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The effect of dilution with steam on the burning velocity and structure of premixed hydrogen flames
Twenty-first Symposium (International) on Combustion/The Combustion Institute, 1986/pp. 1811-1819
T H E EFFECT OF D I L U T I O N W I T H S T E A M O N T H E B U R N I N G V E L O C I T Y A N D S T R U C T U R E OF P R E M I X E D H Y D R O G E N FLAMES G.W. KOROLL AND S.R. MULPURU High-Temperature Chemistry Branch, Atomic Energy of Canada Limited, Whiteshelt Nuclear Research Establishment, Pinawa, Manitoba ROE ILO CANADA
A comparative study of the effects of diluents on the burning velocity of H~-Oz mixtures has been carried out focusing on the extraordinary effect of steam on burning velocity and flame structure. Burning velocities are measured by the nozzle-burner, cone angle method with particle tracking by laser doppler anemometry for a range of stoichiometries and diluent fractions (He, Ar, N> steam). New data are given for H2-air mixtures containing up to 50% steam. The tollowing correlation is obtained, which accurately predicts the physical effects of diluents (flame cooling and heat transport) on burning velocity: S~(~o/a) ]~2 = Suo(1 -X/XL). Here, S,, is the laminar burning velocity, ot is the thermal diffusivity, X is the mole fraction of diluent, XL is the diluent fraction sufficient to inert the mixture, and suffix 0 denotes the undiluted mixture. This correlation underestimates the burning velocity for steam diluent by 20%, indicating that steam influences the burning velocity by mechanisms other than flame cooling and heat transport. Using a one-dimensional flame model, we calculated in detail the changes to the flame structure caused by the addition of steam and determined that steam effects a redistribution of heat release in the flame. This is caused by the high third-body efficiency of steam in the exothermic reaction, H + O2 + M --+ HOz + M. Thus steam increases in the rate of this reaction and, subsequently, the rates of a cycle of exothermic reactions involving HOe in the preheat region of the flame. The result is a steeper temperature profile (i.e., a thinner flame) and an increased burning velocity. Sensitivity analysis indicates this mechanism produces the same effect on burning velocity as is observed experimentally upon adding steam.
1. Introduction T h e l a m i n a r b u r n i n g velocity, the local flame velocity relative to the u n b u r n t gas a n d n o r m a l to the flame front, is one o f the most useful f u n d a m e n t a l p a r a m e t e r s c h a r a c t e r i z i n g a combustible m i x t u r e 1, but b u r n i n g velocity data in the p r e s e n c e o f steam are f r a g m e n t a r y . Liu and M a c F a r l a n e 2, o b t a i n e d b u r n i n g velocity data for H2-air-steam m i x t u r e s c o v e r i n g a t e m p e r a t u r e r a n g e b e t w e e n 25~ a n d 250~ but limited to m i x t u r e s c o n t a i n i n g less that 15% steam. Despite w i d e s p r e a d advocacy o f steam for controlling c o m b u s t i o n processes 3 a n d the natural o c c u r r e n c e o f steam as a c o n s t i t u e n t in safetyrelated analysis 4,s, the m e c h a n i s m s by which steam influences c o m b u s t i o n are not well u n d e r stood. S t e a m is usually c o n s i d e r e d to behave as a simple d i l u e n t in combustion, l o w e r i n g the b u r n i n g velocity to the e x t e n t that it acts as a heat sink, and r e d u c e s the flame t e m p e r a t u r e . T h e limited data available indicate, h o w e v e r , that the r e d u c t i o n o f b u r n i n g velocity in the presence o f steam is n o t c o m m e n s u r a t e with changes to the
heat capacity o f the m i x t u r e . David and M a n n 6 o b s e r v e d moist flame t e m p e r a t u r e s to be h i g h e r than dry flame t e m p e r a t u r e s tbr o p e n H=,-air flames. Kuehl 7 observed an increase in b u r n i n g velocity u p o n r e p l a c i n g N2 with H 2 0 vapor in low-pressure Hz-air flames and postulated that steam accelerates b u r n i n g by increasing the radiative heat t r a n s p o r t f r o m the hot combustion p r o d u c t s to the water v a p o r in the u n b u r n t gas. O t h e r s o f f e r e d chemical kinetic interpretations o f the result 8'9. Muller-Dethlefs and Schlader 1~ studied the effect o f steam on the b u r n i n g velocity o f p r o p a n e and ethylene flames and c o n c l u d e d that steam did not act as an inert diluent but instead gave rise to greater heat release that c o u n t e r a c t e d the cooling effect o f the a d d e d steam. No m e c h a n i s m was offered, but the data are n o t e w o r t h y because they indicate that the a n o m a l o u s b e h a v i o u r of water v a p o r a p p e a r s to be c o m m o n to H2 and hydroc a r b o n flames. We have carried out an e x p e r i m e n t a l and theoretical investigation o f the influence o f steam on the b u r n i n g velocity o f p r e m i x e d
1811
1812
LAMINAR FLAMES
hydrogen flames. I n this paper, we report new data for the b u r n i n g velocities of H2-air-steam mixtures containing up to 50% steam. And, a comparative study of b u r n i n g velocities of three-component mixtures is made in which the influence of steam is examined in the context of a systematic replacement of diluents with different physical properties in H2-O2 mixtures. Using this approach, the physical effects that diluents have on b u r n i n g velocity by changing transport properties and adiabatic flame temperatures are established, a n d the existence and magnitude of chemical kinetic effects of steam diluent are identified. T h e kinetic mechanisms are assessed using a one-dimensional reactive flow model.
__
flame
ocket
] inert gas
III
burner
lo
c o m p r e s s e d gases
lhermoelecfric moss flow controller
2. Methods
2.1 Experimental T h e b u r n i n g velocities were measured by the nozzle-burner/schlieren cone angle method with particle tracking of the u n b u r n t gas velocity by dual-beam, laser doppler anemometry 241. Gas composition was maintained by thermoelectric mass-flow controllers individually calibrated for each gas to within - 0 . 1 % . A uniform nonfluctuating volume flow of steam was provided by evaportion of a precisely metered flow of distilled, degassed water. Steam content was verified to within 0.2% in separate tests in which steam was condensed at the b u r n e r exit at a rate that matched the input mass flow. The b u r n e r was fitted with an a n n u l a r chamber over its entire length (0.85 m) through which water/ ethylene glycol was circulated from a constanttemperature reservoir, to provide accurate control of the final u n b u r n t gas temperatures and to cool the nozzle (see Fig. 1). Prior to final temperature control, the gases containing steam were maintained at 120~ to prevent condensation. T h e b u r n e r diameter for all H2-air-steam experiments was 5 mm. For the faster b u r n i n g H2-O2-steam mixtures, it was necessary to use a 3-mm b u r n e r to avoid exceeding the critical Reynolds n u m b e r for laminar flow. The effect of flame curvature on the measured b u r n i n g velocity was quantified using burners with different diameters (hence flames of different radii of curvature). T h e measured b u r n i n g velocity of 42% Hz-air at 25~ was 3.82 m . s-* on a 2 m m b u r n e r , 3.55 m 9 s-1 on a 3 m m b u r n e r , 3.38 on a 4 m m b u r n e r and 3.28 on a 5 mm burner. Further increases in the nozzle diameter had a negligible effect on b u r n i n g velocity. This is consistent with the work of
sou cel
sleom
I
,ooeport,oleoeoero,or
FIG. 1. A schematic drawing of the burner and gas-handling system. France and Pritchard 1~, who observed no curvature effect for diameters between 8 mm and 12 mm. Our results using the 5-mm b u r n e r for H2-air mixtures at 25~ at atmospheric pressure, agree closely with those of Edmondson and Heap ~2 using a 10.4-mm b u r n e r and France and Pritchard ~a using a 7-mm burner, and with the calculations of Warnatz 14.
2.2 One-Dimensional Flame Model B u r n i n g velocities, heat release, temperature and species profiles in laminar H 2 - 0 2 flames were calculated by solving the one-dimensional conservation equations for overall continuity, individual species continuity and energy. T h e numerical method departs from that of earlier workers 14 ' l o"' 16 in employing Eulerian coordinates and has been described elsewhere 17. Temperature-dependence of transport properties and rate constants are included in the calculation. The reaction scheme is from Warnatz 15 with rate parameters from Baulch et al. Is. T h e calculation begins with user-defined initial profiles of species mass fractions and temperature. With a suitable grid-point system, the differential quotients are replaced by finitedifference expressions. T h e grid Peclet n u m b e r , IU1 9 &~/D, is kept less than 2 to resolve the interactions of convection and diffusion. Here, U is the flow velocity, Ax is the grid interval and D is a diffusion coefficient. Since the ratio [U[/D
HYDROGEN FLAMES DILUTED WITH STEAM decreases in the direction of the b u r n t gases, the grid interval can increase in the direction of the burnt gases, while satisfying the Peclet number restriction. T h e space derivatives are discretized on this non-uniform grid, using central differencing. T h e time derivative is discretized by first-order backward differencing. T h e non-linear reaction rate terms are linearized using a Taylor expansion, and the resulting matrix of linear equations is solved to advance the solution by a time step. T h e stiffness of the kinetic system is m a n a g e d by a variable time step obtained by the criterion [/1 At ~ 1, where ~1 is a parameter that represents a time constant for the changing species concentrations and temperature. This criterion insures that At is varied to resolve the fastest chemical timescale. Thus, the solution is "marched" forward, step by step, in time until a s t e a d y state is reached. T h e b u r n i n g velocity, which then remains the only unknown, is extracted from the steady-state solution.
