The effect of pressure on the laminar burning velocity of methane-oxygen-nitrogen mixtures

INFLUENCE OF PRESSURE ON FLAME SPEED 83

5. GERSTEIN, M.: Ref. 4, pp. 35-43. 6. BURGOYNE, J. H., AND WEINBERG, F.: Ref. 4,

pp. 294-302. 7. BURGOYNE, J. H., AND WEINBERO, F.: Proc.

Roy. Soc. 224A, 286 (1954). 8. WRIGHT, F. H.: California Insti tute of Tech-

nology, Pasadena, Ph.D. Thesis, 1948. 9. CULLEN, I~. E. : Trans. Am. Soc. Mech. Engrs.,

75, 43 (1953). 10. MORGAN, G. H., AND ~4~ANE, W. t~.: Ref. 4,

pp. 313-320. 11. LEwis, B.: Selected Combustion Problems,

AGARD, 176 ft. London, Butterworth, 1954. 12. BARTHOLOMI~, E.: Z. Elektrochem., 53, 191

(1949). 13. GERSTEIN, M., LEVINE, O., AND WONG, E. L.:

J. Am. Chem. Soc., 73, 418 (1951).

14. GRAY, K. L., LINNETT, J. W., AND MELLIStt, C. E.:Trans. Faraday Soc., 48, 1155 (1952).

15. PICKERING, H. S., AND LINNETT, J. W. : Trans. Faraday Soc., 47, 1101 (1951).

16. CONAN, H. l:~., AND LINNETT, J. W. : Trans. Faraday Sou., 47, 981 (1951).

17. DUGGER, G. L., AND SIMON, D. M.: NACA RM E52J13 (1953).

18. AUSLOOS, P., AND VAN TIGGELEN, A.: Bull. soc. chim. Belges, 60, 433 (1951).

19. JAHN, G.: Der Ziindvorgang in Gasgemischen. Berlin, Oldenbourg, 1934.

20. SMITH, F. A.: Chem. Revs., 21,389 (1937). 21. WHEATLEY, P. J., AND LINNETT, J. W.: Trans.

Faraday Sou., 48, 338 (1952). 22. DAMKOftLER, G.: Z. Elektrochem., 4i6, 601

(1940).

9

THE EFFECT OF PRESSURE ON THE LAMINAR BURNING VELOCITY OF METHANE-OXYGEN-NITROGEN MIXTURES

By DONALD SMITH ANn JOHN T. AGNEW

Introduction

The laminar burning velocity, commonly sym- bolized by Su, is recognized as one of the most basic parameters in the science of combustion. Considerable effort is being made to develop adequate theories by means of which this param- eter can be calculated for a given fuel-oxidant mixture. The adequacy of these theories is in- variably tested by comparison with experimental results. More experimental data is needed, par- ticularly relative to the effect of pressure on the laminar burning velocity of hydrocarbon fuels. Very little experimental data exists in the pressure range above one atmosphere. The data re- ported here covers a pressure range up to 20 atmos. The pressure coefficient of burning velocity has been determined in a 10-in. spherical bomb for three mixtures; CH4 + 202, CH4 + 20~ + 2.25N~, and CH4 + 20~ + 7.56N~ (methane-air), all mixtures being initially at room temperature.

Description of Experimental Methods

These studies have been carried out by means of the constant-volume bomb method. This

method was chosen primarily for two reasons First, propagation of the flame front is every where perpendicular to the unburned gas, a strict requirement for accurate measurements of the laminar burning velocity. Secondly, the bomb method is well adapted for studies in the high pressure range. I t is realized that the bomb method has some disadvantages, chief among which is the question of full energy release in the thin reaction zone. This must be assumed in order to make the calculation of the adiabatic explosion pressure, P~, and ultimately the value of Su.

