CO/HJN2 D I F F U S I O N FLAMES M. C. DRAKE General Electric Corporate Research and Development Center Schenectady, New York 12301
The stretched laminar flamelet approach to turbulent diffusion flames is tested by comparison of instantaneous and conditionally-averaged Raman measurements in turbulent H2 and CO/H2/N~ jet diffusion fames with stretched laminar opposed-flow diffusion flame model calculations and measurements. The H2 turbulent jet diffusion flame measurements close to the fuel nozzle show instantaneous temperatures 300K less than equilibrium, peak OH concentrations three times larger than equilibrium, and substantial coexistence of H2 and 02. Quantitatively similar effects are calculated by David, et al., for lightly stretched (c~ = 100 s -l) opposedflow laminar H2 diffusion flames. The turbulent flame data lie in a narrow band between the highly stretched ~ = 12,000 s -1 laminar flame calculation and the adiabatic equilibrium curve and approach adiabatic equilibrium downstream in the flame. Localized extinction is relatively unimportant in simple H2 turbulent jet diffusion flames since only a few instantaneous Raman measurements are dose to that calculated at extinction (c~ = 12,000 s-~). With a fuel consisting of 40%CO/30%H2/30%N> experimental data in both the turbulent jet flame and a laminar opposed flow diffusion flame show even larger nonequilibrium effects. The excellent correspondence between stretched laminar and turbulent flame data suggest that the laminar flamelet approach may provide better predictions than the two-scalar pdf approach of finite-rate chemistry in turbulent reaction zones because partial equilibrium assumptions are not required and localized extinction can be accounted for properly. However, differences between stretched laminar and turbulent flame data suggest that the laminar flamelet approach can overestimate the influence of preferential diffusion in flames containing Hz and may not properly include the slow three body radical recombination reactions which are likely to occur outside of the relatively thin primary reaction zones.
I. Introduction Most c o m b u s t i o n m o d e l s o f t u r b u l e n t diffusion flames have used a c o n s e r v e d scalar-equilibrium chemistry a p p r o a c h 1'2 which accounts for t u r b u l e n t fluctuations using an assumedshape probability density f u n c t i o n o f m i x t u r e fraction { (i.e., e l e m e n t a l mass fraction) but which ignores chemical kinetic effects. However, a m p l e e x p e r i m e n t a l data in t u r b u l e n t j e t diffusion flames (reviewed by Drake and K o l l m a n n 3) d e m o n s t r a t e that finite rate chemistry processes c a n n o t be neglected. Alt h o u g h m o r e c o m p l i c a t e d c o m b u s t i o n models i n c l u d i n g one 4-6 or two 7's reaction progress variables based u p o n partial e q u i l i b r i u m have led to better a g r e e m e n t with e x p e r i m e n t a l data in t u r b u l e n t diffusion flames, the m o d e l results still show significant differences with experiment. 6 T h e laminar flamelet a p p r o a c h provides an alternative way o f i n c l u d i n g finite rate chemis-
try effects in t u r b u l e n t c o m b u s t i o n models. 9-11 In the laminar flamelet a p p r o a c h , t u r b u l e n t flames are assumed to consist o f laminar flamelets stretched and d i s t o r t e d by the turbulence. T h e detailed s t r u c t u r e o f t u r b u l e n t and laminar flamelets are a s s u m e d to be the same, so relationships b e t w e e n m i x t u r e fraction and reactive scalars o b t a i n e d f r o m laminar diffusion flame m o d e l i n g o r e x p e r i m e n t s can be used in t u r b u l e n t c o m b u s t i o n models. However, these m i x t u r e fraction-reactive scalar relationships are not universal a n d are functions o f gradients or flame stretch (usually expressed in terms o f the scalar dissipation rate X = 2 D O~/Ox. O{/Ox). At very low stretch (i.e., very long r e s i d e n c e times) the l a m i n a r flamelet relationships should a p p r o a c h those at equilibrium. At very high stretch, extinction can occur. M e a s u r e d or calculated l a m i n a r flamelet or "stretched laminar flamelet" relationships have b e e n used by Williams, 9 Marble and Broadwell, 12 Liew et al., 13'14 E i c k h o f f a n d G r e t h e 5 and
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TURBULANT COMBUSTION
Peters, 11 to model turbulent diffusion flames. The validity of the laminar flamelet approach in turbulent combustion has been examined using experimental time-averaged thermocoupie or probe sampling measurements. For example, relationships between average temperature and molecular compositions vs. average mixture fraction in turbulent jet diffusion flames of CO 15 and of hydrocarbons 5'16 are compared with measurements or model calculations of laminar diffusion flames. Although reasonable agreement was claimed, 5'15'~6 there is no fundamental reason to believe that laminar flamelet relationships should be valid for conventional time-averaged measurements in turbulent diffusion flames with their large fluctuations in instantaneous mixture fraction and flame stretch. A more fundamentally sound approach of testing the laminar flamelet approach in turbulent jet diffusion flames is to model the fluctuations of ~ and X and to compare the calculated average scalar variables (i.e., temperature, molecular compositions) with those measured experimentally. This approach also leads to reasonable agreement 5 ' 12.14 ' but suffers from uncertainties in the fluid mixing model particularly in determining values of X, the assumed shape of the pdf's of and X, and the assumed relationship between and X. The purpose of the present paper is to provide a more quantitative test of the stretched laminar flamelet approach in H2 and CO/H2/N 2 turbulent jet diffusion flames by comparing instantaneous and conditionaUy-averaged measurements of mixture fraction and scalar variables with laminar flamelet experiments or model calculations. Limitations of the laminar flamelet approach due to preferential diffusion and slow reactions (i.e., three body recombinations) are discussed and the influences of localized extinctions are examined.
II. Approach A. Previous Results on Turbulent Diffusion Flames The characteristics of the turbulent combustor and the initial conditions for the turbulent jet diffusion flames are discussed in detail elsewhere. 6'17'18 For the H~ flames, the fuel jet had an initial average velocity of 285 m/s (corresponding to a cold flow Reynolds number of 8500) and an initial air velocity of 12.5 m/s. For the CO/H2/N2 flame, the initial molar ratio of the fuel was approximately 40%CO/30%HJ 30%N2 with a small amount of CH4 (-0.7%) sometimes added. The initial fuel and air
velocities were 54.6 m/s and 2.4 m/s respectively, chosen to match the Reynolds number (8500) and initial fuel-to-air velocity ratio (22.8) of the H~ flame. The turbulent flame data include qualitative and quantitative imaging (Schlieren, shadowgraph, and planar O H fluorescence); instantaneous measurements of velocity (laser velocimetry); simultaneous measurements of temperature, density, individual major species concentrations and mixture fraction (pulsed Raman); and instantaneous measurements o f OH concentrations (laser saturated fluorescence). Data for H2 flames are summarized in references 17-19 and for CO/H~/N2 flames in references 3, 6, and 20.
B. Data Analysis bz the Present Paper The present paper extends the analysis of turbulent diffusion flame data obtained by pulsed Raman spectroscopy which provides simultaneous measurements of mixture fraction, temperature and concentrations of H2, 02, CO, CO~, Nz and H 2 0 with a spatial resolution of <0.1 m m ~ and a temporal resolution of 2 ~sec. Either instantaneous Raman data or data conditionally-averaged in narrow mixture fraction intervals are compared to stretched laminar flame model calculations or experimental data. Experimental measurements of stretched laminar diffusion flames of H2 are not available, but calculations by David et a1.,21 including detailed chemical kinetics and molecular transport effects have appeared recently. These H2 laminar diffusion flame calculations were obtained at two values of flame stretch (velocity gradients of 100 s -x and 12,000 s -1) where the higher value of flame stretch corresponds to a flame near the extinction limit. Detailed experimental measurements of stretched laminar diffusion flames of CO/H2/N2 fuel have recently been obtained in our laboratory using laser diagnostic and probe sampling techniques. 2z T h e experimental values of flame stretch (velocity gradients (x = 70, 180 and 330 s -1) are believed to be far from the extinction limit for this fuel.
III. Results A. H2 Flames Pulsed Raman data (approximately 30,000 data points) for the simultaneous measurements of temperature and mixture fraction in the Re=8500 turbulent H2 jet flame are shown in Figure 1. T h e solid line in Figure 1 corre-
1581
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sponds to calculated adiabatic e q u i l i b r i u m (AE) conditions for H z - a i r m i x t u r e s . 23 In all cases, the t u r b u l e n t c o m b u s t i o n d a t a in Figure 1 lie in a n a r r o w band. Close to the fuel nozzle (at x/d= 10), the e x p e r i m e n t a l d a t a show t e m p e r a tures considerably above the AE curve in lean flame zones ( m i x t u r e fraction <0.02) a n d considerably below the A E c u r v e in stoichiometric ( m i x t u r e fraction = 0.0283) and rich flame zones. N e a r the c e n t e r o f t h e t u r b u l e n t flame (x/d=50), the R a m a n results are reasonably close to the AE line. F a r d o w n s t r e a m (x/d=200), all o f the rich flame pockets have b u r n e d out a n d the m e a s u r e m e n t s are in g o o d a g r e e m e n t with the AE curve. In o r d e r to m o r e clearly show trends, the R a m a n d a t a at e a c h axial location have b e e n a v e r a g e d in n a r r o w m i x t u r e fraction intervals. Results are shown in F i g u r e 2 for extensive R a m a n data atx/d=lO, 25, 50, 100, 150 a n d 200 in the t u r b u l e n t H2 j e t d i f f u s i o n flame. T h e c o n d i t i o n a l l y - a v e r a g e d data close to the nozzle (x/d= 10 and 25) show t e m p e r a t u r e s as m u c h as 300 K less t h a n those calculated at adiabatic e q u i l i b r i u m and progressively smaller deviations f r o m AE are o b s e r v e d f u r t h e r downstream. T h e t u r b u l e n t H2 flame data are comp a r e d with the results o f calculations o f stretched l a m i n a r H2 d i f f u s i o n flames by David et al., 21 (dashed lines in F i g u r e 2). For a l a m i n a r flame which is not highly stretched (e~= i 0 0 s-S), the calculated p e a k flame t e m p e r a t u r e is 2280 K - - n o t m u c h lower t h a n the peak calculated AE t e m p e r a t u r e o f 2380 K. I n the very highly
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ture and mixture fraction using pulsed laser Raman scattering from the H2 turbulent jet diffusion flame. Each of the ~ 30,000 points represents one time (2 I~s) and space < 0.1mm 3) resolved measurement. Data from three axial positions (x/d= 10, 50 and 200) are shown. The solid line is the calculated relationship between temperature and mixture fraction in H~-air flames under adiabatic equilibrium conditions.