3. R e s u l t s a n d D i s c u s s i o n
3.1 112-02 Diluent Mixtures To u n d e r s t a n d the physical effects of dilution on b u r n i n g velocity, b u r n i n g velocities were measured for H2-O 2 mixtures containing the diluents He, Ar, and N2 at ambient temperature and pressure. Measurements were made for selected ratios of H2-02 with each diluent over the range of diluent fractions that provided a stable flame. Results are shown in Fig. 2, for stoichiometric flames. In all cases, the burning velocity decreased with increasing fraction o f diluent gas and extrapolated smoothly to intercept the x-axis at a point that corre-
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0.8
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Fro. 2. Burning velocities of 2:1 H2-O2 mixtures at 298 K with the diluents He(O), Ar(A) and N2([~). Solids denote the respective inerting diluent fractions from ref. 19.
1813
sponded to the independently measured ~9 inerting fraction for the particular diluent. Yhe results were qualitatively consistent with previous work 13'2~ We assessed the effect of the diluents initially in terms of a well-known general expression ~:~, where b u r n i n g velocity is represented as the product of a transport term and a reaction rate term. S~= - -
\ PCt/
.(reaction rate) 1/2.
(1)
Replacement of one chemically inert diluent for a n o t h e r will alter the t r a n s p o r t term in Eq. (1) if the diluents differ in density p, heat capacity Ct,, or thermal conductivity, X. Diluents differing in heat capacity will also change the rate term to the extent that the)' change the flame t e m p e r a t u r e and thus the rates of high activation energy steps. These are the physical effects constituting "ideal" diluent behaviour, and are different from effects caused by direct or catalytic participation by the diluent h~ reaction kinetics. A practical expression for predicting the physical effects is obtained as follows. T h e transport term is the thermal diffusivity, c~, and is calculated 24 in detail for all mixtures at 298 K. T h e r m a l diffusivities for each mixture containing diluent are normalized with respect to the undiluted mixture, c~,,, to obtain the "relative thermal diffusivity", %/e~, a factor containing the contribution of a d d e d diluent to the transport term of Eq. (1) relative to the undiluted mixture. While c~ is a t e m p e r a t u r e d e p e n d a n t quantity, c~0/c~ is relatively insensitive to temperature. A calculation of %/or at 1000 K indicated an increase relatixe to the 298 K value of 1% to 2% for He, Ar, and N2 diluents, and slightly more for steam, d e p e n d i n g on concentration. Figure 3 shows the result of multiplying the measured burning velocities of mixtures containing He, At, or N2 by the factor (C~o/C0le fbr the respective mixtures. T h e r e is a linear d e p e n d e n c e of the corrected b u r n i n g velocity, S,,(%/o01/2 with a d d e d diluent fraction. Tlae x-intercept of the straight line remains at the diluent fraction corresponding to the flammability limit for downward propagation for the respective diluent, XL, as m e a s u r e d by Kumar and Hollinger 19. Helium and Ar have identical molar heat capacities and, therefore, the same adiabatic flame temperatures, but they differ in their effects on the b u r n i n g velocities through different thermal diffusivities. Nitrogen and Ar have nearly identical thermal diffusivities.
1814
LAMINAR FLAMES change in the b u r n i n g velocity, but, in our experiments when 25% N2 was replaced in a stoichiometric mixture with 25% 02, the burnin~ velocity increased from 6.5 m" s -1 to 8.3 m"
12.0 I0,0
S .-e -~
8.0
S-'.
6.0
Oxygen participates directly in two reactions in the H 2 - 0 2 reaction scheme~5:
4.0
H + O2~OH
+ O
(R1)
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[
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0.1
0.2
0.3
0.4
0.5
0.6
0.7
Mole
fraction
H + 02 + M - ~
I"l~
0.8
diluent
FIG. 3. Burning velocities of 2:1 H2-O= mixtures with He(@), Ar(A) and N2([~) diluents corrected for relative thermal diffusivity. Solid line is the prediction of Eq. (2). Therefore, differences in their effect on burning velocity can be interpreted in terms of different flame t e m p e r a t u r e s arising from their different heat capacities. Since flammability limits are strongly d e p e n d e n t on the heat capacity of the gas mixture, XL values for mixtures with N2 are naturally lower than for mixtures with noble gases. What is important is that a change in the heat capacity of the diluent changes only the slope of the straight line correlation of Su(eo/e) r/2 with the diluent fraction. This behaviour is summarized in Eq. (2).
Su(o~o/~)l/2=Soo(]ff--~).
HO2 4- M
(R2)
09
(2)
Equation (2) has general utility; given the burning velocity of the undiluted mixture, Suo, and the inerting diluent fraction, Xb the burning velocity, S,, can be estimated for any fraction of inert diluent, X. Equation (2) is accurate for lean and rich flames containing He, Ar or N2 that can be stabilized on a burner. It is probably i n a p p r o p r i a t e for near-limit mixtures, but for fast b u r n i n g mixtures Eq. (2) provides the criterion we require for ideal diluent behaviour; it predicts the physical effects of a diluent on b u r n i n g velocity. Behaviour different from that o f Eq. (2) suggests that the diluent contributes to mechanisms other than flame cooling and heat transport. This premise is tested by the case of excess O2. 3.2 Mixtures with Excess 02 Nitrogen and 02 have nearly identical Cp, X and p, so the r e p l a c e m e n t o f N2 diluent with 02 in a stoichiometric mixture will not significantly change the thermal diffusivity or the adiabatic flame t e m p e r a t u r e 25. Equation (2) predicts no
In the mixture containing 50% H2 + 25% 0 2 "k" 25% N2, replacing N2 with 0 2 effectively doubles the concentration of 02 and hence, the rates of reactions (R1) and (R2). The burning velocities were calculated, using the computer model, for the mixture containing 25% N2 and the mixture with N2 replaced by 25% excess O2. T h e calculated burning velocities were, respectively, 6.8 m . s -1 and 8.1 m 9 s -1, in good relative agreement with the values of 6.5 m 9 s -a a n d 8.1 m . s -1 observed experimentally. T h e calculation was repeated for the mixture containing 25% N2 with kl, the rate constant for reaction (R1), artificially doubled in the reaction scheme to simulate the effect o f reaction (R 1) on b u r n i n g velocity when replacing N2 with O2. T h e burning velocity increased from 6.8 m 9 s -] to 7.4 m ' s -1, about half tlae total observed effect of doubling [02]. Finally, k] and k2 were both doubled to simulate the combined effect of both reactions (R1) and (R2) when [02] is doubled. T h e result was a burning velocity o f 8.2 m . s -1, which was nearly the same as the value o f 8.3 m" s -] when [02] was doubled. Thus, the increase in burning velocity when N2 is replaced in a stoichiometric mixture by excess 02 is directly due to the proportional increase in the rates of'reactions (R1) and (R2). T h e case o f O2 "diluent" demonstrates that d e p a r t u r e s from the prediction of Eq. (2) are quantitatively linked to the participation of the diluent in reaction kinetics. 3.3 H2-Air Steam and H2-O2-Steam Mixtures Figure 4 summarizes the results of burning velocities for Hz-air-steam mixtures at 100~ T h e range of H2 concentrations shown is indicative of the range o f mixtures that could be stabilized on the burner. For steam fractions less than 15%, the present results compare favorably with those o f Liu and MacFarlane 2. Their data are consistently higher by a small amount attributable to the flame curvature effect due to their use of a smaller nozzle. T h e effect of steam on flame mechanisms is exa-
HYDROGEN FLAMES DILUTED WITH STEAM mined using the simpler three-component mixtures of H2-O2-steam. In Fig. 5, the b u r n i n g velocities are compared for H2-02 mixtures at 100~ containing N2 and steam. For diluent fractions less than 45%, replacement of N2 with steam increases the b u r n i n g velocity, contrary to what is expected on the basis of the lower adiabatic flame temperature with steam. In Fig. 6, the data for steam are corrected for relative thermal diffusivity a n d plotted with the prediction of Eq. (2) for ideal diluent behaviour. Equation (2) underpredicts the b u r n i n g velocity by 20% (for a mixture containing 25% steam), suggesting that steam, like oxygen, influences the b u r n i n g velocity through mechanisms other than flame cooling and heat transport. Beyond 60% steam, flame cooling mechanisms probably dominate and normal behavior is observed. With the addition of steam there would be an increase in the reverse rates of the partially equilibrated reactions (R3) and (R4), possibly causing an increase [OH]. OH + H2 ~ H2O + H
However, in both cases the reverse reactions are slow (i.e., high activation energy) and the rates are more likely to decrease with added steam due to lower flame temperatures. As a more likely mechanism for the effect, we examined the role of steam as a third-body catahst in the recombination reactions (R2), (RS) and (R6). i
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OH + OH ~-~ H20 + O
1815
I
02
03
(R4)
0.4
0,5
06
0.7
08
Mole fraction diluent
Flo. 5. Burning velocities of" 2:1 H2-O2 mixtures at 373 K with the diluents N2(A) and steam (O).
