December 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
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.
2797
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 . A m , 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 t o 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
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INDUSTRIAL AND ENGINEERING CHEMISTRY
2x18 descriptive and appear to convey different meanings t o different observers. It thus appears fairly evident that the combustion process is so complex that many kinds of measurements will be required to give precise meaning t o these terms. The following comments are, therefore, concerned with (1) indicating the u s e f u l n e s s of t h e r a p i d compression machine as a tool for providing object i v e m e a s u r e m e n t s of autoignition p h e n o m e n a and (2) emphasizing the difficulty of making significant c o m p a r i s o n s o f a u t o i g n i t i o n d a t a obtained by different methods.
T h e rapid compression technique provides a convenieut means of recording the pressure-time and inflammation characteristics of autoigniting mixtures which react too rapidly to he studied in conventional bombs. Autoignition of homogeneous fuel-air mixtures ma> occur in a Iariety of way s. both with regard to the pressuretime history of the piocess and the manner in which the inflammation develops, &3otion pictures show that inflammation does not generally occur uniformly throughout the mixture. The reason for this nonuniformitj is not definitely established, but schlieren photographs re+eal numerous localized temperature gradientb I+hich appear in the mixture. These gradients can he explained on a phj sical basis. In the light of the evidence presented, a re-examination of the meaning of such familiar terms as “dela),” “explosion,” and “flame front,” seems to he called for. A s a start in this direction a rigorous definition of delay is giJen. This definition permits the establishment of a criterion for appraising the ad\ antages and limitations of bombs, rapid compression machines, and shock tubes as apparatus for intestigating autoignition phenomena.
d e m o n s t r a t e d by using ?a-butane a s a f u e l . nButane is a gas at rooin temperature, and the possibility of its condensing under the test condit i o n s is r e m o t e . Nevertheless many bright spots m-ere o b s e r v e d ( F i g u r e IC).
N o n h o m o g e n e i t y of Fuel-Air M i x t u r e . The inixture is agitated in a mixing tank for at least 10 minutes, and a large volume of the mixturc is passed through the cornbustion cylinder (about 80 cylinder volumes) before sealing it off. The pressure ratio between inixing tank and combustion cylinder during the charging process is r e l a t i v e l y high (about 3 : 2 ) a n d , therefore. t h e r e s u l t ine: turbulence in the chamber should enhance the mixing. Sincc the mixture is, then held in the coinbustion chamber for a t least 3 minutes a t a temperature of 150” F. or greater, it is reasonable to suppose that the fuel and air are uniformly distributedespecially so in a gaseous fuel like n-butane. Thus nonhomogeneity does not provide a very likely explanation. If the molecular nature of the niixture is considered, homogeneity takes on a different aspect. In a mixture which is a t a uniforiii temperature and pressure, the average molecular activity will have a k e d value, but for very small volumes the average molecular activity will vary with time. Hence a t any instant the activity in certain of t,hese small volumes will be higher than in others. I n a fuel-air mixture that has been rapidly compressed, the higher level of niolecular activity in these certain sinall voluines niight cause the reaction to be “triggered off,” thus producing bright spots ThiE effect, should be most pronounced near the end of the delay period when the mixture is ready t o explode. If bright spots are formed in this manner, then a uniform autoignition would appear to be impossible even though the fuel and air were perfectly mixed. However, this argument assumes that only a few elementary volumes would have the necessary superiorit,y of molecular activity; but it is just a8 plausible to assume that a large number of such volumes, uniformly distributed through the mixture, could exist at any given instant. I n this event the mixture would ignite simultaneously a t so many points that the inflammation would be indistinguishable from one in which the hole body of mixture ignited simult~aneously.
