Activation energies in high temperature combustion

ACTIVATION ENERGIES IN H I G H T E M P E R A T U R E COMBUSTION formaldehyde and formic acid O~ flames, which should have similar OH concentrations as hydrocarbon flames do not show the effect, which Penner's calculation would lead us to expect. We have no doubt that the anomalous rotational effect in hydrocarbon flames is real, particularly because

231

of the marked change in rotational distribution which occurs when a minute trace of C~H2 is added to a H2-O~ flame at low pressure. Broida's measurements on diluted flames at atmospheric pressure leave no doubt that similar effects can even be detected at 1 arm.

25

ACTIVATION ENERGIES IN HIGH TEMPERATURE COMBUSTION B y JOHN B. F E N N AND HARTWELL F. CALCOTE INTRODUCTION

Most of the recognized theoretical equations for normal burning velocity can be ultimately reduced to the form: S 2 = Fw

(1)

where F is some function of the t r a n s p o r t properties of the system, including diffusion and t h e r m a l conductivity, and w is the rate of chemical reaction in the flame front. I n general, the inherent difficulties of elucidating the reaction rate term h a v e resulted in major emphasis on theoretical analysis of the t r a n s p o r t p h e n o m e n a with a tendency to interpret flame propagation primarily as a transport process. I t has been realized t h a t if and when complete u n d e r s t a n d i n g of the t r a n s p o r t term is achieved, the theory of burning velocity would be extremely useful in attacking the problem of reaction kinetics u n d e r combustion conditions. M e a n while the dependence of b u r n i n g velocity on reaction rate has never been adequately tested. T h e purpose of the present s t u d y is to examine the possibility of determining reaction rate factors, specifically the activation energy, of the chemical processes from b u r n i n g velocity measurements. A simultaneous objective is to establish the relationship between the rate of flame propagation a n d the rate of chemical reaction. In classical form for reaction rate, equation (1) can be rewritten: S 2 = F A t e -F~/nr

(2)

I t is quite likely t h a t the most i m p o r t a n t chemical variable here is the activation energy, E. I n a n y event its determination is of u t m o s t interest. T h e first portion of this paper will deal with a t t e m p t s

to evaluate E b y the conventional means of experimental determination of the t e m p e r a t u r e coefficient of the reaction rate. As will appear presently, this approach is not w i t h o u t difficulty. I n the second p a r t of this paper, use will be made of the relationship between lean limit flame t e m p e r a t u r e and activation energy previously suggested b y one of the authors (1). By applying this concept to burning velocity d a t a for a variety of fuels, a convenient and straightforward deterruination of activation energy is possible. For convenience in following the analysis, a table of symbols and definitions is given here. SYMBOLS AND D E F I N I T I O N S

A = Arrhenius c o n s t a n t A r :- Arrhenius c o n s t a n t modified b y removing t e m p e r a t u r e dependence, or b y including concentration terms from rate expression a0 = initial r e a c t a n t concentration Cp = specific heat a t c o n s t a n t pressure D~ = diffusion coefficient of the i t h species E = activation energy ~f chemical reaction Hc = h e a t of combustion of 1 gram of initial mixture k = reaction rate c o n s t a n t L = n u m b e r of molecules per cc. ml/~rl2 = ratio of original n u m b e r of r e a c t a n t molecules to final n u m b e r of p r o d u c t molecules M = molecular weight N f = mole fraction of combustible in initial mixture No = mole fraction of oxygen in initial mixture

232

LAMINAR COMBUSTION AND DETONATION WAVES

partial pressure of ith component at Ti gas constant linear burning velocity adiabatic equilibrium flame temperature rate of chemical reaction--number of reacting molecules of combustible per second a = constant = E / T / (lean) 0 = Ts (lean)/Ti X = coefficient of thermal conductivity p = gas density Subscripts: 0 = initial mixture I = flame p~ R S TI w

= = = = =

I. D E T E R M I N A T I O N

OF

ACTIVATION

ENERGY

T H E E F F E C T O F INITIAL T E M P E R A T U R E BURNING

.....