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FIG. 4. Burning velocities of H2-air-steam mixtures at 373 K using a 5-mm nozzle.
Mole fraction steam
FIG. 6. Burning velocities of 2:1 H2-02 mixtures at 373 K with steam diluent, corrected for relative thermal diffusivity. Solid line is the prediction of Eq. (2).
1816
LAMINAR FLAMES H + 02 + M---~ HO2 + M
(R2)
H + H + M---~ H2 4- M
(R5)
T{K) 0.24 2800
Burning Velocity 8.9 m's "= O9
H + O H + M---* H20 + M
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(R6)
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The net effect is, 2H2 + 02 ~ 2H20 + 482 kJ. The sensitivity of b u r n i n g velocity to thirdbody efficiency was tested in another computer experiment where the third-body efficiency coefficient for steam was artificially changed in our model to that of N2 (i.e., from 6.0 to 0.4). The results appear in Fig. 7c. The b u r n i n g velocity was very sensitive to the change, decreas!ng from 9.8 m 9 s -1 to 7.8 m . s -a. [HO2] and Q values were virtually the same as for N2 diluent. The high [OH] failed to persist with
0.16
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001
0.04
002
2000
0.12 1600
x IO I o ~ . : . . . . . ."OH ::::::-.-.:-]o.oe
[M] = [H2]+0.4[O2]+0.4[N2]+ 6.0[H20] 15. The high third-body efficiency coefficient of steam in these reactions is well documented 18, particularly for reaction (R2). Reaction (R2) is exothermic and initiates a cycle of exothermic, low-activation reactions of HO2 with H., .OH and O., in all, an important source of heat in the flame 26. We calculated b u r n i n g velocities and flame structures for the stoichiometric mixtures at 100~ containing 25% N2 and for the same mixture with N2 replaced by steam. Nitrogen is retained for comparison because it was earlier demonstrated to behave as a simple diluent. The results are compared in Figs. 7a and 7b. The calculated b u r n i n g velocities with N2 and steam diluents were 8.9 and 9.8 m 9 s -1, respectively, compared with 8.4 and 9.3 m 9 s-1 observed experimentally. It is reasonable that the calculated values were systematically higher by a small a m o u n t because the calculation assumed an adiabatic system. For the mixture with steam diluent, [HO2] is greater by a factor of 3 and [OH] is increased by ~30%. There is a significant redistribution of the heat release, Q, towards the u n b u r n t gas, resulting in a temperature profile also shifted towards the unb u r n t gas. These differences in flame structure between N2 and steam diluents are consistent with an increase in the rate of reaction (R2), resulting from the high third-body efficiency of steam. A typical sequence of reactions consistent with the increased [HO2] and the upstream shift of Q is, H + O 2 + M --~ H O z + M A H = - 196kJ/mol HOg+H ~ 2OH d~H=-160kJ/mol 2(OH+H2)---* 2 ( H 2 0 + H ) AH= 2 ( - 6 3 ) = - 126 kJ/mol
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FIG. 7. Calculated flame structures for 2:1 H2-O2 mixtures at 373 K (a) containing 25% N~ diluent, (b) containing 25% steam diluent, (c) containing 25% steam diluent and the third-body coefficient of steam artificially changed in the code from 6.0 to 0.4 lowered third body efficiency for steam. This indicates that the increased [OH] with added steam does not arise directly via reactions (R3) and (R4) since these d e p e n d on [H20] not third body efficiency. T h e most notable change in flame structure was the nearly 600 K decrease in the temperature profile in the reaction zone, which undoubtedly contributed to the sharp decrease in the b u r n i n g velocity. With the high third body efficiency of steam artificially reduced to that of an ideal diluent such as N2, steam exhibits the effect expected on the basis of its high heat capacity--a reduced b u r n i n g velocity due to a reduced flame temperature in the reaction zone. Moreover, b u r n i n g velocity calculated using the artificially reduced thirdbody efficiency agrees with the prediction of
HYDROGEN FLAMES DILUTED WITH STEAM Eq. (2). H i g h t h i r d - b o d y efficiency appears to be the principal cause o f the n o n - i d e a l behaviour o f steam diluent on b u r n i n g velocity. It r e m a i n s to separate the n e t effect o f t h i r d - b o d y efficiency into the relative effects o f reactions (R5) and (R6) as radical sinks and reaction (R2) as a heat source. C o n s i d e r again the p r e v i o u s r u n where the t h i r d - b o d y coefficient o f steam was r e d u c e d in the code f r o m 6.0 to 0.4. T h i s c h a n g e d [M] and hence the overall rates o f each o f the reactions (R2), (R5) and (R6) by a factor o f V4. T h e effect on calculated b u r n i n g velocity was a decrease, f r o m 9.8 m 9 s -1 to 7.8 m 9 s -1. I n a n o t h e r e x p e r i m e n t , the r e d u c t i o n in t h i r d - b o d y efficiency was c o m p e n s a t e d in reaction (R2) by increasing k2 by a factor o f 4. T h e resulting b u r n i n g velocity was 9.9 m 9 s -~. F r o m this we c o n c l u d e that the c o m b i n e d contribution o f reactions (R5) and (R6) to the effect o f thirdbody coefficient on the b u r n i n g velocity is a decrease by 0.1 m . s -1, a negligible a m o u n t . T h u s , the increased b u r n i n g velocity in the p r e s e n c e o f steam is p r i m a r i l y d u e to an increase in the rate o f reaction (R2) and the resulting increased rate o f h e a t release in a heat-deficient zone o f the flame n e a r the u n b u r n t gas. T h e c o n c u r r e n t d r a i n on chain carriers by reactions (R5) a n d (R6) is o f m i n o r i m p o r t a n c e in its effect on b u r n i n g velocity. F u t h e r m o r e , t h e r e r e m a i n s a vanishingly small role for radiant heat t r a n s p o r t m e c h a n i s m p r o p o s e d by Kuehl or reactions (R3) and (R4) c o n t r i b u t i n g to the o b s e r v e d b e h a v i o u r o f steam diluent.
Conclusions A c o m p a r a t i v e study o f d i l u e n t effects on the b u r n i n g velocity o f H 2 - 0 2 m i x t u r e s was carried out, with emphasis on the effect o f steam diluent. T h e diluents studied r e d u c e the b u r n ing velocity in the o r d e r o f N 2 > A r > H z O > H e . With the e x c e p t i o n o f steam, t h e effect o f diluents o n b u r n i n g velocity c o n f o r m to a correlation based on the t h e r m a l diffusivity o f the m i x t u r e s and flammability limits. New data were given for Hz-air-steam a n d H2-Oz-steam mixtures. S t e a m diluent, by virtue o f its high t h i r d - b o d y efficiency in the reaction H + 02 + M ~ HO2 + M, increases the heat release rate in the p r e h e a t zone o f the flame resulting in an increase in t e m p e r a t u r e in the reaction zone o f several h u n d r e d degrees. T h e increase in b u r n ing velocity caused by this m e c h a n i s m c o u n t e r acts the physical effect o f steam o f r e d u c i n g flame t e m p e r a t u r e .