MIXTURE FRACI'ION
FIG. 2. Data conditionally-averaged in mixture fraction intervals from the H2 turbulent jet diffusion flame at all six axial locations measured. The solid line is the same as in Figure 1. The dotted lines are those calculated by David, et al., 2t for laminar opposed flow H2 diffusion flames under small stretch (t~=100 s-1) and near extinction ((x = 12,000 s-l).
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TURBULANT COMBUSTION
stretched laminar H~ flame close to the extinction limit (c~=12,000 s -1) the peak flame temperature is only 1350 K. Instantaneous R a m a n measurements of mole fractions of H2 a n d 02 near the nozzle (x/d= 10) of the turbulent H2 flame are shown in Figure 3. The solid line in Figure 3 shows that very little overlap of H~ and O2 is expected u n d e r adiabatic equilibrium conditions (at most X(H2) = X(O~)-0.007). T h e fuel-air overlap is calculated 21 to be much greater in stretched laminar diffusion flames a n d to increase with flame stretch [X(H2) --= X(O2)-0.025 at cc = 100 s-1 and X(H2) -= X(02)~0.075 at er = 12,000 s-l]. The pulsed Raman measurements from the turbulent H2 flame in Figure 3 show substantial instantaneous presence of both fuel and air at this flame location (x/d = 10). I n general, the instantaneous turbulent flame data lie between the AE curve and c~ = 12,000 s-1 curve, with most of the data points lying closer to the a = 100 s -I curve. This is in excellent agreement with the temperature vs. mixture fraction data in Figures 1 and 2. The H 2 vs. 02 data (averaged in mixture fraction intervals) in Figure 4 show deviations from the AE curve at x/d =10 and 25 while the data further downstream progressively approach the AE limit, (also similar to the trends observed in Figure 2). The last point of comparison between the H2 turbulent jet diffusion flame data and the stretched laminar flamelet calculations of David et al., 21 is the value of O H concentrations. Absolute OH concentrations were measured in the turbulent H2 flame using single-pulse laser saturated OH fluorescence. '9 The m a x i m u m measured instantaneous O H concentration was 6.2 x 1016 molecules/cc, which is in reasonable agreement with the m a x i m u m value calculated for partial equilibrium conditions (5.5 • 1016 molecules/cc) r9 and with the m a x i m u m of 6.4 x 1016 molecules/cc calculated in a laminar premixed stoichiometric H2-air flame. 24 In the laminar opposed-flow H2 flame calculation, the maximum calculated O H concentration in the c~ = 100 s-1 flame is 6.1 x 1016 molecules/cc, 21 in excellent agreement with the measured maxim u m in turbulent H2-air flames. Near extinction (a = 12,000 s -1) the calculated OH concentration drops, but it remains considerably above the AE value. B. CO/H2/N2 Flames Conditionally-averaged pulsed Raman measurements of temperature and hydrogen element mixture fraction are shown in Figure 5 for the Re = 8500 t u r b u l e n t CO/H2/N2 jet diffusion flame. T h e t u r b u l e n t flame data are
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Fro. 4. Data conditionally-averaged in mixture fraction intervals in the H2 turbulent jet diffusion flame showing the co-presence of H2 and 02. The symbols are the same as in Figure 2. compared with an adiabatic equilibrium flame calculation (solid line) a n d with Raman measurements in the laminar (c~ = 70 and 180 s -1) opposed-flow CO/H2/N2 diffusion flames (dashed line). R a m a n temperature measurements in both the laminar and turbulent flames used the N2 Stokes/anti-Stokes ratio method
LAMINAR FLAMELET ANALYSIS OF DIFFUSION FLAMES which has been shown to agree within experimental error (+50 K) with radiation-corrected coated fine-wire thermocouple measurements in laminar premixed H2-air flames. The Raman measurements in CO/H2/N2 flames have larger uncertainties due to background emissions or laser-induced broad b a n d fluorescence. 2~ However, systematic temperature errors should not markedly affect comparison of laminar and turbulent flame data since both were calculated by the same technique. T h e instantaneous data (not shown) in the turbulent CO/H~/Nz flame fall in bands, although the spread is considerably larger than in Figure 1 for the H2 flame, due at least in part to MEO, BTU GAS TURB. JET FL~ME
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the larger measurement uncertainties in the CO/H2/N2 flame. Also, the t u r b u l e n t CO/H2/N2 flame shows larger deviations from adiabatic equilibrium conditions than the H2 flame. In Figure 5, the peak conditionally-averaged temperature near the nozzle (x/d = 10 and 25) are 3 6 0 - 5 0 0 K lower than the peak AE temperature of 2240 K. Downstream at x/d = 50, the measured temperatures approach the AE values although not as closely as in the H~ flame. T h e conversion of H2 into H 2 0 and of COinto CO2 is monitored separately. Conditionallyaveraged measurements of the fractional conversion of H2 (defined as the mole fraction of H20 divided by the sum of the H2 and H20 mole fraction) are shown in Figure 6 and the corresponding values for CO conversion shown in Figure 7. The conversion of H2 in the laminar and turbulent flames is much closer to equilibrium than the conversion of CO which does not attain equilibrium even at x/d = 50 in the turbulent flame. Although not shown in the present paper, mean O H concentration measurements in this turbulent flame are six times larger than equilibrium at x/d = 10 and remain approximately four times larger than equilibrium at x/d = 50, 6
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FIG. 6. Conditionally-averaged Raman measurements of the conversion of H2 versus mixture fraction in the turbulent jet diffusion flame and laminar opposed-flow diffusion flame with CO/H2/N2 fuel. Symbols are the same as in Figure 5.
I n general, calculations or experimental data from stretched laminar diffusion flames and from turbulent jet diffusion f a m e s show many similar features. This correspondence reinforces the suggestion that stretched turbulent diffusion flames can be modeled as a collection of stretched laminar diffusion flamelets. De-
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TURBULANT COMBUSTION
tailed comparisons o f the laminar and turbulent diffusion flame results are discussed here in terms of four processes (preferential diffusion, superequilibrium, partial equilibrium and localized extinction) which can occur in diffusion flames.
A. Preferential Diffusion Because of its low molecular weight, H2 molecules diffuse much more readily than most other species. T h e preferential diffusion of H2 has been m o d e l e d in laminar H2 diffusion flames 25 and experimentally observed x7'26 and computationally m o d e l e d is in H2 turbulent j e t flames. T h e large deviation from adiabatic equilibrium in fuel-lean regions of the a = 100 s -* laminar flamelet curve in Figure 2 has also been attributed to H2 preferential diffusion. ~l At increased stretch rates, the mixing is faster and thus preferential diffusion is less prominent (see the lean regions of the ~x --- 12,000 s -I curve in Figure 2). Similarly in transitional a n d turbulent H2 diffusion flames, preferential diffusion is smaller and decreases as the j e t Reynolds n u m b e r increases (see Figure 17 of Reference 17). A l t h o u g h deviations from adiabatic equilibrium are observed in Figure l a and in Figure 2 in lean turbulent flame regions at x/d = 10, these deviations are much smaller than in the laminar flamelet calculations. T h u s preferential diffusion is a process which complicates the quantitative comparison of laminar and turbulent diffusion flames containing H2. Although not shown or discussed in the present paper, preferential diffusion effects are also observed in the laminar opposed-flow diffusion flames with CO/H2/N~ fuel. 22
B. Superequilibrium In H2 flames, both the turbulent combustion data and the stretched laminar flamelet calculations show large deviations from adiabatic equilibrium conditions. Most of these deviations are caused by superequilibrium radical formation. Superequilibrium is caused by slow three-body radical recombination reactions (H + O H + M --* H 2 0 + M) which results in excess radical concentrations and r e d u c e d temperatures in laminar p r e m i x e d 24 and diffusion 25 flames. T h e effects are present close to the nozzle (x/d = 10 or 25) in Hz turbulent j e t diffusion flames as well. T h e t u r b u l e n t flame results in Figures I - 4 (either instantaneous or conditionally-averaged) at x/d = 10 a n d 25 fall between the ~x = 100 s -1 a n d ~ = 12,000 s -1 laminar flamelet curves, and the calculated peak O H concentra-
tion at e~ = 100 s -1 is in excellent agreement with the measured o f peak instantaneous O H concentration value. Thus, the superequilibrium process close to the nozzle in turbulent diffusion flames should be representable using laminar flamelet approaches. Downstream in the turbulent H2 j e t flames, the data in Figures 2 and 4 a p p r o a c h adiabatic equilibrium conditions because o f the longer time for three-body recombination reactions to become equilibrated. However, even in a very mildly stretched (~ = 100 s -1) laminar diffusion flame, the residence time is not long e n o u g h for three-body recombination reactions to equilibrate. So, in t u r b u l e n t j e t flames, it seems possible that these recombination reactions could occur over wide regions of the flame and not just in localized laminar flamelets. This could complicate the application of laminar flamelets in m o d e l i n g downstream regions o f turbulent jet flames. I n any case, the comparisons in the p a p e r clearly demonstrate the need for laminar flamelet calculations or measurements over a wide range of flame stretch. In CO/H2/N2 flames, both the turbulent flame data and stretched laminar opposed-flow diffusion flame data show larger deviations from equilibrium than H2 flames. For example, peak conditionally-averaged temperatures at x/d = 10 are decreased by nearly 500 K. Even at x/d = 50, peak t e m p e r a t u r e s near stoichiometric are 200 K below equilibrium. These increased deviations from equilibrium are due in part to increased superequilibrium radical concentrations (i.e., the mean peak O H concentrations are six times larger than at equilibrium at x/d = 10 and r e m a i n four times larger at x/d = 50). 6 A n o t h e r factor in the increased deviations from equilibrium is the CO to CO2 conversion (Figure 7) which is much farther from equilibrium than the H2 to H 2 0 conversion (Figure 6).
