INITIATION OF DETONATION IN GASES G . 6. KISTIAKOWSKY 38, Mass.
Harvard University, Cambridge
T h e field of combustion in gaseous systems is incomplete without the inclusion of the initiation of detonation wales by flames and the mechanism of propagation of such waves. This article is a qualitative review of published theories and facts plus some new thoughts on the structure of stationary detonation waves and the mechanism of initiation of detonation by flames. Qualitative comments on the probable mechanism of spinning and pulsing-that is, nonstationary, detonation w-aves conclude the article. The ideas presented clarify soniewrhat these complex phenomena which are seldom studied by chemists but which are of some importance in combustion engines and are altogether a rather common consequence of nondiffusion flames.
TRONGLY exothermic reactions taking place under nearly adiabatic conditions form flames (deflagrations) or detonations. The flames, in general, propagate more slowly into unburnt medium than do the detonations, but a sharper distinction between the two types of luminous phenomena is furnished by a different criterion. Relative to a system of coordinates moving with the zone of exothermic chemical reactions of a flame, the velocity of the unreacted medium into the zone is smaller than the velocity of the burnt gases out of it. In a detonation wave the reverse is the case. The intermediate case in which the two are equal is apparently unrealizable as a stationary state. The difference in velocities necessitates also a difference in pressures: The pressure in front of the flame is higher than behind; in detonations the pressure ahead of the wave is lower than in the wave itself. From the kinetic point of view the distinction between flames and detonations is also clear, although in detail both classes of phenomena are still largely unexplored. The propagation of flames relies on transport phenomena, a diffusion into the unreacted medium of chain carriers or of thermal energy. Zeldovich (22),in an important theoretical analysis of detonations, was the first to point out that the propagation of the zone of chemical reactions with the wave depends on the spontaneous ignition of the medium by the adiabatic compression in the shock front. The concept of detonation waves as mechanical shocks in unreacted medium, followed by the zone of chemical reactions, the whole maintaining stationary character, was independently developed by von Neumann (11, 20). He determined the theoretical conditions under which temperature, velocity, and other parameters of the waves should be in accord with the Chapman-Jouguet equation (1g, 15) and when deviations should be expected. According to these hydrodynamic considerations. the shock front, by spontaneous ignition, continuously creates a fresh deflagration behind itself: therefore. the question of the adequacy of flame velocities to keep up Tvith detonation waves is irrelevant to the problem. Furthermore, the medium, between the sKock front and the plane in which chemical reactions reach the state of thermodynamic equilibrium, moves Kith such velocity in the direction of wave propagation that the shock front advances with subsonic velocity relative to it. Since the de-
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flagration zone is subsonic with respect to the shock front, the energy released by the flame can be transmitted to the former and so maintain it at a stationary intensity. This support of the shock front by the deflagration is entirely equivalent to what exists in an ordinary flame. In bot’h phenomena the pressure on the side of the unreacted medium-i.e., immediately behind the shock front in a detonation-is higher than on the back side of the chemical reaction zone; the temperature ahead of the reaction zone is lower; the mass velocity of the medium, relative to a stationary frame of reference, is greater; hence, relative to the deflagration front, the unburnt medium enters it slower than burnt gases leave it. The essential difference is that within a detonation the deflagration does not, have to depend on transport mechanisms to keep up with the pressure wave, because the latter adiabatically heats fresh medium to spontaneous ignition. Sumerous experiments have demonstrated that shock waves are able to ignite explosive media (3,x?l,$6). I t has been also shown that when the temperature of a mechanical shock entering an explosive medium exceeds its conventional “ignition temperature” by a few hundred degrees, instant detonation is the result (1). Since the calculated shock t’emperatures in strong detonations are much higher, no doubt can exist that in detonation waves the shocks are able to maintain deflagration, When external energy losses are negligible, the duration (and therefore t’he thickness) of the deflagrat’ion zone is of no consequence. Figure l a shows schemat8icallythe pressure distribution in a detonation wave in which the reaction start8 immediately behind the shock front. The rarefaction