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Acknowledgment This work was conducted at the Whiteshell Nuclear Research Establishment (WNRE) of Atomic Energy of Canada Limited (AECL), Pinawa, Manitoba. Financial support from Ontario Hydro, HydroQuebec, New Brunswick Electric Power Commission and AECL-CANDU Operations in a joint funding agreement with AECL-WNRE (COG-CANDEV 1984/85 number 435) is gratefully acknowledged. REFERENCES 1. RALLIS, C.J. AND GARFORTH,A.M.: Prog. Energ Combust. Sci. 6, 303 (1980). 2. Lm, D.D.S. AND MACFARLANE, R.: Comb. Flame 49, 59 (1983). 3. DRYER, F.L.: Sixteenth Symposium (Int'l) on Combustion, P. The Combustion Institute, Pittsburgh, PA 1976. 4. LIE, D.D.S., HARRISON, W.C., TAMM, H., MACFARLANE, R. AND CLEGG, L.J.: "Canadian Hydrogen Combustion Studies Related to Nuclear Reactor Safety Assessment;" Atomic Energy of Canada Limited Report, AECL-6994 (1980). 5. SHERMAN,M.P. et al; "The Behaviour of Hydrogen During Accidents in Light Water Reactors;" NUREG/CR- 1561, SAND80-1495 (1980 August). 6. DAVID, W.T. AND MANN, J.: Nature 150, 521 (1942). 7. KUEHL, D.K.: A.R.S.J. 32, 1724 (1962). 8. LEVY, A.: A I A A J . 1, 1239 (1963). 9. DIXon-LEwis, G. AND WILLIAMS, A.: AIAAJ. 1, 2416 (1963). 10. MULLER-DETHLEFS, K. AND SCHLADER, A.F.: Comb. Flame 27, 205 (1976). 11. FRANCE, D.H. AND PRITCHARD, R.: J. Inst. Fuel 49, 79 (1976). 12. EDMONDSON, H. AND HEAP, M.P.: Conlb. Flame 16, 161 (1971). 13. FRANCE, D.H. AND PRITCHARD, R.: Gaz W~irme International 26, (12), (1977). 14. WARNATZ, J.: Ber. Bunsenges. Phys. Chem. 82, 643 (1978). 15. WARNATZ,J.: Comb. Sci. Tech. 26, 203 (1981). 16. STEPHENSON, P.L. AND TAYLOR, R.G.: Comb. Flame 20, 231 (1973). 17. MULPCRU, S.R.; Spring meeting of the Combustion Institute Western Section, 1985 May 30, Waterloo, Ontario, Canada. 18. BAULCH,D.L., DRYSDALE,D.D., HORNY,D.G. AXD LLOYD, A.C.; Evaluated Kinetic Data for High Temperature Reactions; V. 1; Butterworths, London, 1972. 19. KUMAR, R.K. AND HOLLINGER, T.: J. Fire Sci. J u l y - A u g (1985). 20. FRIEDMAN,R.: Third Symposium (Int'l) on Combustion; p. 110, The Combustion Institute. Pittsburgh, PA, 1949.
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LAMINAR FLAMES
21. MELLISH, C.E. AND LINNETT, J.W.: Fourth Symposium (Int'l) on Combustion; p. 407 (1953). 22. MORGAN,G.H. AND KANE, W,R.: Fourth Symposium (Int'l) on Combustion, The Combustion Institute, Pittsburgh, PA, p. 313 (1953). 23. GLASSMAN, I.: Combustion, Academic Press Inc., 1977. 24. MASON, E.A., AND SAXENA, S.C.: The Physics of Fluids; I, 361 (1958) from Bird, R.B., Steward,
W.E., and Lightfoot, E.N.: Transport Phenomena, John Wiley and Sons Inc., N.Y. and London, 1960 25. GORDON,S. AND McBRIDE, B: National Aeronautics and Space Administration Report, NASA SP-273 (1971). 26. DIXON-LEwis, G.: Phil. Trans. Roy. Soc. A292 45-99 (1979).
COMMENTS H.S. Mukunda, Indian Institute of Science, India. With respect to some of the results on H2-Air, how do your results compare with earlier measurements and theory summarised in GAMM workshop? The earlier work seems to suggest that the diffusion model is responsible for differences. What is your diffusion model and is it appropriate? Author's Reply. Comparing our burning velocity measurements obtained on the 5 mm burner with those of previous workers, for H2-air mixtures over the range of 20% to 60% H2 in air, we find the best agreement (better than 4%) with the results of Edmondson and Heap 12 who used a 10.4 mm burner, France and Pritchard ~ who used a 7 mm burner and with the calculations of Warnatz. ~4 We do not have the GAMM workshop results but we have compared our model calculations for H2-air and H 2 - 0 2 with measured values from different sources assembled by Warnatz. ~ Ours are within the scatter in the measured values and within 7% of Warnatz calculated values. Different diffusion models employed in flame calculations have been compared by Coffee and Heimerl (Ref. 1, below). We have used method V of their paper (Fick's Law generalized to multicomponent mixtures) which has performed well compared with the more involved methods.
REFERENCES 1. COFVEE, T,P. aND HEIMERL,J.: Comb. and Flame, 43, 273 (1981).
P. Gray, University of Leeds, U.K. When values of thermal diffusivity are used to correct or normalize burning-velocities of diluted mixtures, to what temperatures do the values relate? Is it sufficient, for example, to use room temperature values? Is there any problem with mixing rules?
Author's Reply. The values used here relate to room temperature. We did, however, calculate thermal diffusivities, a, at several temperatures up to 1000~ (using the mixing rule for thermal conductivities from ref. 24 in the text). While c~ is strongly temperature dependent, we found (aJa) v2 to be quite insensitive to temperature. For example, with mixtures of H2 - 02 containing He, Ar, and N2 diluents, calculated values of (aJa) v2 at room temperature and at 1000~ differ by less than 3%. No significant improvement or worsening of our simple correlation was realized using the high temperature values. Mixtures containing steam appeared much more sensitive in this respect. The values for (ao/a) v2 at 1000~ were as much as 7% lower than the room temperature value. This could be partly due to the mixing rule for thermal conductivity being less precise for steam, a polar molecule.
C.K. Wu, Academy of Sciences, China. Since very small nozzles (3 mm dia) are used, the flame stretch effect (compression effect) must be quite pronounced and the flame curvature not negligible. These would cause a higher value of flame velocity measured with the approach velocity--cone angle method than the one-dimensional code. But if these factors were considered and corrections made, then the experimental flame speeds would be even further away from the computed values. Would you comment on the effect of such factors on the results of this study? Author's Reply. We have given experimental results for the effect of nozzle diameter on the measured burning velocity which show that beyond 5 mm diameter the effect is negligible for H2 flames. The 5 mm nozzle was used for all the H~-air-steam results. For smaller than 5 mm diameter nozzles, necessary for the very fast H2-O2flames, curvature effects are not negligible and have been corrected for by subtracting the experimentally-measured effect of the smaller nozzle (i.e., 0.27 m 9 s t for the 3 mm nozzle). In answer to your question, then, the data
H Y D R O G E N FLAMES D I L U T E D W I T H S T E A M have b e e n corrected for stretch a n d c u r v a t u r e effects, to t h e e x t e n t that these are related to nozzle diameter. T h a t o u r data are lower t h a n t h e calculated values is n o t u n e x p e c t e d since t h e calculation a s s u m e s adiabatic conditions.
C.K. Law, University of California at Davis, USA. Stretch effects are probably quite p r o m i n e n t in y o u r flame response because o f t h e high mobility o f h y d r o g e n a n d because o f t h e very small nozzles you used. If such stretch effects are not systematically substracted out, a t t e m p t s at extracting kinetic inform a t i o n o u t o f your stretch-influenced data m a y not be too m e a n i n g f u l .
1819
Author's Reply. Stretch effects, to the extent that they are related to t h e d i a m e t e r o f the b u r n e r nozzle were systematically s u b t r a c t e d o u t on the basis o f m e a s u r e m e n t s we have m a d e with different d i a m e t e r nozzles. We gave, in o u r description o f the a p p a r a t u s , e x p e r i m e n t a l results s h o w i n g t h e d e p e n d e n c e o f m e a s u r e b u r n i n g velocity on nozzle d i a m e t e r where the m e a s u r e m e n t s for 42% H2-air a p p r o a c h an asymptotic value at a b o u t 5 m m diameter. All H2-air-steam results were o b t a i n e d on the 5 m m nozzle. W h e r e use o f a smaller nozzle was necessary to m a i n t a i n l a m i n a r flow, for e x a m p l e , with the very fast H2-02 flames, the effects o f nozzle d i a m t e r are not negligible a n d have b e e n corrected by subtracting the e x p e r i m e n t a l l y - m e a s u r e d effect o f the smaller nozzle (i.e., 0.27 m . s -1 for t h e 3 m m nozzle.)
