An improved soap bubble method of measuring flame velocities

IMPROVED SOAP BUBBLE METHOD OF MEASURING FLAME VELOCITIES

329

39

AN IMPROVED SOAP BUBBLE METHOD OF MEASURING FLAME VELOCITIES By R. A. STREHLOW AND JOSEPH G. STUART INTRODUC'Il ON

Flame velocity determinations using the bubble method were first made by Stevens (1) in 1923. He devised the procedure of using a soap bubble as a constant pressure bomb for containing an exploding mixture. He ignited the bubble at the center with a spark gap and photographed the flame along a horizontal diameter with a drum camera. This space velocity was converted to a flame velocity by dividing it by the volume expansion of the bubble as determined from an initial and final size measurement. The same procedure was used on a study of the carbon monoxide-oxygen system by Flock and Roeder (2) in 1935. Because of the low luminosity of most flame fronts, direct photography is not generally applicable and in 1951 Pickering and Linnett (3) extdnded the method to flames of low luminosity by using a schlieren system to follow the flame front. This method inherently possesses most of the properties of a good method for determining flame velocities. I t is convenient since it requires only a small quantity of gas for each determination. I t is well suited for exact mathematical analysis and the velocity calculations do not require consideration of pressure effects, wall effects, or the effect of an angle between the gas flow and the flame movement. At present the method has certain disadvantages. These are 1) aqueous bubbles contaminate the mixture with an unknown amount of water vapor; 2) afterburning of the hot product gases in air causes difficulties in final size measurement; 3) dead space in the bubble and spark gap holder causes slight initial contamination of the bubble; 4) gas diffusion through the bubble causes a composition change in the bubble mixture before firing; 5) nonisotopic flame propagation during the bubble explosion may effect the accuracy of flame velocity determinations; 6) there are indications that the inertia of the bfibble becomes important at high space velocities; 7) convective rise of the hot combustion gases makes slow flame speed determinations difficult if not impossible; and 8) a bubble method cannot be used with gases which attack the bubble. The first three of these problems have been elimi-

nated by improvements in the method. Problems 4, 5, and 6 are discussed in the report and represent limits of the method. Problems 7 and 8 limit the method to relatively fast flames in gas systems which do not attack the bubble.

THEORY

OF

THE BUBBLE METHOD

Linnett has mentioned that the final flame size measurement contributes the most to the error in the calculated results. The equations below were originally worked out in an attempt to find a method of calculating a burning velocity without the use of a final size measurement. Consider a sphere of combustible gas with an initial radius ro. Assume the sphere is ignited at the center and an infinitely thin flame front propagates at constant velocity to its surface. This process is assumed to take place at constant pressure and the sphere therefore expands to a new volume during the process. The volume of reactive gas that has been burned at any instant, h , after the flame has started is the volume enclosed by the flame at this instant minus the increase in volume of the bubble. V = ~ , ~ [~'~ -- (r~ -- r~)]

(1)

when rj- = radius of flame at t = h rb = radius of bubble at t = h ro = initial radius of bubble at to 9 The volume burned by a flame is equal to the burning velocity, S, times the flame area times the elapsed time V = SAAt.

If the surface area is not constant with time we can write d V = S A ( t ) dl

or V = S

~t t2

A ( t ) dt.

1

However in the case of a spherical flame A = 47rr/~

(2)

330

LAMINAR COMBUSTION AND DETONATION WAVES

and rj = S,t, where S, is a constant called the space velocity. Therefore V

= 4~S~2 S

f0'

t2

dt = ~,~,S~. St ~.

If we now let rf = rb = r2, the final radius, we get Stevens original express/on for the flame velocity

(3)

,s = s. \7.~1

Combining equations (1) and (3)

(6)

Furthermore 4~ = Vo/V2 when V0 and V~ are initial and final volume respectively. Since the mass of gas in both the initial and final volumes is the same and

Ir? -- (r~ - ro~)]%~ = % . ' S ~ S t ~ or

Srflt.

[ry3 - (rb'~ - ro3)] =

s.~

g V o P = Mo 10

RTo

V2P = ~g RT2

I

r where P is the pressure, M the molecular weight, g the mass of gas, R the gas constant, and T tl3e absolute temperature, we get 1 _

r

x.

