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Changes in the shape of flames propagating in tubes
CHANGES IN SHAPE OF FLAMES PROPAGATING IN TUBES
403
52
C H A N G E S IN T H E S H A P E OF F L A M E S PROPAGATING IN T U B E S By H. GUI~NOCHE Am) M. JOUY (Translated by Ruth F. Brinkley) 1.
INTRODUCTION.
Combustion of a gas mixture confined in a vessel of some given shape and ignited at a point generally takes p!ace along a front which propagates at a velocity that depends both on the initial nature, composition, pressure and temperature of the mixture, and on the dimensions, shape and limiting conditions of the vessel. These various factors act either directly or indirectly on the shape of the flame front. i n a tube, it is assumed that the burning velocity, V0s (velocity of the flame with respect to the unburned gas), the propagation velocity, D, the area of the flame front, ~, and the area of the cross section of the tube, S, have the following relation:
in the well-known behavior of flame propagation. The present paper simply presents the experimenta! results obtained in tubes both with regard to the shape of the flame front in uniform propagation and to its deformatkm in the nonsteady state. 2.
EXPERIMENTAL
a. IIigh-speed photographs of the flame front can be obtained by different procedures, depending on the rate at which the flame propagates and on its luminosity. For mixtures having a low propagation velocity, we have adopted the classic method of a rotating sector activated by a synchronous motor. A plane mirror placed over the tube at an angle of 45 ~ makes it possible to record a horizontal projection of the flame front so that two simul.
Vos = DS/~2. This implies that (a) V0s is constant over the entire surface~otherwise V0s represents only the average velocity along the surface of the flame; (b) the unburned gas is quiescent or flows at a constant rate (case of tubes that arc partially open at the end opposite to the flame); (c) the surface of the flame front travels with a translational, uniform movement. Although the first condition must still be assumed, the two others can readily be attained. I t then becomes possible to study the stable form of the flame front, a study which is essential to the understanding of flame propagation. Without these precautions, except in rare cases, propagation is no longer uniform and becomes vibratory. Theoretical investigation of vibratory problems is not easy because both the law of cooling of the burned gas and the effect of vibrations on flame deformation are unknown. It is possible, however, to observe experimentally the disturbances in the flame front, the interdependence of the flame surfaces and the vibrations in the tube, which result ' Such a flame is not stable in the ordinary sense as the location of the ridges which the flame shows shift continually in the plane in which it is stabilized. Changing the flow or the composition changes the number of these cells, and the flame often begins to vibrate and appears to rotate around the tube axis, its center remaining virtually fixed.
METIIODS
TABLE T . u b e .n o . . . . . . . . . . . . .
.
1 .
.
1 2 .
3
4
Length, L, cm.. I 56 I 57 / 98 I 100 Inner diameter, ] I I [ r .......... I 2.9 [ 2.9p 4 [ 2 Ignition source..I Flame [Spark [Spark[Spark taneous pictures o[ the flame along orthogonal directions are obtained. A lens with an f: 2.9 aperture and a focal length of 135 mm projects the image of the horizontally propagating flame on a fixed photographic plate. The two resulting pictures are enlarged to the same linear dimensions. I n addition, a device of the Mallard and Le Chatelier type placed on the other side of the tube gives another aspect of propagation. The following air-acetylene mixtures were used: C~.H2 + 5.25 air; Co.H2 + 6.7 air; C~H,. + 11.9 air; C~Ho + 15.7 air; C~II2 + 21.2 air. Table 1 gives the dimensions of the tubes, which are cylindrical, and the ignition source. The tubes first are evacuated to about 10-1 mm Hg and then filled at room temperature and atmospheric pressure from a mixture in a storage tank. b. When the tubes are wide open at the ignition end, the flame front is photographed and its rate
404
LAMINAR COMBUSTION AND DETONATION WAVES
of progress measured at the beginning of propagation, where the combustion movement is roughly uniform. However if the velocity is rendered constant by adjusting the limiting conditions (1), these measurements can be made at any point along the tube, thus making it possible to determine D by a method similar to that of Berthelot and Vieille (2). Gerstein, Levine, and Wong (3)used a similar procedure to determine the propagation velocity of a large number of hydrocarbon-air mixtures. To study uniform propagation of the flame front, we made use of diaphragms whose size varied according to the nature of the mixture and the tube dimensions. In this way the ignition end of the tube could be decreased when the other end was closed and the opposite end should be decreased when the ignition end was left open. 3. RESULTS