T H E EFFECT OF D I L U T I O N W I T H S T E A M O N T H E B U R N I N G V E L O C I T Y A N D S T R U C T U R E OF P R E M I X E D H Y D R O G E N FLAMES G.W. KOROLL AND S.R. MULPURU High-Temperature Chemistry Branch, Atomic Energy of Canada Limited, Whiteshelt Nuclear Research Establishment, Pinawa, Manitoba ROE ILO CANADA
A comparative study of the effects of diluents on the burning velocity of H~-Oz mixtures has been carried out focusing on the extraordinary effect of steam on burning velocity and flame structure. Burning velocities are measured by the nozzle-burner, cone angle method with particle tracking by laser doppler anemometry for a range of stoichiometries and diluent fractions (He, Ar, N> steam). New data are given for H2-air mixtures containing up to 50% steam. The tollowing correlation is obtained, which accurately predicts the physical effects of diluents (flame cooling and heat transport) on burning velocity: S~(~o/a) ]~2 = Suo(1 -X/XL). Here, S,, is the laminar burning velocity, ot is the thermal diffusivity, X is the mole fraction of diluent, XL is the diluent fraction sufficient to inert the mixture, and suffix 0 denotes the undiluted mixture. This correlation underestimates the burning velocity for steam diluent by 20%, indicating that steam influences the burning velocity by mechanisms other than flame cooling and heat transport. Using a one-dimensional flame model, we calculated in detail the changes to the flame structure caused by the addition of steam and determined that steam effects a redistribution of heat release in the flame. This is caused by the high third-body efficiency of steam in the exothermic reaction, H + O2 + M --+ HOz + M. Thus steam increases in the rate of this reaction and, subsequently, the rates of a cycle of exothermic reactions involving HOe in the preheat region of the flame. The result is a steeper temperature profile (i.e., a thinner flame) and an increased burning velocity. Sensitivity analysis indicates this mechanism produces the same effect on burning velocity as is observed experimentally upon adding steam.
1. Introduction T h e l a m i n a r b u r n i n g velocity, the local flame velocity relative to the u n b u r n t gas a n d n o r m a l to the flame front, is one o f the most useful f u n d a m e n t a l p a r a m e t e r s c h a r a c t e r i z i n g a combustible m i x t u r e 1, but b u r n i n g velocity data in the p r e s e n c e o f steam are f r a g m e n t a r y . Liu and M a c F a r l a n e 2, o b t a i n e d b u r n i n g velocity data for H2-air-steam m i x t u r e s c o v e r i n g a t e m p e r a t u r e r a n g e b e t w e e n 25~ a n d 250~ but limited to m i x t u r e s c o n t a i n i n g less that 15% steam. Despite w i d e s p r e a d advocacy o f steam for controlling c o m b u s t i o n processes 3 a n d the natural o c c u r r e n c e o f steam as a c o n s t i t u e n t in safetyrelated analysis 4,s, the m e c h a n i s m s by which steam influences c o m b u s t i o n are not well u n d e r stood. S t e a m is usually c o n s i d e r e d to behave as a simple d i l u e n t in combustion, l o w e r i n g the b u r n i n g velocity to the e x t e n t that it acts as a heat sink, and r e d u c e s the flame t e m p e r a t u r e . T h e limited data available indicate, h o w e v e r , that the r e d u c t i o n o f b u r n i n g velocity in the presence o f steam is n o t c o m m e n s u r a t e with changes to the
heat capacity o f the m i x t u r e . David and M a n n 6 o b s e r v e d moist flame t e m p e r a t u r e s to be h i g h e r than dry flame t e m p e r a t u r e s tbr o p e n H=,-air flames. Kuehl 7 observed an increase in b u r n i n g velocity u p o n r e p l a c i n g N2 with H 2 0 vapor in low-pressure Hz-air flames and postulated that steam accelerates b u r n i n g by increasing the radiative heat t r a n s p o r t f r o m the hot combustion p r o d u c t s to the water v a p o r in the u n b u r n t gas. O t h e r s o f f e r e d chemical kinetic interpretations o f the result 8'9. Muller-Dethlefs and Schlader 1~ studied the effect o f steam on the b u r n i n g velocity o f p r o p a n e and ethylene flames and c o n c l u d e d that steam did not act as an inert diluent but instead gave rise to greater heat release that c o u n t e r a c t e d the cooling effect o f the a d d e d steam. No m e c h a n i s m was offered, but the data are n o t e w o r t h y because they indicate that the a n o m a l o u s b e h a v i o u r of water v a p o r a p p e a r s to be c o m m o n to H2 and hydroc a r b o n flames. We have carried out an e x p e r i m e n t a l and theoretical investigation o f the influence o f steam on the b u r n i n g velocity o f p r e m i x e d
1811
1812
LAMINAR FLAMES
hydrogen flames. I n this paper, we report new data for the b u r n i n g velocities of H2-air-steam mixtures containing up to 50% steam. And, a comparative study of b u r n i n g velocities of three-component mixtures is made in which the influence of steam is examined in the context of a systematic replacement of diluents with different physical properties in H2-O2 mixtures. Using this approach, the physical effects that diluents have on b u r n i n g velocity by changing transport properties and adiabatic flame temperatures are established, a n d the existence and magnitude of chemical kinetic effects of steam diluent are identified. T h e kinetic mechanisms are assessed using a one-dimensional reactive flow model.
__
flame
ocket
] inert gas
III
burner
lo
c o m p r e s s e d gases
lhermoelecfric moss flow controller
2. Methods
2.1 Experimental T h e b u r n i n g velocities were measured by the nozzle-burner/schlieren cone angle method with particle tracking of the u n b u r n t gas velocity by dual-beam, laser doppler anemometry 241. Gas composition was maintained by thermoelectric mass-flow controllers individually calibrated for each gas to within - 0 . 1 % . A uniform nonfluctuating volume flow of steam was provided by evaportion of a precisely metered flow of distilled, degassed water. Steam content was verified to within 0.2% in separate tests in which steam was condensed at the b u r n e r exit at a rate that matched the input mass flow. The b u r n e r was fitted with an a n n u l a r chamber over its entire length (0.85 m) through which water/ ethylene glycol was circulated from a constanttemperature reservoir, to provide accurate control of the final u n b u r n t gas temperatures and to cool the nozzle (see Fig. 1). Prior to final temperature control, the gases containing steam were maintained at 120~ to prevent condensation. T h e b u r n e r diameter for all H2-air-steam experiments was 5 mm. For the faster b u r n i n g H2-O2-steam mixtures, it was necessary to use a 3-mm b u r n e r to avoid exceeding the critical Reynolds n u m b e r for laminar flow. The effect of flame curvature on the measured b u r n i n g velocity was quantified using burners with different diameters (hence flames of different radii of curvature). T h e measured b u r n i n g velocity of 42% Hz-air at 25~ was 3.82 m . s-* on a 2 m m b u r n e r , 3.55 m 9 s-1 on a 3 m m b u r n e r , 3.38 on a 4 m m b u r n e r and 3.28 on a 5 mm burner. Further increases in the nozzle diameter had a negligible effect on b u r n i n g velocity. This is consistent with the work of
sou cel
sleom
I
,ooeport,oleoeoero,or
FIG. 1. A schematic drawing of the burner and gas-handling system. France and Pritchard 1~, who observed no curvature effect for diameters between 8 mm and 12 mm. Our results using the 5-mm b u r n e r for H2-air mixtures at 25~ at atmospheric pressure, agree closely with those of Edmondson and Heap ~2 using a 10.4-mm b u r n e r and France and Pritchard ~a using a 7-mm burner, and with the calculations of Warnatz 14.
2.2 One-Dimensional Flame Model B u r n i n g velocities, heat release, temperature and species profiles in laminar H 2 - 0 2 flames were calculated by solving the one-dimensional conservation equations for overall continuity, individual species continuity and energy. T h e numerical method departs from that of earlier workers 14 ' l o"' 16 in employing Eulerian coordinates and has been described elsewhere 17. Temperature-dependence of transport properties and rate constants are included in the calculation. The reaction scheme is from Warnatz 15 with rate parameters from Baulch et al. Is. T h e calculation begins with user-defined initial profiles of species mass fractions and temperature. With a suitable grid-point system, the differential quotients are replaced by finitedifference expressions. T h e grid Peclet n u m b e r , IU1 9 &~/D, is kept less than 2 to resolve the interactions of convection and diffusion. Here, U is the flow velocity, Ax is the grid interval and D is a diffusion coefficient. Since the ratio [U[/D
HYDROGEN FLAMES DILUTED WITH STEAM decreases in the direction of the b u r n t gases, the grid interval can increase in the direction of the burnt gases, while satisfying the Peclet number restriction. T h e space derivatives are discretized on this non-uniform grid, using central differencing. T h e time derivative is discretized by first-order backward differencing. T h e non-linear reaction rate terms are linearized using a Taylor expansion, and the resulting matrix of linear equations is solved to advance the solution by a time step. T h e stiffness of the kinetic system is m a n a g e d by a variable time step obtained by the criterion [/1 At ~ 1, where ~1 is a parameter that represents a time constant for the changing species concentrations and temperature. This criterion insures that At is varied to resolve the fastest chemical timescale. Thus, the solution is "marched" forward, step by step, in time until a s t e a d y state is reached. T h e b u r n i n g velocity, which then remains the only unknown, is extracted from the steady-state solution.