C. Partial Equilibrium In turbulent combustion (and often in laminar f a m e s as well), the superequilibrium process is m o d e l e d assuming that only the threebody recombination reactions are out o f equilibrium and that all two-body radical reactions (i.e., H2 + O H ~ H + H20) are equilibrated. This partial equilibrium of two-body reactions (or radical pool concept) permits the deviations from equilibrium to be expressed in terms of a single reaction progress variable .q.4,6,7 Partial equilibrium assumptions can be tested directly in the stretched laminar flamelet calculation. In the ~ = 100 s -1 flame with a peak t e m p e r a t u r e of 2285 K, the calculated 21 radical concentrations are in partial equilibrium (i.e.,
LAMINAR FLAMELET ANALYSIS OF DIFFUSION FLAMES agree closely with equations 1 - 3 in reference 19) while the radical concentrations in the ~ = 12,000 s -1 flame with a peak t e m p e r a t u r e of 1350 K are far from partial equilibrium. This result agrees with experiments ~7 and detailed kinetic modeling 24 in stoichiometric laminar p r e m i x e d H2-air flames where partial equilibrium prevailed when t e m p e r a t u r e s were greater than 1500 K but deviated markedly at lower temperatures. Some combustion models for CO containing flames include CO in the radical pool. This can lead to even larger deviations from partial equilibrium because the reaction CO + OH --+ CO2 + H is slower than two-body shuffle reactions in H2 flames. Warnatz 2s has demonstrated in calculations o f laminar prernixed flames that partial equilibrium for CO only holds at temperatures greater than 1800 K. A two-scalar thermochemical model (assuming partial equilibrium with CO in the radical pool) by Correa et al., 6 has been c o m p a r e d with the same turbulent CO/H~/N2 j e t flame data. T h e two-scalar model predicted peak mean temperatures and O H concentrations in good a g r e e m e n t with experiments, overpredicted mean temperatures and O H concentrations in lower t e m p e r a t u r e fuel-rich flame zones and predicted a much faster a p p r o a c h to equilibrium than measured. T h e discrepancies may be due to deviations from partial equilibrium. T h e reasonable c o r r e s p o n d e n c e in Figures 5 - 7 between the stretched laminar diffusion flame and turbulent diffusion flame data suggests that the stretched laminar flamelet concept may more accurately r e p r e s e n t turbulent diffusion flames than two-scalar p d f models because the laminar flamelet a p p r o a c h does not require partial equilibrium assumptions. D. Localized Extinction Extinction occurs in laminar opposed-flow diffusion flames when the gradients are so large that radical and thermal loss processes d o m i n a t e radical generation reactions such as H + O~ -+ O H + O. In laminar Hz flames, the calculated limiting velocity g r a d i e n t for extinction 21 is ~ 12,000 s -1. T h e instantaneous data from the turbulent H2 diffusion flame in Figures 1 and 3 lie above the limiting temperature curve for c~ = 12,000 s -1 (Figure 2) and below the limiting H z - O z curve for c~ = 12,000 s -1 (Figure 3). This suggests that localized extinction is not occurring in the turbulent H2 flame. (The few data points out of many thousand measurements which fall above the c~ = 12,000 s -1 curve in Figure 3 could arise from experimental e r r o r due to b a c k g r o u n d lumi-
1585
nosity or photon statistical uncertainties. This is particularly true of data points in the u p p e r left h a n d corner of Figure 3 where the measured mole fraction of H2 is less than 0.01.) The absence of localized extinction in this turbulent H2 j e t flame is substantiated by planar laser induced OH fluorescence imaging which indicate fully continuous reaction zones. 29 T h e presence or absence of localized extinction in the turbulent CO/H2/N2 diffusion flames can not be d e t e r m i n e d because calculations or measurements of laminar flames near the extinction limit are not presently available to compare with instantaneous Raman measurements. T h e stretched laminar opposed-flow diffusion flame data in CO/H2/N2 flames (shown in Figures 5 - 7 ) are believed to be from flames far from the extinction limit. T h e absence of localized extinction effects for turbulent H2 j e t diffusion flames demonstrated in this paper are in sharp contrast to the extensive localized extinction found in pilotflame stabilized CH4 turbulent jet diffusion flames using planar fluorescence imaging 3~ and pulsed Raman scattering. ~l T h e two findings are not contradictory. In a simple jet (with no pilot flame stabilization) extinction is most likely to occur at the nozzle exit where the shear rates are highest. Increasing the shear rate by increasing the fuel velocity causes the flame to blow off before extensive localized extinction occurs downstream. Pilot-flame stabilization permits attached flames at high stretch rates so substantial localized extinction can occur. T h e stretched laminar flamelet approach to turbulent combustion modeling might be expected to apply even u n d e r conditions of localized e x t i n c t i o n - - p r o v i d e d experiment or model calculations of the laminar diffusion flame structures are available near the extinction limit, However, published versions of laminar flamelet models do not account specifically for the partial fuel-air mixing and subsequent burning which occurs subsequent to localized extinction. V. C o n c l u s i o n s
T h e present and previous papers have shown that finite rate chemistry processes are important in turbulent j e t diffusion flames, even for I-I2 and CO/H2/N2 fuels where the chemical kinetic rates are reasonably fast and for jet Reynolds numbers (Re = 8500) where the fluid mixing rates are relatively slow. Finite rate chemistry processes in turbulent diffusion flames are expected to be even more important when the chemical rates are slower (hydrocar-
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T U R B U L A N T COMBUSTION
boa fuels) or w h e r e the mixing is faster (higher Reynolds n u m b e r flows). T h e stretched l a m i n a r flamelet concept in turbulent flames was tested in this p a p e r by c o m p a r i n g i n s t a n t a n e o u s and conditionallyaveraged R a m a n m e a s u r e m e n t s in t u r b u l e n t H2 and CO/H~/N2 j e t diffusion flames with Hz stretched laminar flamelet calculations ~1 and CO/HE/N,. stretched l a m i n a r flame m e a s u r e meats. 2u T h e excellent c o r r e s p o n d e n c e between stretched l a m i n a r and t u r b u l e n t flame data suggest that the l a m i n a r flamelet a p p r o a c h may provide better predictions than a twoscalar p d f a p p r o a c h o f finite rate chemistry in turbulent reaction zones because partial equilibrium assumptions are not r e q u i r e d and localized extinction can be accounted for properly. H o w e v e r , d i f f e r e n c e s between stretched laminar and t u r b u l e n t flame data suggest that the laminar flamelet a p p r o a c h might overestimate the influence o f p r e f e r e n t i a l diffusion in turbulent flames c o n t a i n i n g H2 and may not properly include the effects o f t h r e e - b o d y r e c o m b i n a t i o n reactions which are so slow that they are likely to o c c u r outside o f the relatively thin reaction zone.
Acknowledgments This research was sponsored by the Air Force Office of Scientific Research (AFOSR) under Contract F49620-85-C 0035 (Dr. Julian Tishkoff, Program Manager) and by the Basic Research Department of the Gas Research Institute under Contract 5081-263-0600 (Mr. James Kezerle, Program Manager). The technical assistance of Frank Hailer and helpful discussions with Drs. Charles Fenimore, Robert Pitz and Wei Shyy are gratefully acknowledged. REFERENCES 1. LIBBV, P. A. ANn WILLIAMS, F. A.: ed., Turbulent Reacting Flows, Springer-Verlag, New York, 1980.
7. BILGER, R. W. AND STARNER, 8. H.: Combust.
Flame, 51, 155, 1983. 8. CORREA, S. M.: "A Model for Nonpremixed Turbulent Combustion of CO/H2 Jets," IX International Symposium on Combustion Processes, Wisla-Jawornik, Poland, to appear in Archivuum Combustionis. 9. WILLIAXIS,F. A.: "Recent Advances in Theoretical Descriptions of Turbulent Diffusion Flames," Turbulent Mixing in Nonreactive and ReactiveFlows, (S, N. P. Murthy, ed.) Plenum Press p. 189, 1974. 10. CARRIER, G. F., FEYOELL,F. E. ANn MARBLE,F. E.: SIAM J. App. Math, 28, 463, 1975. 11. PETERS, N.: Progress in Energy and Combustion Science, I0, 319, 1984. 12. MARBLE, F. E. AND BROADWELL, J. E.: "A Theoretical Analysis of Nitric Oxide Production in a Methane/Air Turbulent Diffusion Flame," EPA600/7-80-018, 1980. 13. LIrw, S. K., BRAY, K. M. C., ANt) MOSS, J. B.: Comb. Sci. Tech. 27, 69, 1981. 14. LIEW, S. K., BRAY, K. M. C., ArqO MOSS, J. B.: Comb. Flame 56, 199, 1984. 15. RAZDAr,', M. K. AND STEVENS,J. G.: Combust. Flame 59, 289, 1985. 16. JEr,'c, S-M., CHENO, L-D., ANn FAEXH, G. M.: Nineteenth Symp. Int. Comb. p. 349, The Combustion Institute, 1982. 17. DRAKE,M. C., PITZ, R. W., AID LAPP, M.: "Laser Measurements on Nonpremixed Hydrogen-Air Flames for Assessment of Turbulent Combustion Models," AIAA Paper 84-0544, 1984; AIAA J. 24, 905, 1986. 18. DRAKE,M. C., BILGER, R. W. ANDST,~RNER, S. H.:
Nineteenth Syrup. (Int.) on Combustion, p. 459, The Combustion Institute, 1982. 19. DRAKE, M. C., PITZ, R. W., LAPP, M., FENIMORE,
20.
21.
2: JONES, W. P. AND WHITELAW, J. H.: Combust.
Flame 48, 1, 1982. 3. DRAKE,.~[. C. AND KOLLMANN,W.: "Slow Chemistry Nonpremixed Flows," Evaluation of Data on
Simple Turbulent Reacting Flows, (W. C. Strahle, ed.) AFOSR TR-85 0880, Sept. 1985; to appear in Prog. Energy Comb. Sci.. 4. JANICKA,.]. AND KOLLMANN,W.: Combust. Flame 44, 319, 1982. 5. EICKHOFF, H. E. AND GRETHE, K.: Combust. Flame 35, 267, 1977. 6. CORREA, S. M., DRAKE, M. C., PITZ, R. W., AND
SHYY, W.: Twentieth Syrup. Int. Comb., p. 337, The Combustion Institute, 1984.
22.
23.
24. 25.
C. P., L~CHT, R. P., SWEE,','EY, D. W. and LAURENDEAU, N. M.: Twentieth Syrup. Int. Comb. p. 327, The Combustion Institute, 1984. DRAKE, M, C., PITZ, R. W., CORaEA, S. M. AND LAPP, M.: Twentieth Symp. Int. Comb., p. 1983, The Combustion Institute, 1984. DAVID,T., GASKELL,P. H. AND DtxoN-LEwIs, G.: "Structure and Properties of Methane-Air and Hydrogen-Air Counterflow Diffusion Flames," submitted for publication. DRAKE, M. C.: "Kinetics of Nitric Oxide Formation in Laminar and Turbulent Methane Combustion," Gas Research Institute Final Report, GRI-85/0271, 1985. GORDON,S. ANn MCBRIDE, B.J.: "Computer Program for Calculation at Complex Chemical Compositions, Rocket Performances, Incident and Reflected Shocks and Chapman-Jouget Detonations," NASA SP273, NTIS N71-37775, 1971. WARNATZ,J.: Comb. Sci. Tech. 26, 203, 1981. MILLER,J. A. AND KEE, R. J.: J. Chem. Phys. 61, 2534, 1977.
