48 PAYMAN THE PROPAGATION OF FLAME IN VI.-The Ppopagatiort- of Flame in Complex Gaseous Mixtures. Part I V. The Uniform Movement of Flame in Mixtuq*es of Methane, Oxygen and Nitrogen. ‘‘ Maximum-speed Mix-tures” of Methane and Hydrogen in Air. By WILLIAM PAYMAN. IT is customary to describe the inflammation of a gas mixture containing hydrogen and oxygen for example as the “ burning of hydrogen in oxygen.” This phrase is purely a relative one it being of course equally correct to regard the combustion as the burning of oxygen in hydrogen. Thus the upper limit of in-flammability of hydrogen in oxygen is the lower limit of inflammability of oxygen in hydrogen. Mixtures of a combustible gas with air can be considered in a similar way. I f however we state that the combustible gas, hydrogen for example is burning in air the alternative expression would be that the oxygen is burning in a mixture of nitrogen and hydrogen.A comparison can in fact be made over a range of inflammable mixtures between hydrogen and air on the one hand, and on the other mixtures of oxygen with a mixture (or “ atmo-sphere ”) containing nitrogen and hydrogen in constant pro-portions. For all practical purposes atmospheric air may be regarded as a mixture of oxygen and nitrogen in constant proportions. To investigate thoroughly the mode of combustion of complex in-flammable gas mixtures it is evidently desirable to examine their behaviour with atmospheres ” other than air the simplest problem being no doubt the combustion of a pure inflammable gas such as methane in pure oxygen.The uniform movement during the propagation of flame in mixtures of methane with different atmospheres containing less oxygen than air has been examined by Mason and Wheeler (T., 1917 111 1044). The present research deals with mixtures con-taining more oxygen than air and with mixtures with pure oxygen. The detonation-wave in such mixtures has been studied by Dixon (Phil. Trans. 1893 184 97). The speed of propagation of flame by detonation is of a different order from that during the initial, uniform movement of flame which is supposed to be mainly effected by the conduction of heat from the burning to the adjacent unburn COMPLEX QASEOUS MIXTURES. PART N. 49 layer of gas mixture. The speed of the detonation-wave is however, uniform.The two modes of propagation of flame “uniform move-ment ” and ‘‘ detonation-wave,” may be compared with respect to mixtures of hydrogen and air. The speed of the detonation-wave in the mixture of air with hydrogen containing the correct pro-portions for complete combustion is 1930 metres per second in a tube 9 mm. in diameter (value extrapolated from those determined by Dixon Zoc. c i t . ) whilst the speed of the uniform movement of flame in the same mixture (in a horizontal glass tube 2.5 cm. in diameter) is 4.8 metres per second (Haward and Otagawa T., 1916 10.9 83). Maximum-speed Mixtwes.-If we neglect losses of heat to the walls of the containing vessel the speed of propagation of flame during the uniform movement can be regarded as depending mainly on two factors namely (1) the rate of conduction of heat from layer to layer of the mixture which in turn depends on the difference in temperature of the burning and the unburnt gases and on their thermal conductivities and (2) the rate of reaction of the combining gases which for a given combustible gas will vary with the composition of the mixtures (presumably according to the usual laws of mass action) and with the temperature pro-duced by the reaction.A third factor might be added namely, the ignition-temperature of the mixtures but this is perhaps dependent on the other factors. The mixture of hydrogen and air for complete combustion that. is to say the mixture having the greatest heat of combustion, contains 29.6 per cent. of hydrogen but the mixture in which the speed of the uniform movement of flame is greatest contains about 38 per cent.or nearly 10 per cent. in excess. This fact is usually explained by reference t o the high thermal conductivity of hydrogen which is 31.9 x 10-5 as compared with 5-22 x 10-5 for air. A similar displacement of the maximum-speed mixtures is, however observed with all inflammable gases when mixed with air including (as was shown in Part I11 of this series of papers) gases such as carbon monoxide the thermal conductivities of which are less than that of air.