-
EXPERIMENTAL
The NIT rapid compression machine and auxiliary apparatus have been described in considerable detail in earlier papers (3,6, 17). The fuels used were: n-heptane (CIH,~),primary reference fuel; iso-octane (2,2,3-trimethylpentane), primary reference fuel ; and n-butane (C&), 99% mole fraction purity. Each prepared sample of fuel-air mixture was placed in the combustion chamber of the rapid compression machine and allowed to come to equilibrium temperature and pressuie. The mixture was then suddenly compressed to a smaller voluine and held a t this smaller volume until reaction was complete. The experimentally determined value of “delay” is defined as the time interval from the end of the quick compression to the conipletion of the reaction-i.e., the time of maximum explosion pressure. NONUNIFORMITY OF AUTOIGNITION PROCESS Previous work ( 1 7 ) has shown that the autoignition of coiiipressed fuel-air mixtures is not necessarily a uniform reaction The specimen flame photographs of Figure 1 illustrate that autoignition does not always occur simultaneously in all parts of the chamber. The early stages of the reaction generally display a number of bright spots which indicate, presumably, regions where the autoignition is more advanced than elsewhere. An autoignition free from bright spots, like that shown in Figure Id, is a rarity, although even here zones of varying intensity may be observed. Considerable effort has been expended in attempts t o determine the nature of these bright spots. The following possibilities have been examined : Condensed Droplets of Liquid Fuel in Mixture. The explanation afforded by this possibility is unsatkfactory. This was
(b)
Figure 1. (a)
Benzene;
(E)
Specimen Flame Photographs
(b) Iso-octane; (c)
n-Butane;
(d) n-Heptane
December 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
1.l
0
9.9
2799
3.3
Time, Milliseconds
Figure 9.
Flame Photographs of Hydrogen-Air Mixture
Test conditions: initial pressur6, 15.5 Ib,/ra. inch) initial temp., 150’ F.i compression ratio, 1% fuel-air ratio, 0.099
Dust Particles. I t is difficult to demonstrate that dust particles do not influence bright-spot formation. About all that can be done in this connection is to filter the air as carefully as possible. The filters used in this work will remove more than 99.9% of all particles greater than 0.3 micron. There is the possibility, of course, that dust in the form of iron or lead is scraped off the cylinder walls or piston during compression, but the detection of this small amount of dust is difficult. However, when the concentration of iron or lead dust in the cylinder is increased many fold by deliberately adding filings, the brightspot phenomenon in the early stages of development is not noticeably affected. All mixtures give off a bright yellow light during autoignition. When specimen inflammations were examined with a speotrograph, the presence of a strong sodium-D line was revealed in each instance. This sodium contamination could be accounted for if the atmosphere contained salt crystals small enough (0 3 micron) t o pass through the filter or if the cylinder itself were contaminated in some way, It was mentioned earlier (17) that a small amount of grease was used on the piston when first pressing it into the cylinder, after lead plating. This was a sodium-base grease, and, therefore, the next time the piston was lead-plated, a graphitewater mixture, which gave no evidences of sodium, was used as the
lubricant. The cylinder was thoroughly cleaned and scoured with a mild abrasive, and an attempt was made to “burn off” any residual traces of sodium on the surfaces by firing mixtures (using spark ignition) with the piston a t the top of the cylinder. Also, the glass window was replaced by a quartz window to remove the possibility of glass particles, containing Aodium, contaminating the mixture. In spite of these efforts all fuels, including hydrogen, continued to emit the characteristic yellow light. With a sodium-contaminated mixture it cannot be definitely stated that the bright spots represent centers where the reaction is more advanced than elsewhere because the spots may only represent centers where the sodium concentration is greater than elsewhere. Then even though the reaction may have progressed .to the same extent in all parts of the chamber, the regions of higher sodium concentration will glow more brilliantly and will . expose the film first. Carbon Particles. It has been reported by King ( 7 ) and Olsen and Miller (19)that free carbon may be formed during autoignition. This information was used by the present authors (17) as the basis of another possible explanation of the bright spots Since then, however, flame photographs of hydrogen-air mixtures have been obtained (Figure 2). These photographs
2800
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0
5
86
141
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16
28
i 14
259
Time, Milliseconds
Figure 3.
