SELF-IGNITION AND COMBUSTION IN GASES

A. S. Sokolik, Leningrad

The extraordinary diversity of combustion phenomena and their importance for the most important areas of modern technology have brought into being a powerful stream of research—experimental and theoretical—seeking to give an objective physico-chemical description of various types of combustion. The most urgent and at the same time the most difficult task is to find the connection between the course of various combustion phenomena (for example, self-ignition, flame propagation, detonation) and the kinetics of the chemical processes (i.e., the complex chain of oxidative reactions) that underlie every combustion phenomenon and precede the appearance of flame. In this direction only the first steps have been taken, for the most part merely posing the problem of investigation and indicating its paths, but still extremely far from such theoretical generalizations as would make possible prediction, even for the simplest cases—for example, calculation of the temperature, limiting pressure, or delay of self-ignition, the rate of flame propagation, detonation limits, etc., under any specified physico-chemical conditions.

The creation of a general theory of combustion is hindered not only by the complexity of the phenomenon, associated with the simultaneous influence of purely physical factors (heat transfer and hydrodynamics) and the chemistry of preflame processes, but also by the present state of the kinetics of chemical reactions itself.

Despite the successes in the development of this field of physical chemistry, especially in the elaboration of a general theory of chain reactions, we are still compelled to use more or less hypothetical schemes even when considering the simplest chemical systems, such as $\mathrm{H_2 + O_2}$ or $\mathrm{CH_4 + O_2}$. Let us consider, as an example, one of the schemes giving the sequence of elementary reactions for the combustion of methane, proposed by Semenov¹ and Norrish².

According to this scheme, the reaction chain begins with the reaction of $\mathrm{CH_4}$ molecules with atomic oxygen (which, consequently, presupposes a preliminary dissociation of oxygen molecules into atoms):

\[ \mathrm{CH_4 + \frac{1}{2}O_2 \to CH_2 + H_2O.} \]

Chain propagation then proceeds through the radicals $\mathrm{CH_2}$ and $\mathrm{O}$—atoms:

\[ \mathrm{CH_2 + O_2 \to HCHO + O}; \]

\[ \mathrm{O + CH_4 \to H_2O + CH_2}. \]

In addition to this main chain, the formation of new chains is possible (i.e., chain branching), for example, as a result of the oxidation of formaldehyde:

\[ \mathrm{HCHO + O_2 \to H_2O + CO + O}; \]

\[ \mathrm{O + CH_4 \to CH_2 + H_2O}. \]

Let us note that this scheme figures, along with others, only as one of the possible mechanisms of the reaction, and, what is still more important, the individual stages of this scheme have not been established by any direct experiment, but have received only a number of indirect experimental confirmations, such as, for example, the establishment of the existence of the free radical $\mathrm{CH_2}^{3}$.

Thus, our present-day conceptions of the concrete mechanism of pre-flame reactions are in no case based on indisputable experimental material and are only probable hypothetical schemes.

The most important tasks of investigation are therefore, on the one hand, the deciphering of the chemical nature of pre-flame reactions, and, on the other hand, the elucidation of those regularities which connect the course of combustion with the general reaction-kinetic characteristic of the combustible mixture.

In the present article, works of the first kind are excluded from consideration, as being essentially chemical works, despite their undoubted significance both for the theory of combustion and for certain technical problems (especially for the problem of the occurrence of detonation in an internal-combustion engine). In the main, however, the review is devoted to those investigations of recent years in which new combustion phenomena or new methods of their experimental study are established, as well as to works that have shed new light on already known phenomena.

1. Self-ignition of gaseous mixtures

A gradual increase in the temperature of a combustible mixture at constant pressure, or an increase in pressure at constant temperature, leads to such an increase in the reaction rate that the rate of heat liberation from the reaction begins, even if only slightly, to exceed the rate of heat transfer to the walls of the reaction vessel. As a result there arises a progressive self-heating of the combustible mixture, leading to an even greater, spontaneous increase in the reaction rate and to the practically instantaneous liberation of the heat of reaction in some volume of gas, i.e., to its self-ignition.

This conception of the limiting conditions of self-ignition was formulated by Van’t Hoff^4 in the following words: “The temperature of self-ignition is that temperature at which the initial

heat loss, due to thermal conductivity, etc., is equal to the heat which the transformation forms in the same time (p. 114).