~RO~

Z,,o~ l

I

l

ON

VELOCITY

As already pointed out most theories of flame propagation contain an expression for the rate of chemical reaction in the flame front which can presumably be represented in the classical Arrhenius form. I t should thus be possible to employ the temperature effect on burning velocity to calculate the activation energy., E, of the chemical reactions in the flame front by the usual plot of the logarithm of a rate vs. the reciprocal temperature or log f(T) vs. 1/T where the slope gives E. To do this it is necessary to express the burning velocity equations relating thermodynamic, transport, and chemical kinetic parameters of the system in terms of their variation with temperature. This type of analysis has been carried out for the Tanford-Pease theory and for the Zeldovich, Frank-Kamenetsky-Semenov theory of burning velocity as representative cases. Tanford-Pease. For the stoichiometric mixtures discussed here, this theory, which emphasizes diffusion of active particles, can be expressed (2):

S2 = ~

(4) The temperature dependence of the Arrhenius constant A can be represented by A~T ~ where x is determined from partition functions in accordance with the theory of absolute reaction rates. Thus for the reaction of an atom with a polyatomic molecule x = - ~ and for the reaction of a diatomic molecule with a polyatomic molecule x = - ~ . At ordinary temperatures the variation of A is usually ignored because it is insignificant compared to the exponential term. At flame temperatures, however, the relative variation can be quite large, especially in the case of low activation energies.

k, p, D~ L

(3)

This equation is essentially in the form of equation (2) where the transport properties are represented by the diffusion coefficient D and the reaction rate term by kp, k = Ae - E / ~ r . The following assumptions are introduced: (1) The diffusion of only one species is significant. (2) D is proportional to TL In actuality the exponent is probably somewhere between ~ and 2. (3) L is inversely proportional to T. This is equivalent to assuming the perfect gas law.

'

42

i

-

43 i

io 4

FIG. 1. Temperature effect on burning velocity for n-pentane-air flames by Tanford-Pease equation. (5) The temperature in the flame front at which reaction is assumed to occur is considered to be proportional to the adiabatic flame temperature, i.e. it is equal to KT~. (Tanford and Pease assumed K to be 0.7.) With these assumptions, equation 3 can be written in common logarithmic form: 2logS-

21ogT0--

(x-

1) I o g T /

-logp =f(T) --

-E 2.303RK T s

+

constant

(4)

This is the equation of a straight line relation between the left hand side f ( T ) and 1/T~ where the slope is - E / 2 . 3 0 3 R K . I n figure 1 it is applied to burning velocity data for stoichiometric mixtures of normal pentane with air obtained by the bunsen burner method (3). The diffusing species was considered to be H, OH, and O separately

ACTIVATION ENERGIES IN HIGH TEMPERATURE COMBUSTION and then altogether. The value of x was taken as -~.~ except for OH alone when it was assigned the value - ~ . In the collective case the variation in D between species was accounted for by setting in equation (4) p = 1.9PH + 0.28Port + 0.40Po where the numbers are the diffusion coefficients at 298~ and it is assumed that their relative values are unchanged with temperature. Adiabatic flame temperatures and equilibrium concentrations were calculated in accordance with standard procedures. If K is assigned a value of unity, then average slopes of the curves in figure 1 give values of activation energy as follows: Eoa = 50 kcal./mol

D proportional to Tz, E n becomes 23-30 and EH,on,o about 28 with a much greater curvature than shown in figure 1. Very straight lines can be obtained by assuming the coefficient of log To as unity, x equal to 1/~, and D proportional to T2. The activation energies are then En = 37.2 and Emon,o = 39.7. The most reasonable values for EH would thus appear to lie between 23 and 30 kcal/mol with somewhat higher values for the other activation energies. All of this assumes a value of unity for K which means that most of the reaction occurs very near the adiabatic flame temperature as TABLE