Schlieren Photographs of Dry A i r Compression
Test conditions: initial pressure, 1 5 . 5 IbJsq., inch; initial temp., 150' F.; compression ratio, 12.6
ah017 that the presence of carbon is not necessary for the formation of bright spots. Hydrogen. Another possibility is that hydrogen might in some way be responsible for the bright spots. I n this connection carbon monoxide-air mixtures rvere autoignited, but again, many bright spots were obtained. Radiation. The effect of a small piece of radioactive cobalt60 on the formation of the bright spots n'as studied. The cobalt was placed outside the window !There it as estimated that the incidence of gamma rays \vas increased by a factor of about lo4. Twelve sets of flame photographs, using n-heptane with and lr-ithout benefit of gamma radiation, rr-ere taken, but no correlation between bright-spot frequency and radiat,ion was observed, and there \vas no appreciable change in the pressure-time records. Contact of Piston with Cylinder Head. Observation of a great many flame photographs reveals that the bright spots almost always start near t,he circumference of the chamber. It was a t first thought that this might be caused by the seating of the piston on the impact ring a t the end of the stroke. The ring of gas in this region must' be subjected t o an extremely high compression, and it is reasonable to suppose that this action might trigger off the ignition. T o test this supposition, the impact ring n-as bored out so that the pist,on could not make contact ivith it, but the bright spot,s continued to start a t the edges n-ith about the same frequency. Temperature Gradients. Perhaps the most convincing explanation of the bright spots is derived from recent experiments in which schlieren photography was used to record the happenings in the cylinder. When the schlieren apparatus is used, the combustion chamber piston is replaced by one having a ~pherical, chrome-plated head. The spherical surface acts as the mirror for the schlieren optical system and is in focus only when the piston is a t the end of its stroke. N o pressure unit is used in this piston. This apparatus was first used t o study the compression of air. Clean, dry air was placed in the cylinder and, after allon-ing sufficient time for the attainment of temperature equilibrium,
was compressed rapidly. Schlieren photographs taken during this p'rocess are shown in Figure 3. The first frame, marked "0 milliseconds," corresponds t o the instant a t which the piston seats The photographs show that the compressed air is not optically homogeneous, indicating density gradients. These density gradients must be caused by temperature rather than pressure, because pressure gradients n-oulti disappear in a few milliseconds, ivhereas the observed graili s persist for a t least 250 milliseconds. The schlieren apparatus is adjusted so that each dark spot represents a rcgion in n-hith the temperature is higher than in the immediatc surrounding,.. Gnfortunately, the magnitudes of fhe temperature gradient. &?eunknown and t'he schlieren apparatus in its present form does not permit of a quantitative evaluation. The localized hot epots may provide R clue t o the bright spots which appear in the flame photographs. Ili this event the origin of the bright spots can be explained 011 purely physical grounds. I t is appayent that the temperature gradiente persist for a sufficient period of time to esist concurient1~-with the bright spots which first appear near the end of the delay, The existence of thest. t,emperaturegradients may be explained by assuming that the piston, in descending, scrapes off the boundary layer of air from the cylinder walls, producing a turbulent region at the periphery of t h e chamber [sce author's reply t o Lichty's discussion ( I r ) ] . The boundary layer may be hotter than the gas in the interior of the cylinder before rompression, because the mixture is heated by hot fluid surrounding the cylinder walls. But as the piston descends, the tcniperature of the gas in the center of the cylinder riws, reaching a value of about 1000" F. (for a compresssion ratio of 10) a t the end of the stroke, vhereas t'he temperature of the boundary layer a t the cylinder wall remains essentially constant a t 150" F. The mixing of these hot and cold layers of gas may be responsible for the niott,led appearance ehown in the figures. Schlieren Photographs with Iso-octane. Schlieren photographs for the autoignition of iso-octane are shown in Figure 4. The firpt picture corresponds t o the instaut a t which the piston
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0
1.I
3.0
4.4
1.2
10.1
11.7
12.6
14.2
14.6
13.1
14.0 Time, Milliseconds
Figure 4.
