the influence of pressure on flame speed

74 STRUCTURE AND PROPAGATION OF LAMINAR FLAMES

tion order (about 1.7) is close to the value used to correlate blowout data for combustion in the homogeneous reactor (1.8).*

However, this type of reasoning probably only partially explains the variation of m with fuel and oxygen concentrations. It would indeed be for- tuitous if the complex of reactions occurring in a hydrocarbon flame could under all conditions be described by a single global reaction order.

In conclusion, it appears that the interrelation- ships among pressure dependences of the various flame propagation properties are rather well described by simple thermal considerations, Thus experimental determinations of a single flame property may suffice to describe the behavior of the other properties. The quenching distance is most easily measured with good precision. In fact,

* J. P. Longwell and M. A. Weiss: Ind. Eng. Chem., 47, 1634 (1955).

in precise low pressure measurements of the other properties quenching effects must be considered and minimized.t

t Additional references : J. Manton and B. B. Milliken : Proceedings of the

Gas Dynamics Symposium on Aerothermochemis- try, Aug. 22-24, 1955, p. 151. Northwestern Uni- versity, Evanston, 1956.

R. Friedman and W. C. Johnston: J. Appl. Phys., 21, 791 (1950).

B. Lewis and G. Von Elbe: Combustion, Flames and Explosions of Gases. New York, Academic Press, Inc., 1951.

J. E. Garside and B. Jackson : Fourth Symposium (International) on Combustion, p. 545. Baltimore, The Williams & Wilkins Co., 1953.

B. D. Fine: NACA TN 3833. A. L. Berlad: J. Phys. Chem., 58, 1023 (1954).

8

THE INFLUENCE OF PRESSURE O N FLAME SPEED"

By MITCHELL GILBERT

1. I n t r o d u c t i o n

The modern theory of flame propagation indicates that the pressure is an important parameter arising primarily in the effective over-all order of the chemical reactions. Variation of the flame speed with P% where 0 _> n _> -½, suggests second- to first-order kinetics, and 0 _< n _< ½ suggests second- to third-order kinetics. Second- order processes would be expected to occur most frequently, and flame speed independent of pressure should result. However, a complicating factor is the relative behavior of diffusive and thermal transport processes. If the ratio of these effects (expressed as the Prandtl number divided by the Schmidt number) is truly independent of temperature and local chemical composition, then theory predicts flame speed invariant with pressure for second-order kinetics. Variations of the ratio probably occur, and it may be expected that the correlation mentioned above will not be pre-

This paper presents the results of one phase of research carried out at the Jet Propulsion Lab- oratory, California Institute of Technology under Contract No. DA-04-495-Ord 18, sponsored by the Department of the Army, Ordnance Corps.

cise. I t may be noted that flame temperatures and equilibrium compositions depend sufficiently on pressure to cause variations in the Schmidt and Prandtl numbers.

In the present paper, experimental data on the effects of pressure are presented, in the range of pressure below one atmos, for eight fuels. No startling effects are noted and the data are valuable primarily for adding to the completeness of the literature. However, in the course of the experiments an opportunity arose to examine the influence of the method of measuring flame speed. I t was found that, in some previously observed results at subatmospherie pressures, deviations from a linear logarithmic law, In U = a d- n In P, occurred. These results were commonly ascribed, by various investigators including the present author as well, to quenching influences of the burner port or wall. Recent experiments at this Laboratory, however, indicated that these quenching influences were minor. Thus, by using a schlieren-type method for determining flame area, it is shown that the luminous-cone boundary is not proper for determining flame speed, although at elevated pressures no significant error

INFLUENCE OF PRESSURE ON FLAME SPEED 75

is introduced through its use. The new method of measuring flame speed involves deflections of wire-grid shadows to determine the flame boundary. In addition a measure of flame thickness is provided.