According to this conception, an explosion proper must necessarily be preceded by a period of relatively slow increase in the rate of the chemical reaction, corresponding to an equally slow rise in temperature, sometimes practically imperceptible. This period (it is called the induction period, or ignition delay) can be observed visually, for example when admitting a combustible mixture into a vessel placed in a furnace and provided at one end with a window. Under certain conditions, as for mixtures of methane or ethane with air at temperatures of about \(500^\circ\mathrm{C}\), an explosion may occur only many minutes after the mixture has been admitted into the heated bomb. This means that for self-ignition it is not sufficient merely to heat the mixture to some temperature exceeding the limiting one; a definite time must necessarily be allowed for the self-acceleration of the pre-flame reaction, corresponding to the magnitude of the induction period. For many practical cases the very possibility of an explosion is decided precisely by the time factor.

Let us consider, as an example, the question of using explosion-proof electric lamps in an atmosphere containing combustible gases—for example, in coal workings, where methane may be present, or on oil tankers, where vapors of various hydrocarbons included in petroleum and its refined products (pentane, etc.) may be present in the atmosphere. If the glass envelope of a lamp is accidentally destroyed in such an atmosphere, an explosion may occur from contact of the gas with the filament, heated to a temperature of about \(3000^\circ\mathrm{C}\), i.e. manifestly higher than the minimum self-ignition temperature of any combustible mixture (for methane it is below \(800^\circ\mathrm{C}\); for pentane it may fall to \(500\text{–}450^\circ\mathrm{C}\)). To prevent an explosion, such lamps are equipped with special automatic switches which break the current circuit at the moment when the protective bulb surrounding the electric lamp and filled with inert gas under excess pressure is destroyed. Immediately after the current is switched off, cooling of the filament begins, and penetration to it of the combustible mixture, partially diluted with inert gas, will occur at some point on the cooling curve, at a temperature the lower the faster the filament cools (the smaller its thermal inertia). But, as measurements show, this temperature of the filament at the moment of contact with the combustible mixture is always considerably higher than the minimum self-ignition temperature; therefore the possibility of preventing an explosion will be determined first of all by how long the induction period is which corresponds to the given temperature conditions. Indeed, when applied to methane or pentane, which, as experience shows, self-ignite with a relatively long delay (several seconds), it is possible to create lighting apparatus that is completely explosion-proof. But the same lamps prove to be unquestionably explosion-hazardous in an atmosphere containing hydrogen (for example, in potash mines), in accordance with the fact that for this gas

the autoignition delay times are extremely short (on the order of 0.01 sec), although its minimum autoignition temperature differs little from that of pentane (also about 500°C).

Fig. 1. Autoignition in an aliphatic bomb (Dixon and Bradish)

The existence of an autoignition delay is manifested in the fact that, under no experimental conditions, does autoignition occur simultaneously in a sufficiently large volume of gas heated to the autoignition temperature. If, for example, a combustible mixture is heated

warms to the autoignition temperature by adiabatic compression, then, as Dixon already observed\(^5\) (photographing the process of flame development on a film moving in a direction perpendicular to the axis of the bomb), autoignition always arises at some point. This is the result of the inevitable nonuniformity in the distribution of temperatures and, especially, of active centers, so that in some relatively small part of the volume with the maximum temperature and concentration of active molecules, conditions are created for an earlier completion of the induction period\(^1\). The flame that has arisen here, as photographic recording in Fig. 1 shows, spreads through the rest of the gas volume almost in the same way as occurs when a cold gas is ignited by an electric spark.

2. Basic laws of autoignition

As follows from the definition of autoignition, it is due to the fact that an increase in temperature at constant pressure gives a considerably greater increase in the reaction rate and in heat release (according to Arrhenius’ law: \(w \sim Q_a = Ae^{-\frac{E}{RT}}\)) than the heat losses due to heat transfer, which may be taken as proportional to the temperature difference between the gas and the surroundings \([Q_b = k(T - T_0)]\). In exactly the same way, a stronger increase in the reaction rate and in heat release also occurs with an increase in pressure at constant temperature, when heat transfer by thermal conduction does not change at all with pressure, while the reaction rate is proportional to some power of the pressure (for example, \(w \sim ap^2\) for a bimolecular reaction). From this it already follows with obviousness that the autoignition temperature cannot be regarded as a physical constant for a given mixture, and that its value may vary within wide limits depending on the conditions of heat removal (the diameter of the vessel, the nature of heat transfer from the gas to the walls of the vessel, etc.).