Schlieren Photographs of Autoignition
of Iso-octane
Test conditionr: initial pressure, 15.5 Ib./sq. inchi initial temp., 1 5 0 ’ F.i compression ratio, 12.6, fuel-air ratio, 0.095
seats. These pictures exhibit a mottling effect similar to the compressed-air pictures of Figure 3. In frame 1.1 of Figure 4, however, a series of concentric rings may be observed taking shape These rings become more pronounced in the next four pictures but lose their identity in frame 11.7. In frame 13.1 two prominent centers of activity may be observed. These regions spread rapidly, and in frame 14.2 they have become hot enough to glow from their own combustion and therefore may be interpreted as representing the spread of what a direct flame photograph would reveal as “inflammation ” Also in frame 14.2 the character of the mottling at the left of the chamber has changed radically, indicating perhaps that another inflammation zone has started In the last picture the field is glowing with sufficient intensity (from its own combustion light) to indicate that the combustion is complete. The time interval between the first and the last pictures corresponds to the delay period. (The interval occupied by the direct flame photographs corresponds only to the last part of the delay period.) It is not known whether the boundary of the circular regions in frames 13.1 and 14.0 represents the “flame front” as would be recorded by direct photography or whether this boundary represents, for a considerable depth, a region of nonluminous activity. This con-
fusion can be reduced by taking simultaneous flame and schlieren photographs in which the light emitted by the flame is not superimposed on the schlieren photograph and vice versa. The photographic apparatus is currently being redesigned to accomplish this end. Thc two more or less rectangular spots of light, appearing in the center of all these pictures, are due to spurious reflections in the optical system and can be ignored. Schlieren Photographs with Benzene. A series of schlieren photographs for the autoignition of benzene is shown in Figure 5 . These pictures lend support t o the view that the bright spots observed in the flame photographs are associated with innumerable temperature gradients in the unburned mixture. The bright spots, which first appear in frame 5.8, glow with sufficient intensity to expose the film directly. They appear a t the periphery where mottling is also most, pronounced. Close inspection will reveal that these bright spots are roughly rectangular in shape. This distortion occurs because the bright spots lie inside the focal point of the mirror, and, therefore, the reflected light is divergent. The camera aperture is rectangular in shape and smaller than the divergent beam; hence a blurred rectangular spot appears in the photograph
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Vol. 43, No. 12
0
1.6
2,8
4.6
5.8
6.3
1.0
8.1
10.0
12.1
17.4
‘
38.2
Time, Millisecond:
Figure 5.
Schlieren Photographs of Autoignition of Benzene
Test conditions: initial ptessure, 15.5 Ib./sq. inch; initial temp., 1 503 F.; compression ratio, 1P.6; furl-air ratio, 0.040
T W O - S T A G E R E A C T I O N AND EFFECT OF TETRAETHYLLEAD
The tendency of some fuels, notably paraffins, to undergo autoignition in two or more distinct stages has been notcd by many investigators (5, 10, 12, 14, 15, I?), Experimentt 111th the M I T rapid compression machine ( 1 7 ) shoaed that tetrdethjllead may increase or decrease the ignition delay, depending on the temperature of the mixture. Mole recent experiments show that when a two-fitage reaction is obtained with n-heptane, the addition of tetraethyllead alxays increases the duration oi the second stage, This effect is shovin in Figure 6. Thus tetraethyllead may increase, decrease, or have no effwt in the first stage of n-heptane autoignition, depending o n the conditionb of temperature and pressure, but it always increases the second stage. As a result of these two effects, the over-all delay may be increased or decreased by the addition of tetraethyllead. These observations suggest a somewhat more complex situation than that indicated in ( 6 ) . PRESSURE-TEMPERATURE-TIME C O N S I D E R A T I O N S
The experimental results described in this paper, in addition t o those described bv man]’ other observers using bombs or rapid compression machines, shoJr- that the “delay” is an important characteristic of the autoignition proem. The term has been
used here t o indicate the time required for the mixture t o complete the reaction. When the mixture reacts suddenly, the delay is represented by the t’ime interval between the end of compression and the instant at which the sudden reaction occurs, I n other instances, lvhere there is no discontinuity in the trace, the delay is measured by the time interval between the end of compression and the instant a t which maximum pressure is att,ained. It is assumed that the amount of react’ion occurring during compression is small compared with that occurring after compression. This assumption becomes less valid as the interval between the end of compression and the instant. of maximum pressure approaches zero. Moreover, it is possible to vary the test conditions t o produce pressure-time records having the same numerical values of delay but exhibiting entirely different shapes during the delay. Under these conditions it becomes questionable whether the delay can be effectively used as a parameter--.that is, vhether the delay, 1%-hichaccounts for only one variable (time), can be employed as a parameter t o correlate autoignition histories which actually involve three variables (pressure, temperature, and time). The following remarks are directed an attempt to a n s ~ ~this e r question: Idealized Considerations. Consider a given homogeneous combustible mixture of fixed volume, isolated from its surround-
2803
INDUSTRIAL AND ENGINEERING CHEMISTRY
December 1951
Figure 6.
