The dependence of flame propagation in H2O2N2 mixtures on temperature, pressure, and initial composition

Int. J, Hydrogen Energy. VoL 10. No. ] 1. pp. 749-755, 1985.

0360-3199/85 $3.00 + 0.00 Pergamon Press Ltd. © 1985 International Association for Hydrogen Energy

Printed in Great Britain.

THE D E P E N D E N C E OF F L A M E PROPAGATION IN H2-O2-N2 MIXTURES ON T E M P E R A T U R E , PRESSURE, AND INITIAL COMPOSITION F. BEHRENDT and J. WARNATZ Angewandte Physikalische Chemic der Universitiit Heidelberg und Sonderforschungsbereich 123, Im Neuenheimer Feld 253, D-6900 Heidelberg, W. Germany (Received 4 April 1985)

AbstraetmHydrogen combustion in premixed flames is simulated with aid of a reaction mechanism consisting of 25 elementary reactions. Concentration-, pressure-, and temperature-dependence of flame velocities in Hz--O~ N2 mixtures are described in a wide range of conditions. Furthermore, NO formation in H2-air flames is reproduced. A sensitivity analysis is presented demonstrating the influence of the elementary reactions involved in the mechanism.

A cp h r t T v w x z a )~, p

these reasons, this system shall be studied in this p a p e r once more.

NOMENCLATURE area ratio binary diffusion coefficients specit~c heat capacity specific enthalpy mass scale chemical rate of formation time temperature velocity mass fraction mole fraction cartesian space coordinate mixture heat conductivity species thermal conductivity density

CALCULATION METHOD For a quantitative treatment of premixed laminar flat flames the corresponding conservation equations imust be solved in their one-dimensional form. ConserVation of enthalpy and of mass of species i leads to the! time dependent equations [9-11]: OT OT OT p " ~ ' [ = - p v ' ~ ' ~ - j s ~'~z

LL(zo___r + cp Oz \

INTRODUCTION There are several reasons to study the combustion in hydrogen-oxygen-nitrogen mixtures in detail: (1) Hydrogen combustion may play an important part in future technologies. Therefore, a detailed knowledge of hydrogen flames at various conditions (especially at conditions experimentally inaccessable) is desirable; (2) The oxohydrogen reaction system with its chain-branching processes plays a predominant part in hydrocarbon combustion [1, 2]; (3) The hydrogen flame is the only system relevant to technology for which a complete detailed set of elementary reactions can be presented [3--6] in contrary e.g. to hydrocarbon combustion; (4) Hydrogen-air flames are suitable candidates for the study of Zeldovich-NO formation without disturbance by NO formed via hydrocarbon radicals [2]. A study of hydrogen flames has been published several years ago [7]. In the meantime, the mechanism and transport model used in this publication has become obsolete. Furthermore, a new interpretation of experimental results on flame velocities in the hydrogenoxygen-nitrogen system seems to be necessary [8]. For

Z,,h, cp

(1)

Oji + ri Oz

(2)

Oz.]

Owi Owi p - ~ = - pv Oz

where the diffusion fluxes Ji and the mean diffusion flux Jn are given by Owi 0In T ~,cp,iji ( 3 ) Ji = - D i, M p " ~ g - D r , i ' - - ~ - z ,. In = CO A simplified transport model given by equation (4)

D,,M = ~ x j / ~ j , ;~=½

.

~ xv~ + Zx~/,~i

(4)

j-~i

is used, because comparison with multicomp0nent transport models leads to errors relatively small if compared to that caused by uncertainties in the reaction mechanism [9, 12, 13]. For freely propagating flames, the fluxes ji vanish at the cold boundary, if it is placed far enough into the unburnt gas region. Accordingly, the boundary conditions are given by [1, 12, 14]:

749

wi.c = w i , , ; Tc = T,.

