Slow Uniform Propagation of Flame

In 1882 Mallard and Le Chatelier gave the results of an investigation into the rate of propagation of flame in mixtures of air and a combustible

Upper and Lower Flash-Points

Substance	Boiling - Point, ° C.	Lower Flashpoint, ° C.	Lower Constant, k.	Upper Flashpoint, ° C.	Upper Constant, k
Hexane	64	-26	0.734	1	0.813
Heptane	98	-1	0.734	17	0.783
Benzene	80	-12 (solid)	0.739	10	0.802
Toluene	109	10	0.743	30	0.794
Turps	150	38	0.736	55	0.775
Methyl alcohol	64	-1	0.809	32	0.906
Ethyl alcohol	78	11	0.810	32	0.870
Acetone	56	-18	0.777	2	0.837
Ether	34	-41	0.756	-27	0.802

	Ignition Temperature, ° C.
Carbon - Diamond	800-850
Carbon - Graphite	690
Carbon - Charcoal	345
Sulphur - in air	248-363
Sulphur - in oxygen	257-282
Phosphorus - red	255-260
Phosphorus - yellow	c. 60.

gas such as hydrogen and methane. It was observed that if the combustible mixture was ignited at the closed end of a horizontal tube, open to the air at the other end, the flame tended to travel with increasing velocity towards the open end. In a detonating mixture of hydrogen and air a speed of 300 metres per second was registered. If, on the other hand, the combustible mixture was ignited at the open end, the flame was observed to travel for a short distance at a uniform speed. This was followed by a vibratory movement, in the course of which the flame travelled backwards and forwards in an irregular manner, the mean speed from point to point along the tube being usually greater than that of the uniform movement. These vibrations usually continued to the end of the tube, but sometimes, during a particularly violent

vibration, the flame might be extinguished, owing to contamination of the as yet unburnt mixture with the products of combustion.

The initial slow propagation of flame can be maintained at a uniform speed over a considerable distance of travel from the point of ignition with all combustible mixtures of gases under ordinary conditions of temperature and pressure, provided suitable precautions are taken. The conditions most favourable to obtain and maintain this uniform movement are that the inflammable mixture should be contained in a long, straight, and horizontal tube open at one end and closed at the other; and that ignition should be effected at the open end of the tube by a source of heat not greatly exceeding in temperature the ignition- temperature of the mixture, and not productive of mechanical disturbance of the mixture. The speed of the uniform movement then depends on the composition of the mixture and on the diameter of the containing tube. Above a certain (small) diameter the material of which the tube is made does not appreciably affect the speed of the flame. With a tube of given diameter the speed of the uniform movement of flame in a mixture may - according to Mason and Wheeler - be regarded as a definite physical constant for that mixture.

Apparatus used by Wheeler (1914)

Several methods have been adopted for the measurement of flame speeds. If the flames are sufficiently actinic to affect a photographic plate, permanent records may be obtained on revolving drums bearing the films. Mallard and Le Chatelier employed this method in their researches on mixtures of carbon disulphide with nitric oxide or oxygen, the flames of which are well known to be highly actinic, whilst Mason and Wheeler were able to apply the method with conspicuous success to mixtures of acetylene and air. The actual flame speed is obtained by comparison with the waves made simultaneously on the photographic drum by means of a tuning-fork of known frequency.

For the examination of flames, such as those of mixtures of methane and air, which are non-actinic, various devices have been employed. A useful one used by Wheeler consisted in filling a horizontal tube with the gaseous mixture, the ends of the tube being closed, as shown in fig., by flanged end-pieces, bearing taps. S₁, S₂, S₃ . . . were screen wires of copper, 0.025 mm. in diameter, threaded vertically across the tube through fine holes pierced through the walls.

In order to avoid including in the measurements of the speed of the flame any impetus that might be given by the igniting spark, the first screen-wire was fixed 40 cm. from the point of ignition. Other screen- wires were fixed 50, 100, 200, 300, and 400 cm. respectively from the first.

The method of recording the time of passage of flame along the tube was electrical. Each screen-wire carried a small electric current, the interruption of this current when the flame melted the wires being recorded by the movement of an electro-magnet.