The use of the constant-volume bomb technique has been discussed in detail by Lewis and yon Elbe, 1 by Manton, von Elbe, and Lewis, 2 and by Manton and Millikan2 The basic relation- ships employed for the determination of Su are as follows:

P" \M,T~/ (1)

P - - Pi n - (2)

P ~ - Pi

(3)

84 STRUCTURE AND PROPAGATION OF LAMINAR FLAMES

drb/dt Su =

l I ~ A ) (4) 1 + ~ - 1

In these equations:

n = fraction of total charge burned rb = flame radius

P i = initial pressure P = actual instantaneous pressure at any

time t drb/dt = slope of curves shown in Figures 3, 4,

and 5 k~ = ratio of specific heats for the unburned

charge T, = Thermodynamic equilibrium flame

temperature for adiabatic constant volume combustion

Pe = Thermodynamic equilibrium pressure corresponding to Te

Mb = moles of burned gas M~ = moles of unburned gas Ti = initial temperature

Equation 2, which states that the fraction of charge burned is proportional to the pressure rise is only true for adiabatic conditions and for small values of n, of the order of one per cent. This is the order of n during the first few centimeters of flame travel in the constant-volume bomb. Pe is evaluated on the assumption of complete combustion, allowing for dissociation of C02 and H20 to 02, CO, H2 and OH. P~ is always greater than the actual maximum pressure observed due to lack of adiabatic conditions during the late stages of the combustion process.

The investigators mentioned above have shown that the method gives quite reliable and accurate results by taking both pressure data and photographic flame travel data simultaneously. Manton and Millikan 3 have presented very interesting results concerning the pressure coef- fieient of burning velocity for a wide range of hydrocarbon-oxygen-inert gas mixtures at atmospheric pressure and below.

In the constant-volume bomb technique, the use of pressure-time data for the determination of S~ is somewhat difficult since a very sensitive pressure gauge is required to record the small pressure rise associated with the first few centimeters of flame travel (during which travel the determination of burning velocity is made). At the same time, this sensitive pressure gauge must be protected against the ultimate high pressure which develops upon completion of combustion

of the entire charge. For example, with an initial pressure of one atmosphere, the pressure rise at the time Su is determined might be of the order of 0.005 atmos., whereas the total pressure rise would be of the order of 6 atmos.

A different method for determining the flame position as a function of time was used in this work, utilizing ionization gaps located at stra- tegie positions. Four positions of the ionization gaps were utilized and were spaced at approximately equal intervals along a radius of the spherical cavity. The outermost gap was approximately four-tenths of the way from the central ignition gap to the vessel wall. As the flame front passed the ionization gaps, a corresponding de-

OSCILLOSCOPE

- - - ~ 1 I _~o~oo, ooc OHMS '1

I1~ ----)°~Ms I MERCURY V45T ]a. r--------- MANOMETER OL S J~ ~ SPARK

I ~ )GAGE NDOW

1 I ~ / ~ SPARK [ i l- _J

FIG. 1. Diagram of apparatus.

flection was observed on an oscilloscope screen and recorded with a drum camera. Figure 1 is a diagrammatic sketch of the experimental apparatus including the electrical cireuit used to produce the sequence of events on an oscilloscope screen. Figure 2 is a typical oscilloscope traee and Figures 3, 4, and 5 are typical experimental results for the three mixtures studied, the data in these figures being for an initial pressure of one atmos. For the stoiehiometric methane-air mixture sphericity of propagation was confirmed by locating an ionization gap at a constant distance from the ignition gap along a number of radii. The spark ignition gap was 0.010 in. for pressures up to 10 atmos, and 0.003 in. at 20 atmos. The ionization gaps were 0.020 in. placed perpendicular to the direc- tion of propagation. Both the spark gap and ionization gaps were between pointed steel

LAMINAR BURNING VELOCITY OF METHANE-OXYGEN-NITROGEN MIXTURES 85

electrodes 0.0625 in. in diameter. The ignition spark was a pure capacitance spark generated by 0.00625 gf at 4560 v, or an energy of 65 mj. The spark gap was energized by closing a snap switch, so that the 65 mj of energy were actually dissi- pated across two gaps, the external switch and the internal gap. The minimum ignition energy for a stoichiometrie methane-air mixture, with bare steel electrodes forming a 0.010 in. gap is of the order of 8 mj. I

and that the value for n for a stoichiometric methane-air mixture is about -0.09. This value of n is based upon measurements at two pressures, 1.0 and 0.1 atmos. The data shown in

2.0

I.C

I 1.2

x kx

J

c:"t,t += O'Z+T.SSNz

IO lh CH BOMB

¢ I2 IS ~0

Time - millile¢o~¢ilt

FzG. 3. Experimental flame travel data for methane-Mr mixture.