a. Uniform propagation 1. The flames often appear as ellipsoids, at least in narrow tubes and for mixtures with low burning velocities. Coward and Hartwell (4) calculate the area of the flame front by matching it to a portion of ellipsoid whose plane of symmetry is the vertical plane through the axis of the tube and whose main axis is inclined over the horizontal. I t appears that this interpretation does require discussion because under conditions of uniform propagation the flame rarely assumes the position described and discussed by these authors. I t has the appearance of a "spoon" tangent to the inner wall of the tube, which takes up some position in the tube and travels the length of the tube maintaining a constant area. The accompanying photographs (figs. 1-12) show the position and shape of the flame in the various tubes used. Views h are projections of the flame front in a horizontal plane and views v are projections in a vertical plane. The time interval between two successive positions of the flame is designated as At. The diameter of the ignition opening and the opposite opening are d~ and d j , respectively. 2. If the effect of convection of the burned gas on the flame shape is doubtful, it is a rough approximation, in cases where the appearance of the flame appears to justify such an analogy, to compare the flame to the ellipsoid whose equation is given by Coward and Hartwell. Such an approximation gives some idea of the true area of the flame surface, but the degree of accuracy is not known. Moreover, in many instances, the curvature of the front does not have a constant sign over the entire
surface (fig. 4) making the flame area calculated from the contour less than the true value. Finally~ the stroboscopic method is defective if the burned gas is actinic enough to impress the photographic plate. This is the case for the stoichiometric airacetylene mixture (fig. 6). The area of the flame front is increased by an amount which cannot be determined because it depends on the emission of the gas, the sensitivity of the photographic emulsion, the dimension of the stroboscopic slit and the aperture of the camera lens. These considerations limit the significance of the results obtained with this experimental method. However the burning velocity can be determined .in this way (a) if the flame surface is well defined and smooth; (b) if the flame travels into a quiescent mixture or a mixture with a constant flow rate, as shown by any optical method (5); (c) if the flame has a simple geometrical shape such as a spherical segment. This last condition can be obtained--it occurs much more readily in mixtures with a low acetylene content--but the reasons for its occurrence are not known. For the same set of experimental conditions, except possibly the spark, the flame front may be unsymmetrical or approximately symmetrical (fig. 7). However there does exist a relation between the shape of the initial flame front and its appearance in the subsequent frames. When the flame has an axis of symmetry and when this axis coincides with that of the tube, the surface of the first fiont is very nearly a spherical segment, in contrast to the case of an unsymmetrical flame. As under conditions of uniform propagation once the movement is established no force acts on the combustion surface (the piston represented by the burned gas has a velocity of zero), it may be assumed that this surface will retain its initial shape over its entire course, this shape depending on the way in which the spark flashes. This is similar to what is observed when a flame is forced back very gradually into a vertical tube whose upper rim presents an irregular section. The flame re-enters the tube unsymmetrically and advances slowly by translation, keeping its classical "spoon" shape. When action on the flow ceases, the flame becomes stabilized in this shape and clings to the hot points of the wall.
b. Vibratory propagation When propagation is vibratory, the flame surface undergoes changes. The tube with its two columns of unburned and burned gas forms a
CHANGES
IN SHAPE OF FLAMES
PROPAGATING
IN TUBES
F l o s . 1-12 1/ sec, C2HH2 -~- 5. 25 air Fro. 1. T u b e No. 1, di = 12 m m , d l = 0, At = ,:~o FIG. 2. T u b e No. 1, di = ~p, d.t = 12 ram, At = 1/~o sec, C~Hto + 5 . 2 5 air F i e . 3. T u b e No. 1, di = ,p, dy = 12 m m , At = ~ o sec, C~I-I~ + 5. 25 a i r FIG. 4. T u b e No. 2, di = 12 m m , d.r = 0, At = /1~0, 1 sec, C2I'I2 + 5 . 2 5 air F~G. 5. T u b e No. 4, di = 8 m m , d.r = 0, At = ~ o o sec, C2H2 + 15. 7 air FIG. 6. T u b e No. 2, di = 14 m m , d., = 0, At = ~ o o sec, Cei.i~ + 1 1 . 9 air F~G. 7. T u b e No. 2, di = 12 ram, d l = 0, At = )~o sec, C2I-I2 + 5 . 2 5 air FIG. 8. T u b e No. 1, di = ~, di = 0, At = 1/.5o, 1 sec, C2H~ + 5. 25 air FIG. 9. T u b e No. 1, di = 7 m m , ds = 0, At = 1/~o sec, C2H~ + 5 . 2 5 air F~c. 10. T u b e No. 3, di = 16 m m , dr = 0, At = )~o sec, C~H~ + 5. 25 air FIG. 11. T u b e No. 4, di = 10 m m , d! = 0, At = I/~o sec, C~I.I~ + 5. 25 a i r FIG. 12. T u b e No. 2, di = 14 m m , dy = 0, At = 1/(o o sec, C2H2 + 1 5 . 7 air