Effect of Tetraethyllead on First and Second Stages of Autoignition of n-Heptane
Test conditions: initial pressure, 11.3 Ib./sq. inch; initial temp., 148’ F.; compresaion ratio, 9.06; fuel-air ratio, 0.066
ings as regards heat and work. Experience indicates that, with the passage of time, the state of the mixture (physical and chemical) will change, however slowly, until a definite end state is reached. This process is variously described as “slow burning,” “autoignition,” “combustion,” or even as “an explosion,” the particular designation depending on whether the events under consideration occur early or late in the process and to what extent the time scale is magnified. A “reference state” may be specified by measuring the pressure, temperature, and composition of the mixture a t a given instant. If the process is reproducible, then the mixture can describe only one pressure-temperature-time path between this reference state and the end state. For simplifying the discussion, only reproducible processes will be considered here. A representative pressure-temperature-time path, projected on the pressuretime plane, would appear somewhat as indicated in Figure 7 . PRESSURE
represent all possible pressure-temperature-time paths which a mixture of given composition can possibly have. In Figure 9, a-n corresponds to a-m in Figure 7 . Although theoretically it may be possible to write a mathematical expression describing any one of these paths, practically, there is no method available. However, the time duration of a given path provides useful information, and since this can be measured ahd expressed by a number, it will be referred to h e r e inafter as the “absolute delay,” defined as the time interval between a given reference state and the correspondin end state. The time intervals (tm-to), (t,.-t~), ( t ~ t ~and ) , (&-by in Figure 8 represent the absolute delays of the pressure-temperature-time paths associated with reference states a,b, c, and d, respectively. Since a unique pressure-tem erature-time path is associated with every reference state, a n f e v e r y such path has a definite value of absolute delay, then every reference state is associated with a definite value of absolute delay. But the c o n v e r s e namely, that every value of absolute delay is associated with only one reference state-is obviously not true, since the definition of a reference state implies simply that the associated pressuretemperature-time path is different in shape, but not necessarily different in time duration, from that of any other reference state. Hence there will be many reference states in the pressuretemperature plane, to, having the same value of absolute delay, and if a smooth curve is drawn through all points representing a given value of absolute delay, the result will be a line of constant absolute delay. The general appearance of a family of these lines can be sketched (Figure 10) by notin that along a line of constant pressure in plane to the absolute felay will increase ae the temperature decreases, and along a line of constant temperature the delay will increase as the pressure decreases. This argument ignores reactions for which “explosion peninsulas” exist.