L A M I N A R FLAMELET ANALYSIS OF DIFFUSION FLAMES 26. DRAm~, M. C., LAPP, M., PENNEY, C. M., WARSHAW, S. AND GERHOLD, B. W.: Eighteenth Symp. Int. Comb., p. 1521, T h e Combustion Institutel 1981. 27. HYNES, A. J., STEINBERG, M., AND SCHOFIELD, K.: J. Chem. Phys. 80, 3921, 1984. 28. WARNATZ, J.: Ber. Bunsenges. Phys. Chem. 83, 950, 1979. 29. KYCHAROW, G., HOWE, R. D., HANSON, R. K., DRAKE, M. C., PITZ, R. W., LAee, M., mad PENNEY, C. M.: Science 224, 382, 1984.
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30. DIBBLE, R. W., LONG, M. B., a n d MASRI, A.: "Two Dimensional Imaging o f C2 in Turbulent Nonpremixed Flames," T e n t h Int. Colloquium on Dynamics o f Explosions and Reactive Systems, Berkeley, CA, August 1985. 31. DIBBLE, R. W., MASRI, A. AND BILGER, R. W.: "Spontaneous Raman Measurements in Laminar and T u r b u l e n t N o n p r e m i x e d Flames o f Methane," submitted for publication.
COMMENTS R. W. Bilger, University of Sydney, Australia. 1. In the absence o f simultaneous m e a s u r e m e n t o f O H and major species, how can you tell if partial equilibrium is breaking down? 2. T h e plots o f reactive scalars vs. mixture fraction do not, o f themselves, imply flamelets. Distributed reaction zones would also show a similar scatter o f data. To me, a "flamelet" implies that the local normal to mixture fraction surfaces undergoes a monotonic progression in mixture fraction t h r o u g h the reaction zone. O n the scalar vs. mixture fraction plot, this maps as a single valued curve. A distributed reaction zone can have an up and down variation o f m i x t u r e fraction along such a normal and this maps as a multivalued and even crossing curve on the scalar mixture fraction plot. T h e r e is no way o f telling from the data on such plots w h e t h e r t h e r e are flamelets or distributed reaction zones. T h e r e is possibly a way o f distinguishing flamelets from distributed reaction zones in a system such as your CO/H~ flame, where m o r e than one progress variable is necessary to describe the state o f the mixture. For each data point, it should be possible to assign two values o f "a" (the flamelet stretch parameter) c o r r e s p o n d i n g to, say, the progress o f the CO reaction and o f the heat release as d e t e r m i n e d from the flamelet library. If these are equal, we may have flamelets. I f not, the progress o f the CO and H2 reactions are not correlated as in flamelets and we do not have flamelets. It is possible to have folded flamelets with overlapping reaction zones (and, hence, a distributed reaction zone) which has all reaction progress variables correlated as in a flamelet, but this is unlikely.
Author's Reply. 1. T h e H2 turbulent jet diffusion flame measurements are not sufficient to tell if partial equilibrium in the radical pool is breaking down. However, as explained in the paper, partial equilibrium can be tested directly in the stretched laminar flamelet calculations. I f the two body shuffle reactions
H + 02 ~ O H + O O + H2~.~-OH + H OH + H2 ~ H20 + H are equilibrated, then the calculated concentrations o f O and H should he given by [O] = 0.152 exp(8391/T)[OH]2/[HzO] [H] = 8.906x10 -3 exp(16223/T)[OH]3/ ([O~][H=O], = 0.2419 exp(7400/T)[OH][H2]/[H20]
lean rich
T h e s e relationships a p p e a r to be true in the high t e m p e r a t u r e regions o f the a = 100 s -~ H2 laminar f a m e , but not in the ~ = 12,000 s t flame. I f the laminar flamelet model is valid for turbulent diffusion flames, a similar breakdown in partial equilibrium may be i n f e r r e d in highly stretched regions o f turbulent H2 diffusion flames. Even larger deviations from partial equilibrium can be expected in CO/H~/N2 diffusion flames because the reaction C O -~- O H ~- C O 2 ~- H
is much slower than the three reactions listed previously. T h e deviations f r o m partial equilibrium (particularly for CO) are the likely cause for the differences between two-scalar p d f model calculations and experimental data in low t e m p e r a t u r e , fuel-rich regions o f turbulent CO/H~/N2 jet diffusion flames. 2. In essence, this c o m m e n t says that present experimental data are insufficient to determine w h e t h e r laminar flamelets or distributed reaction zones are the d o m i n a n t form o f combustion in these simple turbulent jet diffusion flames. I strongly disagree. T h e experimental data in this paper and in previously published work are consistent with laminar flamelet combustion and are not consistent with distributed reactions. T h e most direct evidence for laminar flamelets in simple turbulent H~ diffusion flames comes from instantaneous two-dimensional images of O H concentrations using planar laser i n d u c e d fluorescenceJ Since O H concentrations are localized in reaction
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T U R B U L A N T COMBUSTION
zones of diffusion flames, O H images provide instantaneous reaction zone shapes and distributions. T h e images show a smooth progression from laminar (Re = 660), transitional (Re = 1600) and turbulent (Re = 8500) H2 diffusion flames. As Re increases, the instantaneous flame fronts get thinner and more highly convolved, but remain highly localized in continuous laminar flamelets. Taking a slice normal to the flame front, as Professor Bilger suggests, gives a smooth distribution of OH concentrations which monotonically increase to a maximum near the center of the flame front and then monotonically decrease. The OH images do not appear to be consistent with distributed reaction zones which are expected to give irregular distributions of O H concentrations across the flame front, widely dispersed OH concentrations throughout the flame, and highly discontinuous flame fronts. The present paper starts with the existence of laminar flamelets and asks whether the pulsed Raman data are consistent with stretched laminar flamelets. As Professor Bilger comments, the local normal to mixture fraction surfaces undergoes a monotonic progression in mixture fraction through the reaction zone, which on scalar vs. mixture fraction plots corresponds to a single valued curve. However, this single valued curve corresponds to one value of scalar dissipation or flame stretch. A different value of flame stretch corresponds to a different scalar vs. mixture fraction relationship. So the spread in the data on temperature vs. mixture plots (Fig. la) or the H~ vs. 02 plots (Fig. 3) can be qualitatively explained by fluctuations in flame stretch which occur in turbulent H2 diffusion flames. The pulsed Raman data may not be consistent with distributed reaction zones where a broader range of temperatures for a given mixture fraction might be expected. The experimental data from planar laser induced fluorescence and from pulsed Raman scattering demonstrate clearly that localized extinction is not important in this simple H2 turbulent jet flame. These data could provide a valuable test of turbulent combustion models using the laminar flamelet approach (such as that of Rogg, et al.2), because the most empirical parts of the model dealing with localized extinction and subsequent partial premixing would not need to be included. Although it appears clear that simple turbulent jet diffusion flames b u r n in laminar flamelets, the situation is not resolved for lifted turbulent jet diffusion flames or for flames stabilized by pilot flames or recirculation. For example, in pilot flame stabilized turbulent jet diffusion flames, C2 fluorescence imaging 3 and pulsed Raman measurements 4 show extensive localized extinction. Whether subsequent combustion occurs as partially premixed laminar flamelets or as distributed reactions remains to be determined.
REFERENCES 1. KYCHAKOFF, G., HOWE, R.D., HANSON, R.K, DRAKE, M.C., PITZ, R.W., LAPP, M., and PENNEY, C.M., Science, 224, 382 (1984). 2. ROGG, B., BEHRENBT, F., and WARNATZ,J,, this Symposium. 3. DIBBLE, R.W., LONG, M.B., and MASRI, A., "Two Dimensional Imaging of C2 in Turbulent Nonpremixed Flames," T e n t h Int. Colloquium on Dynamics of Explosions and Reactive Systems, Berkeley, CA (1985). 4. DIBBLE, R.W., MASRI, A. and BILGER, R.W., "Spontaneous Raman Measurements in Laminar and T u r b u l e n t Nonpremixed Flames of Methane," submitted for publication.
F. A. Williams, Princeton University, USA. Your results are very interesting in strongly suggesting the relevance of the flamelet view to turbulent hydrogenair diffusion flames. T h e kinds of comparisons with theoretical calculations that you have made are, in my opinion, essential as a first step in testing the concepts. Having obtained this degree of understanding of attached flames, you can now go on to make measurements of lifted flames. As you know, currently there is considerable uncertainty concerning the degree of mixing that occurs between the jet exit and the point of flame inception. Since measurements of the kind that you are making can shed a great deal of light on the question, I certainly hope that you will be able to proceed to test lifted flames. Author's Reply. I agree that this paper represents the first step in testing the applicability of the laminar flamelet concept in turbulent jet diffusion flames. The next step could be the quantitative comparison of a detailed stretched laminar flamelet calculation of H2 and CO/H2/N2 jet diffusion flames with experimental measurements--- both averaged at individual flame locations and conditionally averaged in mixture fraction intervals. T h e wide range of scalars (~, T, X(major species), p, and X(OH)) which have been measured in the turbulent H2 and CO/H2/N2 jet diffusion flames should provide a reasonable test of the model. An even more direct test of laminar flamelet model calculations would involve the comparison of model calculations and experiments of scalar dissipation conditioned upon the presence of the reaction zone (ie. • This type of measurement has not been obtained but appears feasible in some H2 turbulent jet diffusion flames using two dimensional OH fluorescence imaging. Your suggestion of pulsed Raman measurements of lifted turbulent jet diffusion flames is one of several potentially fruitful research directions.
LAMINAR FLAMELET ANALYSIS OF DIFFUSION FLAMES Another is measurements in pilot flame stabilized turbulent jet flames with H2 and CO/H2/N2 fuels at much higher Reynolds number. I expect these measurements will show localized extinction effects, and
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detailed experiment-model comparisons could test the applicability of stretched laminar flamelet models which include localized extinction, partial fuel-air premixing, and subsequent combustion.