405
406
LAMINAR COMBUSTION AND DETONATION WAVES
resonator that can vibrate in (2k + 1))~/4 or in k(X/2), according to its limiting conditions. Diaphragms have little effect on the frequency of the vibrations, but they affect the amplitudes, at least for mixtures with low burning velocities. The law of changes in frequency as a function of the diameter of the opening is similar to that given by Bouasse (6) for resonance in a tube filled with a single gas. The dimensions of the tube do not influence the character of the propagation. Thus, for a tube that is closed downstream and open upstream (ignition), the frequency most often observed is the fundamental frequencY , but in many cases the first harmonic is present; this harmonic never lies between the consecutive node and antinode of the movement. Similarly, with a tube that is wide open at both ends, two propagation patterns may appear, regardless of the dimensions of the tube (figs. 13 and 14).
FIGS. 13 and 14. d~ = d/ = ~ = 20 mm, L = 56 cm. I t is clear that the shape and area of the flame depend on the vibratory system. Thus the flame straightens up in the tube and tends to become thinner and more symmetrical when it reaches a region of vibratory disturbances. Simultaneously the so-called multicellular structure appears. This had been observed previously by Markstein (7). I t should be noted, however, that although our setup does not allow observation of the flame front during large-amplitude vibrations, this flame structure appears to be characteristic of the transition from a state of uniform propagation to a state of large-amplitude vibrations, which we will call an oscillatory state. This is indicated also by photographs of Schmidt, Steinicke and Neubert (8) who investigated the combustion of propane-air mixtures using an optical method with a high frequency spark as a light source. According to Markstein (7), the cell dimensions depend on the amplitude of the vibratory motion. We believe that it depends rather on the number of cells, and that this amplitude increases with the state of division of the flame front. This can be verified by studying the deformation of the
flame front as a function of the diameter d~ of the open end (figs. 8 and 9). Finally it should be noted that such flames appear regardless of the diameter of the tube or the mixture composition (figs. 10, 11 and 12). Recently Manton, von Elbe and Lewis (9) published an interpretation of cellular flames based on the influence of diffusion phenomena on the burning velocity. As the profile of a uniformly propagating flame has not been established, it seems hazardous to a t t e m p t to justify or reject such a view. Nevertheless the results obtained by us, as well as the "stabilization" of a multicellular flame in a cylindrical t u b e ) suggest rather that this phenomenon is due to hydrodynamic instability. REFERENCES 1. See, for instance, COWARD,H. F., HARTWELL, F. J., AND GEORCESON,E. H. M.: J. Chem. Soc., 1482 (1937), or GU~NOCHE, H., AND LAF~'I~E, P., Compt. Rend. 222, 1594 (1946), and GU~NOCrlE, H., AI~ MANSON, N., ibid. 230, 726 (1950). 2. BERTttELOT, M., AND VmlLLE, P.: Compt. Rend. 94, 101 (1882). 3. GERSXXlN,M., LEVlNE, O., AND WONO, E.: J'. Am. Chem. Soc. 73, 418 (1951). 4. COWARD,H. F., ANI) HARXWELL, F. J.: J. Chem. Soc., 2676 (1932). 5. GuENoclm, H.: Compt. Rend. 232, 2316 (1951). 6. BOUASSE, H.: Tuyaux et r6sonateurs, Delagrave, Paris (1928). 7. MARKSTEIN, G. H.: J. Aeronaut. Sci., 18, 428 (1951). 8. SCHmDT, E., STEImCKE, H.: Am) NEUBERT, U.: VDI-Fors. 431, B17 (1951). 9. MANTON, f., VON ELBE, G., AND LEWIS, B.: J. Chem. Phys. 20, 153 (1952). DISCUSSIONBY EDWARDBURKE* The authors state that orifices were used over the downstream end of the flame tube to reduce vibrations. For the purposes of the present paper this would seem acceptable since no burning velocities are reported; however we found that orifices are unsatisfactory where accurate burning velocities are desired. While we found that the orifices did reduce the vibration, they introduced considerable uncertainty into the measurement of flame speed. This is based on measurements done in connection with our study of the burning velocities of acetylene, which we reported in 1951,t wherein we employed tubes of approximately the same dimensions as those used by the authors of this paper. * Research Laboratories, Westinghouse Electric Corp., East Pittsburgh, Pa. t Friedman, R. and Burke, E., Industrial & Engineering Chemistry, Vol. 43, p. 2772, Dec. 1951.