wave behind the deflagration is imagined to be prevented by having a piston, in the rear, move forward with the same velocity as the mass velocity of the burnt gases in the plane of completion of the deflagration (the Chapman-Jouguet plane). This velocity is less than the velocity of the shock front by t’hesonic velocity of burnt gases. Figure 16 is a schematic representation of a more realistic case. In the absence of the piston, the pressure drops as a rarefact’ion wave behind the deflagration zone because the burnt gases return into the space traversed by the detonation wave. As the forward velocity of the medium is retarded in the rarefaction wave, the shock front moves relative to it faster than with sonic velocity. If any chemical reactions remain incompleted by then, their further progress cannot be transmitted to the shock front as a cont,inuous pressure wave because such wave can advance with no more than sonic velocity. Consequently in “young” detonation waves, in which the rarefaction is steep, less energy is transmitted to the shock front and the detonation wave is weaker. With its progress through the medium the pressure gradient in the rarefaction wave decreases ( 1 9 ) , and a greater portion of the deflagration can occur within the subsonic region, ahead of the Chapman-Jouguet plane, even though chemical reaction rates may remain unchanged. Thus the speed of the detonation rises asymptot’icallyto the stationary value when complete equilibrium is attained in the Chapman-Jouguet plane. Evidence of this occurring in gaseous systems has been reported (1). The effect of the finite lateral extent of detonation waves in tube esperiments and under other practically realizable conditions is also important. As pointed out by Zeldovich (dx?),lateral effects equivalent to the rarefaction wave in their consequences, may 2794
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place permanently the tail end of the reaction zone into the supersonic region and so detract the energy there released from the shock front. The consequence is a stationary reduction in detonation velocity, observed in narrow pipes. It has been commonly observed that the deflagration of gaseous media upon sudden heating is preceded by induction periods of varying duration. These have been interpreted as either the period of self-heating of the gas by the initial reaction, in the case of the so-called thermal evplosions (16), or as the period of the build-up of concentrations of chain carriers, in the case of branching chain explosions. In both, the induction periods decrease with rising temperature, but in the second case their functional dependence on temperature may be quite complex. Because induction periods are the rule, rather than the exception, it is illusory to assume that in all detonations the deflagration follows immediately upon the shock front. Hence a more correct representation of the normal structure of detonation waves is shown by Figure IC. The region immediately following the shock front is in the state of “induction” with negligible chemical reaction taking place. There, to maintain the shock front stationary, the pressure, temperature, and mass velocities must all have only negligible gradients. Upon the induction period follows deflagration, to which apply all the comments made in connection with Figure l b . In comparison with the problem of stationary detonation waves, their initiation mechanism presents many additional complications. In the search for a t least a qualitative understanding, it seems desirable to consider first a somewhat unrealistic case of an infinite plane deflagration spreading into the medium from a stationary wall under conditions of vanishing energy losses to the outside. It will be assumed in accordance
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Figure I. Schematic Drawings Showing Pressure Distribution in Detonation Waves (a, 6,and c) and in Process of Initiation (d and e) Narrow regions between dotted lines indicate deflagration zone
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with observations that the flame velocity i? increased by rising temperature of the medium, but that the flame velocity has a finite, subsonic limit with respect to burnt gases (17). The gaseous medium is considered to expand on passing through the deflagration zone. Since the stationary boundary in the rear of deflagration prevents the burnt gases from moving rearward, the passage of the deflagration sets the unburnt medium into forward motion. The disturbance advances as a compressional wave (19, 15) with sonic velocity. The deflagration is burning, therefore, in a slightly compressed and heated medium, and its velocity increases, resulting in additional acceleration of the unburnt medium and hence in further compression and heating. An important contributory factor in this accelerating regime is the selfinduced turbulence of the flame front, predicted by Landau (IS),and due to the dynamic instability of a system in which a medium of