S T R E T C H E D L A M I N A R FLAMELET ANALYSIS OF T U R B U L E N T H2 A N D CO/HJN2 D I F F U S I O N FLAMES M. C. DRAKE General Electric Corporate Research and Development Center Schenectady, New York 12301
The stretched laminar flamelet approach to turbulent diffusion flames is tested by comparison of instantaneous and conditionally-averaged Raman measurements in turbulent H2 and CO/H2/N~ jet diffusion fames with stretched laminar opposed-flow diffusion flame model calculations and measurements. The H2 turbulent jet diffusion flame measurements close to the fuel nozzle show instantaneous temperatures 300K less than equilibrium, peak OH concentrations three times larger than equilibrium, and substantial coexistence of H2 and 02. Quantitatively similar effects are calculated by David, et al., for lightly stretched (c~ = 100 s -l) opposedflow laminar H2 diffusion flames. The turbulent flame data lie in a narrow band between the highly stretched ~ = 12,000 s -1 laminar flame calculation and the adiabatic equilibrium curve and approach adiabatic equilibrium downstream in the flame. Localized extinction is relatively unimportant in simple H2 turbulent jet diffusion flames since only a few instantaneous Raman measurements are dose to that calculated at extinction (c~ = 12,000 s-~). With a fuel consisting of 40%CO/30%H2/30%N> experimental data in both the turbulent jet flame and a laminar opposed flow diffusion flame show even larger nonequilibrium effects. The excellent correspondence between stretched laminar and turbulent flame data suggest that the laminar flamelet approach may provide better predictions than the two-scalar pdf approach of finite-rate chemistry in turbulent reaction zones because partial equilibrium assumptions are not required and localized extinction can be accounted for properly. However, differences between stretched laminar and turbulent flame data suggest that the laminar flamelet approach can overestimate the influence of preferential diffusion in flames containing Hz and may not properly include the slow three body radical recombination reactions which are likely to occur outside of the relatively thin primary reaction zones.
I. Introduction Most c o m b u s t i o n m o d e l s o f t u r b u l e n t diffusion flames have used a c o n s e r v e d scalar-equilibrium chemistry a p p r o a c h 1'2 which accounts for t u r b u l e n t fluctuations using an assumedshape probability density f u n c t i o n o f m i x t u r e fraction { (i.e., e l e m e n t a l mass fraction) but which ignores chemical kinetic effects. However, a m p l e e x p e r i m e n t a l data in t u r b u l e n t j e t diffusion flames (reviewed by Drake and K o l l m a n n 3) d e m o n s t r a t e that finite rate chemistry processes c a n n o t be neglected. Alt h o u g h m o r e c o m p l i c a t e d c o m b u s t i o n models i n c l u d i n g one 4-6 or two 7's reaction progress variables based u p o n partial e q u i l i b r i u m have led to better a g r e e m e n t with e x p e r i m e n t a l data in t u r b u l e n t diffusion flames, the m o d e l results still show significant differences with experiment. 6 T h e laminar flamelet a p p r o a c h provides an alternative way o f i n c l u d i n g finite rate chemis-
try effects in t u r b u l e n t c o m b u s t i o n models. 9-11 In the laminar flamelet a p p r o a c h , t u r b u l e n t flames are assumed to consist o f laminar flamelets stretched and d i s t o r t e d by the turbulence. T h e detailed s t r u c t u r e o f t u r b u l e n t and laminar flamelets are a s s u m e d to be the same, so relationships b e t w e e n m i x t u r e fraction and reactive scalars o b t a i n e d f r o m laminar diffusion flame m o d e l i n g o r e x p e r i m e n t s can be used in t u r b u l e n t c o m b u s t i o n models. However, these m i x t u r e fraction-reactive scalar relationships are not universal a n d are functions o f gradients or flame stretch (usually expressed in terms o f the scalar dissipation rate X = 2 D O~/Ox. O{/Ox). At very low stretch (i.e., very long r e s i d e n c e times) the l a m i n a r flamelet relationships should a p p r o a c h those at equilibrium. At very high stretch, extinction can occur. M e a s u r e d or calculated l a m i n a r flamelet or "stretched laminar flamelet" relationships have b e e n used by Williams, 9 Marble and Broadwell, 12 Liew et al., 13'14 E i c k h o f f a n d G r e t h e 5 and
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TURBULANT COMBUSTION
Peters, 11 to model turbulent diffusion flames. The validity of the laminar flamelet approach in turbulent combustion has been examined using experimental time-averaged thermocoupie or probe sampling measurements. For example, relationships between average temperature and molecular compositions vs. average mixture fraction in turbulent jet diffusion flames of CO 15 and of hydrocarbons 5'16 are compared with measurements or model calculations of laminar diffusion flames. Although reasonable agreement was claimed, 5'15'~6 there is no fundamental reason to believe that laminar flamelet relationships should be valid for conventional time-averaged measurements in turbulent diffusion flames with their large fluctuations in instantaneous mixture fraction and flame stretch. A more fundamentally sound approach of testing the laminar flamelet approach in turbulent jet diffusion flames is to model the fluctuations of ~ and X and to compare the calculated average scalar variables (i.e., temperature, molecular compositions) with those measured experimentally. This approach also leads to reasonable agreement 5 ' 12.14 ' but suffers from uncertainties in the fluid mixing model particularly in determining values of X, the assumed shape of the pdf's of and X, and the assumed relationship between and X. The purpose of the present paper is to provide a more quantitative test of the stretched laminar flamelet approach in H2 and CO/H2/N 2 turbulent jet diffusion flames by comparing instantaneous and conditionaUy-averaged measurements of mixture fraction and scalar variables with laminar flamelet experiments or model calculations. Limitations of the laminar flamelet approach due to preferential diffusion and slow reactions (i.e., three body recombinations) are discussed and the influences of localized extinctions are examined.
II. Approach A. Previous Results on Turbulent Diffusion Flames The characteristics of the turbulent combustor and the initial conditions for the turbulent jet diffusion flames are discussed in detail elsewhere. 6'17'18 For the H~ flames, the fuel jet had an initial average velocity of 285 m/s (corresponding to a cold flow Reynolds number of 8500) and an initial air velocity of 12.5 m/s. For the CO/H2/N2 flame, the initial molar ratio of the fuel was approximately 40%CO/30%HJ 30%N2 with a small amount of CH4 (-0.7%) sometimes added. The initial fuel and air
velocities were 54.6 m/s and 2.4 m/s respectively, chosen to match the Reynolds number (8500) and initial fuel-to-air velocity ratio (22.8) of the H~ flame. The turbulent flame data include qualitative and quantitative imaging (Schlieren, shadowgraph, and planar O H fluorescence); instantaneous measurements of velocity (laser velocimetry); simultaneous measurements of temperature, density, individual major species concentrations and mixture fraction (pulsed Raman); and instantaneous measurements o f OH concentrations (laser saturated fluorescence). Data for H2 flames are summarized in references 17-19 and for CO/H~/N2 flames in references 3, 6, and 20.
B. Data Analysis bz the Present Paper The present paper extends the analysis of turbulent diffusion flame data obtained by pulsed Raman spectroscopy which provides simultaneous measurements of mixture fraction, temperature and concentrations of H2, 02, CO, CO~, Nz and H 2 0 with a spatial resolution of <0.1 m m ~ and a temporal resolution of 2 ~sec. Either instantaneous Raman data or data conditionally-averaged in narrow mixture fraction intervals are compared to stretched laminar flame model calculations or experimental data. Experimental measurements of stretched laminar diffusion flames of H2 are not available, but calculations by David et a1.,21 including detailed chemical kinetics and molecular transport effects have appeared recently. These H2 laminar diffusion flame calculations were obtained at two values of flame stretch (velocity gradients of 100 s -x and 12,000 s -1) where the higher value of flame stretch corresponds to a flame near the extinction limit. Detailed experimental measurements of stretched laminar diffusion flames of CO/H2/N2 fuel have recently been obtained in our laboratory using laser diagnostic and probe sampling techniques. 2z T h e experimental values of flame stretch (velocity gradients (x = 70, 180 and 330 s -1) are believed to be far from the extinction limit for this fuel.
III. Results A. H2 Flames Pulsed Raman data (approximately 30,000 data points) for the simultaneous measurements of temperature and mixture fraction in the Re=8500 turbulent H2 jet flame are shown in Figure 1. T h e solid line in Figure 1 corre-
1581
LAMINAR FLAMELET ANALYSIS OF DIFFUSION FLAMES HYDAOGEN TURB. JET FLAME
RE=8500
X/D.10 f
Iooo
1< 84
lee
MIXTURE FRACTION
HY(14tOGEN Tq4q~ JET FLAME
...v
ii~O~O
X/O~
~,.~,~ ,.-..~.~,
,,
|-
~
JET FLAME
t~=aNO
XA)=~O0
sponds to calculated adiabatic e q u i l i b r i u m (AE) conditions for H z - a i r m i x t u r e s . 23 In all cases, the t u r b u l e n t c o m b u s t i o n d a t a in Figure 1 lie in a n a r r o w band. Close to the fuel nozzle (at x/d= 10), the e x p e r i m e n t a l d a t a show t e m p e r a tures considerably above the AE curve in lean flame zones ( m i x t u r e fraction <0.02) a n d considerably below the A E c u r v e in stoichiometric ( m i x t u r e fraction = 0.0283) and rich flame zones. N e a r the c e n t e r o f t h e t u r b u l e n t flame (x/d=50), the R a m a n results are reasonably close to the AE line. F a r d o w n s t r e a m (x/d=200), all o f the rich flame pockets have b u r n e d out a n d the m e a s u r e m e n t s are in g o o d a g r e e m e n t with the AE curve. In o r d e r to m o r e clearly show trends, the R a m a n d a t a at e a c h axial location have b e e n a v e r a g e d in n a r r o w m i x t u r e fraction intervals. Results are shown in F i g u r e 2 for extensive R a m a n data atx/d=lO, 25, 50, 100, 150 a n d 200 in the t u r b u l e n t H2 j e t d i f f u s i o n flame. T h e c o n d i t i o n a l l y - a v e r a g e d data close to the nozzle (x/d= 10 and 25) show t e m p e r a t u r e s as m u c h as 300 K less t h a n those calculated at adiabatic e q u i l i b r i u m and progressively smaller deviations f r o m AE are o b s e r v e d f u r t h e r downstream. T h e t u r b u l e n t H2 flame data are comp a r e d with the results o f calculations o f stretched l a m i n a r H2 d i f f u s i o n flames by David et al., 21 (dashed lines in F i g u r e 2). For a l a m i n a r flame which is not highly stretched (e~= i 0 0 s-S), the calculated p e a k flame t e m p e r a t u r e is 2280 K - - n o t m u c h lower t h a n the peak calculated AE t e m p e r a t u r e o f 2380 K. I n the very highly
HYORO(3EN TURB, JET FLAME
RE=8~O0
X/0=10-200
DATA, AVEI~kGEO IN MIXTURE FRACTION INTERVALS ~m
200o
a
O~tNAn Fl~mtL~r
0
le
9
im im ~o
. 9 o
soo MtXTtJ~t FRACTK~
..