To ~

=

26

ErLomo = 30 Because of the non-linearity of the curves these values are only approximate. However, they are significantly higher than the 9.9 kcal/mol calculated by Dugger for propane (4). His procedure was different. He chose the "best" value of E to fit the calculated "burning velocity vs. initial temperature curve" to experimental data. This method can be demonstrated to be somewhat insensitive. Moreover, Dugger initially neglected entirely the variation of the reaction rate constant k with temperature. Although in later papers the exponential is taken into account, the temperature effect on A is still neglected. As has already been pointed out, in the case of high temperatures and low activation energies the variation in A is comparable with that of the exponential term. The terms for hydrogen atom diffusion in equation 4, plotted in figure 1, are tabulated in table 1. The last three lines in this table indicate the dependence off(T), and eventually the activation energy, upon the various terms. Since f ( T ) essentially involves numbers of the same order of magnitude it is rather sensitive to small differences. However, the coeff• of the log T~ term which is the most questionable is also the least important. If it had been assumed that D was proportional to T ~ this coefficient would be 2 giving E n = 27, and EH,on,o = 37 kcal/mole. The non-exponential term in the Arrhenius expression could have been taken from kinetic theory of gases. Then x would be I~ and assuming

1

Term84 m equation (4) for the Tanford-Pease expression 2 log S

:~ log T l : log pn

2 log To

Eo = 27 EH

233

298 3. 2608 4. 9484 373 3. 5706 5.1434 433 3,7844 5.2730 483 3.9610 5. 3680 498 4.0070 5.344 523 4.0868 5.4370 548 ~ 4. 1598 5.4770

5.0355 5.0444 5.0513 5.0574 5.0588 5.0619 5.0652

f(T)

]--3.3372 i -3.2328 i --3.15813 -3.1051 --3.0915 i--3.0758 ~--3.0458

6.6851 6.7044 6. 7207 6.7533 6.7629 6.7875 6.7932

Per cent change over temperature range

--

,

2.3

18.0

0.59

Ii 9.4

I 1.6

Numerical change over temperature range --

0.8990

0.5286

0.0297

0.2914 0.1081

Per cent of final answer

830

490

i

27

270

1 i

argued by Semenov (5). Of course, the higher the activation energy the better the argument. With reaction occurring at some mean temperature in the flame front, for example where K = 0.7, the activation energy, Er~, would be in the range of 16 to 21 kcal/mol. In brief, the Tanford-Pease expression cannot be readily employed to give a reliable value of the activation energy because the temperature variation of some of the terms is not sufficiently well known. In addition the arbitrary choice of a mean temperature at which reaction occurs places an additional uncertainty in the interpretation. The assumption that T is proportional to TI is surely not a necessity; some other relation might be more reasonable. The equation could be improved by integrating the reaction rate over the tempera-

234

LAMINAR COMBUSTION AND DETONATION WAVES

ture range in the flame front without essentially altering the physical picture upon which the theory is based. Zeldovich-Frank-Kamenetsky-Semenov. Assuming a bimolecular reaction, the final equation according to these workers is (5) :

With these assumptions, written in logarithmic form: 2logS--

21ogT0--

equation 5 can be

51ogTl

+ 3 l o g ( T I -- To) = f ( T ) E -

2.303RTI

I n this equation A ' is the Arrhenius constant with temperature dependence removed, A = A~T-L The Arrhenius constant was not integrated over

I

2 log S

2 log To

5 log T/ i

3.2608 3. 5706 3. 7844 3.9610 4.0070 4.0868 4.1598

4. 9484 5. 1434 5. 2730 5.3680 5.3944 5.4370 5.4776

16.7850, 9.8880 16.8145 9.8586 16.8375 9.8349 16.85801 9.8154 16 8645 9.8100 16.87301 9. 7986 16.8840 k 9.7896

23

80

3 log

I

-f(T)

--8.5846 --8.5287 I--8.4912 [--8.4496 !--8.4419 --8.4246 --8.4122

If

i o 59 i l O

0.8990

0.5286

-BE

I

0.0990 0.0984

520

i

310

57

57

i

44

:1o 4

Fro. 2. Temperature effect on burning velocity for n-pentane-air flames by Semenov's equation.