I M E

R|

Ro

II

R/R o

I

I

I

1.0 1.2 1.4 [6

[

I

I

18 2.0 2.2

:

Fro. 1. Theoretical bubble motion for constant space velocity and expansion ratios of 6, 8, and 10. This yields S

r/J1 = 7

rift

However since

r~--ra~

(4)

rl

= space velocity = 5",

S = S~II

r~-- r~]

and since S and S, are both constants for any particular flame, 3

3

rb -- r0 _ c o n s t a n t = 4~. r.~f

(7)

Since Mo - - M2 and To is usually close to 300~ and T2 runs from 1800 to 3000~ 1 / r usually lies between 6 and 10. Using equation (5) the radius of the bubble ro = 1 is plotted against time in figure 1 for a constant value of the space velocity and for 1/4) = 6, 8, and 10. Equations (5) and (6) indicate two separate and independent ways of calculating the expansion ratio of a bubble explosion from measurable quantities. However an analysis of the errors shows that Stevens' original method (equation 6) has much better accuracy than the other method. In fact, the errors introduced by the calculation with equation (5) are at least six times the errors resulting if one uses equation (6). Unfortunately, the calculation errors are also quite large if one tries to find the asymptotic velocity of the bubble as the flame approaches it and subtract this from the flame space velocity. Therefore, from a mathematical point of view, the original Stevens method is by far the best method available for calculating a flame velocity from an experimental bubble photograph.

(5)

r~

1

i o T2 M2 To

APPARATUS

AND PROCEDURE

The photographs were Radio 35 mm oscilloscope with a 5 inch lens and an of 40 inches focal length. 100 watt zirconium arc

taken with a General drum camera equipped 8 inch schlieren system The light source was a lamp. The horizontal

IMPROVED SOAP BUBBLE METHOD OF MEASURING FLAME VELOCITIES camera slit was 0.023 inch wide, which corresponded to a ~{ inch slit at the bubble, and was so adjusted that the edge which ends the exposure cuts the image of the spark gap in half. This adjustment yields a true radius of the flame as a function of time. For all other adjustments the simple procedure of using Ar:/At to calculate a space velocity is incorrect. For example, with no s/it at all one can easily show that the sine, not the tangent, of the half angle is equal to Ar~/At and to measure a true radius of the flame in this case one must measure to the centerline along a line perpendicular to the flame line on the photograph. The bubbles were blown with a non-aqueous bubble mixture of very low vapor pressure developed at the Ballistic Research Laboratories (4). The mixture is a redistilled dry glycerine solution containing 5 per cent by volume of Nopco 1179 (Nopco Chemical Company, Harrison, New Jersey), a synthetic non-aqueous detergent. This sosution has a vapor pressure of less than 20 microns. The bubbles were blown upwards in an airtight box (4.5 cu ft) which could be filled with argon to eliminate afterburning. The bubble and spark gap holder are shown in figure 2. The bubble holder was fixed in space and the spark gap moved down and up for blowing and firing the bubble. The bubble was blown by first letting a small amount of bubble solution into and past the bore of the three2way stopcock A. The stopcock was then turned and this slug of liquid was forced ahead of the reactive gas into the mouth of the holder, using positive pressure supplied by a mercury leveling bulb. The solution easily covers and fills the two small holes (0.030 in.) which hold the 0.025 inch tungsten spark gap wires and forms a bubble. After blowing a bubble approximately 4.5 cm in diameter the glass spark gap holder C can be raised to position and fired. The time required to blow and ignite a bubble from the instant it started to form in the mouth ranged from five seconds to ten seconds in all experiments. The bubbles were formed and exploded near the center of a large box 21 inches square, which was swept free of air by displacement with argon. The parallel beam of the schlieren system passed through two selected lucite windows in the sides of the box. The spark gap was raised and lowered from the outside of the box with wires. The gas mixtures used for this report were made in a one-liter capacity mixing bulb. The heavy gas was first led into the evacuated bulb and its

331

pressure was read. The system leading to the bulb was then evacuated and the light gas was forced in at a higher pressure. The final pressure was read and the composition calculated from the ideal gas law. The mixtures were allowed to stand at least two hours before they were used for a burning velocity determination. All mixtures were made directly from tank gases with no additional purification. The air was taken from the room through a drying tube. The manufacturer's purity on the tanks was: ethylene-99.5 per cent, propane--99.9 per cent, nitrous oxide--98.0 per cent, and hydrogen (electrolytic) --99.8 per cent. The spark was fired by discharging a 0.01 mfd condenser charged to 6,000 volts, through a high voltage thyratron. The firing operation was syn-

TO BUBBLE

ONE iI~t4

0.025 )NCH TUNGSTEN WIRE

FIG. 2. Bubble holder with sliding spark gap chronized to the position of the moving drum and the opening of the shutter by suitable circuits. A standard distance on the film was supplied by two two-millimeter rods whose center lines were 17.788 cm apart in the parallel schlieren beam. The timing marks were supplied by a Sylvania l130B cold crater lamp pulsed at a known frequency. A 1,000 cy.cle Hewlitt-Packard secondary frequency standard was used for millisecond timing spots. The apparatus is also provided with a variable frequency oscillator and oscilloscope for synchronizing the timing light to any desired frequency. The oscilloscope is used to monitor the V.F.O. frequency to some convenient multiplier sub-multiple of the standard 1,000 cycle frequency. The flashing tube is operative to 15,000 cycles per second. A five-millimeter rod was used to blank the field at the center of the record to allow a uniform contrast for the timing marks.