INFLUENCE OF I N E R T GASES ON FLAME PHENOMENA
407
more, we found that if a sufficiently careful procedure of flame initiation is employed, a smooth flame front with a uniform mean velocity can always be obtained. It is stated that the flame area varies randomly from one run to the next. However, in the report,~ it is shown that, for any given mixture, the flame area bears a nearly constant ratio to the tube cross-section. Furthermore, the highly repeatable flame speeds shown in figure 2 provide further confirmation of the suitability of the tube method of measuring burning velocities. An indication is given that the method is unreliable because of the vibrations of the flame front. We found that the mean velocity of the vibrating flame is substantially independent of the amplitude of the vibrations, and that it is only necessary to follow the progress of the flame through a considerable number of oscillations. This further indicates that it is preferable to tolerate the vibrations rather than to eliminate them with orifices.
Our use of orifices was suggested by the paper of Guenoche and Manson~;; we were unable to duplicate their experimental findings over a wide range of the ratio of orifice diameter to tube diameter. Since the accurate measurement of burning velocity was the object of our study, we could not tolerate this uncertainty, and so all of our experiments were done with a closed downstream end. Difficulty was experienced by the authors, in that the flame fronts were often irregular. Furthermore, it is stated that spark ignition was used for some series of experiments, while flame ignition was used for others. In our work with acetylene we used only flame ignition, since our calculations indicated that spark ignition was unsuitable because reflections of the shock wave produced by the spark would perturb the flame. Further:~ Guenoche, J. and Manson, N., Comptes Rendus, Vol. 230, p. 726. Feb. 1950.
53
THE INFLUENCE OF INERT GASES ON SOME FLAME PHENOMENA By C. E. MELLISH AZ,rD J. W. LINNETT INTRODUCTION
One of the great difficulties in studying the mecha n i s m of flame propagation is t h a t it is impossible to alter one p r o p e r t y only of a n inflammable mixture while leaving all others unaffected. P r o b a b l y one of the simplest a n d smallest changes t h a t can be m a d e is the substitution of one kinetically i n e r t gas for another. I n particular, the substitution of one Group O gas for another (e.g. helitlm for argon) in a mixture will alter the properties of the mixture in as controlled a n d limited a m a n n e r as possible. T h e object of this p a p e r is to consider the effect of such inert gas substitutions. T h e inert gases t h a t will be examined in greatest detail will be helium, argon a n d nitrogen, b u t carbon dioxide will also be considered to a certain extent. I n t h e experimental p a r t of this p a p e r two sets of results will be presented: (1) T h e b u r n i n g velocities ( f u n d a m e n t a l flame speeds) of ethylene + oxygen + i n e r t gas mixtures, the inert gases being helium, argon or mixtures of these; (2) T h e upper limits of inflammability of hydrogen + air + inert gas mixtures and of hydrogen + nitrous oxide + i n e r t
gas mixtures, the inert gases being helium, argon a n d nitrogen. I n the next section the results t h a t have been obtained b y other workers for the effects o[ inert gases on various properties of flames will be summarized. I n the last two sections the effects of changing inert gases on different properties (burning velocities, limits, m i n i m u m ignition energies, etc.) will be compared a n d the similarities and differences in b e h a v i o u r discussed a n d summarised. E X P E R I M E N T A L METHODS
1. Burning velocity determinations These were obtained b y the soap b u b b l e m e t h o d using the procedure described b y Pickering, Linn e t t a n d Wheatley (1). Preliminary experiments were carried o u t to ensure t h a t the soap film was a satisfactory enclosing m e d i u m for mixtures containing helium. A mixture containing 7.7 per cent ethylene, 19.4 per cent oxygen a n d 72.9 per cent helium was tested. This mixture was used to blow a n u m b e r of bubbles which were fired after v a r y i n g intervals of time from 6 to 31 seconds. T h e b u r n i n g
403
52
C H A N G E S IN T H E S H A P E OF F L A M E S PROPAGATING IN T U B E S By H. GUI~NOCHE Am) M. JOUY (Translated by Ruth F. Brinkley) 1.