---/LlF END STATE
REFERENCE
STATE
I ’0
+rn
TIME
Figure 7. Pressure-Tom erature-Time Path of Hypothetical Combustible Mixture Frojected on Pressure-Time Plane A t to the mixture has pressure pa, temperature T a and composition Ca; mixture burns adiabatically, and at constant volume, histor; of mixture before to is ignored; state of the mixture beyond t m does not change
S o w assume that the mixture a t a, instead of being allowed to run its adiabatic, constanbvolume course to m, is heated or compressed instantaneously to a new state a t higher pressure and temperature. Also, assume that the composition of the mixture does not change during this instantaneous process, If the mixture is now allowed to react adiabatically and a t constant volume, a new and different pressure-temperature-time path will be described. This path, projected in the pressure-time plane, might a p ear somewhat as indicated by b-r in Figure 8. gimilarly, every point on the line to may be assumed to represent a different physical state of the same mixture, and from each such point a unique adiabatic, constant-volume, pressure-temperature-time path will begin. In three-dimensional pressure-temperature-time space, line to represents the intersection of the pressure-temperature plane a t to with the pressure-time plane (Figure 9), and therefore the foregoing argument can be extended to every point in this pressuretemperature plane. That is, a t any point in the plane: (1) the chemical composition of the mixture will be the same, and (2) the physical state of the mixture will be different. Therefore, a unique adiabatic, constant-volume, pressure-temperature-time path will begin a t each point in the plane and will extend in the direction of increasing pressure, increasing temperature, and increasing time. The state of the mixture be ond the end state for any given path will be represented by a {ne parallel to the time axis, extending to infinity. The totality of such paths will
PRESSURE 4
I - -
d Figure 8.
I
I
1
I
‘S
+I
tm
+n
TIME
Pressure-Temperature-Time Paths of Combustible Mixture Projected on Pressure-Time Plane
A t each Doint on line to comrrosition of mixture is same and (I uniaue Dresswetemperature-time path begins; states represented b y points b, c, and d ‘ m a i be considered to b e derived lrom some arbitrary state b y compressing, expanding, heating, or cooling the mixture instantaneously
EXPERIMENTAL CONSIDERATIONS
By heating or compressing a given mixture as rapidly as possible so that a number of selected reference states are approximated, a series of actual pressure-temperature-time paths can be ob-
INDUSTRIAL AND ENGINEERING CHEMISTRY
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tained. These paths will approach the ideal paths as the heating, or compressing, time is decreased. Some experimentally measured values of delay for stoichiometric n-heptane-air mixtures obtained by Maccormac and Townend ( I I ) , using a bomb, and Roegener (16), Teichmann (It?), and the authors, using rapid compreasion machines are plotted in Figure 11on temperature-pressure coordinates.
Vol. 43, No. 12
TEMPERATURE
TIME
i ‘
I
PRESSURE
pa
Figure I O .
Lines of Constant Absolute Delay in Pressure-Time Plane to
Points a b and e correspond to points a, b, and e pf Fi ure 8 Point e ha; the same value of sbrolute delay as point b gut th; shapes of the pressure-temperature-timo paths associated with a and b are dilierent ‘0
/
PRESSURE
Figure 9. Pressure-Temperature-Time Path of Hypothetical Reaction of Figure 7 Each point in plane at to represents diaerent physical state of same mixture, each point also marks the besinning of a unique prPioure.temperature-time path
There is an obvious disagreement betvieen the results obtained with the two rapid compression machines. However, this discrepancy becomes smaller a t the larger values of delay. This trend emphasizes the fact that even a rapid compression machine does not produce the instantaneous compression which is assumed in the definition of absolute delay. The compression time used by Roegener in these tests was 0.010 t o 0.012 second, approximately twice that used bJ- the authors. The discrepancies in Figure 11 are in the proper direction if this difference in compression time is assumed to be the disturbing factor That is, it would be expected that a longer compression time would give a shorter delay a t a given reference-state pressure and temperature, since more reaction will occur during the longer compression process leaving less