* Consider the effect of mass action when methane burns in a given atmosphere of nitrogen and oxygen. Let this atmosphere contain a per cent. of oxygen. According to the law of mass action the rate of reaction will be proportional to CCHc x CZo1:.Let the mixture in which the rate has its maximum value contain 2- per cent. of methane. * The value for the thermal conductivity of carban monoxide i s 4.99 x 10-50 Then PAYMAN THE PROPAGATION OF FLAME IN CCH( x Po = x) x (100 - 2)-> ( C 100 l2 Since a is constant the term into which it enters will be at a maximum when z(lOO-x)2 is a t a maximum. That is to say, provided it remains constant the composition of the atmosphere does not affect the methane content required to give the expression CC‘H+ x Po its maximum value. It can be shown that this ex-pression reaches a maximum when x the percentage of methane, is 33.3. Similarly with hydrogen and any atmosphere of oxygen and nitrogen of constant proportion the factor representing the effect of mass action is a t a maximum when the mixture contains 66.7 per cent.of hydrogen. I n every instance with a given atmosphere when this remains unaltered the maximum effect of the mass-action factor is theoreti-cally attainable with mixtures containing more combustible gas than is required- for complete combustion (except with an atmosphere of pure oxygen when the mixture for complete combustion is also, theoretically that for the maximum effect of mass action). The rate of chemical reaction increases rapidly with rise of temperature. I n a series of mixtures of a combustdble gas with an atmosphere of constant composition the highest calorific effect is produced by the mixture containing combustible gas and oxygen in combining proportions.This factor will therefore act in an opposite sense to mass action and will diminish the “displace- . ment ” of the maximum-speed mixture caused by the latter factor. For this reason the amount of displacement will be influenced by the cooling effect of excess of combustible gas and the higher the specific heat of this excew gas at the temperature of reaction the less will be the displacement.“ When oxygen burns in an “atmosphere” of constant composi-tion composed of nitrogen and a combustible gas the displacement of the maximum mixture should take place towards mixtures con-taining excess of oxygen. This can be tested experimentally. Just as the whole series of inflammable mixtures of methane and air can be obtained by starting with the mixture containing the reacting gases in combining proportions and adding either methane or air to it in the same way a series of mixtures of oxygen with an “atmosphere” of nitrogen and methane can be obtained, by adding excess of oxygen or excess of “atmosphere” to the * This consideration accounts for the wider “ displacement ” obtained with carbon monoxide than with hydrogen when mixed with air COMPLEX GASEOUS MIXTURES.PART IV. 51 mixture of methane and air in combining proportions which may be termed the " basic mixture." This procedure has the advantage of enabling a direct comparison to be made between methane-air and oxygen-" atmosphere " mixtures the two series having a common point. The results of two such series of determination of the speed of the uniform movement of flame in mixtures of oxygen with (i) an atmosphere of nitrogen and methane and (ii) one of nitrogen and hydrogen are given in table I.The determinations were carried out in a horizontal glass tube 1-5 metres long and 2-5 cm. in diameter. TABLE I. Speed of Uniform Movement of Flame in Mixtures of Oxygen with Mixtures of Constant Composition (" A tmospheres ") of iVitrogen and a Combustible Gas. Methane as the combustible gas. Hydrogen as the combustible gas. Basic mixture 9.5 per cent. CH,; 19-0 per cent. 0,; 71.5 per cent. N,. Methane. Per cent. 6.67 7.61 8.29 8.75 9.07 9-18 9.50 9.67 Oxygen. Per cent. 43.3 46.2 39.5 25.6 22.9 22.0 19.0 17-8 Speed. Cm. per sec. 36.0 61.9 84.3 97-3 91.4 85-4 66.7 37.5 ,-Basic mixture 29.6 per cent.H,; 14.8 per cent. 0,; 55.6 per cent. N2-Hydrogen. Oxygen. Speed. Per cent. Per cent. Cm. per sec 16.06 53.7 171 21-76 37.3 488 25.72 25-9 660 29.60 14.8 410 30-50 12.2 234 It will be seen that the displacement of the maximum-speed mixture in both series of experimentkl as anticipated is towards mixtures containing an excess of oxygen. In table I1 the dis-placements are compared with those found with the combustible gases burning in air. TABLE 11. Displacement of Maximum-spe ed Mixtures . Methane. & OS-N CH4-N, constant. constant. Methane. Oxygen. Per cent. Per cent. Mixture for maximum speed of Mixture in combining propor-Displacement . . . . . . . . . . . . . . uniform movement of flame 9.9 34.8 tions.