(5)

750

F. B E H R E N D T AND J. W A R N A T Z Table 1. Molecular parameters Species H O H., Oz H.,O N:

(I0 -t° m)

e/k(K)

2.05 2.75 2.92 3.46 2.60 3.62

145 80 38 107 572 97

# (Debye)

H e r e the i n d i c e s u a n d c d e n o t e the u n b u r n t gas and the cold gas at the b u r n e r s u r f a c e . T h e h o t b o u n d a r y c o n d i t i o n s are g i v e n by a m e a n v a l u e of that d e f i n e d by c o n d i t i o n s of v a n i s h i n g s l o p e and of c o n s t a n t s l o p e b o t h of t e m p e r a t u r e a n d mass f r a c t i o n p r o f i l e [14]. T h e i n p u t data for the d e t e r m i n a t i o n of the t r a n s p o r t p r o p e r t i e s ( L e n n a r d - J o n e s p o t e n t i a l p a r a m e t e r s 6 and e, d i p o l e m o m e n t /~, p o l a r i z a b i l i t y o~, and r o t a t i o n a l r e l a x a t i o n c o l l i s i o n n u m b e r Z,o,, see [10]) are g i v e n in T a b l e 1. T h e r m o c h e m i c a l data are t a k e n from the

a'(10-3° m3)

Zro, (298 K)

0.79 1.60

280 3.8 4.0 4.0

1.844 1.76

J A N A F T a b l e s [15] a n d a d d e n d a . T h e m e c h a n i s m and rate data are d i s c u s s e d in the next s e c t i o n .

REACTION MECHANISM T h e e x t e n s i v e l i t e r a t u r e on the h y d r o g e n - - o x y g e n r e a c t i o n s h a l l n o t be d i s c u s s e d h e r e in d e t a i l , s i n c e t h e r e are c o m p r e h e n s i v e r e v i e w s on the e l e m e n t a r y r e a c t i o n s and rate coefficients in this s y s t e m [3, 6, 16, 17]. An a p p r o p r i a t e c o m b i n a t i o n of the s p e c i e s t a k i n g

Table 2. Reaction mechanism Number 1 2 3 4 5 6 7 8 9(a) 9(b) 10 11 12 13 14 15 16 17 18 19 20 21 22 23

24 25 26 27 28

Reaction OH H H O O H OH H20

H H H O H H H O OH HO2

HO2 OH HzO2 HzO2 H2 H20 2 H20 2 H202 O N N

+ H2 + H20

+ 02 + OH + H2

~ H20

+ + --~ OH + --* H + ~ OH + ---* O + ~H20 + --, OH + + M" ---, H2 + + H2 ~ H2 + +M'---,H20 + + M' ---* 02 + + M' ~ HO2 + " , OH + -'-" H2 + ~OH + ~H20 + -'* OH

+ OH + OH + O + H + H + OH + O + O2 + HOz + HO2 +HO2 + HO2 + HO2 -'-" H202 + M' --*H + OH + M ' - - ~ H 2 0 2 + M' ~OH + H "-" H2 + HO2 ---" H202 + H "-* H20 + O ~ OH + OH -" H20 + N2 "-'NO + 02 ----, NO + OH ~NO

H H2 O O2 H H2 O OH M" H2 M' M' M' OH 02 02 02

+ 02

+ + + + + + + + + + +

02 + M' M' OH + M' HO2 H OH HO2 HO2 N O H

k = A ( T / K )b exp( - E / R T ) M' = 1.00 (Hz) + 6.50 (HzO) + 0.40 (02) + 0.40 (N2) M" -- 6.50 (HzO) + 0.40 (02) + 0.40 (Nz)

A ( c m , mol, s)

T-Exp

1.00 E + 08 4.60 E + 08 7.80 E + 15 4.70 E + 14 1.50 E + 07 6.70 E + 06 1 . 5 0 E + 09 1.50 E + 10 1.80 E + 18 9.70 E + 16 2.20E+22 2.90 E + 17 2.00 E + 18 1.50 E + 14 2.50 E + 13 2 . 0 0 E + 13 2 . 0 0 E + 13 2.00 E + 12 5 . 0 0 E + 15 3 . 3 0 E + 22 3 . 0 0 E + 17 1.70 E + 12 7.30 E + 11 1.00 E + 13 2.80 E + 13 7.00 E + 12 1 . 8 0 E + 14 6.40 E + 09 3 . 0 0 E + 13

1.60 1.60 -0.55 -0.55 2.00 2.00 1.14 1.14 -1.00 -0.60 -2.00 -1.00 -0.80 0 0 0 0 0 0 -2.00 0 0 0 0 0 0 0 1.0 0