332

LAMINAR COMBUSTION AND DETONATION WAVES

Kodak Super X X or lineograph film was used and developed with a fine grain developer. Figure 3A shows a typical photograph of a bubble explosion taken with this system. THE METHOD OF MEASUREMENT Wc have used the original Stevens method of measuring a space velocity and initial and final size to determine the normal burning velocity from a bubble explosion. This method was chosen because the simplified theoretical equations for this

measurement was the point where a line thi'ough the straight portion of the flame edge intersected the extrapolated final size line. An example is given in figures 3A and 3B. Comparator readings of the flame edges were taken at each timing mark after the spark image until the change in readings was small and rather uniform. As soon as the flame edge was unreadable, readings were shifted to the bubble edge as shown on one side of the trace. The readings were then plotted on an enlarged scale and the final size was read off of a graph

65Z0

-,5'~6N, FIHlU..SIZE"

-,;

,,:,,x,,,N/

~ ~

|

S6

64

62

60

58

56

54

~l

50

GOMPARATOR RF_..ADING-MILLIMETERS

FIG. 3. Film no. 141C. 6.53 per cent ethylene-air mixture; argon atmosphere; timing light = 1000 flashes per econd; standard distance, 17.788 cm at bubble equals 23.38 mm comparator reading; initial diameter = 6.91 mm, s/4, = (13.84/6.91) ~ = 8.033; space velocity (from graph) = &D/2 &t = 12.87 X 17.788/23.38 N .02 = 489.5 lm/sec; So = 489.5/8.033 -~ 60.9 era/see. A. Left. Bubble explosion. B. Right. Graph of comparator reading. C

System show that it is the only method with a reasonable calculation accuracy. When we started measuring flame velocities using the bubble method the question immediately arose as to what was the correct point for measuring final size. This is a particularly difficult question because 1) errors are magnified by the process of cubing the measurement, and 2) the final size increases slowly with time after the flame is extinguished. (This happens even in an inert atmosphere and is due to the pressure and velocity field which exists when the flame extinguishes.) The procedure adopted was to measure the diameter as a function of time after the flame extinguishes and then extrapolate the linear portion of this curve back to some significant time and call this the final size. The point chosen for

similar to figure 3B. As a sample, the calculation of So for this particular film (141C) is given below figure 3. Figures 4A and 4B show two types of records which were not read. In figure 4A the bubble broke very unsymmetrically and could possibly have disturbed the symmetrical gas motion. In figure 4B the bubble was not centered to the spark and was therefore discarded. The usual determination at one concentration consisted of about 12-16 photographs of which possibly seven to nine con-. formed to the geometry of figure 3A and ~vere read. One other type of record was discarded in calculating the final results. When we were measuring flame velocities in a region of non-isotropic propagation we found that the flame velocities So

IMPROVED SOAP BUBBLE METHOD OF MEASURING FLAME VELOCITIES showed a total variation of up to +15 per cent. It was also noticed that these individual results with a large variation always came from a flame photograph where the space velocities were grossly different on the two sides of the record. This large variation disappeared when the difference in the two space velocities on one film was less than five per cent of the average space velocity for that film. Therefore all films which were read and showed space velocity differences of more than five per cent were not used in determining the final average flame velocity, S0.

333

the bubble wall and the configuration of our schlieren systeln. Pictures taken with gists of different index of refraction in the babble showed different positions for the true e:lges. Fortunately for ethylene-air or propane-air mixtures at low concentration the index of refraction is quit? close to that of air and the correction is useable without further evaluation. We have not yet evaluated this for other systems such as the H.o--N20 system and this must necessal'[ly be done before accurate data caa be reported.