The electric current passing through the screen-wires was sufficient to raise them nearly to red heat. This arrangement ensured the rapid melting of the wires as soon as the flame touched them, and therefore gave very uniform results; wires made from metals or alloys of low melting-point, which could not be drawn so fine or of so uniform a diameter as copper, were found to be unsatisfactory.

All electrical connections through the screen-wires and chronograph having been established, the left-hand end-piece of the explosion-tube was removed (by sliding it downwards) and the mixture ignited at the now open end by passing an induction-coil spark at A.

Speed of Uniform movement of flame in tubes of different diameter.

As is evident from the results shown graphically in figs., the size of the tube exerts an important influence upon the flame speed. In tubes of small diameter, say less than about 5 cm., the cooling effect of the walls results in appreciable retardation of the flame speed. It will be observed that there is not much difference in speed in tubes from 5 to 10 cm. in diameter, whereas when the diameter of the tube is only 2.5 cm., the speed is reduced by about 30 per cent. Cooling by the walls thus interferes with the measurement of the true speed of the uniform movement of flame in mixtures of methane and air unless the diameter of the tube exceeds about 5 cm.

When, however, the diameter is increased above 10 cm., the speed of the flames is affected by the coming into play of another factor, namely, convection. This is noticeable with the fastest moving flames in tubes 10 cm. in diameter, the visible effect being a turbulence of the flame front. This is essentially a swirling motion in a direction nearly normal to the direction of translation of the flame front, which, as in tubes of smaller diameter, progresses at a uniform speed for about 150 cm. before backward and forward vibrations are set up. This swirling motion appears ab initio, and is due to rapid movement of the hot gases from below upwards by convection. In tubes of comparatively small diameter (5 to 9 cm.) this rapid movement is suppressed.

Influence of tube diameter upon the flame speed.

With tubes of diameter ranging from 9 cm. to 17 cm. there is an apparent retardation in the influence of the size of the tube. This was first observed by Parker in 1915, but, as is evident from fig., this effect is only temporary, for the maximum effect is not even reached with a diameter of 96.5 cm. But it may reasonably be objected that a pipe of so great a diameter is no longer to be regarded as a tube. On the other hand, there is a lower limit to the diameter of the tube that will allow a flame to pass through.

If the diameter of the tube is sufficiently small,|the flame dies out after travelling a short distance. Still further reduction in the diameter of the tube renders it impossible for the flame to spread from the point of ignition. This was discovered by Davy, and constituted the starting- point of his researches 011 the construction of his well-known safety lamp for use in coal mines. He found that in tubes 1/7-inch in diameter (i.e. 3.63 mm.) explosive mixtures of firedamp and air could not be fired as no flame would pass along.

Analogous results were obtained by Mallard and Le Chatelier, who found the speeds of flame in a mixture of methane and air containing 10.4 per cent, of methane, using tubes of glass of different diameters, to be as follow:

Diameter of tube, mm	3.2	5.5	8.0	9.5	12.2
Speed of flame, cm. per sec.	nil	22	39	41	47

Influence of tube diameter upon the propagation of flame.

The methane was impure, it is true, but the result closely agrees with that found by Davy with firedamp. A more thorough investigation of the subject by Payman and Wheeler, whilst yielding analogous results, has revealed several interesting features. One of the most important of these is that the apparent limits of inflammability of methane in air become narrowed as the diameter of the tube decreases, until with a diameter of 4.5 mm. only one of the seventeen mixtures tested, namely, that containing 9.95 per cent, of methane, would propagate flame. With 10.15 per cent, methane no flame would pass, whilst with 9.5 per cent, methane the flame only travelled 20 cm. and then became extinguished. With a tube of diameter 3.6 mm. no flame propagation occurred with any of the inflammable mixtures. The results obtained with 9.95 and 9.0 per cent, methane are shown in fig. The nature of the tube itself is important, as Davy himself was aware. Metal tubes, on account of their greater cooling effect, are more efficient extinguishers of flame than glass. Since wire-gauze may be regarded as a series of thin, transverse sections of narrow metallic tubes joined together, the bearing of these results upon Davy's safety lamp is apparent.