0.1724

-

the temperature range with w but was considered as independent of temperature. To obtain the temperature dependence of equation 5 the following assumptions were made: 1. He C~(TI - To) where Cp is an average specific heat for the products between To and TI and is assumed constant. 2. X is proportional to T. In actuality the exponent is probably somewhere between 1/~ and 1. 3. p0 and a0 are inversely proportional to T. This is equivalent to assuming the perfect gas law. 4. X/C~Dp = constant approximately. 5. A', Cp , (m,/m~_) and E are constant. =

i

4.3

~

, 2o

Per cent of final answer -

-8.s

42

Numerical change over temperature range --

I

~ig

Per cent change over temperature range

-

I

-e 4

Terms in equation (6) for the Zeldovich-FrankKamenetsky-Semenov__ expression

298 373 433 483 498 523 548 iI

(6)

Equation (6) has been plotted in figure 2 and the terms tabulated in table 2. The slope gives an activation energy of 41.2 kcal/mole. Practically the same remarks concerning accuracy of the data can be made for the results in table 2 as were made for the results in table I.

TABLE 2

T~ ~

+ constant

If A t is given the temperature dependence of a diatomic molecule reacting with a polyatomic molecule, i.e. Tj -'~ and X and D assumed dependent upon T '~ and T ~ respectively a straight line just as good as that reported in figure 2 is obtained, giving E = 27 kcal/mole. The thermal theory would thus appear to give a range of activation energies from 27 to 41 kcal/mol. Although a better straight line is obtained with the thermal theory than with the diffusion theory, the indeterminacy of the final result is ess, ntially the same. II.

DETERMINATION OF ACTIVATION ENERGY CORRELATION BETWEEN

BY A

LEAN FLAMMABILITY

"LIMITS A N D B U R N I N G V E L O C I T Y

The essence of the previous section is that from expressions of the form of equation 2 it is possible to get activation energy values by the variation of

ACTIVATION ENERGIES IN HIGH TEMPERATURE COMBUSTION S with Ts as the initial temperature changes. However, an inherent difficulty consists in relatively large temperature coefficients of the nonexponential terms in the equation. Consequently, the accuracy of the results is strongly dependent upon how well the particular theory used describes the transport phenomena involved as well as the accuracy with which the temperature dependence of the various terms is known. In this section attention will be directed at the variation in S with activation energy by changing the fuel. In order to pursue this attack it becomes necessary to make use of an approximate relationship between lean limit flame temperature and activation energy (1) namely E = a T s (lean)

235

will apply in large measure to many of the theories which have been suggested including the TanfordPease expression. As a first step equation (2) can be taken in its simple form with the following assumptions: 1. The transport properties represented by the term F are invariant over the chemical systems to be examined. 2. The concentration and frequency factor are unimportant so that A r is constant.

--

.o

\

o * FUELS WITH G AND R 9 FUELS WITH G , H A N O 0 Q 9 FUELS WITH G,H AND CI,

Hz _ _

0

S,O~

N

_ _

(7)

where a is a constant specific to the particular method or apparatus used for determining the lean limit flame temperature. In the earlier paper mentioned c~ was found to be 16.0 for temperatures calculated from lean limit measurements made in this laboratory with downward propagation in a 2.5 cm. tube. This evaluation of a was accomplished by applying a simple theory of minimum spark ignition energy to experimental data for a large number of fuels. An analogous approach will be made here using the same lean limit data as before but in conjunction this time with burning velocity considerations. In brief, equation (7) will be combined with a form of equation (2) in order to evaluate a from experimental values of burning velocity. Now it is necessary to note that the combustion wave or flame front to which the general equation (2) relates involves a sharp temperature gradient from the initial temperature To to the final temperature Ts. Therefore, the evaluation of both the transport and reaction rate terms depends fundamentally on integrating over this temperature range. Moreover, most of the terms in the integral are directly or implicitly functions of the temperature. Consequently, the mathematical procedures become extremely complex. Therefore, the problem has always been to make the appropriate simplifying assumptions which will permit a reasonably straightforward calculation. In what follows the picture developed by Zeldovich, Frank-Kamenetsky and Semenov will be utilized as a thoughtful compromise between the classical over-simplifications of Mallard and Le Chatelier and the comprehensive but complex treatment of Hirschfelder, et al. (6). Actually the considerations

~ o , ooc - -

i

o

GS

o~

I,OOC

4

5 TEMPERATURE

.S RATIO,

e

7

8

9

Tf ( L E A N ) Tf (MIXTURE)