3. R e s u l t s a n d D i s c u s s i o n
3.1 112-02 Diluent Mixtures To u n d e r s t a n d the physical effects of dilution on b u r n i n g velocity, b u r n i n g velocities were measured for H2-O 2 mixtures containing the diluents He, Ar, and N2 at ambient temperature and pressure. Measurements were made for selected ratios of H2-02 with each diluent over the range of diluent fractions that provided a stable flame. Results are shown in Fig. 2, for stoichiometric flames. In all cases, the burning velocity decreased with increasing fraction o f diluent gas and extrapolated smoothly to intercept the x-axis at a point that corre-
~'~ O.0
~ 0~-..~
--o..o
"E 4.0
o
I OA
P 0.2
I
I
I
I
0.~,
0.4
0.5
0.6
L ~ _ J 0.7
0.8
0.9
Mole fraction diluent
Fro. 2. Burning velocities of 2:1 H2-O2 mixtures at 298 K with the diluents He(O), Ar(A) and N2([~). Solids denote the respective inerting diluent fractions from ref. 19.
1813
sponded to the independently measured ~9 inerting fraction for the particular diluent. Yhe results were qualitatively consistent with previous work 13'2~ We assessed the effect of the diluents initially in terms of a well-known general expression ~:~, where b u r n i n g velocity is represented as the product of a transport term and a reaction rate term. S~= - -
\ PCt/
.(reaction rate) 1/2.
(1)
Replacement of one chemically inert diluent for a n o t h e r will alter the t r a n s p o r t term in Eq. (1) if the diluents differ in density p, heat capacity Ct,, or thermal conductivity, X. Diluents differing in heat capacity will also change the rate term to the extent that the)' change the flame t e m p e r a t u r e and thus the rates of high activation energy steps. These are the physical effects constituting "ideal" diluent behaviour, and are different from effects caused by direct or catalytic participation by the diluent h~ reaction kinetics. A practical expression for predicting the physical effects is obtained as follows. T h e transport term is the thermal diffusivity, c~, and is calculated 24 in detail for all mixtures at 298 K. T h e r m a l diffusivities for each mixture containing diluent are normalized with respect to the undiluted mixture, c~,,, to obtain the "relative thermal diffusivity", %/e~, a factor containing the contribution of a d d e d diluent to the transport term of Eq. (1) relative to the undiluted mixture. While c~ is a t e m p e r a t u r e d e p e n d a n t quantity, c~0/c~ is relatively insensitive to temperature. A calculation of %/or at 1000 K indicated an increase relatixe to the 298 K value of 1% to 2% for He, Ar, and N2 diluents, and slightly more for steam, d e p e n d i n g on concentration. Figure 3 shows the result of multiplying the measured burning velocities of mixtures containing He, At, or N2 by the factor (C~o/C0le fbr the respective mixtures. T h e r e is a linear d e p e n d e n c e of the corrected b u r n i n g velocity, S,,(%/o01/2 with a d d e d diluent fraction. Tlae x-intercept of the straight line remains at the diluent fraction corresponding to the flammability limit for downward propagation for the respective diluent, XL, as m e a s u r e d by Kumar and Hollinger 19. Helium and Ar have identical molar heat capacities and, therefore, the same adiabatic flame temperatures, but they differ in their effects on the b u r n i n g velocities through different thermal diffusivities. Nitrogen and Ar have nearly identical thermal diffusivities.
1814
LAMINAR FLAMES change in the b u r n i n g velocity, but, in our experiments when 25% N2 was replaced in a stoichiometric mixture with 25% 02, the burnin~ velocity increased from 6.5 m" s -1 to 8.3 m"
12.0 I0,0
S .-e -~
8.0
S-'.
6.0
Oxygen participates directly in two reactions in the H 2 - 0 2 reaction scheme~5:
4.0
H + O2~OH
+ O
(R1)
2.0 I
I
I
I
I
[
I
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Mole
fraction
H + 02 + M - ~
I"l~
0.8
diluent
FIG. 3. Burning velocities of 2:1 H2-O= mixtures with He(@), Ar(A) and N2([~) diluents corrected for relative thermal diffusivity. Solid line is the prediction of Eq. (2). Therefore, differences in their effect on burning velocity can be interpreted in terms of different flame t e m p e r a t u r e s arising from their different heat capacities. Since flammability limits are strongly d e p e n d e n t on the heat capacity of the gas mixture, XL values for mixtures with N2 are naturally lower than for mixtures with noble gases. What is important is that a change in the heat capacity of the diluent changes only the slope of the straight line correlation of Su(eo/e) r/2 with the diluent fraction. This behaviour is summarized in Eq. (2).
Su(o~o/~)l/2=Soo(]ff--~).
HO2 4- M
(R2)
09
(2)
Equation (2) has general utility; given the burning velocity of the undiluted mixture, Suo, and the inerting diluent fraction, Xb the burning velocity, S,, can be estimated for any fraction of inert diluent, X. Equation (2) is accurate for lean and rich flames containing He, Ar or N2 that can be stabilized on a burner. It is probably i n a p p r o p r i a t e for near-limit mixtures, but for fast b u r n i n g mixtures Eq. (2) provides the criterion we require for ideal diluent behaviour; it predicts the physical effects of a diluent on b u r n i n g velocity. Behaviour different from that o f Eq. (2) suggests that the diluent contributes to mechanisms other than flame cooling and heat transport. This premise is tested by the case of excess O2. 3.2 Mixtures with Excess 02 Nitrogen and 02 have nearly identical Cp, X and p, so the r e p l a c e m e n t o f N2 diluent with 02 in a stoichiometric mixture will not significantly change the thermal diffusivity or the adiabatic flame t e m p e r a t u r e 25. Equation (2) predicts no
In the mixture containing 50% H2 + 25% 0 2 "k" 25% N2, replacing N2 with 0 2 effectively doubles the concentration of 02 and hence, the rates of reactions (R1) and (R2). The burning velocities were calculated, using the computer model, for the mixture containing 25% N2 and the mixture with N2 replaced by 25% excess O2. T h e calculated burning velocities were, respectively, 6.8 m . s -1 and 8.1 m 9 s -1, in good relative agreement with the values of 6.5 m 9 s -a a n d 8.1 m . s -1 observed experimentally. T h e calculation was repeated for the mixture containing 25% N2 with kl, the rate constant for reaction (R1), artificially doubled in the reaction scheme to simulate the effect o f reaction (R 1) on b u r n i n g velocity when replacing N2 with O2. T h e burning velocity increased from 6.8 m 9 s -] to 7.4 m ' s -1, about half tlae total observed effect of doubling [02]. Finally, k] and k2 were both doubled to simulate the combined effect of both reactions (R1) and (R2) when [02] is doubled. T h e result was a burning velocity o f 8.2 m . s -1, which was nearly the same as the value o f 8.3 m" s -] when [02] was doubled. Thus, the increase in burning velocity when N2 is replaced in a stoichiometric mixture by excess 02 is directly due to the proportional increase in the rates of'reactions (R1) and (R2). T h e case o f O2 "diluent" demonstrates that d e p a r t u r e s from the prediction of Eq. (2) are quantitatively linked to the participation of the diluent in reaction kinetics. 3.3 H2-Air Steam and H2-O2-Steam Mixtures Figure 4 summarizes the results of burning velocities for Hz-air-steam mixtures at 100~ T h e range of H2 concentrations shown is indicative of the range o f mixtures that could be stabilized on the burner. For steam fractions less than 15%, the present results compare favorably with those o f Liu and MacFarlane 2. Their data are consistently higher by a small amount attributable to the flame curvature effect due to their use of a smaller nozzle. T h e effect of steam on flame mechanisms is exa-
HYDROGEN FLAMES DILUTED WITH STEAM mined using the simpler three-component mixtures of H2-O2-steam. In Fig. 5, the b u r n i n g velocities are compared for H2-02 mixtures at 100~ containing N2 and steam. For diluent fractions less than 45%, replacement of N2 with steam increases the b u r n i n g velocity, contrary to what is expected on the basis of the lower adiabatic flame temperature with steam. In Fig. 6, the data for steam are corrected for relative thermal diffusivity a n d plotted with the prediction of Eq. (2) for ideal diluent behaviour. Equation (2) underpredicts the b u r n i n g velocity by 20% (for a mixture containing 25% steam), suggesting that steam, like oxygen, influences the b u r n i n g velocity through mechanisms other than flame cooling and heat transport. Beyond 60% steam, flame cooling mechanisms probably dominate and normal behavior is observed. With the addition of steam there would be an increase in the reverse rates of the partially equilibrated reactions (R3) and (R4), possibly causing an increase [OH]. OH + H2 ~ H2O + H
However, in both cases the reverse reactions are slow (i.e., high activation energy) and the rates are more likely to decrease with added steam due to lower flame temperatures. As a more likely mechanism for the effect, we examined the role of steam as a third-body catahst in the recombination reactions (R2), (RS) and (R6). i
i
i
i
i
i
140
E ~
r2
o, ,A~,~
~.,0=o ~
a
2 I
I
OI
i
=
16
(R3)
OH + OH ~-~ H20 + O
1815
I
02
03
(R4)
0.4
0,5
06
0.7
08
Mole fraction diluent
Flo. 5. Burning velocities of" 2:1 H2-O2 mixtures at 373 K with the diluents N2(A) and steam (O).
i
% steom 00% <>12%
i~ I
I
i
i
i
=
,
i
I
0.2
03
04
0.5
06
0 ,'
0,8
a 22% x 33%
4.0
z~ 4 3 %
9 50% E
3.0
E
O
12
_o I-
14(
IC 8
2.0
6 4
1.0 2 i
0.I 01 .