2. Experimental Technique

Flame speeds were measured in a vacuum system described in detail elsewhere. 1 Bunsen-type flames were established on long cylindrical duets. Some of the ducts were provided with short nozzle inserts in order to increase the range of duet diameter for the experiments. This was necessary because the variation of the stability limits of low-pressure flames requires increase in burner size as the pressure is lowered. 1, 2 The con- trol of pressure and flow are such as to produce flames of remarkable stability. In addition, low- pressure flames are relatively free of influence due to the nature and behavior of the external atmosphere.

Most of the flame speeds reported here were measured by determining the area of the inner boundary of the luminous cone. A single convex lens, with a 9-in. focal length and 5-in. diameter, projected the flame image onto a transparent plastic screen, and the inner boundary was visually traced. Magnification was 1:1. Flow volume divided by area gives a flame speed aver- aged over the surface.

Some lack of agreement in pressure dependence of flame speed has been noted among various investigators. Consequently, some flame-speed measurements were repeated using a schlieren technique, since this method, for experimental and theoretical reasons, has found wide acceptance. Experiments evaluating flame-speed measurement techniques indicate that the sehlieren cone, from the point of view of providing a boundary most consistent with the definition of flame speed, is satisfacto~T because the temperature rise is quite small up to this boundary. Furthermore, geometric assumptions appear to be satisfied because the stream lines remain parallel up to the schlieren boundary. Broeze, a Linnett, 4 and Ger- stein '~ summarize the physical considerations involved and make strong arguments for the validity of the schlieren boundary.

An interesting variation of the ordinary sehlieren method was used. Instead of a knife- edge stop in a double-mirror Z-system, one can interpose a grid of parallel wires. The grid is conveniently placed between the image plane of

the flame and the image of the light source. Bur- goyne and ~,Veinberg 6. 7 in a simpler version of this technique, used parallel open slits to study a fiat flame. These authors and Wright s discuss the formation of the slit image and wire shadow on the image plane. It is clear that deflections in the shadow or slit are produced by index-of- refraction gradients normal to the light path. The magnitude of the deflection is essentially the counterpart of the intensity variation produced on the image plane by the combination of a re- fracting source and a schlieren knife-edge. Figure

Fro. 1. Wire-shadow patterns produced by a propane-air flame (mole ratio 0.044, pressure 249 mm Hg abs).

1 shows the wire shadow pattern deflected by a flame. The associated diffraction pattern is also visible. A grid composed of 0.010-in. wires about ~/g in. apart was used to produce the patterns of Figure 1.

The peak deflections are of interest. It can be shown that the peak intensity of the ordinary schlieren image and the peak deflections of the wire shadows represent the maximum of the function

(1/~) (d~/dx) sin 0

o r

(-- 1/T x) (dT/dz)


for the beam at right angles to the gradient. Thus the schlieren boundary, or the boundary defined by the locus of peak deviations in Figure 1, is seen theoretically to represent a flame boundary of lower temperature than the inner luminous cone, and lies farther upstream than the luminous boundary. Indeed, it lies far enough upstream toward the unburned gas to provide a good determination of the flame speed, and supporting evidence is presented in this paper. Right and left photographs such as Figure 1 were taken for some of the flames, and comparison was made between flame speeds determined by the inner

and Weinberg in that deflections can be magnified enormously by bringing the wire grid closer to the image plane of the schlieren light source. At, low pressures the gradients are diminished and deflections become quite small, but by changing the grid position respectable deflections can again be obtained. The wire shadows concurrently separate, and a closer grid construction must be employed if the flame image is to be defined by a sufficient number of peaks.

The conical-cylindrical geometry of the flame introduces some optical distortion,-primarily in the colder region of the flame where the light beam

8C

7(;

6(;

50

5 4o d i,i i,i O.

','30

-J U.