230

4

O0 0,4 0.8 I .~ 1.6 2.0

Time - millisecond=

FIG. 4. Experimental flame CH4 + 20~ + 2.25N~ mixture.

S.ar ~t

J

c~4, z oz* Z.~N 2 IO INCH BC ~B

2.4 2.8 3.2

travel data for

FIG. 2. Typical oscilloscope trace.

Effect of P r e s s u r e o n t h e L a m i n a r

B u r n i n g V e l o c i t y

Figure 6 shows the results of our work and of several other investigators as to the effect of pressure on S= for a stoichiometric methane-air mixture. The Wolfhard data may not be accurately represented since it was transferred from a slide projected by Dr. Wolfhard at a recent lecture at Purdue University. However, his values, obtained by a burner method were, in general, somewhat lower than ours. The Egerton and Lefebvre data 4 were obtained by a tube method. Manton and Millikan 3 have suggested that the variation of burning velocity with pressure for most hydrocarbon-oxygen-inert gas mixtures may be represented by the relation;

.~ i.6

~1.2

~- oA

2 7

z X X X , ~

c%+z% 0 INCH BOMB

2

O~ 0,2 0.4 0.6 0.8 1,0

Time - m i I l i x¢ond l

FIG. 5. Experimental flame methane-oxygen mixture.

travel data for

Figure 6 for these investigators is an extension of this equation, with the -0 .09 exponent, to a pressure of 20 atmos. Our data would indicate that the pressure dependency is not representable by the simple relationship shown in Equation 5. As shown in Figure 6, our data is accurately represented by the relationship;

8 6 STRUCTURE AND PROPAGATION OF LAMINAR FLAMES

S~_u = eO.3(~_po.~4) (6)

where S~ is the laminar burning velocity at pressure, P, and S~ is the laminar burning velocity at a pressure of one atmos.

This equation gives a value of 44.4 cm/sec for S~ at 0.1 atmos., which checks quite closely the experimental value of Manton and Millikan.

~c I s ' ,,.sO.,:,°.s'<'/ I o I J / ~ . : e "[$~,,i-~+-A,~.,,+,.3

+ ~ ' ' - . +

, o , / v , "-..-.-. I w°/f~¢'~l . I - - " " \ o . I

+",.-,,++,..++.~',. +'+~" " '..'.x'~ I (re+~.~3 " \ , \ 1

+o I t "~

C//~ + ZO~ + ? .~ ~V~ I (me~h,~ .e - ~ i r )

- 3 -?. - I o I ~. 3 ~ I ~ P

FIG. 6. Burning velooity +s m function of pres sure for stoiehiometric methane-air mixture.

z ~

ZIC~

! 1oc

leo

I 0 * • ~ p e r l m e n f o l

x -c~l¢(~lat"ed

S /

,ll /

/ - 5 . o23 O - O - ° ' ' 4 s )

/ / I

/ CH÷ +Z O~ + Z . Z S N z

-2 - I o I L 5 ~ l n P

FZG. 7. B u r n i n g v e l o c i t y as a f u n c t i o n of pressure for 42.8 per cent nitrogen mixture.

Figure 7 shows the results obtained for the CH4 Jr- 202 + 2.25N2 mixture. I t will be noticed immediately that the values of S~ are much higher than for the methane-air mixture, and further- more that the pressure coefficient is now positive rather than negative. An equation which accurately fits the curve shown in Figure 7 is;

S_u_ = eO.3(l_p-O.145) (7)

Both equations 6 and 7 have the same general

form;

S~ - - = e b(l-e=) (8) Su~

where b and x are experimentally determined con- stants. The rather striking result was that the constant b was within one per cent of 0.3 for both the methane-air and the CH4 + 202 + 2 . 2 5 N ~

mixtures. The third mixture studied was a stoichiometric

methane-oxygen mixture. There is considerable

40.6

+0,4

4 0 . l

0

-0,1

-0 .4

.-0.6

0,1

0,4

0,|

0 0

cM~+z o~ + YN~

i \ \

J I

x / I I _ : b 0 - p x) /

$ % - ,..,. /

/ /

In S.,

FIG. 8. Relationship between burning velocity the experimental parameters b and x, and the nitrogen content of the mixture.