Ft

One mea,~, rement difficulty which was not anticipated at the start and caused a systematic error in early results was the measurement of initial size. I t is not too noticeable on the photographs (figs. 3A, 4A and 4B) but the edge of the initial bubble is surrounded by a white edge which is quite wide. Some question as to what we were reading when we read t~e inside edge of this white region came up during the initial data-taking period. For this reason a series of still photographs were taken using incident light at the same time as a schlieren strip photograph. These showed that the true edge of the bubble coincides with the mid-point of this white region within one per cent total variation for air bubbles blown in argon. This effect is no doubt due to the high density of

This white region is completely absent on all final size edges and the point of greatest density change was always read as the edge. RESULTS AND DISCUSSION

Table 1 gives the results of two flame velocity determinations in a seven and one-half to eight per cent ethylene-air mixture. The only change made between the two runs (except for a slight change in per cent composition) was a change of the surrounding gas atmosphere. The space velocities are essentially equal in these two cases but the expansion ratios differ by a large factor. The increased expansion, when the bubble is immersed in air, has been noted before (3) and is due to the afterburning of the hot product gases in the atmosphere. Pickering and Linnett (3) m e a s u r e

334

LAMINAR COMBUSTION AND DETONATION WAVES TABLE 1 Composition 8.0% Ethylene in Air Atmosphere-Argon

Film No.

Ss

88A . 88C 89A 95B 97C 101A 101C 104C 107A Average

.

1/4,

5.~ 4 9.05 527 8.28 543 8.29 558 8.01 545 7.80 505 7.47 523 8.23 548 7.93 513 8.39 [538 8.16

.

Composition 7.78% Ethylene in Air Atmosphere-Air Film No.

S

62.4 63.6 65.5 69.7 69.9 67.6 63.6 69.1 61.2 65.8

71A 71B 72A 74B 75C 76A 79C 82A 82B Average

i 5'~

"\\

/

\

/

g

S

1502 9.12 55.0 i 516 9.85 52.4 521 9.76153.4 629 9.69 64.5 533 10.18 52.3 510 9.5053.7 534 9.21 58.0 523 9.65 54.2 528 9.66 54.6 i533 - - 55.3

/i I

l/q~

i

I

---lP--C,~IN

I Al~ klllkll~

,--<~-PI~R~

A~

---- (IIIIIT[IN

9

\

LIIINITI

klVIIi! Alt

T i n s IIEPq~T

PER CENT [TICYI.EN[

FIG. 5. Flame velocities (So) for ethylene-air mixtures. TABLE 2 Fuel in_ _air

,/,

I S,,

So (other investigators)

so

per cent

Ethy!ene 6 6.5 7.0 7.5 8.0 Propane 4.03

56.6(A) 61.1(B) 65.6 (A) 67.8(B) 67.2 (A)

65.5 (B) 68.3" (C) 67.5(B)

.5 44.6(D)

(39)* (C)

7.7~ 484 62.4 ::t= .4 7.9~ 525 66.2::k .8 3.12 557 6 8 . 6 • 1.3 ~ . l f 538 6 5 . 8 • .8 5.65 268 4 0 . 4 •

55.6(B)

* Maximum flame velocity. A. Pickering and Linnett: Trans. Faraday Soc., 47, 989 (1951). B. Conen and Linnett: Trans. Faraday Soc., 47, 981 (1951). C. Gerstein, Levine and Wong: J. Am. Chem. Soc., 73, 418-22 (1951). D. Anderson and Feln: Univ. of Wisconsin, CM 517 (Dec. 1.5 1948).

their expansion ratios in an air atmosphere, but do it by finding a slight indentation of the outer edge which they call the final size. This should correspond to a point where the true flame stops and the afterburning starts. We tried their method but had difficulty in finding the indentation of most records. We therefore developed the measure-' ment method described above which requires that the bubbles be blown in an inert atmosphere. We feel that this extrapolation method should give a correct result because all we did was replace the region on the photograph where the flame is extinguished by the theoretically correct straight lines. In other words, before the flame starts to slow down everything is proceeding as the theory predicts (straight flame line) and also after the flame is completely extinguished the theory once again holds (except for the slight expansion rate we noticed which would appear in a more elaborate theory). We therefore just extrapolated the theory into a region where the finite thickness of the flame causes a slow change instead of the predicted discontinuity. The only assumption made is that the flame reaction goes to completion at the edge of the bubble even though the flame is slower due to lack of fuel and cooling effects of the surrounding gas. However, this assumption is needed for any type of bubble flame velocity measurement. A plot of some experimental values of So for ethylene-air mixtures is shown in figure 5. Table 2 lists our values of So as well as those of other investigators for four ethylene-air mixtures a n d for a stoichiometric propane-air mixture. The probable errors are given with our results. The larger error in the results at the higher ethylene concentrations seems to be caused by non-isotropic propagation. This view is supported by the fact that a high percentage of the records for these mixtures showed large differences in the two space velocities calculated from the two flame edges in one photograph. A few records had differences in S., as high as 20 per cent of S, or about 100 cm/sec. Since the scatter in the So value went up fast as AS,/S, increased we rejected all results where AS, was greater than five per cent of S, .. This figure was chosen because we found that the S, percentage difference in most cases was either below five per cent or above ten per cent, and in the zero to five per cent region the scatter in So values was approximately uniform even though it was still quite high. The question as to whether non-isotropic propagation shifts the calculated flame velocity in any