20 , ,

<1

4 0 5 0

-.......4

D • 0 ~

El [

v 0.685-in. NOZZLE INSERT 0 0.877-in. DUCT O 1.O0-in. NOZZLE INSERT O 1.25-in. DUCT ~. 1.50-in.NOZZLE INSERT A 1.86-in. DUCT <] 2.32-in. DUCT

OPEN POINTS: LUMINOUS CONE AREA SOLID POINTS: WIRE SHADOW METHOD

J I 6 0 7 0 8 0 9 0 I00

FIG. 2. Flame

, ° ' ' ~ " : o . a : oaez

2O0 3OO 4O0 PRESSURE, mm Hg obs

speed vs pressure for two propane-air mixtures.

500 6 0 0 700 8 0 0

luminous-cone area and by the area defined from the locus of peak deflections of the wire shadows.

Brief discussion may be made of some additional factors involved in using the shadow deflection method. First, the peak deviations are determined at the central bright line of the wire shadow. Second, although the trace of a single wire is, in principle, capable of giving the refrac- tive index or temperature distribution in the reaction zone of the flame, as pointed out by Burgoyne and Weinberg, 6'r the quantitative accuracy is not as yet very great. For purposes of measuring flame speed, however, the maximum deflection point (determined by a tangent to the peak, parallel to the undeviated shadow) is quite definitive. The present optical system has a significant advantage over that used by Burgoyne

must pass through the reaction zone twice at a small angle to the gradient, and then through a long path length of cooler gas. It can be shown that in the region of maximum deflection the perturbing effects of the flame geometry are small, due to variation of path length and variation of gradient along the path (a slight upstream shift is caused). Good over-all temperature dis- tributions can probably be obtained only for plane flames. Further consideration of the properties of the wire-shadow technique and its physical applications will be deferred to a later publication.

3. R e s u l t s a n d D i s c u s s i o n

The figures show flame speeds for a large number of systems. Most of the data give flame speeds.

I N F L U E N C E O F PRESSURE O N F L A M E SPEED 77

obtained from the area of the inner luminous boundary. The flame speeds for the faster-burning flames appear to be independent of pressure below one atmosphere, while the slower-burning flames show a behavior characterized by U ~ P~'. Such a power law is valid if the data can be repre- sented by straight lines in the log plots, despite an obvious falling off toward low pressures (Figs. 2 to 8).

The use of the straight line in Figures 2, 3 and 4 stems from the observation that as the duet size s increased the straight-line behavior of the data is extended. I t would appear that for extremely

the solid points in Figures 2, 3 and 4) was used with some low-pressure flames previously studied by the luminous-cone method, it was noted that the data do not exhibit the deviation from the power law. At extremely low pressures there is some indication, as would be expected, that a falling off of flame speed occurs part of which may be attributable to the quenching implied in Cullen's analysis based on the effects of burner rim.

The linear logarithmic behavior of the wire- shadow data suggests a more natural explanation for the falling off of the luminous-cone-boundary

o

bJ (D

..I

'1

50

0 0 0 r l , , 0 ~ ~ 0 . 1 8 " mole ratio

• , , ~ I ,~ ~ v -,~ ~ N - ~ - - ~ . . v C H ~ -,- -w-+.....q:

---- d ;;,z!,;o

. . o - " _ ~ o.o~, '

60

+ 0 .377- in . NOZZLE INSERT A 0.50-in, DUCT

0.685- in. NOZZLE INSERT 0 0.877-in. DUCT ,"') REFS. 13,15,16,17 0 I .O0-in, NOZZLE INSERT ~" o 1.25-in, DUCT ~" ~- 1.50-in, NOZZLE INSERT d C3He/Oz+Nz MIXTURE

REF.13(O.0398 mole ratio) O" • REEl4 OPEN POINTS: LUMINOUS CONE AREA I SOLID POINTS: WIRE SHADOW METHOD I

I I I I I 70 80 90 IO0 200 300 400 500 600 700 800 900

PRESSURE, mm Hg abe FIG. 3. Flame speed vs pressure for ethylene-air, propylene-air, and isobutylene-air.

large ducts a linear asymptote should be valid. An at tempt to explain the deviation of the data from a power law was made by Cullen2 Assuming that a quenching effect exists, arising from the burner port or wall, Cullen derived an expression which seemed to indicate that for Peeler numbers below 200, based on the observed flame speed, burner exit diameter, and operating pressure, the data would fall away from the linear asymptote. The correlation was quite convincing; the present author had reached the same conclusion on the basis of early experimental data at this Labora- tory, but the present research shows that the correlation is invalid.