lower density (the burnt gases) exerts a force on a denser medium in front. The continuing acceleration of the medium leads, in a well understood manner, to the formation of a shock wave a t the front of the disturbance. The pressure distribution in a system becomes as indicated by Figure Id. The shock advances with supersonic velocity relative to the undisturbed medium, but with subsonic velocity relative to the medium between the shock front and the deflagration. The deflagration may be either stabilized in a nearly stationary state or it may cause detonation: Let the maximum flame velocity be V and the expansion ratio on the deflagration be R. If a state is established in which the flame is stationary, the mass velocity of the unburnt medium must be V R throughout the region between the deflagration and the shock front, To this mass velocity corresponds a definite shock temperature and when this is below the ignition temperature of the medium, the flame should reach a stationary velocity. Of course, the shock continues to outdistance the flame and the medium in between must eventually ignite spontaneously owing to its additional heating by finite reaction rates a t finite temperatures. This may happen, however, so much later that in the meantime a steady flame propagation will result. The limits of gaseous compositions outside which this is observed could be called detonability limits a t infinite tube diameter. Let the product V R now correspond to such shock intensity that spontaneous ignition after a short induction period does occur. As the deflagration is accelerating and the shock front is growing in intensity, the moment must arrive when the induction period becomes equal to the time the medium spends in passing from the shock to deflagration. This is the instant of the initiation of detonation because thereafter the deflagration is propagated by the spontaneous ignition mechanism of detonations. The negative pressure gradient back of the shock (Figure I d ) causes its further intensification; this leads to shorter induction periods and so the distance between the shock and the deflagration starts to decrease. Flames overtaking advance shocks have indeed been repeatedly observed in tube experiments ( l a ) , but it is not certain that this is relevant to the case considered. While the distance between the shock and the deflagration is decreasing, the detonation wave is not as yet in a stationary state and is propagating with rising velocity because of increasing shock intensity. The attainment of the stationary state should be a gradual procem, the conditions illustrated in Figure Id asymptotically flowing into those of Figure IC, as the shock intensity attains the value determined by the Chapman-Jouguet equations. Because of the negative temperature gradient between the deflagration and the shock, it is rather improbable that in this idealized case a spontaneous shock ignition ahead of the existing deflagration could occur. The consequences of such event are better discussed, therefore, in connection with the initiation of detonation in tubes of finite diameter. Here the processes behind the shock front are complicated by the heat losses to the walls as well as by the formation of a velocity gradient across the
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tube in laminar flow and of the turbulent boundary layer Extensive experimental ’data-for instance, the observations of Shchelkin (18) that the distance of flame travel to the initiation of detonation is proportional to the diameter of the tube and is much shorter in rough tubes-demonstrate the profound importance of the interaction of the originally quiescent medium with the tube walls during the initiation period. In the opinion of Zeldovich (23) the most important contributing factor is the velocity gradient in the streaming gas, from the axis to the periphery of the tube. This gradient causes the deflagration zone to change from a plane into a paraboloid, thereby increasing its area and thus its rate of propagation. The discussion presented earlier for the infinite plane deflagrations applies as an approximation to the tubes of finite diameter. The events start by an acceleration period, well known from many observations, and then lead either to the establishment of a state resembling a stationary propagation of deflagration or to the initiation of detonation. The latter niay occur by the gradual transition mechanism outlined earlier; hoviever, new possibilities offer themselves. In gaseous media in which the transition to detonation is relatively slow, the distance between the deflagration and the advance shock must become large compared to the tube diameter. The turbulent boundary layer spreads then deeply into the moving medium and turbulence contributes to the deflagration velocity ( 2 3 ) . On the other hand, heat losses to the walls should produce a positive temperature gradient from the vicinity of the deflagration to the shock, although both are accelerating and, therefore, pressure