(Basic3 mixture) ...... 9-6 19.0 0.4 5.8 Hydrogen. A7 OS-N HS-N, constant. constant. Hydrogen. Oxygen. Per cent. Per cent. 38.5 23.4 29-6 14-8 8.9 8-52 PAYMAN THE PROPAGATION OF FLAME IN The addition of either combustible gas or oxygen to the basic mixture results in an increase in speed of the flame. According t o the laws of mass action it would be expected that the displacement would be greater on the addition of oxygen than on the addition of methane (since one molecule of methane combines with two mole-cules of oxygen for complete combustion); this is found to be so. The displacement should be less wit?h oxygen than with hydrogen (since two molecules of hydrogen combine with one molecule of oxygen) ; experiment again shows this deduction to be correct.The fact that the specific heat of oxygen is lower than that of methane and much lower than that of hydrogen however would have the effect of decreasing proportionally the amount of displacement caused by excess of either of the two last-named gases. Thus the displacement caused by the addition of oxygen is found to be much gIeater than that caused by methane but only a little less than that caused by hydrogen.* The Uniform Movemeizt of Flame in Mixtures of Methane, Oxygen and Nitrogen. The speeds of the uniform movement of flame in mixtures of methane with atmospheres containing 13-7 21 33 50 66 and 100 per cent. of oxygen have been determined. The experiments were carried out in a horizontal glass tube 2.5 cm.in diameter, as used for earlier experiments. A comparatively short tube, 1.5 metres in length was used in order to avoid the development of the detonation-wave. With the fastest speeds of flames how-ever the detonation-wave was developed after the flame had travelled less than a metre so that for some of the experiments i t was necessary to replace the last metre of the glass tube by a piece of lead piping of the same length and internal diameter. Only the slowest speeds up to about 300 cm. per second were determined by means of the automatic commutator and single recording stylus usually employed €or such work in this labora-tory; for faster speeds recourse was had to delicate Deprez indicators with separate styli for each screen-wire recording on a smoked paper chart fixed to a rapidly revolving drum.The fastest speeds in mixtures of methane with pure oxygen were determined photographically by the method described by Mason and Wheeler (T. 1919 115 578). A comparison between the two last-named methods of recording speeds of flames gave closely agreeing results. The results of the determinations are given in table 111 and * These experiments explain why the displacement of the maximum-speed mixture was found to be so small with the mixtures of producer gas and air, as described in Part 111 TABLE 111. Speed of Uniform Movement of Flame in Mixtures of Methane with Oxygen in a Horizontal Glass Tube 2.5 cm. Atmosphere. 13.7 per cent. 0,. 7 Per cent. CH,. 6.33 6.41* 6.70 6.90 7.02 - Speed (om.per sec.). Flame about I6 om. 21.9 21.0 19.1 Flame about 6 cm. Atmosphere. 33 per cent. 02. 7 Per cent. CH,. 6-69 6.78 6.87 8-44 11-01 14*58* 18.01 21-51 25.12 25.41 -'-Speed (cm. per sec.). Flame about 10 cm. 23.0 23.9 97.6 168 232 200 49.1 18.9 Flame about 15 cm. Atmosphere. 50 per cent. 0,. & Per cent. Speed CH,. (cm. per sec.). 5-70 Flame about 8-83 22.8 9.60 160 12-48 40 1 15-38 735 19*84* 967 24.01 711 28-47 171 33-58 44 38.78 18.9 39-26 Flame about 15 cm. 16 cm. Per CH,. 