INTRODUCTION.
Combustion of a gas mixture confined in a vessel of some given shape and ignited at a point generally takes p!ace along a front which propagates at a velocity that depends both on the initial nature, composition, pressure and temperature of the mixture, and on the dimensions, shape and limiting conditions of the vessel. These various factors act either directly or indirectly on the shape of the flame front. i n a tube, it is assumed that the burning velocity, V0s (velocity of the flame with respect to the unburned gas), the propagation velocity, D, the area of the flame front, ~, and the area of the cross section of the tube, S, have the following relation:
in the well-known behavior of flame propagation. The present paper simply presents the experimenta! results obtained in tubes both with regard to the shape of the flame front in uniform propagation and to its deformatkm in the nonsteady state. 2.
EXPERIMENTAL
a. IIigh-speed photographs of the flame front can be obtained by different procedures, depending on the rate at which the flame propagates and on its luminosity. For mixtures having a low propagation velocity, we have adopted the classic method of a rotating sector activated by a synchronous motor. A plane mirror placed over the tube at an angle of 45 ~ makes it possible to record a horizontal projection of the flame front so that two simul.
Vos = DS/~2. This implies that (a) V0s is constant over the entire surface~otherwise V0s represents only the average velocity along the surface of the flame; (b) the unburned gas is quiescent or flows at a constant rate (case of tubes that arc partially open at the end opposite to the flame); (c) the surface of the flame front travels with a translational, uniform movement. Although the first condition must still be assumed, the two others can readily be attained. I t then becomes possible to study the stable form of the flame front, a study which is essential to the understanding of flame propagation. Without these precautions, except in rare cases, propagation is no longer uniform and becomes vibratory. Theoretical investigation of vibratory problems is not easy because both the law of cooling of the burned gas and the effect of vibrations on flame deformation are unknown. It is possible, however, to observe experimentally the disturbances in the flame front, the interdependence of the flame surfaces and the vibrations in the tube, which result ' Such a flame is not stable in the ordinary sense as the location of the ridges which the flame shows shift continually in the plane in which it is stabilized. Changing the flow or the composition changes the number of these cells, and the flame often begins to vibrate and appears to rotate around the tube axis, its center remaining virtually fixed.
METIIODS
TABLE T . u b e .n o . . . . . . . . . . . . .
.
1 .
.
1 2 .
3
4
Length, L, cm.. I 56 I 57 / 98 I 100 Inner diameter, ] I I [ r .......... I 2.9 [ 2.9p 4 [ 2 Ignition source..I Flame [Spark [Spark[Spark taneous pictures o[ the flame along orthogonal directions are obtained. A lens with an f: 2.9 aperture and a focal length of 135 mm projects the image of the horizontally propagating flame on a fixed photographic plate. The two resulting pictures are enlarged to the same linear dimensions. I n addition, a device of the Mallard and Le Chatelier type placed on the other side of the tube gives another aspect of propagation. The following air-acetylene mixtures were used: C~.H2 + 5.25 air; Co.H2 + 6.7 air; C~H,. + 11.9 air; C~Ho + 15.7 air; C~II2 + 21.2 air. Table 1 gives the dimensions of the tubes, which are cylindrical, and the ignition source. The tubes first are evacuated to about 10-1 mm Hg and then filled at room temperature and atmospheric pressure from a mixture in a storage tank. b. When the tubes are wide open at the ignition end, the flame front is photographed and its rate
404
LAMINAR COMBUSTION AND DETONATION WAVES
of progress measured at the beginning of propagation, where the combustion movement is roughly uniform. However if the velocity is rendered constant by adjusting the limiting conditions (1), these measurements can be made at any point along the tube, thus making it possible to determine D by a method similar to that of Berthelot and Vieille (2). Gerstein, Levine, and Wong (3)used a similar procedure to determine the propagation velocity of a large number of hydrocarbon-air mixtures. To study uniform propagation of the flame front, we made use of diaphragms whose size varied according to the nature of the mixture and the tube dimensions. In this way the ignition end of the tube could be decreased when the other end was closed and the opposite end should be decreased when the ignition end was left open. 3. RESULTS