9

FIe. 3. Burning velocity and lean limit flame temperature. 3. Practically the entire reaction proceeds at the adiabatic flame temperature, Ts. This approximation was suggested by Zeldovich and Semenov. 4. The activation energyE is taken as a T s (lean). In log form, equation (2) thus becomes: log S 2 -- l o g f ( F A ' )

aO

(8)

2.303R If the above assumptions are not too overwhelming a plot of log S 2 against the ratio, 0, of the lean limit flame temperature to the adiabatic flame temperature of the mixture for which S is determined should be linear. Figure 3 shows such a plot. The data used are in table 3. The values of lean limit flame temperature and stoichiometric flame temperature are the same ones used pre-

236

LAMINAR COMBUSTION AND DETONATION WAVES

TABLE 3 Temperature, burning velocity and activation energy for various fuels with stoichiometric amounts of air

Fuel

!1: T/ i] 0 r S AEi-et ] Flame T/(lean) i Burning ration Temp. T j ( ~ ' Velocity Energy

WS' Acetaldehyde . . . . . Acetone . . . . . . . . . . . . . Acetylene . . . . . . . . . . . Acrolein . . . . . . . . . . . . . Allyl chloride . . . . . . . .

2300 2210 2580 2340 [ 2270

cm/sec. !kcat/raol

0. 729 .771 9 .656 9839

41.4 42.6 144.0 65.9 32.4

27 27 20 25 31

Benzene . . . . . . . . . . . . . i 2340 Butadiene 1,3 . . . . . . . i 2365 n-Butane . . . . . . . . . i 2280 n-Butyl chloride . . . . . . 2225 Carbon disulfide . . . . . . 1 2250

735 671 771 779 9

47.8 49.6 44.8 31.6 58.8

27 25 28 28 16

Cyclohexane Cyclopentane . . . . . . . . Cyclopropane . . . . . . . . Diethyl ether . . . . . . . . Dimethoxy methane..

2225 I 2235 I 2350 I 2305 2220

.750 9745 .700 9

43.5 45.3 54.2 48 9 46.6

27 27 26 26 25

2,2 Dimethylbutane.. 2,2 Dimethylpropane. Ethane . . . . . . . . . . . . . . Ethyl acetate . . . . . . . Ethylene . . . . . . . . . . .

i 2220 2220 2195 2125 2340

9769 .784 .730 .800 9630

39.9 34.8 44.5 37.0 749

27 28 26 27 24

Ethylene oxide . . . . . . 2425 Furan . . . . . . . . . . . . . . . . 2390 Hydrogen . . . . . . . . . . . . 2345 Isopentane . . . . . . . . . . 2250 Isopropyl chloride . . . . . 2205

.610 88.8 .645 62.5 .421! 170.0 9735 40.0 .840 27.4

24 25 16 27 30

Isopropyl ether . . . . . . . Isopropyl mercaptan., Methane . . . . . . . . . . . . Methyl acetylene . . . . . Methyl ethyl ketone..

2250 2250 2200 2450 2210

.771 .79 9760 9653 .748

38.3 33.0 38 9 70.8 43 9

28 28 26 25 26

Methyl sulfide . . . . . . . 2230 2275 n-Pentane . . . . . . . . . . . n-Pentene-2 . . . . . . . . . ] 2320 Propionaldehyde . . . . . 2310 Propane . . . . . . . . . . . . . 2260

9720 .716 .713 .678 .732

33.0 43.6 47.8 49.5 44.0

26 26 26 25 26

n-Propyl chloride . . . . . 2205 Propylene . . . . . . . . . . . ] 2320 Propylene oxide . . . . . . i 2360 Triptane . . . . . . . . . . . . [12250