5.70 5.84 8.79 11-15.07 18-25* 29.29 34.65 40.02 46.93 47-47.6 54 PAYMAN THJG PROPAGATION OF FLAME diagrammatically in Pig. 1. For the values for mixtures with air, reference should be made t o the table in P a r t 11 (T.1919 115, 1448). The mixture marked with an asterisk in each column is that which contains methane and oxygen in combining proportions. Fig. 1 may be compared so far as its general characteristics are concerned with the similar diagram given by Mason and Wheeler (loc. cit. p. 1048) for mixtures of methane with atmospheres con-taining less oxygen than air. It should however be noted that these authors determined the speeds in a tube 5 cm. in diameter. The most striking results are those for mixtures of methane with FIU. 1. Methane per cent. pure oxygen. It will be seen that the maximum speed of the uniform movement of flame is obtained as was anticipated with the mixture containing methane and oxygen in combining propor-tions (CH,+20,).This result is in sharp distinction from what obtains 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 remem-bered that the uniform movement gives place to the detonation-wave after quite a short distance of travel of the flame [ To face p. 54 COMPLEX OASEOUS Ml’STUSb!S. PART 1V. 55 In table I V a comparison is made between the speed of the uniform movement and that of the detonation-wave in the five mixtures used by Dixon (Zoc. cit. p. 181). TABLE IV. Comparison of the Speeds of the Detonation-wave and the Uniform Movement in Mixtures of Methane and Oxygen.Composition of mixture. 2CH + 80s 2CH4 + 60, 2CH4 + 402 2CH4+ 30, ZCH,+ 202 Speed metres per second. - Detonation wave. Uniform movement. Tube 2-5 cm. diam. Tube 0.9 cm. diam. 1963 18 2146 33 2322 66 2470 25 2528 2 The addition of methane to the mixture for complete combus-tion (CH,+20,) is thus seen to increase the speed of the detonation-wave but markedly to decrease the speed of the uniform movement of flame. This effect is well illustrated by photographs of the flames (1) in a mixture containing just sufficient oxygen for complete combus-tion of the methane and (2) in a mixture containing rather more methane (40 per cent.). In the latter mixture (Fig. a) the uniform movement persisted over about 25 cm.of travel of the flame which then vibrated rapidly for a short time (0.06 sec.) without moving further along the tube. The vibrations were followed by a rapid acceleration of the flame resulting in the detonation-wave which shattered the glass tube a t about 25 an. distance from the lead extension piece. The bright band at the bottom of the photograph is caused by the ‘ I retonation-wave.” * Although the speed of the uniform movement of flame is slower in a mixture containing 40 per cent. of methane than in one con-taining 33 per cent. the detonation-wave is developed sooner in the former. With the 33 per cent. mixture the uniform move-ment extends across the whole width of the photograph (Fig. 3). The incidence of the detonation-wave a short distance further along the tube (within the lead extension piece) is indicated by the bright band due to the retonation-wave a t the bottom of the photograph.f * A compression-wave sent back simultaneously with the development of the detonation-wave through the burnt or still burning mixture (Dixon, Phil. Trans. 1902 200 316). t The length of tube photographed wag 30 cm. and the speeds of the film were 692 and 762 om. per second for Fig. 2 and Fig. 3 respeotively $6 PAYMAX THE PROPAGATION OF FLAME IN It must be admitted that the displacement of the maximum-speed mixture away from that required for complete combustion is not! very great in mixtures of methane and air. A better test) of the soundness of the coriclusion that with pure oxygen the maximum-speed mixture and the complete-combustion mixture should coincide should be obtained with a combustible gas like hydrogen.With this gas it will be remembered the maximum-speed mixture with air is displaced by as much as 10 per cent. Experiments were theref ore made with mixtures of hydrogen and pure oxygen. Three mixtures were examined and the speeds are recorded in table V with the speeds of the detonation-wave in the same mixture for comparison. TABLE V . Comparison of the Speeds of the Detonatiowave and the Uniform Movement in Mixtures of Hydrogen and Oxygen. Speed metres per sec. - -. Hydrogen. Detonation-wave. Uniform movement. Tube 2.5 cm. dirtm. Per cent. Tube 0.9 cm. &am. (Dixon). 