a. Uniform propagation 1. The flames often appear as ellipsoids, at least in narrow tubes and for mixtures with low burning velocities. Coward and Hartwell (4) calculate the area of the flame front by matching it to a portion of ellipsoid whose plane of symmetry is the vertical plane through the axis of the tube and whose main axis is inclined over the horizontal. I t appears that this interpretation does require discussion because under conditions of uniform propagation the flame rarely assumes the position described and discussed by these authors. I t has the appearance of a "spoon" tangent to the inner wall of the tube, which takes up some position in the tube and travels the length of the tube maintaining a constant area. The accompanying photographs (figs. 1-12) show the position and shape of the flame in the various tubes used. Views h are projections of the flame front in a horizontal plane and views v are projections in a vertical plane. The time interval between two successive positions of the flame is designated as At. The diameter of the ignition opening and the opposite opening are d~ and d j , respectively. 2. If the effect of convection of the burned gas on the flame shape is doubtful, it is a rough approximation, in cases where the appearance of the flame appears to justify such an analogy, to compare the flame to the ellipsoid whose equation is given by Coward and Hartwell. Such an approximation gives some idea of the true area of the flame surface, but the degree of accuracy is not known. Moreover, in many instances, the curvature of the front does not have a constant sign over the entire
surface (fig. 4) making the flame area calculated from the contour less than the true value. Finally~ the stroboscopic method is defective if the burned gas is actinic enough to impress the photographic plate. This is the case for the stoichiometric airacetylene mixture (fig. 6). The area of the flame front is increased by an amount which cannot be determined because it depends on the emission of the gas, the sensitivity of the photographic emulsion, the dimension of the stroboscopic slit and the aperture of the camera lens. These considerations limit the significance of the results obtained with this experimental method. However the burning velocity can be determined .in this way (a) if the flame surface is well defined and smooth; (b) if the flame travels into a quiescent mixture or a mixture with a constant flow rate, as shown by any optical method (5); (c) if the flame has a simple geometrical shape such as a spherical segment. This last condition can be obtained--it occurs much more readily in mixtures with a low acetylene content--but the reasons for its occurrence are not known. For the same set of experimental conditions, except possibly the spark, the flame front may be unsymmetrical or approximately symmetrical (fig. 7). However there does exist a relation between the shape of the initial flame front and its appearance in the subsequent frames. When the flame has an axis of symmetry and when this axis coincides with that of the tube, the surface of the first fiont is very nearly a spherical segment, in contrast to the case of an unsymmetrical flame. As under conditions of uniform propagation once the movement is established no force acts on the combustion surface (the piston represented by the burned gas has a velocity of zero), it may be assumed that this surface will retain its initial shape over its entire course, this shape depending on the way in which the spark flashes. This is similar to what is observed when a flame is forced back very gradually into a vertical tube whose upper rim presents an irregular section. The flame re-enters the tube unsymmetrically and advances slowly by translation, keeping its classical "spoon" shape. When action on the flow ceases, the flame becomes stabilized in this shape and clings to the hot points of the wall.
b. Vibratory propagation When propagation is vibratory, the flame surface undergoes changes. The tube with its two columns of unburned and burned gas forms a
CHANGES
IN SHAPE OF FLAMES
PROPAGATING
IN TUBES
F l o s . 1-12 1/ sec, C2HH2 -~- 5. 25 air Fro. 1. T u b e No. 1, di = 12 m m , d l = 0, At = ,:~o FIG. 2. T u b e No. 1, di = ~p, d.t = 12 ram, At = 1/~o sec, C~Hto + 5 . 2 5 air F i e . 3. T u b e No. 1, di = ,p, dy = 12 m m , At = ~ o sec, C~I-I~ + 5. 25 a i r FIG. 4. T u b e No. 2, di = 12 m m , d.r = 0, At = /1~0, 1 sec, C2I'I2 + 5 . 2 5 air F~G. 5. T u b e No. 4, di = 8 m m , d.r = 0, At = ~ o o sec, C2H2 + 15. 7 air FIG. 6. T u b e No. 2, di = 14 m m , d., = 0, At = ~ o o sec, Cei.i~ + 1 1 . 9 air F~G. 7. T u b e No. 2, di = 12 ram, d l = 0, At = )~o sec, C2I-I2 + 5 . 2 5 air FIG. 8. T u b e No. 1, di = ~, di = 0, At = 1/.5o, 1 sec, C2H~ + 5. 25 air FIG. 9. T u b e No. 1, di = 7 m m , ds = 0, At = 1/~o sec, C2H~ + 5 . 2 5 air F~c. 10. T u b e No. 3, di = 16 m m , dr = 0, At = )~o sec, C~H~ + 5. 25 air FIG. 11. T u b e No. 4, di = 10 m m , d! = 0, At = I/~o sec, C~I.I~ + 5. 25 a i r FIG. 12. T u b e No. 2, di = 14 m m , dy = 0, At = 1/(o o sec, C2H2 + 1 5 . 7 air