E(kJ/mol) 13.80 77.70 70.38 0 31.60 23.30 0 72.20 0 0 0 0 0 4.20 2.90 0 0 0 191.20 0 190.00 15.70 78.10 15.00 26.80 6.00 319.0 26.2 0

THE DEPENDENCE OF FLAME PROPAGATION part in this reaction yield about 80 reactions which can occur theoretically. However, about 50 of these are negligible as can be shown by relatively simple arguments (large activation energy, etc.). The remaining 30 reactions are then included in the calculations. On the basis of these calculations further reactions can be eliminated by the criteria discussed elsewhere [1, 5]. The result of this elimination procedure is given in Table 2. There are 25 reactions remaining. Reactions (1) to (8) are the well known H2--O2 chain reactions together with their reverse reactions. Besides, there are the recombination Reactions (9) to (12), the HO2 consumption Reactions (13) to (18) and formation and consumption of H202, Reactions (19) to (25). It should be mentioned that H20 2 closely fails to be an unimportant by-product according to the criteria mentioned above. Reactions (9), (11), (22) and (24) are listed for completeness, though unimportant at all conditions used in this paper.

the point of maximum adiabatic flame temperature adjacent to the stoichiometric composition. This is caused by the fact that flame propagation in this System is not purely thermal (as it is at high pressures ilarger than about 50 bar), but partially promoted by diffusion of the light chain carrier H into the cold gas.

P R E S S U R E D E P E N D E N C E OF THE F L A M E VELOCITY The pressure dependence of the H2--O2 flame x~elocity is complicated by the occurrence of two competing oxidation mechanisms represented by H+

O2-* O H + O

(R3)

OH + H 2 ~ H20 + H

(R1)

O + H2 ~ OH + H

(R5)

O 2 + M ~ HO2 + M

(R12)

H + HO2 ~ OH + OH

(R13)

OH + H2--> H~O + H.

(R1)

and by H+

C O N C E N T R A T I O N D E P E N D E N C E OF THE F L A M E VELOCITY The concentration dependence of the flame velocity in H2-O2-N2 mixtures at P = 1 bar and T, -- 298 K is shown in Fig. 1. Parameter is the N2 content of the initial mixture. There is good agreement with experimental results. The values given by Jahn [18] are included without correction due to systematic errors [8, 19]. It is typical of H2--O2--N2 flames, that the point of maximum flame velocity lies relatively far in the rich domain of initial mixture composition if compared with

751

Here the first mechanism leads to strong chain-branching of active particles enhancing combustion, Whereas the second mechanism has chain-terminating character. The competition of the different reaction order~ of the rate-controlling reactions (R3) and (R12) lea~s to a pressure dependence of flame velocities shown in Fig. 2 in a log-log presentation for stoichiometric Hv-Oz--N2 mixtures. It is interesting to compare these calculations with corresponding results of the Zeldovich theory [20]. This

Vul m / s I v~i,n/sl 10

o

O

X02 / { X o z ÷ X N 2 ) = 1

i

i

i

i

a XH2

0.2 o.~ 0.6 o.e 1 Fig 1. Concentration dependence of flame velocity for different N : - O : mixtures. 1: pure H~-O:; 2: 40% O: in oxidant; 3: H ~ a i r : 4:12.5 % O2in oxidant. Points: experimental results;

lines: calculations.

0.1 i

~

i

i

i

0.01

01

1

10

10o

P[ bur]

Fig. 2. Pressure dependence of flame velocity. 1: pure Hr-O2; 2: Hr-air; 3: 23.4% 02 in oxidant. Points: e~erimen~al results (for reference [7]); lines: calculations.

752

F. BEHRENDT AND J. WARNATZ

theory (assuming one-step kinetics) gives for the pressure dependence of the flame velocity

(6)

v. = K . p(n-2)/2,

where n is the order of the one-step reaction assumed. K is a function of the thermal conductivity coefficient a = A/pep at the burnt gas temperature, which is approximately equal to the mean diffusion coefficient @. Furthermore, K is dependent on the mean reaction time r. The reaction mechanism (Table 2) includes reactions only of the order two and three. According to formula (6) this would lead to a pressure dependence

v - p m with 0 < m < 0 . 5

(7)

in contrary to the results shown in Fig. 2. Negative values of m (at high pressures) show a breakdown of the Zeldovich theory, as derived by Dixon-Lewis, Isles, and Walmsley [21]. (The results given by Warnatz [7] showing a different picture at high pressures, must be corrected due to an incorrect formulation of the Eucken corrections of the heat conductivities.) T E M P E R A T U R E D E P E N D E N C E OF THE F L A M E VELOCITY As expected (see e.g. [22] for CH4 flames) the flame velocity is a strong function of unburnt gas temperature (see Fig. 3). Unfortunately, measurements only for stoichiometric mixtures of H2 with pure 02 are available in the literature [23].