When recently the wire-shadow technique (see

data. This explanation is based on the increase in separation between the inner luminous boundary and the schlieren or wire-shadow boundary, as the pressure is reduced. Assume, in Figure 9, that the solid cone represents the wire shadow, or true boundary, and that the dotted cone represents the inner luminous boundary. If the separation of these boundaries is 5 (experimentally ~ should be of the order of reaction-zone thickness), then mean free path considerations dictate that 8 cc l / P , or 8 = 8oPo/P, where ~0, P0 represent flame thickness and pressure at i atmos. The ratio of flame areas, the luminous-cone area to wire- shadow cone area, is then, for ~ << r.

78 S T R U C T U R E A N D P R O P A G A T I O N O F L A M I N A R FLAMES

AI , 28 280P0 ~ ] + - - = 1 + - -

,4~ r r P (~)

If it is assumed that the power law holds, then

U[P] = U o ( P / P o ) ~ = ( Q / A w ~ ) ( P / P o ) ~ (2)

¢o =co ~o ~oo sod ¢,oo ~0o coo ~oo

PRESSURE, mm H~ ob~

FIG. 4. Flame speed vs pressm'e for methane-air stoichiometric mixture.

......... ioli°!i

~ o 20o ~oo 4oo ~o ~co 70o sod sco PRESSURE, mm Hq obs

FIG. 5. Flame speed vs pressure for acetylene- air and acetylene-oxygen-nitrogen mixtures.

d CzMz/0 a • 0 05s moJe ro~o

I°eso r,o zo eo 90 ~ ~oo 4oo PRE~URE, mm H~ Obs

FIG. 6. Flame speed vs pressure for an acetylene-oxygen mixture, 0.5-in. duct.

Thus the use of the flame area Ale instead of the correct one, A~: , would result in an apparent flame speed

U'[P] = ( Q / A I o ) ( P / P o ) ~ (3)

and using Equations (1) and (2)

U ' = Uo ( P / P o ) ~ (4) 1 + (2~oPo/rP)

The denominator of the right-hand side of Equa- tion (4) determines the deviation of the flame speed from a power law. In fact, the deviation at any pressure is

A U = U - U ' ~ ( 2 U o S o / r ) ( P / P o ) ~-~ (5)

and upon examination it is seen that the observed deviation from the power law can, through the use of Equation (5), give a measure of 30 :

~o = ( r A U / 2 U o ) ( P / P o ) ~-~ (6)

For example, for the methane-air flame n =

I v o.665-ia NOZZt.E INSERT I

o 0 e77 - i~ OUGT 1 D I.ZS-in. D~T ® R.f re

i

. . . . . , • ,.2_~.Z,° _ _ ®

U H a ~ • 0.5 ~ l e rat~ ° " " ! - 2 o ®

4¢¢ m o m a

r-.m ;~URE, mm x~ or,

FZG. 7. Flame speed vs pressure for anamonia- oxygen mixtures.

I I 0 C C0/02

o

.i

v SER? 0 0877-in DUCT

-- 0 1.00 o in. NOZZLE INSERT ~ ~5-i~ DUCT

,® Ref 19 (CO MOISTURE CONTENT, 135%)

i a

CO/AIR = I mole rotio

O V V 7 ®

~co 200 300 400 ~co Boo mo ec~

PRESSURE, mm Hg obs

FIG. 8. Flame speed vs pressure for carbon monoxide-oxygen and carbon monoxide-air mixtures.

--0.27, U0 = 36 cm/sec, and at 162 mm Hg abs the luminous-cone-area flame speed deviates from the linear asymptote by about 12 cm/sec in an 0.877-in.-diameter duct (Fig. 4). The calculated value of 80 is 0.026 era. Morgan and Kane ~° measured the distance from the schlieren boundary to what is effectively the middle of the luminous cone. Thus their measurement should be two to four times 80. Morgan's and Kane's value of 0.048 cm is therefore comparable with this author's calculated value.