405
406
LAMINAR COMBUSTION AND DETONATION WAVES
resonator that can vibrate in (2k + 1))~/4 or in k(X/2), according to its limiting conditions. Diaphragms have little effect on the frequency of the vibrations, but they affect the amplitudes, at least for mixtures with low burning velocities. The law of changes in frequency as a function of the diameter of the opening is similar to that given by Bouasse (6) for resonance in a tube filled with a single gas. The dimensions of the tube do not influence the character of the propagation. Thus, for a tube that is closed downstream and open upstream (ignition), the frequency most often observed is the fundamental frequencY , but in many cases the first harmonic is present; this harmonic never lies between the consecutive node and antinode of the movement. Similarly, with a tube that is wide open at both ends, two propagation patterns may appear, regardless of the dimensions of the tube (figs. 13 and 14).
FIGS. 13 and 14. d~ = d/ = ~ = 20 mm, L = 56 cm. I t is clear that the shape and area of the flame depend on the vibratory system. Thus the flame straightens up in the tube and tends to become thinner and more symmetrical when it reaches a region of vibratory disturbances. Simultaneously the so-called multicellular structure appears. This had been observed previously by Markstein (7). I t should be noted, however, that although our setup does not allow observation of the flame front during large-amplitude vibrations, this flame structure appears to be characteristic of the transition from a state of uniform propagation to a state of large-amplitude vibrations, which we will call an oscillatory state. This is indicated also by photographs of Schmidt, Steinicke and Neubert (8) who investigated the combustion of propane-air mixtures using an optical method with a high frequency spark as a light source. According to Markstein (7), the cell dimensions depend on the amplitude of the vibratory motion. We believe that it depends rather on the number of cells, and that this amplitude increases with the state of division of the flame front. This can be verified by studying the deformation of the
flame front as a function of the diameter d~ of the open end (figs. 8 and 9). Finally it should be noted that such flames appear regardless of the diameter of the tube or the mixture composition (figs. 10, 11 and 12). Recently Manton, von Elbe and Lewis (9) published an interpretation of cellular flames based on the influence of diffusion phenomena on the burning velocity. As the profile of a uniformly propagating flame has not been established, it seems hazardous to a t t e m p t to justify or reject such a view. Nevertheless the results obtained by us, as well as the "stabilization" of a multicellular flame in a cylindrical t u b e ) suggest rather that this phenomenon is due to hydrodynamic instability. REFERENCES 1. See, for instance, COWARD,H. F., HARTWELL, F. J., AND GEORCESON,E. H. M.: J. Chem. Soc., 1482 (1937), or GU~NOCHE, H., AND LAF~'I~E, P., Compt. Rend. 222, 1594 (1946), and GU~NOCrlE, H., AI~ MANSON, N., ibid. 230, 726 (1950). 2. BERTttELOT, M., AND VmlLLE, P.: Compt. Rend. 94, 101 (1882). 3. GERSXXlN,M., LEVlNE, O., AND WONO, E.: J'. Am. Chem. Soc. 73, 418 (1951). 4. COWARD,H. F., ANI) HARXWELL, F. J.: J. Chem. Soc., 2676 (1932). 5. GuENoclm, H.: Compt. Rend. 232, 2316 (1951). 6. BOUASSE, H.: Tuyaux et r6sonateurs, Delagrave, Paris (1928). 7. MARKSTEIN, G. H.: J. Aeronaut. Sci., 18, 428 (1951). 8. SCHmDT, E., STEImCKE, H.: Am) NEUBERT, U.: VDI-Fors. 431, B17 (1951). 9. MANTON, f., VON ELBE, G., AND LEWIS, B.: J. Chem. Phys. 20, 153 (1952). DISCUSSIONBY EDWARDBURKE* The authors state that orifices were used over the downstream end of the flame tube to reduce vibrations. For the purposes of the present paper this would seem acceptable since no burning velocities are reported; however we found that orifices are unsatisfactory where accurate burning velocities are desired. While we found that the orifices did reduce the vibration, they introduced considerable uncertainty into the measurement of flame speed. This is based on measurements done in connection with our study of the burning velocities of acetylene, which we reported in 1951,t wherein we employed tubes of approximately the same dimensions as those used by the authors of this paper. * Research Laboratories, Westinghouse Electric Corp., East Pittsburgh, Pa. t Friedman, R. and Burke, E., Industrial & Engineering Chemistry, Vol. 43, p. 2772, Dec. 1951.