Consideration of the curves shown in fig. shows that the flame-speeds of mixtures of methane and ail steadily rise to maximum values as the percentage of the combustible gas is raised from its lower limit of 5.6 to about 10 per cent. Further addition of methane reduces the speed until the flame is extinguished just beyond the upper limit value.

This was to be anticipated for, beyond a certain value, excess of the combustible gas will usually function as a diluent. The shape of the curve, therefore, is typical.

Flame speeds in methane-air mixtures diluted with nitrogen. (Mason and Wheeler, 1917.)

Interesting results are shown in fig., which gives the flame speeds of mixtures of methane and oxygen with varying proportions of the neutral diluent nitrogen. Not only does the lower methane limit fall slightly with increase of oxygen, but it will be observed that there are great increases in the upper-limit values and in the flame speeds.

Flame speeds in methane-air mixtures enriches with oxygen.

By decreasing the percentage of nitrogen from that present in the atmosphere to nil, the flame speeds show enormously enhanced values. This is clear from the data shown graphically in fig.

The author points out that the most striking results are those for mixtures of methane with pure oxygen. The speed is then 5500 cm. per second - more than fifty times that attained in air. It will be further observed that the maximum speed of the flame is obtained with the mixture in which the methane and oxygen are present in combining proportions, namely, CH₄ + 2O₂. This result is in noteworthy distinction to that obtaining when the detonation-wave is developed in mixtures of methane and oxygen, for the mixture in which the speed of the detonation-wave is greatest contains equal proportions of methane and oxygen. The difference is the more striking when it is remembered that the uniform movement may give place to the detonation-wave after quite a short distance of travel of the flame.

The flame-speeds of combustible mixtures of hydrogen and air are less easy to determine since the flame travels more rapidly and in some mixtures the explosion-wave may be set up after the flame has travelled but a short distance (about 2 metres) from the end of the tube.

Flame speeds of hydrogen in air. (Haward and Otagawa, 1916.)

Nevertheless a series of determinations has been published, and these are shown in fig. Glass tubes of three diameters were employed namely, 9, 11.5, and 25 mm. respectively. The curves show that an increase in diameter enhances the flame speed only in those mixtures in which the hydrogen is not present in considerable excess. It is interesting to note that the maximum flame speed is not attained with the mixture containing the hydrogen and oxygen in combining proportions, namely, 29.5 per cent, of hydrogen, but with a mixture containing about 40 per cent, of hydrogen. This is in peculiar contrast to the results obtained with mixtures of methane and oxygen. Le Chatelier suggested that as the thermal conductivity of hydrogen is six times that of air, it may well be that with mixtures containing more than one-third of their volume of hydrogen, the enhanced conductivity of the mixture more than compensates for its lower heating value.

Flame speeds in combustible mixtures of paraffin hydrocarbons. (Payman, 1919.)

Measurements have also been made of the speed of the uniform movement in mixtures of air with each one of the hydrocarbons of the paraffin series up to and including pentane. The determinations were carried out with horizontal glass tubes, 2.5 cm. in diameter, and the results are shown diagrammatically in fig. With the exception of methane, the maximum speeds are approximately the same, namely, about 82 cm. per second. The value for methane is rather lower than this, being 67 cm. per second. Owing to the few data available for the thermal constants of the paraffin hydrocarbons, it is not easy to explain this difference. In each instance, the mixture having the maximum speed of flame contains more combustible gas than is required for complete combustion.

The higher and lower limit speeds tend to approach the same value of 20 cm. per second for all the gases. It is interesting to note that in every case, except that of methane, the maximum flame speed occurs with a mixture containing more of the combustible gas than is required for complete combustion.

Flame speeds of carbon monoxide, hydrogen, and methane.

Rusults obtained with carbon monoxide and air, and with mixtures of thee two with other combustible gases are shown graphically in fig.

In the following table are given the maximum uniform flame speeds of various combustible mixtures, together with the flame speeds at approximately the upper and lower limits in horizontal tubes of diameter 2.5 cm.