I
2
I
0.4
I
I
0.6
I
0.8
Volume fraction H2/H2 + air
FIG. 4. Burning velocities of H2-air-steam mixtures at 373 K using a 5-mm nozzle.
Mole fraction steam
FIG. 6. Burning velocities of 2:1 H2-02 mixtures at 373 K with steam diluent, corrected for relative thermal diffusivity. Solid line is the prediction of Eq. (2).
1816
LAMINAR FLAMES H + 02 + M---~ HO2 + M
(R2)
H + H + M---~ H2 4- M
(R5)
T{K) 0.24 2800
Burning Velocity 8.9 m's "= O9
H + O H + M---* H20 + M
H"
(R6)
O.O06
~-
//-. ~
0004
where
/H02
0.oo
~
.~'~ ~
0.
~
~-~.
/~=/ "
0
The net effect is, 2H2 + 02 ~ 2H20 + 482 kJ. The sensitivity of b u r n i n g velocity to thirdbody efficiency was tested in another computer experiment where the third-body efficiency coefficient for steam was artificially changed in our model to that of N2 (i.e., from 6.0 to 0.4). The results appear in Fig. 7c. The b u r n i n g velocity was very sensitive to the change, decreas!ng from 9.8 m 9 s -1 to 7.8 m . s -a. [HO2] and Q values were virtually the same as for N2 diluent. The high [OH] failed to persist with
0.16
"....
001
0.04
002
2000
0.12 1600
x IO I o ~ . : . . . . . ."OH ::::::-.-.:-]o.oe
[M] = [H2]+0.4[O2]+0.4[N2]+ 6.0[H20] 15. The high third-body efficiency coefficient of steam in these reactions is well documented 18, particularly for reaction (R2). Reaction (R2) is exothermic and initiates a cycle of exothermic, low-activation reactions of HO2 with H., .OH and O., in all, an important source of heat in the flame 26. We calculated b u r n i n g velocities and flame structures for the stoichiometric mixtures at 100~ containing 25% N2 and for the same mixture with N2 replaced by steam. Nitrogen is retained for comparison because it was earlier demonstrated to behave as a simple diluent. The results are compared in Figs. 7a and 7b. The calculated b u r n i n g velocities with N2 and steam diluents were 8.9 and 9.8 m 9 s -1, respectively, compared with 8.4 and 9.3 m 9 s-1 observed experimentally. It is reasonable that the calculated values were systematically higher by a small a m o u n t because the calculation assumed an adiabatic system. For the mixture with steam diluent, [HO2] is greater by a factor of 3 and [OH] is increased by ~30%. There is a significant redistribution of the heat release, Q, towards the u n b u r n t gas, resulting in a temperature profile also shifted towards the unb u r n t gas. These differences in flame structure between N2 and steam diluents are consistent with an increase in the rate of reaction (R2), resulting from the high third-body efficiency of steam. A typical sequence of reactions consistent with the increased [HO2] and the upstream shift of Q is, H + O 2 + M --~ H O z + M A H = - 196kJ/mol HOg+H ~ 2OH d~H=-160kJ/mol 2(OH+H2)---* 2 ( H 2 0 + H ) AH= 2 ( - 6 3 ) = - 126 kJ/mol
t
0.20 2400
T ~
0.008
00 004
003
,2oo 800 40O
Distonce into The Florae (cm)
j
8urnin9 Velocity 9.8m.$ "t O*OIC ~t i
O,OOE O-OOE
..~
BO
//'
2 0.004
\,\
T~ ~
I
Q
T(K)
0.20
2400
016
2000
.~.H.
~ - - - ~ ............. 0.,2 , ~ o o ~'~. o ioo8,2oo __c ..........
"OH xlO- - - ' ....
...
.....
o.00~ ' J 0.0
~
'
"
.......... 001
~ . . . . . . 0.02 0 03
qo o 0.04
4oo
DisTonce into the FlOrae (era) i
Q
Burning VelociTy 7,Bm,s "1 H"
001
o=-
T(K)
0 20
2400
0 .I 6
2000
0,12
1600
/ /'
~ O9 ,/
_~0.006
T ~---
o
/:f/
9~0 004
9
--
~~ " /f
0.002
09
O.O1
0.02
. 008
,20o
- - -.7_.-.:...-.=
" .-.--:6;;-~,o-'
003
- o04
coo
004
Disfonce info the Flome(cm)
FIG. 7. Calculated flame structures for 2:1 H2-O2 mixtures at 373 K (a) containing 25% N~ diluent, (b) containing 25% steam diluent, (c) containing 25% steam diluent and the third-body coefficient of steam artificially changed in the code from 6.0 to 0.4 lowered third body efficiency for steam. This indicates that the increased [OH] with added steam does not arise directly via reactions (R3) and (R4) since these d e p e n d on [H20] not third body efficiency. T h e most notable change in flame structure was the nearly 600 K decrease in the temperature profile in the reaction zone, which undoubtedly contributed to the sharp decrease in the b u r n i n g velocity. With the high third body efficiency of steam artificially reduced to that of an ideal diluent such as N2, steam exhibits the effect expected on the basis of its high heat capacity--a reduced b u r n i n g velocity due to a reduced flame temperature in the reaction zone. Moreover, b u r n i n g velocity calculated using the artificially reduced thirdbody efficiency agrees with the prediction of
HYDROGEN FLAMES DILUTED WITH STEAM Eq. (2). H i g h t h i r d - b o d y efficiency appears to be the principal cause o f the n o n - i d e a l behaviour o f steam diluent on b u r n i n g velocity. It r e m a i n s to separate the n e t effect o f t h i r d - b o d y efficiency into the relative effects o f reactions (R5) and (R6) as radical sinks and reaction (R2) as a heat source. C o n s i d e r again the p r e v i o u s r u n where the t h i r d - b o d y coefficient o f steam was r e d u c e d in the code f r o m 6.0 to 0.4. T h i s c h a n g e d [M] and hence the overall rates o f each o f the reactions (R2), (R5) and (R6) by a factor o f V4. T h e effect on calculated b u r n i n g velocity was a decrease, f r o m 9.8 m 9 s -1 to 7.8 m 9 s -1. I n a n o t h e r e x p e r i m e n t , the r e d u c t i o n in t h i r d - b o d y efficiency was c o m p e n s a t e d in reaction (R2) by increasing k2 by a factor o f 4. T h e resulting b u r n i n g velocity was 9.9 m 9 s -~. F r o m this we c o n c l u d e that the c o m b i n e d contribution o f reactions (R5) and (R6) to the effect o f thirdbody coefficient on the b u r n i n g velocity is a decrease by 0.1 m . s -1, a negligible a m o u n t . T h u s , the increased b u r n i n g velocity in the p r e s e n c e o f steam is p r i m a r i l y d u e to an increase in the rate o f reaction (R2) and the resulting increased rate o f h e a t release in a heat-deficient zone o f the flame n e a r the u n b u r n t gas. T h e c o n c u r r e n t d r a i n on chain carriers by reactions (R5) a n d (R6) is o f m i n o r i m p o r t a n c e in its effect on b u r n i n g velocity. F u t h e r m o r e , t h e r e r e m a i n s a vanishingly small role for radiant heat t r a n s p o r t m e c h a n i s m p r o p o s e d by Kuehl or reactions (R3) and (R4) c o n t r i b u t i n g to the o b s e r v e d b e h a v i o u r o f steam diluent.
Conclusions A c o m p a r a t i v e study o f d i l u e n t effects on the b u r n i n g velocity o f H 2 - 0 2 m i x t u r e s was carried out, with emphasis on the effect o f steam diluent. T h e diluents studied r e d u c e the b u r n ing velocity in the o r d e r o f N 2 > A r > H z O > H e . With the e x c e p t i o n o f steam, t h e effect o f diluents o n b u r n i n g velocity c o n f o r m to a correlation based on the t h e r m a l diffusivity o f the m i x t u r e s and flammability limits. New data were given for Hz-air-steam a n d H2-Oz-steam mixtures. S t e a m diluent, by virtue o f its high t h i r d - b o d y efficiency in the reaction H + 02 + M ~ HO2 + M, increases the heat release rate in the p r e h e a t zone o f the flame resulting in an increase in t e m p e r a t u r e in the reaction zone o f several h u n d r e d degrees. T h e increase in b u r n ing velocity caused by this m e c h a n i s m c o u n t e r acts the physical effect o f steam o f r e d u c i n g flame t e m p e r a t u r e .