gradient in this legion is negative. This situation should be conducive to the generation of an autoignition in the region between the shock and the original deflagration front; such autoignitions have indeed been repeatedly observed ( 2 , 14). The autoignition, once started, moves into unburnt medium, forming two new deflagration fronts. Figure l e attempts to indicate the resultant pressure distribution. The backward moving deflagration eventually meets the original one which terminates both. In the meantime, however, the forward moving deflagration advances on the initial shock because its own pressure wave, added to the compression caused by the shock, results in a shortening induction period. Thus a detonation wave associated with this deflagration may be formed in the region already compressed and set into motion by the original shock. The mass velocity within this detonation nil1 be quite high, approaching the sum of that given by the ChapmanJouguet equation and that caused by the first shock. Its velocity, relative to a stationary frame of reference, may therefore be far in excess of the Chapman-Jouguet value, and when it overtakes the first shock, a sudden rise of shock velocity to values in excess of the Chapman-Jouguet theory must result. Eventually the wave then slows down to the Chapman-Jouguet value because of stability considerations. Observations of such phenomena have been recorded in the literature (1,s). The effects of turbulence on the transition to detonations have been extensively treated in a number of publications (18, 93, 24) and nil1 not be considered here except to note that, of course, the turbulence has the net effect of accelerating the rate of combustion in a deflagration and, therefore, increases the mass flow of unburnt medium in a tube. On the other hand, turbulence, by converting directed mass motion into random motion of volume elements, acts as a rarefaction wave behind a shock. Evidently the first of these effects is overwhelming, since the run-up distance to detonation is reduced by decreasing tube dianieter. The extremely short run-up distances, observed by Shchelkin ( 1 8 )in tubes with macroscopically rough ~ a l l ssuggest , that an auxiliary factor may be reflections of shock waves under oblique angles from the uneven malls. It is well known (9) that on oblique angle reflection, the pressure of the reflected wave may be substantially more than double that of the in-
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cident one. Here are possibilities for ,oca1 ignitions which might lead to rapid initiation of detonation. The initiation of detonations in gaseous media which are in the state of turbulence a t the instant of the ignition, as is the case in internal combustion engines, involves no new principles, but is still less amenable to treatment. That turbulence is of utmost importance under these conditions is shown by the observation that the speed of combustion is proportional to the speed of the engine ( 4 ) . As the turbulence accelerates the progress of deflagration, it undoubtedly results in a complex pattein of pressure waves and shocks. The interaction of the latter can lead to still higher local pressures and temperatures and thus to autoignitions. A11 this encourages rapid initiation of detonation, but experimental evidence to date does not seem to be conclusive as to whether true detonations are involved in knocking engines or whether knocking is due to shocks induced by rapidly accelerating flames. Observations with pressure-sensitive gages of the phenomena taking place when mechanical shocks, slightly too n eak to initiate instantaneous stable detonation, enter explosive media ( I ) , illustrate some of the points brought out in the pleceding discussion. Comparatively weak shocks .irere obserived to be slowly accelerated over the entire distance of observations, approximately 100 em. in a 10-em. diameter tube. A deflagration starting a t the boundary between the inert and the reactive media after a long induction period and propagating a t an accelerating rate, seems to be the most plausible explanation. Under somewhat different conditions such ,hocks, after traveling as far as 60 em., were observed to be d d e n l y accelerated to velocities in excess of Chapman-Jouguet value and finally leveled off to this stationary velocity. Here an autoignition nithin the explosive medium seems to be the most self-consistent explanation. Unexplained remain the ieasons n h y one or the other of these phenomena does take place in a given experiment. Recent, still unpublished, experiments by H. Knight and RI. Malin in this laboratory provide an interesting link between the phenomena of initiation and the pulqating detonations. The latter have been observed by others (6, ?) in poorly balanced explosive mixtures, using relatively narrow tubes. Their occurrence has been associated with that of the spinning detonation. Knowing that drying diminishes flame relocities in carbon monoxide-oxygen mixtures and