discrepancy in the literature both as to the actual value of S~ for this mixture at one atmos pressure and as to the pressure coefficient of the burning velocity. Wolfhard (5) has indicated that his results with the burner method show little, if any, pressure dependency of S~ for this mixture. We have measured Su for the CH+ + 205 mixture at only two pressures, 0.1 and 1.0 atmos. The values obtained were 386 and 564 cm/sec re- spectively, indicating a positive pressure dependency for this mixture. In order to compare the magnitude of this pressure dependency with that obtained with the other two mixtures investigated, the method shown in Figure 8 was used.

LAMINAR BURNING VELOCITY OF METHANE-OXYGEN-NITROGEN MIXTURES 87

The upper curve in this figure is a plot of the pressure exponent, x, in equation 8 as a function of in Su~ (the atmospheric pressure value). The values of x of 30.54 and -0 .145 are for the methane-air and CH4 + 202 + 2.25N~ mixtures. The data of Manton and Millikan indicate that a CH4 + 202 + 5N2 mixture should have zero pressure dependency and a burning velocity of approximately 80 era/see. This point has been in- cluded on the curve and the curve then extra- polated to In S ~ equal to 6.34 (S,1 equal to 564 cm/sec) which was obtained experimentally. This extrapolation resulted in a value for x of -0 .21 . Using this value of x and the experimental S~

IlO0~

I000

@- experim~tal 9OO ; - cellculaf~

80o / /

/

/ 700 ]

/ , / :3 6 0 0

U)

/ .~oo / . / /

400 / ~ f /

/

3o~: -3 -Z -I o~J o.i~ o~s

/ /

/ /

/

, /

/

~Z

I % "b"

_ S . ' - o . ~ ( ' l - P - o ' Z / )

cH, + Z O,

I FIG. 9. Burning velocity as a function of pres-

sure for stoichiometric methane-oxygen mixture.

values at 0.i and 1.0 atmos of 386 and 564 era/see, an equation of the same form as equation 8 was derived for the methane-oxygen mixture as

S~ = e0.62(l_p-0.21) (9) Su 1

This equation has been plotted in Figure 9 along with the Manton and Millikan equation for this mixture, the dotted portion of each curve indicating an extension of the experimental data according to the appropriate equation. I t is for this mixture that the greatest deviation exists (in the low pressure experimental range) between the data of Manton and Millikan and our data. Singer and Heimel (see Lewis and yon E l b e / p . 467) using the burner cone frustrum method obtained a value of approximately 450 cm/see for

Su of a stoiehiometric methane-oxygen mixture at a pressure of one atmosphere.

The lower curve in Figure 8 is a plot of the b value in Equation 8 as a function of In S,I for the three mixtures investigated, the value for the methane-oxygen mixture being subject to the methods described above. I t is, of course, almost impossible to draw any conclusions from such sparse data, but it is interesting to note that a minimum in the b curve is indicated in the region where Manton and Millikan have observed zero pressure dependence. These results also indicate a definite positive pressure dependence of Su for the methane-oxygen mixture.

S u m m a r y and Conclusions The laminar burning velocity of a stoichio-

metric methane-air mixture (71.6 per cent nitrogen) decreases markedly as the pressure is increased from one to twenty atmos. This pressure relationship is not representable by a single value of n in the relationship given in Equation 5. The burning velocity for the CH4 + 202 + 2.25 N~ mixture (42.8 per cent nitrogen) increases as the pressure increases from 0.5 to 5.0 atmo~. Ex- perimentM data show also that a stoichiometrie methane-oxygen mixture has a positive pressure dependence. Equations 6, 7, and 9 accurately represent the pressure dependence of laminar burning velocity for these three mixtures, respec- tively, all of these equations being of the general form given in Equation 8. I t should be noted that the form of Equation 8 is such that a negative value of x indicates a positive pressure dependence and vice versa.