12~os-~
I
J
FIG. 1, Instantaneous measurements of tempera-
ture and mixture fraction using pulsed laser Raman scattering from the H2 turbulent jet diffusion flame. Each of the ~ 30,000 points represents one time (2 I~s) and space < 0.1mm 3) resolved measurement. Data from three axial positions (x/d= 10, 50 and 200) are shown. The solid line is the calculated relationship between temperature and mixture fraction in H~-air flames under adiabatic equilibrium conditions.
MIXTURE FRACI'ION
FIG. 2. Data conditionally-averaged in mixture fraction intervals from the H2 turbulent jet diffusion flame at all six axial locations measured. The solid line is the same as in Figure 1. The dotted lines are those calculated by David, et al., 2t for laminar opposed flow H2 diffusion flames under small stretch (t~=100 s-1) and near extinction ((x = 12,000 s-l).
1582
TURBULANT COMBUSTION
stretched laminar H~ flame close to the extinction limit (c~=12,000 s -1) the peak flame temperature is only 1350 K. Instantaneous R a m a n measurements of mole fractions of H2 a n d 02 near the nozzle (x/d= 10) of the turbulent H2 flame are shown in Figure 3. The solid line in Figure 3 shows that very little overlap of H~ and O2 is expected u n d e r adiabatic equilibrium conditions (at most X(H2) = X(O~)-0.007). T h e fuel-air overlap is calculated 21 to be much greater in stretched laminar diffusion flames a n d to increase with flame stretch [X(H2) --= X(O2)-0.025 at cc = 100 s-1 and X(H2) -= X(02)~0.075 at er = 12,000 s-l]. The pulsed Raman measurements from the turbulent H2 flame in Figure 3 show substantial instantaneous presence of both fuel and air at this flame location (x/d = 10). I n general, the instantaneous turbulent flame data lie between the AE curve and c~ = 12,000 s-1 curve, with most of the data points lying closer to the a = 100 s -I curve. This is in excellent agreement with the temperature vs. mixture fraction data in Figures 1 and 2. The H 2 vs. 02 data (averaged in mixture fraction intervals) in Figure 4 show deviations from the AE curve at x/d =10 and 25 while the data further downstream progressively approach the AE limit, (also similar to the trends observed in Figure 2). The last point of comparison between the H2 turbulent jet diffusion flame data and the stretched laminar flamelet calculations of David et al., 21 is the value of O H concentrations. Absolute OH concentrations were measured in the turbulent H2 flame using single-pulse laser saturated OH fluorescence. '9 The m a x i m u m measured instantaneous O H concentration was 6.2 x 1016 molecules/cc, which is in reasonable agreement with the m a x i m u m value calculated for partial equilibrium conditions (5.5 • 1016 molecules/cc) r9 and with the m a x i m u m of 6.4 x 1016 molecules/cc calculated in a laminar premixed stoichiometric H2-air flame. 24 In the laminar opposed-flow H2 flame calculation, the maximum calculated O H concentration in the c~ = 100 s-1 flame is 6.1 x 1016 molecules/cc, 21 in excellent agreement with the measured maxim u m in turbulent H2-air flames. Near extinction (a = 12,000 s -1) the calculated OH concentration drops, but it remains considerably above the AE value. B. CO/H2/N2 Flames Conditionally-averaged pulsed Raman measurements of temperature and hydrogen element mixture fraction are shown in Figure 5 for the Re = 8500 t u r b u l e n t CO/H2/N2 jet diffusion flame. T h e t u r b u l e n t flame data are
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LAMINAR FLAMELET ANALYSIS OF DIFFUSION FLAMES which has been shown to agree within experimental error (+50 K) with radiation-corrected coated fine-wire thermocouple measurements in laminar premixed H2-air flames. The Raman measurements in CO/H2/N2 flames have larger uncertainties due to background emissions or laser-induced broad b a n d fluorescence. 2~ However, systematic temperature errors should not markedly affect comparison of laminar and turbulent flame data since both were calculated by the same technique. T h e instantaneous data (not shown) in the turbulent CO/H~/Nz flame fall in bands, although the spread is considerably larger than in Figure 1 for the H2 flame, due at least in part to MEO, BTU GAS TURB. JET FL~ME
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1583
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the larger measurement uncertainties in the CO/H2/N2 flame. Also, the t u r b u l e n t CO/H2/N2 flame shows larger deviations from adiabatic equilibrium conditions than the H2 flame. In Figure 5, the peak conditionally-averaged temperature near the nozzle (x/d = 10 and 25) are 3 6 0 - 5 0 0 K lower than the peak AE temperature of 2240 K. Downstream at x/d = 50, the measured temperatures approach the AE values although not as closely as in the H~ flame. T h e conversion of H2 into H 2 0 and of COinto CO2 is monitored separately. Conditionallyaveraged measurements of the fractional conversion of H2 (defined as the mole fraction of H20 divided by the sum of the H2 and H20 mole fraction) are shown in Figure 6 and the corresponding values for CO conversion shown in Figure 7. The conversion of H2 in the laminar and turbulent flames is much closer to equilibrium than the conversion of CO which does not attain equilibrium even at x/d = 50 in the turbulent flame. Although not shown in the present paper, mean O H concentration measurements in this turbulent flame are six times larger than equilibrium at x/d = 10 and remain approximately four times larger than equilibrium at x/d = 50, 6
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10
MIXTURE FRACTION
FIG. 6. Conditionally-averaged Raman measurements of the conversion of H2 versus mixture fraction in the turbulent jet diffusion flame and laminar opposed-flow diffusion flame with CO/H2/N2 fuel. Symbols are the same as in Figure 5.
I n general, calculations or experimental data from stretched laminar diffusion flames and from turbulent jet diffusion f a m e s show many similar features. This correspondence reinforces the suggestion that stretched turbulent diffusion flames can be modeled as a collection of stretched laminar diffusion flamelets. De-
1584
TURBULANT COMBUSTION
tailed comparisons o f the laminar and turbulent diffusion flame results are discussed here in terms of four processes (preferential diffusion, superequilibrium, partial equilibrium and localized extinction) which can occur in diffusion flames.
A. Preferential Diffusion Because of its low molecular weight, H2 molecules diffuse much more readily than most other species. T h e preferential diffusion of H2 has been m o d e l e d in laminar H2 diffusion flames 25 and experimentally observed x7'26 and computationally m o d e l e d is in H2 turbulent j e t flames. T h e large deviation from adiabatic equilibrium in fuel-lean regions of the a = 100 s -* laminar flamelet curve in Figure 2 has also been attributed to H2 preferential diffusion. ~l At increased stretch rates, the mixing is faster and thus preferential diffusion is less prominent (see the lean regions of the ~x --- 12,000 s -I curve in Figure 2). Similarly in transitional a n d turbulent H2 diffusion flames, preferential diffusion is smaller and decreases as the j e t Reynolds n u m b e r increases (see Figure 17 of Reference 17). A l t h o u g h deviations from adiabatic equilibrium are observed in Figure l a and in Figure 2 in lean turbulent flame regions at x/d = 10, these deviations are much smaller than in the laminar flamelet calculations. T h u s preferential diffusion is a process which complicates the quantitative comparison of laminar and turbulent diffusion flames containing H2. Although not shown or discussed in the present paper, preferential diffusion effects are also observed in the laminar opposed-flow diffusion flames with CO/H2/N~ fuel. 22
B. Superequilibrium In H2 flames, both the turbulent combustion data and the stretched laminar flamelet calculations show large deviations from adiabatic equilibrium conditions. Most of these deviations are caused by superequilibrium radical formation. Superequilibrium is caused by slow three-body radical recombination reactions (H + O H + M --* H 2 0 + M) which results in excess radical concentrations and r e d u c e d temperatures in laminar p r e m i x e d 24 and diffusion 25 flames. T h e effects are present close to the nozzle (x/d = 10 or 25) in Hz turbulent j e t diffusion flames as well. T h e t u r b u l e n t flame results in Figures I - 4 (either instantaneous or conditionally-averaged) at x/d = 10 a n d 25 fall between the ~x = 100 s -1 a n d ~ = 12,000 s -1 laminar flamelet curves, and the calculated peak O H concentra-
tion at e~ = 100 s -1 is in excellent agreement with the measured o f peak instantaneous O H concentration value. Thus, the superequilibrium process close to the nozzle in turbulent diffusion flames should be representable using laminar flamelet approaches. Downstream in the turbulent H2 j e t flames, the data in Figures 2 and 4 a p p r o a c h adiabatic equilibrium conditions because o f the longer time for three-body recombination reactions to become equilibrated. However, even in a very mildly stretched (~ = 100 s -1) laminar diffusion flame, the residence time is not long e n o u g h for three-body recombination reactions to equilibrate. So, in t u r b u l e n t j e t flames, it seems possible that these recombination reactions could occur over wide regions of the flame and not just in localized laminar flamelets. This could complicate the application of laminar flamelets in m o d e l i n g downstream regions o f turbulent jet flames. I n any case, the comparisons in the p a p e r clearly demonstrate the need for laminar flamelet calculations or measurements over a wide range of flame stretch. In CO/H2/N2 flames, both the turbulent flame data and stretched laminar opposed-flow diffusion flame data show larger deviations from equilibrium than H2 flames. For example, peak conditionally-averaged temperatures at x/d = 10 are decreased by nearly 500 K. Even at x/d = 50, peak t e m p e r a t u r e s near stoichiometric are 200 K below equilibrium. These increased deviations from equilibrium are due in part to increased superequilibrium radical concentrations (i.e., the mean peak O H concentrations are six times larger than at equilibrium at x/d = 10 and r e m a i n four times larger at x/d = 50). 6 A n o t h e r factor in the increased deviations from equilibrium is the CO to CO2 conversion (Figure 7) which is much farther from equilibrium than the H2 to H 2 0 conversion (Figure 6).