From the foregoing analysis, the reason for the accidental correlation found by Cullen 9 becomes clear. The correlation with Peclet number, p D U c p / k , can be reduced to purely a function of Reynolds number by noting that the Prandtl


number is practically constant with pressure and varies only slightly for similar hydrocarbon fuel- air mixtures. Now, if one recognizes the fact that 50 in Equation (4) is an inverse function of flame speed, then it follows that the quantity 5oPo/rP can also be replaced by a function of the Reynolds number. Thus, the observations of Cullen 9 are rexplained without recourse to quenching as their origin.

Figures 10 through 17 summarize flame speed for sonle faster-burning systems. Propane-oxygen .and acetylene-oxygen systems could, because of the high flame speeds, be burned down to pressures of a few millimeters of mercury. Part of the effects noticed at very low pressures may be at- *ributed to true quenching. For example, in

-~ 2 r = FIG. 9. Diagram of a conical flame.

Figures 13 and 16, flat flames are observed to yield lower flame speeds than conical flames, at a given pressure and burner diameter. I t is not un- reasonable to assume that this is partly due to the greater value of the ratio of wetted perimeter to flame area for the flat flame as compared with the conical flame. That the effect seems accentu- ated in the smaller (1.25-in.) duct is consistent with the expected increase in wetted-perimeter/ flame-area ratio as duct size is decreased.

Nevertheless, for a given duct even the very- low-pressure data are influenced by the deviation introduced through use of the luminous-cone boundary. Referring to Figures 15d and 17, one can estimate the reaction-zone thickness 60 for the propane-oxygen system. At 10 mm Hg abs, the deviation in flame speed from a linear behavior (in this case n ~ 0) is about 75 cm/sec; Uo = 325 em/sec at a mole ratio of 0.11. The

calculated value of D0 is 0.003 cm, which compares with 0.0094 cm observed by ~.iorgan and Kane at a mole ratio of 0.20 (a mixture having the same flame speed as the 0.11 mixture). As predicted, their value is about three times 50 •

Stone consideration can be given to the ques-

~60

150

~30

izo

E

WQ" 1~0

c~ I00

<[ E 9o

o

/ 80 / 0 THIS REPORT, 0.50- in. DUCT,

/ 250 mm Hgobs 70 13 Ref.20, I otmosphere

X Ref21, AVERAGE VALUE 60

~ s~roIc HI()METRIC

0.04 0.06 0~08 O.IC, 0.12 0.14 0.16 0.18 MOLE RATIO

Fz~. 10. Effect of mole ratio on flame speed of acetylene-air mixtures.

c

12o

E o HX

8 m

8Q HH,/O,. ,.,5 MOLE RA~O

0 THIS REPORTt 0.877- in. DUCT, I00 mm Hg obs

O Ref. 18, latmosphere

I t I I I I o.O2 I~1~ O .O6 0.1~ 0.10 0.12 0.14 0.16 0.18

MOLE RATIO, N2/(NH3+O=+N2I

Fia. 11. Effect of nitrogen addition on flame speed of an ammonia-oxygen mixture.

tion of the flame speed vs pressure behavior of the very-fast-burning systems. Lewis" has indicated that in these systems U ~ P~ where n > 0. The flame speed should then fall appreciably as the pressure is reduced. For example, one can roughly estimate that acetylene-oxygen flame speed should decrease by a factor of 1.5 between 760 and 100 mm Hg. A good check is not available since the present data are for very lean mixtures

80

700

600

=~ SO0

E o 400

. 0

~ 30{1

¢ 0

STRUCTURE AND PROPAGATION OF LAMINAR FLAMES

J ' ~ - - 3 mm Hg dos / f ~ \ , ~ . i

OJO 020 0~0 0.40 0.~0 MOLE RATIO, CzH=/O z

(o) Flot Flarnl$ on 2.37-in. Duct

(o)