1817
Acknowledgment This work was conducted at the Whiteshell Nuclear Research Establishment (WNRE) of Atomic Energy of Canada Limited (AECL), Pinawa, Manitoba. Financial support from Ontario Hydro, HydroQuebec, New Brunswick Electric Power Commission and AECL-CANDU Operations in a joint funding agreement with AECL-WNRE (COG-CANDEV 1984/85 number 435) is gratefully acknowledged. REFERENCES 1. RALLIS, C.J. AND GARFORTH,A.M.: Prog. Energ Combust. Sci. 6, 303 (1980). 2. Lm, D.D.S. AND MACFARLANE, R.: Comb. Flame 49, 59 (1983). 3. DRYER, F.L.: Sixteenth Symposium (Int'l) on Combustion, P. The Combustion Institute, Pittsburgh, PA 1976. 4. LIE, D.D.S., HARRISON, W.C., TAMM, H., MACFARLANE, R. AND CLEGG, L.J.: "Canadian Hydrogen Combustion Studies Related to Nuclear Reactor Safety Assessment;" Atomic Energy of Canada Limited Report, AECL-6994 (1980). 5. SHERMAN,M.P. et al; "The Behaviour of Hydrogen During Accidents in Light Water Reactors;" NUREG/CR- 1561, SAND80-1495 (1980 August). 6. DAVID, W.T. AND MANN, J.: Nature 150, 521 (1942). 7. KUEHL, D.K.: A.R.S.J. 32, 1724 (1962). 8. LEVY, A.: A I A A J . 1, 1239 (1963). 9. DIXon-LEwis, G. AND WILLIAMS, A.: AIAAJ. 1, 2416 (1963). 10. MULLER-DETHLEFS, K. AND SCHLADER, A.F.: Comb. Flame 27, 205 (1976). 11. FRANCE, D.H. AND PRITCHARD, R.: J. Inst. Fuel 49, 79 (1976). 12. EDMONDSON, H. AND HEAP, M.P.: Conlb. Flame 16, 161 (1971). 13. FRANCE, D.H. AND PRITCHARD, R.: Gaz W~irme International 26, (12), (1977). 14. WARNATZ, J.: Ber. Bunsenges. Phys. Chem. 82, 643 (1978). 15. WARNATZ,J.: Comb. Sci. Tech. 26, 203 (1981). 16. STEPHENSON, P.L. AND TAYLOR, R.G.: Comb. Flame 20, 231 (1973). 17. MULPCRU, S.R.; Spring meeting of the Combustion Institute Western Section, 1985 May 30, Waterloo, Ontario, Canada. 18. BAULCH,D.L., DRYSDALE,D.D., HORNY,D.G. AXD LLOYD, A.C.; Evaluated Kinetic Data for High Temperature Reactions; V. 1; Butterworths, London, 1972. 19. KUMAR, R.K. AND HOLLINGER, T.: J. Fire Sci. J u l y - A u g (1985). 20. FRIEDMAN,R.: Third Symposium (Int'l) on Combustion; p. 110, The Combustion Institute. Pittsburgh, PA, 1949.
1818
LAMINAR FLAMES
21. MELLISH, C.E. AND LINNETT, J.W.: Fourth Symposium (Int'l) on Combustion; p. 407 (1953). 22. MORGAN,G.H. AND KANE, W,R.: Fourth Symposium (Int'l) on Combustion, The Combustion Institute, Pittsburgh, PA, p. 313 (1953). 23. GLASSMAN, I.: Combustion, Academic Press Inc., 1977. 24. MASON, E.A., AND SAXENA, S.C.: The Physics of Fluids; I, 361 (1958) from Bird, R.B., Steward,
W.E., and Lightfoot, E.N.: Transport Phenomena, John Wiley and Sons Inc., N.Y. and London, 1960 25. GORDON,S. AND McBRIDE, B: National Aeronautics and Space Administration Report, NASA SP-273 (1971). 26. DIXON-LEwis, G.: Phil. Trans. Roy. Soc. A292 45-99 (1979).
COMMENTS H.S. Mukunda, Indian Institute of Science, India. With respect to some of the results on H2-Air, how do your results compare with earlier measurements and theory summarised in GAMM workshop? The earlier work seems to suggest that the diffusion model is responsible for differences. What is your diffusion model and is it appropriate? Author's Reply. Comparing our burning velocity measurements obtained on the 5 mm burner with those of previous workers, for H2-air mixtures over the range of 20% to 60% H2 in air, we find the best agreement (better than 4%) with the results of Edmondson and Heap 12 who used a 10.4 mm burner, France and Pritchard ~ who used a 7 mm burner and with the calculations of Warnatz. ~4 We do not have the GAMM workshop results but we have compared our model calculations for H2-air and H 2 - 0 2 with measured values from different sources assembled by Warnatz. ~ Ours are within the scatter in the measured values and within 7% of Warnatz calculated values. Different diffusion models employed in flame calculations have been compared by Coffee and Heimerl (Ref. 1, below). We have used method V of their paper (Fick's Law generalized to multicomponent mixtures) which has performed well compared with the more involved methods.
REFERENCES 1. COFVEE, T,P. aND HEIMERL,J.: Comb. and Flame, 43, 273 (1981).
P. Gray, University of Leeds, U.K. When values of thermal diffusivity are used to correct or normalize burning-velocities of diluted mixtures, to what temperatures do the values relate? Is it sufficient, for example, to use room temperature values? Is there any problem with mixing rules?
Author's Reply. The values used here relate to room temperature. We did, however, calculate thermal diffusivities, a, at several temperatures up to 1000~ (using the mixing rule for thermal conductivities from ref. 24 in the text). While c~ is strongly temperature dependent, we found (aJa) v2 to be quite insensitive to temperature. For example, with mixtures of H2 - 02 containing He, Ar, and N2 diluents, calculated values of (aJa) v2 at room temperature and at 1000~ differ by less than 3%. No significant improvement or worsening of our simple correlation was realized using the high temperature values. Mixtures containing steam appeared much more sensitive in this respect. The values for (ao/a) v2 at 1000~ were as much as 7% lower than the room temperature value. This could be partly due to the mixing rule for thermal conductivity being less precise for steam, a polar molecule.
C.K. Wu, Academy of Sciences, China. Since very small nozzles (3 mm dia) are used, the flame stretch effect (compression effect) must be quite pronounced and the flame curvature not negligible. These would cause a higher value of flame velocity measured with the approach velocity--cone angle method than the one-dimensional code. But if these factors were considered and corrections made, then the experimental flame speeds would be even further away from the computed values. Would you comment on the effect of such factors on the results of this study? Author's Reply. We have given experimental results for the effect of nozzle diameter on the measured burning velocity which show that beyond 5 mm diameter the effect is negligible for H2 flames. The 5 mm nozzle was used for all the H~-air-steam results. For smaller than 5 mm diameter nozzles, necessary for the very fast H2-O2flames, curvature effects are not negligible and have been corrected for by subtracting the experimentally-measured effect of the smaller nozzle (i.e., 0.27 m 9 s t for the 3 mm nozzle). In answer to your question, then, the data
H Y D R O G E N FLAMES D I L U T E D W I T H S T E A M have b e e n corrected for stretch a n d c u r v a t u r e effects, to t h e e x t e n t that these are related to nozzle diameter. T h a t o u r data are lower t h a n t h e calculated values is n o t u n e x p e c t e d since t h e calculation a s s u m e s adiabatic conditions.
C.K. Law, University of California at Davis, USA. Stretch effects are probably quite p r o m i n e n t in y o u r flame response because o f t h e high mobility o f h y d r o g e n a n d because o f t h e very small nozzles you used. If such stretch effects are not systematically substracted out, a t t e m p t s at extracting kinetic inform a t i o n o u t o f your stretch-influenced data m a y not be too m e a n i n g f u l .
1819
Author's Reply. Stretch effects, to the extent that they are related to t h e d i a m e t e r o f the b u r n e r nozzle were systematically s u b t r a c t e d o u t on the basis o f m e a s u r e m e n t s we have m a d e with different d i a m e t e r nozzles. We gave, in o u r description o f the a p p a r a t u s , e x p e r i m e n t a l results s h o w i n g t h e d e p e n d e n c e o f m e a s u r e b u r n i n g velocity on nozzle d i a m e t e r where the m e a s u r e m e n t s for 42% H2-air a p p r o a c h an asymptotic value at a b o u t 5 m m diameter. All H2-air-steam results were o b t a i n e d on the 5 m m nozzle. W h e r e use o f a smaller nozzle was necessary to m a i n t a i n l a m i n a r flow, for e x a m p l e , with the very fast H2-02 flames, the effects o f nozzle d i a m t e r are not negligible a n d have b e e n corrected by subtracting the e x p e r i m e n t a l l y - m e a s u r e d effect o f the smaller nozzle (i.e., 0.27 m . s -1 for t h e 3 m m nozzle.)