IMPROVED SOAP BUBBLE METHOD OF MEASURING FLAME VELOCITIES

335

FIG. 6. Fast nitrous oxide hydrogen flames. Timing light frequency = 2,000 cycles per second. A. Upper left. No box, 29.9 per cent H~. B. Upper right. Box, 29.9 per cent H~. C. Lower left. No box, 30.3 per cent N20. D. Lower right. Box 30.3 per cent N20. systematic manner cannot be answered at this time. One effect was noticed, however. In those records which had a large AS#S, the average of the calculated propagation velocity So was higher than that calculated from the useable records. As an example, at seven per cent ethylene the un-

useable records averaged to 69.4 cm/sec So as compared to 66.2 for the good records. Diffusion through the bubble was checked by measuring the rate of change of the bubble diameter when it was blown with different gases in an atmosphere of either air, argon, or carbon di-

336

LAMINAR COMBUSTION AND DETONATION WAVES

oxide. Of the set of gases ethylene, propane, air', argon and carbon dioxide, only carbon dioxide diffused at any measurable rate through a bubble surface. Bubbles blown with combinations not containing carbon dioxide showed no appreciable change in size in one-half hour and since only ten seconds are required to explode a fresh bubble, this check was considered satisfactory. The bubble surface was very permeable to carbon dioxide. As an example, a five cm diameter bubble blown in a carbon dioxide atmosphere increased in volume 48 per cent in three minutes. No diffusion checks have been made on nitrous oxide or hydrogen as yet. Figure 6 shows some preliminary photographs of fast nitrous oxide-hydrogen flames. Those taken in the box show some long term oscillations due to the oscillations of the gas in the box. The bubble was not centered to the box in these experiments and the oscillations show very definitely that the entire ball of hot gas is moving back and forth in the field. This, plus the fact that these oscillations disappear when the box is removed, prove rather

well that the oscillations are due to the container. The high frequency oscillations shown in the 30 per cent hydrogen mixture cannot be adequately explained as yet. These, however, might be due to some interaction of the high density bubble surface with the pressure ~ave caused by the flame front. If this is true the effect will force a~ upper limit on flame velocities which can be determined by the bubble method. ACKNOWLEDGMENT The authors wish to thank Pfc. Leland Watermeier, who did most of the experimental work and calculations that are reported. REFERENCES 1. STEVENS:N. A. C. A., Tech. Rap., 176 (1923). 2. FIOCKAND ROEDER: N. A. C. A,, Tech. Rep. 532 (1935); 553 (1936). 3. PICKERINGAND LINNETT: Trans. Faraday Soc., 47, 9, 989 (1951). 4. KAUFMAN A N D COOK: Ballistic Research Laboratories Tech. Note No. 575 (1952).

40

PREDICTION OF FLAME VELOCITIES OF HYDROCARBON FLAMES By GORDON L. DUGGER ASm DOROTHY M. SIMON INTRODUCTION The ability to predict flame velocities of fuels is of growing importance in the field of aircraft propulsion, since a correlation has been found between combustion efficiency of a ram-jet burner and the laminar flame velocity of the fuel (1). The prediction of P~ame velocities is difficult for three reasons: (1) There is no complete, rigorous theory which can be readily applied. There are, however, a number of approximte equations in the literature which approach the problem of flame propagation from various viewpoints. (2) There are no data on the kinetics of the oxidation process under flame conditions, and very little data on transport properties at high temperatures. (3) Different methods of flame velocity measurement give different values, so that it is difficult to compare data from different sources. The uncertainty in

measurements made by a given method is of the order of 5 per cent. In this report fame velocity measurements made at the NACA (2 through 5) for different hydrocarbons, initial temperatures, and compositions are used with semi-theoretical and empirical methods of flame velocity prediction to show the correspondence between the measured velocities arid the predicted velocities. The semi-theoretical methods are based on the Semenov equation (6), the Tanford and Pease "square root law" (7) and the Manson equation (8). These three equations were derived using different models of the flame propagation process. The Semenov model is essentially a thermal model which includes chemical reaction kinetics; the Tanford and Pease model is based oi1 the diffusion of chain carriers of the oxidation reaction; and Manson used a modification of the