Semenov, proceeding from these considerations, was the first to give a mathematical formulation for the limiting conditions of autoignition as the condition of equality between heat losses and the heat released by the reaction. Graphically this corresponds to the condition of tangency of one of the curves (2 in Fig. 2), showing the change with temperature of the amount of heat released per second at different pressures (according to the law:

\[ Q_a = Ae^{-\frac{E}{RT}} \]

) and of the straight line of heat transfer as a function of the gas temperature at constant bomb temperature—\(T_0\) [corresponding to the law: \(Q_b = k(T - T_0)\)]. The pressure corresponding to curve 2, tangent to the straight line of heat transfer, is the critical minimum pressure at which autoignition is possible at the given bomb temperature. The condition of tangency gives the following relation between

\(^1\) On the mechanism of formation of such temperature fluctuations in a gas, see Semenov (loc. cit., 114) and Norrish\(^6\).

by the critical pressure and the autoignition temperature:

\[ \left(\frac{p}{T_0}\right)^n e^{-\frac{E}{RT_0}}=\text{const} \]

or

\[ \lg \frac{p}{T_0}=\frac{A}{T_0}+B, \]

where

\[ A=\frac{E\lg e}{nR}, \]

and \(B\) is a constant depending on the composition of the mixture and on the physical conditions of the explosion (in particular, the heat-transfer conditions—for example, the diameter of the vessel).

Fig. 2. Derivation of the limiting conditions of autoignition (Semenov)

Semenov’s formula not only gives a relation between the values of the critical pressure and the autoignition temperature, but also gives their dependence on the reaction-kinetic properties of the mixture, determined by the activation energy (the constant \(A\)), and on the physical conditions of the explosion, determined by the constant \(B\), which already indicates a path for precalculating the limits of autoignition.

Subsequently, on the basis of Semenov’s ideas, a more rigorous theory of thermal explosion was developed in the works of Todes \(^{7}\) and Frank-Kamenetskii \(^{8}\), which showed the real possibility of calculating autoignition temperatures and pressures under specific heat-transfer conditions for the simplest types of reactions (for example, for the explosive decomposition of \(N_2O\) \(^{9}\)).

Semenov’s formula was repeatedly confirmed experimentally, first by Zagulin \(^{10}\), and then by a number of other investigators under explosion conditions at low pressures (of the order of several centimeters Hg). Under these conditions a decrease in the critical pressure with increasing autoignition temperature was always observed, in exact agreement with the formula.

Fig. 3. Boundaries of the region of autoignition of hydrocarbons over wide ranges of pressure variation. The dashed line (\(T\)) denotes the boundary according to Townsend’s experiments

Further expansion of the experimental region toward the study of autoignition at higher pressures (especially important for hydrocarbon–air mixtures and as applied to problems of the internal-combustion engine) showed the limited applicability of Semenov’s formula \(^{1}\). This is clearly demonstrated by the form of the boundary curve of the autoignition region shown in Fig. 3, typical for most hydrocarbons. Only a small segment, corresponding to low pressures and high temperatures (\(AB\) in Fig. 3), gives such a decrease of the critical pressure with increasing—

\(^{1}\) See the corresponding remarks in the works of Naylor and Wheeler \(^{11}\) and ours \(^{16}\).

of the ignition temperature, which is required by Semenov’s formula. For the remaining and larger part of the limiting curve, experiment gives other relationships between these explosive parameters—for example, an increase in \(p_{\mathrm{pred}}\) with increasing \(T\) on the segment \(BC\), corresponding to the so-called upper ignition limit (where ignition disappears when the pressure is increased at constant temperature), or the almost complete constancy of the critical pressure when the temperature changes over wide limits—from \(400\)—\(450\) to \(300^\circ\mathrm{C}\) on the segment \(DE\), corresponding to the transition from the so-called high-temperature to the low-temperature ignition zone1; or, conversely, an almost complete constancy of the ignition temperature when the pressure changes over wide limits (from 2 to 30—40 atm) on the segment \(EF\), corresponding to the minimum ignition temperature.