9 .694 9658 9750

27.5 51 9 66.5 40.1

30 26 25 27

]

i

.701

viously (1). T h e b u r n i n g velocities are a compilation of values obtained in this laboratory by the b u n s e n b u r n e r method over the past several years (7)9 W i t h the obvious exception of carbon disulfide all of the points fall fairly close to a s t r a i g h t line 9 Some of the scatter can u n d o u b t e d l y be a t t r i b u t e d to inaccuracies in the experimental data, particularly the lean limit flame temperatures 9 However, the general agreement is remarkable 9 T h e value of obtained from the slope of the s t r a i g h t line is 18. T h e r a t h e r gross assumptions m a d e above will now be modified somewhat 9 B y considering the t r a n s p o r t p h e n o m e n a as comprising essentially conduction of h e a t ahead of the flame front to warm up the approaching mixture, taking account of the variation of reaction rate with temperature, b u t ignoring the effect of changing composition on the reaction rate as fuel is consumed, Semenov arrives a t the following equation: S ~ -_

(9)

2~A'e -(~tRT:)RT~ Cppoao(T/-

To)E

T h i s is essentially the case where the chemical reaction is of zero order. T h e following approximations are now made: 1. ]k/poa, o is proportional to N o . Actually k and p0 are essentially the same for all cases except hydrogen. T h e proportionality relationship with N o , the tool fraction of oxygen is a convenient if not exact result of considering t h a t the actual reacting species to which a0 should relate, are not the fuel molecules themselves b u t some intermediate product, say hydrogen. 2. ( T : / T : - To) is essentially constant. This is true for the present cases within 3 per cent 9 3. Cp is essentially the same for all mixtures. W r i t t e n in log form with E = a T : (lean) and 0 = T: ( l e a n ) / T : , equation (9) becomes: S 20

l o g -No = c o n s t a n t

aO

2.303R

(10)

Figure 4 shows a plot of the log term on the left against 0 where the c o n s t a n t includes all Of the i n v a r i a n t terms. T h e agreement is a b o u t the same as in the former case with the notable exception t h a t the hydrogen p o i n t is more nearly in line 9 Again carbon disulfide is the m a j o r exception. T h e value of a is found to be 16.09 T h u s far the molecularity of the reaction has been ignored together with the effect of changing r e a c t a n t concentration as the reaction proceeds 9

ACTIVATION ENERGIES IN H I G H TEMPERATURE COMBUSTION For the third case a bimolecular reaction is assumed together with Semenov's final equation [see equation (5)] which takes into account the actual concentration of reactants in the combustion zone as determined by diffusion, depletion and true density. The assumptions are as follows:

oool

237

With these assumptions and writing E aT: (lean) and 0 = T: (lean)/T: as before, Semenov's equation for a bimolecular reaction in log form becomes: =

$2o3(T: _ log

Vo)3

No 31 i (m~']2

\m.,_/

;! iiii! !!i! Ti',isNo,

a0

= constant

(1 l )

2.303R

where the constant includes all the terms considered invariant. Figure 5 is a plot of the log .....

_

t

I

I

I

I

I

-

o 9 F~.'ELS WITH

C AND H __ FUELS WITH C . It AND O t~: FbIELS WITH G,H AND GI, - -

,~.

----

i~I176176176 20001 .3

.4

.5

TEMP~'RATURE

6 RATIO .

.7 9

9

.8

/'H2

A

S, OR N

--

g1r ~ iO.OOC - -

--

.9

c

Tf ( L E A N ) T 1 (MIXTURE)

o

~

--

c

Fro. 4. Burning velocity and lean limit flame temperature by simplified Semenov equation.

1:3

~ 1. The chemical reaction rate in the combustion zone can be written .cs z

da dt

_

NoN/p~ Ae-CEmr)

T h a t is, the reaction is assumed to be bimolecular and first order with respect to fuel and oxygen. Obviously the real reacting species are not fuel molecules and oxygen molecules. However, this expression would suffice for any case in which the concentrations of reacting species were proportional to oxygen and fuel concentrations. This same assumption was made in the spark ignition work. I t is less critical here. 2. The diffusion coefficient for the fuel molecules is considered as inversely proportional to the square root of the molecular weight. 3. X, Cp and p are considered the same for all fuel-air mixtures except in the case of hydrogen where ;k is estimated at 1.3 times the value for all other mixtures.

hooc

4

s TEMPERATURE

6 RATIO

,

g

7 =

T# Tf

e I LEAN I (MIXTURE)

'9

.....