O60

~/ / ~ , ° ° 1 s0 o. o

~20mm Hg ab,,

OJO 0.20 0.30 040 0.50 MOLE RATIO, C=H=/O=

(b) Flat Flames On I.Z5-in. Duct

( b )

o6o

70C

60~

50C

6 4oc

u~ 30C

~ 20C

IOC

/,

S

~-15 mm Hg obs

/ ' / ~ % - 5 mm Hg abs

/ / ~ 6 rn m Hg Ibs

:5, 4 mm Hg abs

o i

(cl I I oi

0.10 0.20 0.30 040 0.50 0 ~ O 010 0.20 0.30 0.40 MOLE RATIO, CzH=/O = MOLE RATIO, CIHtJO I

(c) Conical Flomel on 2.37-in, Duct (d) Cmical Flames on 1.25-1n. Duct

/

( i \.Oom.,o

7 (dl

0.50 0~0

FIG. 12. Variation of flame speed with mole ratio for acetylene-oxygen at low pressures (curves represent experimental data with mean scatter 0-2 per cent).

60¢ / ~ / ~ C'J / t " ~ "

~ 500 r f

: ./ -.~ L#~ o- ,:."

~I i °

- - 2,37-in, DUCT O~

tO¢- ~ " - - 1.25-in. DUCT

O.lO 020 0.50 0.40 GSO MOLE RATIO, C=Hz/O 2

FzG. 13. Comparison of acetylene-oxygen flame speeds at low pressures (5-20 mm Hg abs) showing effects of flame shape and duct size.

a"

4o0

i S / /THIS' REPORT

i I(X} mm Hg / 1.25-~rL DUCT

[

I ATMOSPH~E O'licm DUCT t

/ ° I

~o 0do o.zo a3o o4o ~ o 0.60 070 08O MOLE RATIO, CIHI/OI

Fla. 14. Acetylene-oxygen flame speeds, limit- ing values of present research extrapolated using Fig. 12.


¥ ZSO

E '

=-

15C

50

I / - 8 turn H~ abs

/

0.05 O.lO 015 O.ZO MOLE RATIO, C=H=/O=

(¢1) Flat Flome= on Z.37-1n. Ouat

O.Z5

)o

wo

io

,o

~o

%

/

IO m Hg obs

.> mm Hg abs 0

~ 4 0 mm Hg obs u~

I ~05 O.iO 0.15 0.20

MOLE RATIO, CaH=/O=

(b) Fiat FJomqa on 1.2fl-in. Ou¢t

0.25 G$O

350

30C

ZSO

2oc

~u) t5o

IOO

/ / / i f

/ o , / g

6 mm Hg ~bs

0.10 0.15 O.ZO MOLE RATIO, C=Ha/O=

(cl Coni¢ol Flames On 2.37-iR Duct

O0 @05 025 0.30

I

,f'- ./-~ \

40 mrn PR obs ~ ' ~

"-60, 80, I00 mm Hg obs

z

0.05 0.10 0.15 0,20 MOLE RATIO, CaHI/Oz

(dl Conical Flomes on 1.25-in. Ouct

O0 0.25 0.30

FIG. 15. Var ia t ion of flame speed wi th mole ra t io for propane-oxygen a t low pressures (curves represen t exper imental da ta wi th mean sca t t e r less than 1 per cent) .

400

360

300

250

2o0 ¢q

~__j 1 5 0 ~

IGo

.50

.o/~/J / -..

~7',,~o mm FLAT I ~ ] / / 1

2.37- in. DUCT

- - - - - - 1.25-in. DUCT

0.05 ( 0 C 15

'~,mm CONE _ _

~ ",,j \ I

Omm CONE

(J

o

I O25

MOLE RATIO, C5H6/02

F~o. 16. Comparison of propane-oxygen flame 'speeds at low pressures (8-40 mm Hg abs) showing effects of flame shape and duct size.