There is complete agreement of experiments and calculations, if the measurements are corrected to give the correct room temperature value (see Fig. 1). For completeness, calculated results for stoichiometric H_,-air mixtures are added, too. Simple flame theory assuming one-step reaction kinetics (see [20]) yields the formula

v, = ( a i r " F(Ob))1/2

(8)

for the flame velocity vu. Here a = A/pep and F(Ob) is of the order of 1. This expression shows the flame velocity to be dependent on the burnt gas thermal conductivity coefficient a, which is only a weak function of temperature, and on the reaction time r (including the induction period), which therefore must be mainly responsible for the strong temperature dependence of vu. It is not possible to give a simple interpretation of this strong temperature dependence, since for multistep mechanisms r is a complicated function of mixture composition and rate coefficients of the reactions involved. Nevertheless, the similar temperature dependence of the flame velocity v, both in H2-O2-N2 and in hydrocarbon-air mixtures (see [22]) is caused by the predominant influence of the rate-controlling chain-branching reaction H + O2 --~ OH + O

(R3)

in both systems [1].

PARTIAL EQUILIBRIUM Calculations are much better suited for a verification of the hypothesis of partial equilibrium of radical concentrations in the H2-O2 system than measurements because of the difficulty of experimental determination of the radicals H, O, and OH (see Fig. 4 for examples of radical profiles). Assuming partial equilibrium of Reactions (R1) to (R6) the radical mole fractions can be calculated from stable species mole fractions by (for reference see [24])

% / m,s"I 30

{k~k3~sXo2X.2'~°5

20

XH = ~ k~kak6X2H20 j klk3Xo2XH2 XO = k2k4XH20

{k3k 5

10

Xon = ~ k - ~ x o 2 xH2

! I

i

I

I

I

I

r~

- -

600 1000 K Fig. 3. Temperature dependence of flame velocity. 1: pure H202; 2: H2-air. Points: experimental results; lines: calculations. 200

(9)

(10)

)0.5 (11)

Comparison of the mole fractions calculated by (9) to (11) with exact values is given in Fig. 5. The set of formulas (9) to (11) clearly shows partial equilibrium to be established at temperatures above 1700 K, whereas at lower temperatures there are large discrepancies. Thus, partial equilibrium assumptions should be tested very carefully, if they are used at lower temperatures.

THE DEPENDENCE OF FLAME PROPAGATION x

753 portial

.....

1.o

J

Io 9 x~ a' •

~

equilibrium ossumption

c o m p t e t e mechanism used

5= Oz

I

1000 x ~ O z ~

2

o

o

-2 '

~"

05

z/ram

1.0

1.5

x

-4

,/

,

,

,

~

,

'

50o

15oo

,

T/K

2ooo

T/K

1.0

. . . . . . . . . . . 2000

to

x~o'

. - ' ' ' ' ' ' " T 0

2

x

H2

2

x

•

~

•

o

•

e

•

HzO

-6 . . . . . . . . . . /

/,'

Fig.

4.

0.5

'

1.0

'

1.5

z/mm

Mole fractions and temperature in a stoichiometric H2-air flame (P = 1 bar, T = 298 K).

-8

, 500

NO F O R M A T I O N IN H 2 - A I R F L A M E S The H2--air system is well suited for a quantitative test of the Zeldovich mechanism of NO formation since there is no interference by NO formation caused by hydrocarbon radicals (for reference see [26, 27]). Up to the present, NO concentrations in Hz--air flames have been measured in the burnt gas region far away from the flame front (typical dimensions: flame front thickness 3 mm, see Fig. 4, NO measurements 30 mm behind the flame front).