59.9 66-6 75.2 2650 2824 3140 5-74 6.62 5-16 Fig.4 and Fig. 5 are the photographs of the flames in the mixtures containing 75.2 per cent. and 66.6 per cent. of hydrogen respectively.* It will be seen that the photographs are similar in general character to those obtained with the two corresponding mixtures of methane and oxygen. To revert to the experiments with methane the addition of either methane or oxygen like that of the inert gas nitrogen to the mixture of methane with pure oxygen of the composition CH + 20, results in a reduction of the speed of the uniform move-ment of flame. The relative effects of these three gases are shown in Fig. 6. Methane having the highest specific heat of the three, has the greatest retarding effect. Although oxygen and nitrogen have approximately the same specific heat the retarding effect of the former is appreciably less owing to the effect of mass action when the gas added is capable of taking part in the reaction.The application of the “speed generalisation ” was shown in earlier papers to be restricted by the fact that the only data avail-* The speeds of the films were 784 and 816 cm. per second for Fig. 4 rtnd Fig. 6 respectively COMPLEX GASEOUS MIXTURES. PART I V . 57 able for use in the calculations were those respecting mixtures of inflammable gas% with air. Thus with methane-hydrogen-air mixtures no calculations could be made for mixtures in which the speed of flame was greater than 67 cm. per second the maximum speed in mixtures of methane and air. The speeds now obtained in mixtures of methane with atmospheres containing more oxygen than air are often greater than the maximum speed with hydrogen-air mixtures so that the use of these values should render it FIG.6. Gm added to the mixture CH + 20, molecules. possible to calculate the speeds of the uniform movement; of flame in any methane-hydrogen-air mixture. For this purpose however it would be necessary t o determine the speed of flame in mixtures of hydrogen with different atmo-spheres in the same way as has been done for methane and for similar calculations Go be made for mixtures of an industrial gas with air similar determinations would be required for each individual gas present in the industrial gas. Such a series of determinations is outside the scope of the pre-sent work. It is however important to establish the fact that the “speed generalisation” is capable of extension in this manner 58 PROPAGATION OF FLAME IN COMPLEX GASEOUS MIXTURES.To this end a few determinations have been made for methane-hydrogen-air mixtures. To simplify the calculations mixtures of methane and hydrogen with just sufficient air for complete combustion were chosen. A curve similar to the one in Fig. 6 for CH,+20,+zN2 was con-structed for hydrogen (2H + 0 + d,). I f mixtures are selected from these two curves in which the speed of flame is the same and is intermediate between the maximum speeds in methane-air and hydrogen-air mixtures it is possible to mix them in such propor-tions that the resulting mixtures will contain nitrogen and oxygen in the ratio in which they are found in air. This mixture will have the same speed of uniform movement of flame will contain combustible gas and oxygen in combining proportions and will be, in a sense a methane-hydrogen-air mixture. In this way it is possible t o determine the speed of flame in all mixtures of methane and hydrogen with sufficient air for their complete combustion. The results of such calculations with three simple mixtures are recorded in table VI. Speed of TABLE VI. Uniform Movement of FZame. Cm. per sec. Hydrogen-Me theno mixture. Calculated. - From curves. 9 From formula. 85 90 95 135 140 149 240 250 246 Found. The results recorded in the last column are obtained by use of a formula similar to the one used in P a r t I1 (T. 1919 115 1452) for calculating the ma,ximum-speeds of flame in mixtures with air, ‘‘ mixture for complete combustion ” being substituted for ‘‘ maximum-speed ” mixture. The experimental work described in this series of papers was carried out at the Home Office Experimental Station under the general direction of Dr. R. V. Wheeler. ESKDALS, CUMBERLAND. [Received November 12th 1919.