t o occur after compression. Similarlj , the bomb data of Figure 11 may suffer from this ambiguity if the bomb-charging time is an appreciable fraction of the measured delay. , Notice that in the 1o.n- pressure region the bomb data gives three diffeient values of ignition tempeiature for a given pressure. No evidence of this evplosion peninsula has yet been revealed by the MIT rapid compression machine. This difference in the shape of the constant delay curves obtained by the two methods may be due to an essential difference in the chemical processes which lead to explosion. However, an alternate explanation may be found in the vagueness of the terms “explosion limit,” and “slow reaction,” commonly used in reports of ignition delay experiments. It appears certain, for example, that all the reactions represented by the rapid compression machine data would have been called esplosions had they occurred in the bomb experiments. Perhaps it is the differences in the magnitude of the time scale and in the definitions of terms which account for this disagreement in the shapes of the curves obtained by these two methods ( 2 , 4). Figure 11 also reveals that a lack of information exists in the intermediate delay region between 1 second and, say, 50 milliseconds. There are two good reasons for this deficit:
1. With delay values as short as 1 second, the significance of delay in the bomb experiments becomes suspect because of the comparatively long time required t o charge the bomb and bring its contents to the required reference state. 2. With delay values as long as 50 milliseconds, the significance of delay in the rapid compression machine experiments is uncertain because of cooling of the fuel-air mixture after compression. Erratic results m r e obtained from the h l I T machine when working in the long delay regions, and it is believed that this is due primarily to this factor. There appears to be no easy solution to the compression machine’s limitation for long delay work. However, the range of the constant-volume heated bomb could be extended somewhat by refinements in technique and instrumentation. An alternate solution would be the construction of a hybrid machine in which the fuel-air mixture could be compressed quickly and transferred into a bomb whose walls were previously heated to the calculated adiabatic compression temperature. This special device would be operated with only a moderate compression time of, say, 50
1
100
200 PRESSURE,
300
400
500
PSIA
Figure 11. D e l a y of Stoichiometric Mixtures of n-Heptane W h e n Heated or Compressed to Various Temperatures and Pressures
December 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
milliseconds instead of the 5-millisecond time which is used with the MIT rapid compression machine. The remaining uncharted territory of Figure 11 lies in the high temperature and pressure regions with infinitesimal delays. The shock tube (1, 16) appears to be a promising tool for the exploration of this region. The values of delay indicated in Figure 11 give no information concerning the shape of the pressure-temperature-time paths from which these measurements were made. The characteristics of the paths will vary as the pressure and temperature a t the end of compression vary. A complete experimental survey may reveal that there are prominent differences in the shapes of paths associated with different pressure-temperature regions, and therefore it may be desirable to devise a simple nomenclature to distinguish them. Thus, when the experimental evidence is more complete, it may be possible to divide the pressure-temperature reference plane into regions designated “slow-burning,” “two-stage,” or “explosive,” but presentation of typical pressuretime records would also he required to illustrate the meaning of these terms.
ACKNOWLEDGMENT
The authors wish to express their sincere thanks to the Ethyl Corp., the sponsors of the project, and to the staff of the Ethyl Corp. Research Laboratories for their keen interest and cooperation. The authors also greatly appreciate the assistance given by the staff of the Sloan Laboratory for Automotive and Aircraft Engines a t MIT. LITERATURE CITED
Beretz, D. J., Green, E. F., and Kistiakowski, G. B., J . Am. Chem. SOC.,72, 1080, 1086 (1950).
Chamberlain,G. H. N., and Walsh, A. D., “Third Symposium on Combustion, Flame and Explosion Phenomena,” p. 375, Baltimore, Md., Williams & Wilkins Co., 1949. Draper, C. S., and Li, Y . T., J . Inst. Aeronaut. Sci., 16, No. 1Q (1949).