Having no possibility of considering in detail the causes that produce the different course of variation of both explosive parameters—the ignition temperature and pressure—we shall only mention that this by no means indicates an incorrectness of the arguments underlying Semenov’s formula, but is connected either with a special influence of pressure on the development of chain reactions (for example, with enhancement of the breaking of reaction chains and difficulty of ignition, owing to an increase in the number of triple collisions when the pressure is raised), or with the fact that the pre-flame reactions in the low-temperature zone represent a combination of several competing processes which respond differently to changes in temperature and pressure.

But regardless of these causes, the conclusion is indisputable that the ignition temperature is not only not a physicochemical constant of the given combustible mixture (since its value also depends on a number of physical conditions determining the character of heat removal from the reacting gas), but the very concept of ignition temperature has no physical meaning without indication of the pressure corresponding to it.

In exactly the same way, the magnitudes of the ignition temperature and pressure are closely connected with the time factor—the corresponding value of the induction period.

The quantitative relation between the induction period and the ignition temperature was first given by Tizard and Pye[^14] in their fundamental investigation of ignition under adiabatic compression. Subsequently Semenov introduced a more general formula giving the dependence between all three explosive parameters—pressure \((p)\), temperature \((T)\), and induction period \((\tau)\). It follows from the general law of development of the rate of the pre-flame reaction with time: \(w = ae^{\varphi t}\), and the general condition for ignition: \(\varphi \tau = \mathrm{const}\), where the coefficient of self-acceleration of the reaction is \(\varphi = p^n e^{-\frac{\gamma}{T}}\).

The general formula:

$$ \tau p^n e^{-\frac{\gamma}{T}}=\text{const} $$

was first established experimentally by Neumann and Egorov ^15 on the example of spontaneous ignition of methane at low pressures.

As follows from the formula, the induction period must decrease both with an increase in pressure and with an increase in temperature. The influence of the latter is especially great for a sufficiently large value of the temperature coefficient \(\gamma\). Thus, for \(\gamma = 20\,000\) (and in some cases its value is even higher), an increase in temperature by \(10^\circ\) at \(300^\circ\mathrm{C}\) leads to an almost twofold reduction in the delay.

The same relationship between the delay and the spontaneous-ignition temperature may also be considered from another point of view, namely: spontaneous ignition must occur at the lower the temperature (but not below the minimum), the greater the time provided for the development of pre-flame reactions.

But here, too, the extension of the experimental region toward higher pressures showed the limited applicability of this formula in its general form—for example, the constancy of the delay for hydrocarbon–air mixtures in the temperature range \(400\)—\(600^\circ\mathrm{C}\) and, conversely, the constancy of delays with pressure in the low-temperature zone: \(400\)—\(280^\circ\mathrm{C}\) ^16. Investigation of spontaneous ignition of hydrogen–air mixtures at high pressures showed that for them the induction period does not depend on temperature and decreases sharply with increasing pressure over the entire temperature interval studied: \(500\)—\(700^\circ\mathrm{C}\). Thus, spontaneous ignition of hydrogen–air mixtures at \(p > 1\)—\(1.5\) atm is described by the formula: \(\tau p^3 = \text{const}\), independently of the temperature at which spontaneous ignition occurs ^16. The original works give examples of the use of these experimental conclusions for the interpretation of practically important explosive phenomena.

On the basis of the fact that spontaneous-ignition temperatures are not physicochemical constants, a number of investigators have recently shown a tendency to exclude all explosive parameters \((T, p, t)\) altogether from the arsenal of physical chemistry, replacing them with such primary quantities as directly characterize the kinetics of pre-flame reactions—for example, the reaction rate, its activation energy, and the like. This tendency is to some extent justified by the difficulty of constructing a rigorous theory of flame propagation using explosive parameters; but their experimental values, and especially the experimentally established relationships between them, provide correct guidance in considering many technical problems. If, for example, the absolute values of induction periods measured for air mixtures of hydrogen or pentane under certain conditions of a laboratory experiment cannot be transferred to the conditions of a particular explosion (for example, an explosion from the incandescent filament of a lamp), nevertheless the values of the induction periods provide a reliable criterion for assessing the relative explosion safety of equipment in an atmosphere of pentane and hydrogen.