FIo. 5. Burning velocity and lean limit flame temperature by Semenov theory. term on the left of equation (11) against 0. Once again the value of a can be obtained f r o m the slope of the best straight line through the points and turns out to be 16.1. Carbon disulfide remains an exception. Thus no matter what the order of reaction, the rate determining factor appears to be the exponential activation energy term so that essentially the same value of a is obtained. It will be recalled t h a t from spark ignition energy data as utilized in the previous paper a value of 16.0 was obtained for a. The present values of 18.0, 16.0 and 16.1 obtained from burning velocity data compare very

238

LAMINAR COMBUSTION AND DETONATION WAVES

favorably. On the whole, therefore, the concept of a proportional relationship between lean limit flame temperature and activation energy appears to be a fruitful one. Some implications of the anomalous behavior of carbon disulfide are worthy of further discussion. The burning velocity of the fuel appears to be much lower than can be accounted for in terms of reaction rate as determined by activation energy. Therefore, the difference must be attributed to the transport phenomena. This conclusion is supported by the fact that in the theory of minimum spark ignition energy outlined previously where transport processes were less important, the behavior of carbon disulfide was consistent with the other fuels. The question immediately arises as to what transport process could account for the low flame speed of this fuel. An obvious observation is that it is the one fuel of the group studied which has no hydrogen. Tanford and Pease have suggested that the diffusion of hydrogen atoms is important in the mechanism of flame propagation. If this were true of all fuels but carbon disulfide, then the low flame propagation rate for the latter might be expected. Some preliminary work with values of burning velocity for dry carbon monoxide air mixtures indicates that this is indeed the case. If the point for wet carbon monoxide is plotted in any of the figures it falls in line with the other fuels. An estimated value for dry carbon monoxide, obtained by extrapolation, appears to fall on a straight line parallel to the first but passing through the carbon disulfide point, that is a line of the same slope but different intercept. It is readily apparent that all of the undescribed transport properties are in the intercept term of the above equations. The picture of flame propagation thus becomes one in which for a given mechanism (e.g. diffusion of H atoms) the velocity is determined primarily by chemical reaction rate. On the other hand, if the reaction rate is fixed, as is more or less true in the carbon monoxide mixtures discussed by Tanford and Pease, then variation in burning velocity can be effected by altering transport phenomena, i.e. H atom or radical concentrations. However, there are still some dualistic aspects of this picture that are unresolved. I t is difficult to separate in similar systems the dependence of reactive species concentration on temperature from the dependence of reaction rate on temperature. Although the above comments on the theory of burning velocity are somewhat speculative, it

appears that the calculation of activation energy is on firmer ground. The simplicity, consistency, and precision of the method based on lean limit flame temperatures readily gives values whose general range is confirmed by the independent but awkward method of determining the variation in burning velocity with initial temperature. Calculated values of the activation energy for each fuel are given in table 3, assuming that a is 16.0. Again the need for better lean limit data is emphasized.

Acknowledgment The work described in this paper was performed for the Department of the Navy, Bureau of Ordnance Contract NOrd 9756, as part of Project Bumblebee. REFERENCES

1. FENN, J. B.: Ind. Eng. Chem., 43, 2865 (1951). 2. TAN~'ORD,C., AND PEASE, R. N.: J. Chem. Phys., 15, 861 (1947). TANFORD,C.: Third Symposium on Combustion, Flame and Explosion Phenomena, p. 140 Baltimore, The Williams & Wilkins Co. (1949). 3. GIBBS, G., AND CALCOTE, H. F.: Unpublished results on effect of initial temperature on burning velocity. 4. DOGGER,G. L.: J. Am. Chem. Soc., 73, 2398 (1951). J. Am. Chem. Soc., 72, 5271 (1950). See also NACA TN-2374 (1951), TN-2624 (1952), TN2680 (1952). 5. SEm~NOV, N. N.: Thermal Theory of Combustion and Explosion. III. Thermal Theory of Normal Flame Propagation. Prog. Phys. Sci. (USSR), 24, No. 4 (1940). Trans. NACA TM-1026 (1942). 6. HIRSCHFELDER,J. O., AND CURTISS, C. F.: J. Chem. Phys., 17, 1076 (1949). 7. CAI.COTE,H. F., A~rDGIBBS,G.: Unpublished results on the effect of molecular structure on burning velocity. DISCUSSIONBY PHILIP L. WALKER,JR.* The simple theory relating activation energies to lean limit flame temperatures is a definite contribution toward the further clarification of hydrocarbon burning velocities. Recently (Walker and Wright, J. Am. Chem. Soc., 74, 3769, 1952) an attempt was made to correlate the hydrocarbon burning velocities with the thermal combustion theory of Semenov. The authors were handicapped by the lack of any high temperatureactivation energy data for hydrocarbon combustion and resorted to available low temperature hydrocarbon oxidation * Division of Fuel Technology, Pennsylvania State College.