C. Partial Equilibrium In turbulent combustion (and often in laminar f a m e s as well), the superequilibrium process is m o d e l e d assuming that only the threebody recombination reactions are out o f equilibrium and that all two-body radical reactions (i.e., H2 + O H ~ H + H20) are equilibrated. This partial equilibrium of two-body reactions (or radical pool concept) permits the deviations from equilibrium to be expressed in terms of a single reaction progress variable .q.4,6,7 Partial equilibrium assumptions can be tested directly in the stretched laminar flamelet calculation. In the ~ = 100 s -1 flame with a peak t e m p e r a t u r e of 2285 K, the calculated 21 radical concentrations are in partial equilibrium (i.e.,
LAMINAR FLAMELET ANALYSIS OF DIFFUSION FLAMES agree closely with equations 1 - 3 in reference 19) while the radical concentrations in the ~ = 12,000 s -1 flame with a peak t e m p e r a t u r e of 1350 K are far from partial equilibrium. This result agrees with experiments ~7 and detailed kinetic modeling 24 in stoichiometric laminar p r e m i x e d H2-air flames where partial equilibrium prevailed when t e m p e r a t u r e s were greater than 1500 K but deviated markedly at lower temperatures. Some combustion models for CO containing flames include CO in the radical pool. This can lead to even larger deviations from partial equilibrium because the reaction CO + OH --+ CO2 + H is slower than two-body shuffle reactions in H2 flames. Warnatz 2s has demonstrated in calculations o f laminar prernixed flames that partial equilibrium for CO only holds at temperatures greater than 1800 K. A two-scalar thermochemical model (assuming partial equilibrium with CO in the radical pool) by Correa et al., 6 has been c o m p a r e d with the same turbulent CO/H~/N2 j e t flame data. T h e two-scalar model predicted peak mean temperatures and O H concentrations in good a g r e e m e n t with experiments, overpredicted mean temperatures and O H concentrations in lower t e m p e r a t u r e fuel-rich flame zones and predicted a much faster a p p r o a c h to equilibrium than measured. T h e discrepancies may be due to deviations from partial equilibrium. T h e reasonable c o r r e s p o n d e n c e in Figures 5 - 7 between the stretched laminar diffusion flame and turbulent diffusion flame data suggests that the stretched laminar flamelet concept may more accurately r e p r e s e n t turbulent diffusion flames than two-scalar p d f models because the laminar flamelet a p p r o a c h does not require partial equilibrium assumptions. D. Localized Extinction Extinction occurs in laminar opposed-flow diffusion flames when the gradients are so large that radical and thermal loss processes d o m i n a t e radical generation reactions such as H + O~ -+ O H + O. In laminar Hz flames, the calculated limiting velocity g r a d i e n t for extinction 21 is ~ 12,000 s -1. T h e instantaneous data from the turbulent H2 diffusion flame in Figures 1 and 3 lie above the limiting temperature curve for c~ = 12,000 s -1 (Figure 2) and below the limiting H z - O z curve for c~ = 12,000 s -1 (Figure 3). This suggests that localized extinction is not occurring in the turbulent H2 flame. (The few data points out of many thousand measurements which fall above the c~ = 12,000 s -1 curve in Figure 3 could arise from experimental e r r o r due to b a c k g r o u n d lumi-
1585
nosity or photon statistical uncertainties. This is particularly true of data points in the u p p e r left h a n d corner of Figure 3 where the measured mole fraction of H2 is less than 0.01.) The absence of localized extinction in this turbulent H2 j e t flame is substantiated by planar laser induced OH fluorescence imaging which indicate fully continuous reaction zones. 29 T h e presence or absence of localized extinction in the turbulent CO/H2/N2 diffusion flames can not be d e t e r m i n e d because calculations or measurements of laminar flames near the extinction limit are not presently available to compare with instantaneous Raman measurements. T h e stretched laminar opposed-flow diffusion flame data in CO/H2/N2 flames (shown in Figures 5 - 7 ) are believed to be from flames far from the extinction limit. T h e absence of localized extinction effects for turbulent H2 j e t diffusion flames demonstrated in this paper are in sharp contrast to the extensive localized extinction found in pilotflame stabilized CH4 turbulent jet diffusion flames using planar fluorescence imaging 3~ and pulsed Raman scattering. ~l T h e two findings are not contradictory. In a simple jet (with no pilot flame stabilization) extinction is most likely to occur at the nozzle exit where the shear rates are highest. Increasing the shear rate by increasing the fuel velocity causes the flame to blow off before extensive localized extinction occurs downstream. Pilot-flame stabilization permits attached flames at high stretch rates so substantial localized extinction can occur. T h e stretched laminar flamelet approach to turbulent combustion modeling might be expected to apply even u n d e r conditions of localized e x t i n c t i o n - - p r o v i d e d experiment or model calculations of the laminar diffusion flame structures are available near the extinction limit, However, published versions of laminar flamelet models do not account specifically for the partial fuel-air mixing and subsequent burning which occurs subsequent to localized extinction. V. C o n c l u s i o n s
T h e present and previous papers have shown that finite rate chemistry processes are important in turbulent j e t diffusion flames, even for I-I2 and CO/H2/N2 fuels where the chemical kinetic rates are reasonably fast and for jet Reynolds numbers (Re = 8500) where the fluid mixing rates are relatively slow. Finite rate chemistry processes in turbulent diffusion flames are expected to be even more important when the chemical rates are slower (hydrocar-
1586
T U R B U L A N T COMBUSTION
boa fuels) or w h e r e the mixing is faster (higher Reynolds n u m b e r flows). T h e stretched l a m i n a r flamelet concept in turbulent flames was tested in this p a p e r by c o m p a r i n g i n s t a n t a n e o u s and conditionallyaveraged R a m a n m e a s u r e m e n t s in t u r b u l e n t H2 and CO/H~/N2 j e t diffusion flames with Hz stretched laminar flamelet calculations ~1 and CO/HE/N,. stretched l a m i n a r flame m e a s u r e meats. 2u T h e excellent c o r r e s p o n d e n c e between stretched l a m i n a r and t u r b u l e n t flame data suggest that the l a m i n a r flamelet a p p r o a c h may provide better predictions than a twoscalar p d f a p p r o a c h o f finite rate chemistry in turbulent reaction zones because partial equilibrium assumptions are not r e q u i r e d and localized extinction can be accounted for properly. H o w e v e r , d i f f e r e n c e s between stretched laminar and t u r b u l e n t flame data suggest that the laminar flamelet a p p r o a c h might overestimate the influence o f p r e f e r e n t i a l diffusion in turbulent flames c o n t a i n i n g H2 and may not properly include the effects o f t h r e e - b o d y r e c o m b i n a t i o n reactions which are so slow that they are likely to o c c u r outside o f the relatively thin reaction zone.
Acknowledgments This research was sponsored by the Air Force Office of Scientific Research (AFOSR) under Contract F49620-85-C 0035 (Dr. Julian Tishkoff, Program Manager) and by the Basic Research Department of the Gas Research Institute under Contract 5081-263-0600 (Mr. James Kezerle, Program Manager). The technical assistance of Frank Hailer and helpful discussions with Drs. Charles Fenimore, Robert Pitz and Wei Shyy are gratefully acknowledged. REFERENCES 1. LIBBV, P. A. ANn WILLIAMS, F. A.: ed., Turbulent Reacting Flows, Springer-Verlag, New York, 1980.
7. BILGER, R. W. AND STARNER, 8. H.: Combust.
Flame, 51, 155, 1983. 8. CORREA, S. M.: "A Model for Nonpremixed Turbulent Combustion of CO/H2 Jets," IX International Symposium on Combustion Processes, Wisla-Jawornik, Poland, to appear in Archivuum Combustionis. 9. WILLIAXIS,F. A.: "Recent Advances in Theoretical Descriptions of Turbulent Diffusion Flames," Turbulent Mixing in Nonreactive and ReactiveFlows, (S, N. P. Murthy, ed.) Plenum Press p. 189, 1974. 10. CARRIER, G. F., FEYOELL,F. E. ANn MARBLE,F. E.: SIAM J. App. Math, 28, 463, 1975. 11. PETERS, N.: Progress in Energy and Combustion Science, I0, 319, 1984. 12. MARBLE, F. E. AND BROADWELL, J. E.: "A Theoretical Analysis of Nitric Oxide Production in a Methane/Air Turbulent Diffusion Flame," EPA600/7-80-018, 1980. 13. LIrw, S. K., BRAY, K. M. C., ANt) MOSS, J. B.: Comb. Sci. Tech. 27, 69, 1981. 14. LIEW, S. K., BRAY, K. M. C., ArqO MOSS, J. B.: Comb. Flame 56, 199, 1984. 15. RAZDAr,', M. K. AND STEVENS,J. G.: Combust. Flame 59, 289, 1985. 16. JEr,'c, S-M., CHENO, L-D., ANn FAEXH, G. M.: Nineteenth Symp. Int. Comb. p. 349, The Combustion Institute, 1982. 17. DRAKE,M. C., PITZ, R. W., AID LAPP, M.: "Laser Measurements on Nonpremixed Hydrogen-Air Flames for Assessment of Turbulent Combustion Models," AIAA Paper 84-0544, 1984; AIAA J. 24, 905, 1986. 18. DRAKE,M. C., BILGER, R. W. ANDST,~RNER, S. H.:
Nineteenth Syrup. (Int.) on Combustion, p. 459, The Combustion Institute, 1982. 19. DRAKE, M. C., PITZ, R. W., LAPP, M., FENIMORE,
20.
21.
2: JONES, W. P. AND WHITELAW, J. H.: Combust.
Flame 48, 1, 1982. 3. DRAKE,.~[. C. AND KOLLMANN,W.: "Slow Chemistry Nonpremixed Flows," Evaluation of Data on
Simple Turbulent Reacting Flows, (W. C. Strahle, ed.) AFOSR TR-85 0880, Sept. 1985; to appear in Prog. Energy Comb. Sci.. 4. JANICKA,.]. AND KOLLMANN,W.: Combust. Flame 44, 319, 1982. 5. EICKHOFF, H. E. AND GRETHE, K.: Combust. Flame 35, 267, 1977. 6. CORREA, S. M., DRAKE, M. C., PITZ, R. W., AND
SHYY, W.: Twentieth Syrup. Int. Comb., p. 337, The Combustion Institute, 1984.
22.
23.
24. 25.