raises their ignition temperature, Dixon ( 1 0 ) experimented with detonations of such mixtures and concluded that the velocity was materially reduced. Subsequent, n ork on this subject seemed to disprove Dixon’s conclusion ( 3 , 6 , 8 ) but left the problem in an inconclusive state. Such mixtures are indeed an ideal system to explore the effect of chemical reaction rates on initiation and propagation of detonations because the addition of a fraction of 1% of water vapor or hydrogen changes chemical rates many fold (26) without altering significantly the hydrothermodynamic properties of the system The experiments reported here have shon n that in moist mixtures stable detonation waves propagate with velocities that are in, agreement with the predictions of the Chapman-Jouguet equation. Careful drying causes such mixtures to become verv difficult to initiate by mechanical shock. Moreover, although self-propagating waves are formed, which, on the average, travel with a velocity very different from that of moist mixtures, these waves lose stationary character, Ovei an observational distance of 200 em., a quasi-periodic rise and fall in wave velocity is. observed. After a burst of excess velocity the wave gradually slows down below the Chapman-Jouguet value and then the pulse is repeated; the “nave length” is of the order of 20 to 5OJ em. in the 10 em. tube. Since others, evperimenting with narrow tubes, have observed somewhat similar pulsations of only a few centimeters wave length manifested as “spin,” it is evident that the separation of the walls determines the period of these phenomena ( 1 2 ) . Probably the most significant aspect of these observations is that instability of detonation has been shon n to b e
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the consequence of slow reaction velocities alone rather than of hydrodynamic weakness of the detonation wave. Pending the outcome of the simultaneous observations with the pressure gages and a moving film camera, which are now under way, only preliminary remarks on the nature of the pulsations can be offered. It is believed that in dry mixtures the temperature of the stationary (Chapman-Jouguet) shock is not sufficient to start deflagration at any reasonable distance behind the shock front. Indeed, nearly balanced acetylene-oxygen mixtures are needed as the shock initiator to start these waves on their way. Thus, when an initially overdriven wave settles down to its stationary velocity, the deflagration ceases to be maintained behind the shock front and drops behind. Under these circumstances, opposite to the regime of accelerating deflagration, a positive pressure gradient is established between the deflagration and the shock. The latter must, therefore, decay. Since the walls determine the wave length of the pulsations, i t must be assumed that the deflagration continues lagging until it enters a region so far behind the shock that the effects of the walls have penetrated deeply into the interioi of the pipe. Thereafter, by a mechanism which the author is unable to describe a t present, an autoignition occurs in the region between the shock and the original deflagration. This, as pointed out before, must gather momentum, eventually overtake the shock, and produce a transient excessive velocity. Thereupon the cycle repeats itself. In the sense of this interpretation the detonation spin, which is frequently associated with the pulsating waves, might not be the cause but an effect of the latter phenomenon. Since the autoignitions probably occur in a turbulent medium and hence are not plane fronts, it is entirely possible that oblique shocks are formed in the tube: their impacts produce the luminous and extreme-pressure manifestations of detonation spins. The voluminous literature on detonations stretches back some 70 years and has been only incompletely summarized in books. Moreover, much of the modern Russian literature on the subject has not been available to the writer, except in the inadequate form of Chemical Abstracts. It is, therefore, entirely possible that some of the ideas here expressed, without credit to others, have already been piopounded. The writer apologizes in advance for these unintentional omissions and will be grateful to learn of the correct sources.
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ACKNOWLEDGMENT
It is a pleasure to acknowledge interesting discussions with A. Kantrowitz and H. W. Emmons which have materially helped in the formulation of ideas here presented. LITERATURE CITED
(1) Berets, D. J., Greene, E. F., and Kistiakowsky, G. B., J . Am, Chem. SOC.,72, 1086 (1950). (2)Bone, W.A.,and Fraser, R. P., Phil. Trans. R o y . SOC.(London),
230A, 363 (1932). (3)Ibid., 235A,29 (1935). (4) Bouohard, C.L.,Taylor, C. F., and Taylor, E. S.,S.A.E. Journal, 41,515(1987). (5) Campbell, C., and Finch, A. C., J . Chem. SOC.,1928,2094. (6) Campbell,C., Whiteworth, C., and Woodhead, D. W,,Ib%.,1933, 59. (7) Campbell, C., and Woodhead, D. W., Ibid., 1926, 3010; 1927, 1572.