The positive pressure dependence indicates a high order or reaction which is rather disturbing. However, it is to be noted also, that the possible objection that excitation lag might cause false results in the bomb method applies just as well to the methane-air mixture as to the methane- oxygen mixture. Fair agreement among the various investigators exists for the methane-air mixture up to a pressure of 20 atmos, but considerable discrepancy remains regarding the actual values of and the pressure dependency of Su for the methane-oxygen mixture. This lack of agreement will undoubtedly be resolved by more research by the various investigators.

REFERENCES 1. L~wzs, B., AND YON ELBa, G.: Combustion,

Flames and Explosions. New York, Academic Press, Inc., 1951.

2. MANTON, J . , VON E L B E , G., AND LEWIS , B.:

88 STRUCTURE AND PROPAGATION OF LAMINAR FLAMES

Fourth Symposium (International) on Com- bustion. Baltimore, The Williams & Wilkins Co., 1953.

3. MANTON, J., AND MILLIKAN, B. B.: Gas Dy- namics Symposium on Aerothermoehemistry. Evanston, Illinois, August 1955. See also

L~wIs, B. (discussion): Selected Combustion Problems, AGARD, p. 177. London, Butter- worths Scientific Publications, 1954.

4. EGERTON, A., AND LEFEBVRE, A.: Pr0c. Roy. Soc., A222, 206 (1954).

5. Private communication.

10

INFLUENCE OF PHYSICAL AND CHEMICAL FACTORS ON BURNING VELOCITY

By E. S. GOLOVINA AND G. G. FYODOROV

Introduct ion

The principal objective of this study was to determine the effect of the chemical characteris- tics of a combustible mixture on the fundamental burning velocity. Changes in the rate of the chemical process were effected by varying the oxygen content in mixtures containing benzene, hexane or a hexene-hexane fraction (40 per cent hexene and 60 per cent hexane). The oxygen content was changed by replacing nitrogen with oxygen, going from 16.4 per cent 02 to a pure oxygen atmosphere. The experimental method consisted of varying the content of the fuel by replacing nitrogen in fuel--O2-N2 mixtures with a fixed oxygen content. In this way, a system of U~ (normal burning velocity) curves was obtained over the maximum possible range of fuel concentrations, each curve corresponding to a constant oxygen concentration.

Experimental Procedure

The burning velocity measurements were made with a Bunsen-type burner. Because of the high burning velocities in oxygen-containing mixtures and the necessity of maintaining a laminar regime of flow, it was necessary to use narrow burners and decrease the burner diameter f romd = 3 r a m r o d = 2 m m a n d t h e n t o d = 1.45 mm as the oxygen content was increased. Check tests showed that at sufficiently high burning velocities, of the order of those of oxygen flames, changing the burner diameter did not change the normal velocity values appreciably.

With such small burners, the most difficult experimental problem was to obtain a low, stable feed rate for the fuel and to measure it. This problem was solved successfully by using narrow

capillary tubes through which the fuel was fed to a vaporizer, from which its vapors were re- moved by a nitrogen or oxygen stream. Changes in the feed rate of the combustible were effected by varying the location of the capillary tube with respect to the liquid level in the feed reservoir, or by using a capillary tube of a different diameter. The capillary tube made it possible to obtain a stable feed of the combustible with an accuracy of 0.01 cc/min. The burning velocity was determined from photographs of the flame cone on the burner by measuring the angle 2c~ at the apex of the cone and calculating U from the relationship

U = l~ sina

in which W is the mean flow velocity at the burner port. The spectral line-reversal method also was used to measure the temperature at the cone apex for the mixture giving the maximum burning velocity and for the stoichiometric mixture.

The composition and temperature of the combustion products were determined by thermodynamic calculations for a wide range of hexane concentrations and for 02 concentrations varying within the limits mentioned above.

Results

Figure 1 shows the burning velocity in benzene- oxygen mixtures as a function of the fuel content of the mixture expressed in per cent. With the exception of the extreme upper curve, represent- ing C6H6 + 02 mixtures in which the content of each of the components is a variable, the oxygen content for each curve is constant. Similar curves for hexane mixtures are given in Figure 2. The

The effect of pressure on the laminar burning velocity of methane-oxygen-nitrogen mixtures

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