C. P., L~CHT, R. P., SWEE,','EY, D. W. and LAURENDEAU, N. M.: Twentieth Syrup. Int. Comb. p. 327, The Combustion Institute, 1984. DRAKE, M, C., PITZ, R. W., CORaEA, S. M. AND LAPP, M.: Twentieth Symp. Int. Comb., p. 1983, The Combustion Institute, 1984. DAVID,T., GASKELL,P. H. AND DtxoN-LEwIs, G.: "Structure and Properties of Methane-Air and Hydrogen-Air Counterflow Diffusion Flames," submitted for publication. DRAKE, M. C.: "Kinetics of Nitric Oxide Formation in Laminar and Turbulent Methane Combustion," Gas Research Institute Final Report, GRI-85/0271, 1985. GORDON,S. ANn MCBRIDE, B.J.: "Computer Program for Calculation at Complex Chemical Compositions, Rocket Performances, Incident and Reflected Shocks and Chapman-Jouget Detonations," NASA SP273, NTIS N71-37775, 1971. WARNATZ,J.: Comb. Sci. Tech. 26, 203, 1981. MILLER,J. A. AND KEE, R. J.: J. Chem. Phys. 61, 2534, 1977.
L A M I N A R FLAMELET ANALYSIS OF DIFFUSION FLAMES 26. DRAm~, M. C., LAPP, M., PENNEY, C. M., WARSHAW, S. AND GERHOLD, B. W.: Eighteenth Symp. Int. Comb., p. 1521, T h e Combustion Institutel 1981. 27. HYNES, A. J., STEINBERG, M., AND SCHOFIELD, K.: J. Chem. Phys. 80, 3921, 1984. 28. WARNATZ, J.: Ber. Bunsenges. Phys. Chem. 83, 950, 1979. 29. KYCHAROW, G., HOWE, R. D., HANSON, R. K., DRAKE, M. C., PITZ, R. W., LAee, M., mad PENNEY, C. M.: Science 224, 382, 1984.
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30. DIBBLE, R. W., LONG, M. B., a n d MASRI, A.: "Two Dimensional Imaging o f C2 in Turbulent Nonpremixed Flames," T e n t h Int. Colloquium on Dynamics o f Explosions and Reactive Systems, Berkeley, CA, August 1985. 31. DIBBLE, R. W., MASRI, A. AND BILGER, R. W.: "Spontaneous Raman Measurements in Laminar and T u r b u l e n t N o n p r e m i x e d Flames o f Methane," submitted for publication.
COMMENTS R. W. Bilger, University of Sydney, Australia. 1. In the absence o f simultaneous m e a s u r e m e n t o f O H and major species, how can you tell if partial equilibrium is breaking down? 2. T h e plots o f reactive scalars vs. mixture fraction do not, o f themselves, imply flamelets. Distributed reaction zones would also show a similar scatter o f data. To me, a "flamelet" implies that the local normal to mixture fraction surfaces undergoes a monotonic progression in mixture fraction t h r o u g h the reaction zone. O n the scalar vs. mixture fraction plot, this maps as a single valued curve. A distributed reaction zone can have an up and down variation o f m i x t u r e fraction along such a normal and this maps as a multivalued and even crossing curve on the scalar mixture fraction plot. T h e r e is no way o f telling from the data on such plots w h e t h e r t h e r e are flamelets or distributed reaction zones. T h e r e is possibly a way o f distinguishing flamelets from distributed reaction zones in a system such as your CO/H~ flame, where m o r e than one progress variable is necessary to describe the state o f the mixture. For each data point, it should be possible to assign two values o f "a" (the flamelet stretch parameter) c o r r e s p o n d i n g to, say, the progress o f the CO reaction and o f the heat release as d e t e r m i n e d from the flamelet library. If these are equal, we may have flamelets. I f not, the progress o f the CO and H2 reactions are not correlated as in flamelets and we do not have flamelets. It is possible to have folded flamelets with overlapping reaction zones (and, hence, a distributed reaction zone) which has all reaction progress variables correlated as in a flamelet, but this is unlikely.
Author's Reply. 1. T h e H2 turbulent jet diffusion flame measurements are not sufficient to tell if partial equilibrium in the radical pool is breaking down. However, as explained in the paper, partial equilibrium can be tested directly in the stretched laminar flamelet calculations. I f the two body shuffle reactions
H + 02 ~ O H + O O + H2~.~-OH + H OH + H2 ~ H20 + H are equilibrated, then the calculated concentrations o f O and H should he given by [O] = 0.152 exp(8391/T)[OH]2/[HzO] [H] = 8.906x10 -3 exp(16223/T)[OH]3/ ([O~][H=O], = 0.2419 exp(7400/T)[OH][H2]/[H20]
lean rich
T h e s e relationships a p p e a r to be true in the high t e m p e r a t u r e regions o f the a = 100 s -~ H2 laminar f a m e , but not in the ~ = 12,000 s t flame. I f the laminar flamelet model is valid for turbulent diffusion flames, a similar breakdown in partial equilibrium may be i n f e r r e d in highly stretched regions o f turbulent H2 diffusion flames. Even larger deviations from partial equilibrium can be expected in CO/H~/N2 diffusion flames because the reaction C O -~- O H ~- C O 2 ~- H
is much slower than the three reactions listed previously. T h e deviations f r o m partial equilibrium (particularly for CO) are the likely cause for the differences between two-scalar p d f model calculations and experimental data in low t e m p e r a t u r e , fuel-rich regions o f turbulent CO/H~/N2 jet diffusion flames. 2. In essence, this c o m m e n t says that present experimental data are insufficient to determine w h e t h e r laminar flamelets or distributed reaction zones are the d o m i n a n t form o f combustion in these simple turbulent jet diffusion flames. I strongly disagree. T h e experimental data in this paper and in previously published work are consistent with laminar flamelet combustion and are not consistent with distributed reactions. T h e most direct evidence for laminar flamelets in simple turbulent H~ diffusion flames comes from instantaneous two-dimensional images of O H concentrations using planar laser i n d u c e d fluorescenceJ Since O H concentrations are localized in reaction
1588
T U R B U L A N T COMBUSTION
zones of diffusion flames, O H images provide instantaneous reaction zone shapes and distributions. T h e images show a smooth progression from laminar (Re = 660), transitional (Re = 1600) and turbulent (Re = 8500) H2 diffusion flames. As Re increases, the instantaneous flame fronts get thinner and more highly convolved, but remain highly localized in continuous laminar flamelets. Taking a slice normal to the flame front, as Professor Bilger suggests, gives a smooth distribution of OH concentrations which monotonically increase to a maximum near the center of the flame front and then monotonically decrease. The OH images do not appear to be consistent with distributed reaction zones which are expected to give irregular distributions of O H concentrations across the flame front, widely dispersed OH concentrations throughout the flame, and highly discontinuous flame fronts. The present paper starts with the existence of laminar flamelets and asks whether the pulsed Raman data are consistent with stretched laminar flamelets. As Professor Bilger comments, the local normal to mixture fraction surfaces undergoes a monotonic progression in mixture fraction through the reaction zone, which on scalar vs. mixture fraction plots corresponds to a single valued curve. However, this single valued curve corresponds to one value of scalar dissipation or flame stretch. A different value of flame stretch corresponds to a different scalar vs. mixture fraction relationship. So the spread in the data on temperature vs. mixture plots (Fig. la) or the H~ vs. 02 plots (Fig. 3) can be qualitatively explained by fluctuations in flame stretch which occur in turbulent H2 diffusion flames. The pulsed Raman data may not be consistent with distributed reaction zones where a broader range of temperatures for a given mixture fraction might be expected. The experimental data from planar laser induced fluorescence and from pulsed Raman scattering demonstrate clearly that localized extinction is not important in this simple H2 turbulent jet flame. These data could provide a valuable test of turbulent combustion models using the laminar flamelet approach (such as that of Rogg, et al.2), because the most empirical parts of the model dealing with localized extinction and subsequent partial premixing would not need to be included. Although it appears clear that simple turbulent jet diffusion flames b u r n in laminar flamelets, the situation is not resolved for lifted turbulent jet diffusion flames or for flames stabilized by pilot flames or recirculation. For example, in pilot flame stabilized turbulent jet diffusion flames, C2 fluorescence imaging 3 and pulsed Raman measurements 4 show extensive localized extinction. Whether subsequent combustion occurs as partially premixed laminar flamelets or as distributed reactions remains to be determined.
REFERENCES 1. KYCHAKOFF, G., HOWE, R.D., HANSON, R.K, DRAKE, M.C., PITZ, R.W., LAPP, M., and PENNEY, C.M., Science, 224, 382 (1984). 2. ROGG, B., BEHRENBT, F., and WARNATZ,J,, this Symposium. 3. DIBBLE, R.W., LONG, M.B., and MASRI, A., "Two Dimensional Imaging of C2 in Turbulent Nonpremixed Flames," T e n t h Int. Colloquium on Dynamics of Explosions and Reactive Systems, Berkeley, CA (1985). 4. DIBBLE, R.W., MASRI, A. and BILGER, R.W., "Spontaneous Raman Measurements in Laminar and T u r b u l e n t Nonpremixed Flames of Methane," submitted for publication.
F. A. Williams, Princeton University, USA. Your results are very interesting in strongly suggesting the relevance of the flamelet view to turbulent hydrogenair diffusion flames. T h e kinds of comparisons with theoretical calculations that you have made are, in my opinion, essential as a first step in testing the concepts. Having obtained this degree of understanding of attached flames, you can now go on to make measurements of lifted flames. As you know, currently there is considerable uncertainty concerning the degree of mixing that occurs between the jet exit and the point of flame inception. Since measurements of the kind that you are making can shed a great deal of light on the question, I certainly hope that you will be able to proceed to test lifted flames. Author's Reply. I agree that this paper represents the first step in testing the applicability of the laminar flamelet concept in turbulent jet diffusion flames. The next step could be the quantitative comparison of a detailed stretched laminar flamelet calculation of H2 and CO/H2/N2 jet diffusion flames with experimental measurements--- both averaged at individual flame locations and conditionally averaged in mixture fraction intervals. T h e wide range of scalars (~, T, X(major species), p, and X(OH)) which have been measured in the turbulent H2 and CO/H2/N2 jet diffusion flames should provide a reasonable test of the model. An even more direct test of laminar flamelet model calculations would involve the comparison of model calculations and experiments of scalar dissipation conditioned upon the presence of the reaction zone (ie. • This type of measurement has not been obtained but appears feasible in some H2 turbulent jet diffusion flames using two dimensional OH fluorescence imaging. Your suggestion of pulsed Raman measurements of lifted turbulent jet diffusion flames is one of several potentially fruitful research directions.
LAMINAR FLAMELET ANALYSIS OF DIFFUSION FLAMES Another is measurements in pilot flame stabilized turbulent jet flames with H2 and CO/H2/N2 fuels at much higher Reynolds number. I expect these measurements will show localized extinction effects, and
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detailed experiment-model comparisons could test the applicability of stretched laminar flamelet models which include localized extinction, partial fuel-air premixing, and subsequent combustion.