INFLUENCE OF I N E R T GASES ON FLAME PHENOMENA
407
more, we found that if a sufficiently careful procedure of flame initiation is employed, a smooth flame front with a uniform mean velocity can always be obtained. It is stated that the flame area varies randomly from one run to the next. However, in the report,~ it is shown that, for any given mixture, the flame area bears a nearly constant ratio to the tube cross-section. Furthermore, the highly repeatable flame speeds shown in figure 2 provide further confirmation of the suitability of the tube method of measuring burning velocities. An indication is given that the method is unreliable because of the vibrations of the flame front. We found that the mean velocity of the vibrating flame is substantially independent of the amplitude of the vibrations, and that it is only necessary to follow the progress of the flame through a considerable number of oscillations. This further indicates that it is preferable to tolerate the vibrations rather than to eliminate them with orifices.
Our use of orifices was suggested by the paper of Guenoche and Manson~;; we were unable to duplicate their experimental findings over a wide range of the ratio of orifice diameter to tube diameter. Since the accurate measurement of burning velocity was the object of our study, we could not tolerate this uncertainty, and so all of our experiments were done with a closed downstream end. Difficulty was experienced by the authors, in that the flame fronts were often irregular. Furthermore, it is stated that spark ignition was used for some series of experiments, while flame ignition was used for others. In our work with acetylene we used only flame ignition, since our calculations indicated that spark ignition was unsuitable because reflections of the shock wave produced by the spark would perturb the flame. Further:~ Guenoche, J. and Manson, N., Comptes Rendus, Vol. 230, p. 726. Feb. 1950.
53
THE INFLUENCE OF INERT GASES ON SOME FLAME PHENOMENA By C. E. MELLISH AZ,rD J. W. LINNETT INTRODUCTION
One of the great difficulties in studying the mecha n i s m of flame propagation is t h a t it is impossible to alter one p r o p e r t y only of a n inflammable mixture while leaving all others unaffected. P r o b a b l y one of the simplest a n d smallest changes t h a t can be m a d e is the substitution of one kinetically i n e r t gas for another. I n particular, the substitution of one Group O gas for another (e.g. helitlm for argon) in a mixture will alter the properties of the mixture in as controlled a n d limited a m a n n e r as possible. T h e object of this p a p e r is to consider the effect of such inert gas substitutions. T h e inert gases t h a t will be examined in greatest detail will be helium, argon a n d nitrogen, b u t carbon dioxide will also be considered to a certain extent. I n t h e experimental p a r t of this p a p e r two sets of results will be presented: (1) T h e b u r n i n g velocities ( f u n d a m e n t a l flame speeds) of ethylene + oxygen + i n e r t gas mixtures, the inert gases being helium, argon or mixtures of these; (2) T h e upper limits of inflammability of hydrogen + air + inert gas mixtures and of hydrogen + nitrous oxide + i n e r t
gas mixtures, the inert gases being helium, argon a n d nitrogen. I n the next section the results t h a t have been obtained b y other workers for the effects o[ inert gases on various properties of flames will be summarized. I n the last two sections the effects of changing inert gases on different properties (burning velocities, limits, m i n i m u m ignition energies, etc.) will be compared a n d the similarities and differences in b e h a v i o u r discussed a n d summarised. E X P E R I M E N T A L METHODS
1. Burning velocity determinations These were obtained b y the soap b u b b l e m e t h o d using the procedure described b y Pickering, Linn e t t a n d Wheatley (1). Preliminary experiments were carried o u t to ensure t h a t the soap film was a satisfactory enclosing m e d i u m for mixtures containing helium. A mixture containing 7.7 per cent ethylene, 19.4 per cent oxygen a n d 72.9 per cent helium was tested. This mixture was used to blow a n u m b e r of bubbles which were fired after v a r y i n g intervals of time from 6 to 31 seconds. T h e b u r n i n g