Ref. 12,0.2-cm DUCT, I atmosphere..- ~ j

//" " : - l . ~ " [ Ref.NOZZLEIO, 1/16-b.,

300 I at mc~pheee

200 Ref. 22, 0 .2187cm- DUCT, I atmosphere

15o THIS RERORT, 1.25-in. DUCT / ,OOmo,,o.

I c 0 o.t5 o.zo o.z5

O'LOMOLE RATIO, C 3 H e / 0 z

FZG. 17. Propane-oxygen flame speeds, l imi t ing values (low pressure) of present research compared wi th 1-atmos data .


and could not be readily extended to stoichiometric mixtures, and the only comparable data (12) occur at 1 atmos for richer mixtures. How- ever, Figure 14 presents the available fragments of data and shows that it is not at all evident that Bartholom6's data would lie above the low- pressure data if the experimental range of mixtures were extended.

In Figure 17 a comparison of high- and low- pressure data for propane-oxygen again do not suggest any decrease of flame speed as pressure is reduced. Here the data are extensive enough to be more forceful.

With regard to the slope of the flame speed vs pressure data in some of the figures, it may be noted that where the line is drawn through the data obtained only for luminous-cone areas without the confirmation of wire-shadow measurements, the slope is probably underestimated.

4. Conclusions

Experimental data on the variation of flame speed with pressure in the subatmospheric range indicate that slow-burning flames have varying pressure dependence; in general, flame speed in- creases as pressure decreases. Fast flames are independent of pressure. The present data on very fast flames, propane and acetylene with oxygen, on comparison with the iiterature did not indicate any direct pressure dependence sufficient to cause an appreciable decrease of flame speed as pressure is lowered.

Flame boundaries obtained with a wire-shadow technique comparable to a schlieren method indicate that flame speed obeys a power law U cc pn. The data tend to affirm the sehlieren boundary as the correct one for flame-speed measurement. In the eases studied (methane, propane, ethylene), deviations from this power law, observed when the luminous inner boundary is used for flame-speed determination, are shown to be caused by the separation of the schlieren and luminous boundaries as the pressure is lowered. Quenching processes do not appear to be responsible, and in fact probably enter only at considerably lower pressures than those at which deviations from the power law are first observed with the luminous boundary. The range of n observed was 0 _> n _> - ~ .

Simple theory indicates that the deviation of flame speed from the power law provides a measure of the flame thickness. Values so obtained are comparable with other researches.

When kinetics for a particular flame are available, laminar flame theory predicts the pressure dependence of the flame speed. The extent of de- parture of experiment from such theory can, if the flame kinetics have a reasonably firm basis, provide information on the actual variation of transport processes with pressure and other contingent parameters.

Acknowledgments

The author gratefully acknowledges the help of George A. Eriksen, Lieutenant, USN; William McK. Pardee, Lieutenant Commander, USN; and John M. Charles, Lieutenant, USN, who obtained a major portion of the data with great care and fidelity. The valuable discussions with Dr. Hamilton Wright are also acknowledged.

Nomenclature

Alo = area of inner luminous-cone boundary Aws = area of boundary defined by peak deflec-

tions of wire shadows n = exponent of pressure in flame-speed equa-

tion P = pressure P0 = atmospheric pressure Q = total volume flow through flame r = radius of flame base or burner duct T = temperature U = flame speed U' = flame speed observed usinginner luminous-

cone boundary U0 = flame speed at atmospheric pressure x = distance normal to flame front

= flame thickness (distance between schlieren and luminous boundaries)

~0 = flame thickness at atmospheric pressure ~U = U - U' 7/ = gas viscosity

= index of refraction of flame gases p = gas density 0 = angle between light beam and index-of-

refraction gradient

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3. BROEZE, J. J.: Third Symposium (Interna- tional) on Combustion, pp. 146-155. Balti- more, The Williams & Wilkins Co., 1949.

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

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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).

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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 parameter 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 reported 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)

the influence of pressure on flame speed

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