Courant, R., and Friedrichs “Supersonic Flow and Shock Waves” pp. 153-4, New York, lnterscience Publishers, 1948. Dixon, H. B.,Phil. Trans. Roy. SOC.(London),184A,97 (1894). Dorine. Ann. Phws.. 43.417 (1943). Jost, W., “Explosion and Combustion Processes in Gases,” p. 170,New York, McGraw-Hill Book Co., 1946. Landau, L., J. Ezptl.. Theoret. Phys. ( U S S R ) ,14,240 (1944). Le Chatelier, H., Compt. rend., 179,971 (1924). Lewis, B., and Van Elbe, G., “Combustion, Flames, and Explo. sions of Gaaes,” pp. 246-7, New York, Maomillan Co., 1938. Semenov, N., “Chemical Kinetics and Chain Reactions,” New York, Clarendon Press, 1935. Shapiro, A. H., Hawthorne, W. R., and Edelman, G. M., Meteor Rept. No. 14, Mass. Inst. Technology (1947). Shchelkin, K. I.,J . Tech. Phys. (USSR),17, 613 (1947). Taylor, G. I.,Proc. SOC.200A,235 (1949). von Neumann, J., OSRD Rept. No. 549 (May 1942). Wendlandt, R., 2. physiol. Chem., 110, 637 (1924); 116, 227 (1925). Zeldovioh, Ya. B., J . Ezpll. Theoret.Phys., 10,542 (1940). Zeldovich, Ya. B., J . Tech. Phys. ( U S S R ) ,17,3 (1947). Zeldovich, Ya. B., and Roslovski, A., Doklady Akad. Nauk ( U S S R ) ,57, 365 (1947). Zeldovich, Ya. B., and Shylyapintokh, I. Ya., Ibid., 65, 871 (1949). Zeidovich, Ya. B., and Semenov, N. N., J . physiol. Chem. ( U S S R ) ,23,1361 (1949). RECEIVED June 22, 1951. This work was supported under the contract, NR-053-094, T.O. XIX, between the Office of Naval Research and Harvard University.
AUTOIGNITION BY RAPID COMPRESSION J. C. LIVENGOOD AND W. A. LEARY Massachusetts lnstitute
o f Technology, Cambridge-39, Mass.
INVESTIGATION of the autoignition of gases under conditions of rapid compression has been in progress in the Sloan Laboratory for Automotive and Aircraft Engines a t Massachusetts Institute of Technology for several years. The rapid compression technique provides a convenient means of recording the pressure-time histories and the inflammation characteristics of combustible mixtures which react too rapidly t o be studied in conventional bombs. The M I T rapid compression machine was built primarily t o study the physical aspects of autoignition with a view to obtaining a clearer understanding of the knocking or detonation process in engines. Previous papers (6, 8, 9, 17) describing the results of these experiments were, therefore, concerned mainly with emphasizing thp
usefulness of the apparatus as a tool for studying the detonationfuel problem in engines. In the present paper, some additional test results are described. Although these results clarify and extend knowledge of the autoignition process, they also raise questions which call for a reexamination of some fundamental concepts. In attempting to rationalize the rapid compression machine data and correlate them with similar data obtained with bombs, the authors have become keenly aware of the difficulties involved. One difficulty arises from the lack of a consistent nomenclature and another from the absence of definitive experimental measurements. Such terms as “delay,” L‘explosion,” “autoignition,” “flame front,” and “preliminary reactions” are for the most part purely