239

COMBUSTION OF HYDRAZINE data for the correlation. Using a value of 40 kcal./mol for all hydrocarbons, a reasonably good correlation of hydrocarbon burning velocity was obtained, except for ethylene and acetylene. It was concluded, as had Simon (Ind. Eng. Chem., 43, 2718, 1951) from theactive particle diffusion theory correlation, that these two compounds have an anomalous combustion behavior. Using the new activation energies and experimental flame temperatures for propane and ethylene (Jones, Lewis, Friauf and Perrott, J. Am. Chem. Soc., 53, 869, 1931) and acetylene (Behrens and Rossler, Zeit. Naturforsch., 5a, 311, 1950), the relative burning velocities, as predicted by the Semenov equation, have been re-evaluated, as shown in Table A, and compared with the experimental results of Gerstein (J. Am. Chem. Sot., 73, 418, 1951).

TABLE A

Maximum Burning Velocities of Hydrocarbon Flames Vol. Fuel

Hydrocarbon

I Burning Vel. Act Exp. _ _ ' Ener i flame i . g Y J T e m- p 9 Exptl__ Sqm~_~ I

per cent

Propane Ethylene Acetylene

4.5 7.4 10.4

l

l

i'~'o'i [

~

,,,.I ..... ,,,.I,ec.

I

26.1 12158139.0139.0 23.612238168.3

I 71.0

20.412480 1141.0 1152.5

It is seen that the new results suggest that ethylene and acetylene do not give anomalous combustion results, but simply possess lower activation energies than the majority of hydrocarbons for the combustion reaction.

26

THE COMBUSTION OF HYDRAZINE By G. K. ADAMS AND G. W. STOCKS 1. I N T R O D U C T I O N

Hall and Murray (1) have recently published some values of the burning velocity of hydrazinewater mixtures measured at atmospheric pressure by a burner method. The combustion of hydrazine in the absence of oxygen seems to be the only example of a flame maintained by an exothermic decomposition reaction that has been studied and it is of interest to see whether information on the kinetics of the homogeneous decomposition reaction at high temperatures can be obtained from combustion measurements. Halt and M u r r a y found that the products of the decomposition flame corresponded to the reaction N2H4~ --~ 1/~H2 + 1/~N~ + NH3 which has a heat of reaction of 33.2 kilocalories per mole at 300~ and constant pressure. T h e y suggested that the observed flame velocity can be explained on the theory of a thermally activated reaction by a first-order decomposition reaction with an energy of activation of 60 kilocalories per mole corresponding to the primary dissociation reaction (2) : N2H4 ~ 2NH2

As these authors have not attempted to check this theory by measurement of the pressure coefficient of the flame velocity or by a calculation of activation energy from their measurements of the change in flame velocity when the flame is cooled by the addition of water vapour we have thought it worth while to do this. For simplicity, the flame velocity was obtained by measuring the velocity of regression of a liquid surface in a capillary tube, the flame being selfmaintained at the surface of the liquid. This method has been found convenient for the measurement of the rate of combustion of liquid explosives at pressures greater than atmospheric, although the absolute value of the flame velocity cannot be calculated with any accuracy because the area of the flame surface cannot be accurately measured. 2.

EXPERIMENTAL

MEASUREMENTS

2.1 The influence of tube diameter on the rate of

burning in capillary tubes Measurement of the rate of burning of the liquid (expressed as the rate of decrease in the height of the liquid column in cm/sec) for a number of different tube diameters at constant exter-