Jost, W., “Explosion and Combustion Processes in Gases,” pp. 32-46, New York, McGraw-Hill Book Co., 1946. Jost, W., “Third Symposium on Combustion, Flame and Explosion Phenomena,” pp. 424-32, Baltimore, Md., Williams & Wilkins Co., 1949. Jovellanos, J. U., Taylor, E. S., Taylor, C. F., and Leary, W. A., Natl. Advisory Comm. Aeronaut., Tech. Note 2127 (June 1950). King, R. O., Wallace, W. A., and Mahapatra, B., Can. J . Re-
CONCLUSIONS
1. Autoignition may occur in a variety of ways, both with regard to the pressure-time history of the process and the manner in which the inflammation develops. The inflammation does not in general occur uniformly throughout the mixture. The reason for this nonuniformity is not definitely established but may be due to a great many localized temperature gradients which appear in the mixture at the end of compression. 2. In the light of the photographic evidence presented here, a re-examination of the meaning of such familiar terms as “delay,” “explosion,” ‘[flame front,” etc., seems to be called for. As a start in this direction, a rigorous definition of delay has been given. 3. The new definition of delay permits the establishment of a criterion for appraising the advantages and limitations of bombs, rapid compression machines and shock tubes as apparatus for investigating autoignition phenomena. This criterion indicates that certain of the published data on autoignition may be extended beyond the point where the delay has any real significance.
2808
search, F26, 264-76 (1948).
Leary, W. A., Taylor, E. S , Taylor, C. F., and Jovellanos, J. U., Natl. Advisory Comm. Aeronaut. Tech. Note 1332 (February 1948). Ibid., 1470 (March 1948). Levedahl, W. J., and Sargent, G. IT.,Jr., thesis, B.S. Mech Em.. MIT (1948). MacGrmac, M., and Townend, D. T. A., 3. Chem. SOC.(London), 1938, pp. 238-46. Miller, C . D., and Logan, W. 0.. Jr., Natl. Advisory Comm. Aeronaut. Tech. Rept.-785 (1944). Olsen, H. L., and hiIiller, C. D., Ibid., 912 (1948). Pastell, 0. L., “PrecombustionReactions in a Motored Engine,” S.A.E. Quart. Trans., 4, No. 4 (October 1950). Roegener, H., 2.Electrochem., 53, 389-97 (December 1949). Shepherd, W. C. F., “Third Symposium’on Combustion, Flame and Explosion Phenomena,” p. 301-16, Baltimore, Md., Williams & Wilkins Co., 1949. Taylor, C. F., Taylor, E. S., Livengood, J. C., Russell, W. A,, and Leary, W. A., S.A.E. Quart. Trans., 4, KO.2, 232-74 (April 1950). Teichmann, H., 2. Electrochem., 47, S o . 4 (1941). RECEIVED June 27, 1951.
TWO-STAGE AUTOIGNITION OF SOME HYDROCARBONS WILLIAM J. LEVEDAHL
AND
FRANK L. HOWARD
Engine Fuels Section, National Bureau of Standards, Washington, D. C.
HE autoignition theory has been used to explain many of the phenomena associated with knock in an Otto cycle engine.
T
According to this theory the ‘[end gases,” which constitute the last portion of the charge to be traversed by the flame front, are compressed adiabatically by piston motion and by combustion in the flame front until spontaneous ignition occurs. Because of experimental difficulties involved in isolating endgas reactions from those occurring elsewhere in the cylinder, the end-gas reaction has been simulated by compressing the entire contents of the cylinder to cause autoignition in the absence of spark. Pressure records of autoignition in Coordinating Fuel Research test engines have shown two distinct stages in the combustion of diethyl ether, n-heptane, and n-hexane (a, 4 ) . The beginning
of the first stage is recognized by a sudden but small pressure rise; a few milliseconds later the large and rapid rise in pressure accompanying the second stage occurs. Observations made with a rapid compression machine a t the Massachusetts Institute of Technology (6) have also shown this two-stage reaction with n-heptane and iso-octane. By adjusting the compression ratio so that the piston began its downward motion a t or shortly after the beginning of the first stage, it was possible to prevent the second stage of the reaction from occurring. Pastell ( 5 ) found that the same changes in operating variables which caused an increase in the energy liberated by the first-stage reaction also increased the tendency of the fuel to knock in a spark-ignition engine. The experiments described herein were devised to study the