, 1000

,

L

i

, 1500

'

' , 2000

T/K

i

T/K

mox

Io0 XOH

/,,

SENSITIVITY A N A L Y S I S More insight into the reaction mechanism is provided by a systematic variation of rate coefficients in the calculation e.g. of the flame velocity of a stoichiometric H2--air flame at atmospheric pressure (Fig. 6). For each reaction the rate coefficient is enlarged by a factor of two. The ratio of the original and the new flame velocity is given in the illustration. For the large majority of reactions the flame velocity changes by less than 2% (hatched area). For this reason, these reactions are not listed. It is clearly shown that flame propagation is promoted by chain-branching and inhibited by chain-terminating processes; furthermore, reactions with heat release are promoting, too. The difference to corresponding sensitivity analysis in hydrocarbon flames is considerable, caused by the ability of the fuel to act as a radical scavenger [1,25].

~

-6 g"

-0 i

L

i

500

l

1000

i

2000

1500

Fig. 5. Partial equilibrium radical concentrations (open points) compared with exactly calculated ones (full poi0ts) in a stoichiometric Hz-air flame (P = 1 bar, T = 298K).

0.9

1.0

'

~

1.2

1.1

v~

(2x I~) v . (k)

OH

÷ H2

'Jr~,

HzO * H

H

*O2

~

OH

*0

0

+ H2

~

OH

*" H

H

"-OH

÷H

~

H20 "1"1

H

-02

*H

~

HO2 "-PI

H

* HOz

--"

OH

., OH

H

*HO z

--""

Hz

"02

Fig. 6. Influence of enlargement of rate coefficients on the free flame velocity v~ in a stoichiometric H2-air mixture (P = I bar, T = 298 K).

F. BEHRENDT AND J. WARNATZ

754

For the calculation the 'large' rate coefficient

XNo/pp m \

k-- 1.8 x 1014 exp( - 3 1 9 kJ m o l - l / R T ) cm3 (mol. s)-'

\ \ \ e q u i l i b r i u m NO \

1000

(for reference see [29]) has been used for the reaction (R26). Thus, the results presented here support the validity of the 'large' rate coefficient. Nevertheless, the measurement of NO profiles in the flame front itself seems to be desirable with regard to a more exact evaluation of the rate of reaction (R26). Since NO is formed at temperatures T > 1700 K, NO concentrations calculated with the partial equilibrium assumption (for reference see [26]) should be correct if the results described in a preceding section are taken into consideration. On the o t h e r hand, calculations of NO concentrations assuming complete thermodynamic equilibrium [7] lead to completely wrong results, as likewise demonstrated in Fig. 7.

%\ \

100

\\

10

I

I

0.25

I

~ I

I

Xh~

0.30

Acknowledgement--The authors are indebted to the 'Deutsche Forschungsgemeinschaft', the 'Fonds der Chemischen Industrie', and the 'Volkswagen-Stiftung' for financial support.

Fig. 7. NO formation in Hz--air flames. Points: measurements by Hoyermann [27], and by Homer and Sutton [28]; lines: calculations [7]. REFERENCES For stability reasons of the calculation method used in this paper, it is not possible to extend the coordinate system far enough into the burnt gas region to compare calculated and measured NO concentrations. Therefore, the following procedure has been used: First the flame structure is calculated as usual. Then for crossing of the large burnt gas region an isothermal integration (neglecting diffusion) by Gear's method [11], has been performed started with the concentrations calculated at the experimental temperature. The calculations show the N atom mole fraction to be only of the o r d e r of 10-9 showing that in comparison to (R26) reactions (R27) and (R28) are fast enough to lead to quasi-steady-state concentrations of N atoms. This is confirmed by additional calculations assuming this quasi-steady-state. Thus, NO formation is controlled merely by the rate of reaction (R26). N2 + O---> NO + N

(R26)

N + 02 ~ NO + O

(R27)

N + OH ~ NO + H

(R28)

A b o u t 50% of the NO are formed in the flame front region (typical size given in Fig. 4), the remainder in the much larger post-flame region. Figure 7 shows results of these calculations compared with experiments by H o m e r and Sutton [28] and by Hoyermann, J a n d e r and Wagner [27]. There is rough agreement, if approximations in the calculation procedure and the experimental limits of e r r o r are t a k e n into consideration.

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22. 23.

24.

25. 26.

27.

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