A comparative study of the induction periods of autoignition of heavy diesel fuels in a bomb, under conditions generally different from their autoignition in a diesel engine, nevertheless made it possible to evaluate correctly their performance qualities, determined by the so-called “cetane number” 17–19.

Investigation in a bomb of the dependence of the autoignition delay of light motor fuels on pressure and temperature in various temperature zones made it possible not only to draw a number of important conclusions about the conditions for the occurrence of detonation in the Otto engine, but also to establish a direct quantitative dependence between the magnitude of the temperature coefficient \(\gamma\) for the induction period and the critical compression ratio characterizing the detonation properties of motor fuels 20.

3. Studies of short induction periods

Rapid-admission method. Visual measurement of autoignition delays is possible only under limited conditions of either low pressures or low temperatures (near the minimum temperature), with delays no shorter than 2–3 sec. Meanwhile, the greatest practical interest lies in the study of autoignition with short delays. In the work of our laboratory (the first systematic investigations of autoignition at short delays), the rapid-admission method, schematically shown in Fig. 4, was successfully used.

The combustible mixture from the preliminary chamber 1 is admitted into the heated bomb 2 by means of a fast-acting spring valve 3, so that the entire process of filling the bomb takes place within \(3–5 \cdot 10^{-2}\) sec. The short duration of admission is one of the main methodological conditions necessary in the study of short induction periods. The induction period is measured by means of an optical membrane manograph 5 from photographic recordings of pressure, examples of which are given in Fig. 5. The induction period here corresponds to the horizontal part of the pressure diagram from the moment of the end of admission to the sharp rise in pressure during explosion.

Fig. 4. Diagram of the apparatus for studying autoignition.
1 — admission vessel, 2 — bomb, 3 — fast-acting valve, 4 — window for visual observation, 5 — membrane manograph.

But, in addition to estimating the overall magnitude of the induction period, a detailed study of the pre-explosion processes occurring in the gas is extremely important. This is a task of exceptional methodological difficulty, since here it is sometimes necessary to measure negligible changes in pressure caused by the slow reaction in the induction period, simultane-

simultaneously with the recording of explosive pressures on the order of tens of atmospheres. However, the methodological difficulties have been completely overcome by the creation of an optical differential manograph, applied

Fig. 5. Samples of photographic pressure recordings during autoignition

in the work of Neumann and co-workers²¹, Cain²², and, in its most advanced form, in studies of our laboratory (the designs of A. N. Voinov and A. I. Bykov) (Fig. 6).

The manograph is divided by a thin membrane 1 into two chambers, one of which communicates with the bypass vessel 4, and the other with the bomb 6. The bypass vessel is equipped with an electromagnetic valve, which closes the bypass channel under the action of a spring and opens when current is switched on in coil 5. The thin membrane of the manograph is connected with the optical system and is bounded on both sides by thick perforated membranes 2 and 3.

Fig. 6. Diagram of a differential optical manograph for studying the kinetics of pre-explosion processes (design by A. N. Voinov and A. I. Bykov)

When the bypass vessel is filled to a prescribed pressure (up to 10—15 atm), the thin membrane is pressed against the limiter and, together with it, gives a deflection corresponding to the pressure increase during filling of vessel 4. On the film this pressure is recorded by the line a—b in Fig. 7. When the mixture is admitted into the previously evacuated bomb, the pressures in both chambers of the manograph become equalized, and limiter 2, together with the thin membrane, returns to its initial position. The process of pressure equalization in vessels 4 and 6, i.e., the admission process, is recorded on the film by the line b—c, making it possible to control the rate of admission, which, as shown by

experiment, which is especially important for stabilizing the conditions of self-ignition[^13]. Next, the diagram records the moment of switching off the electromagnet \(d\). The bomb is now connected with only one chamber of the manograph. The pressure increase \((e—f)\) due to the reaction is at first recorded only by the thin membrane \(1\), and then, beginning with pressures above \(100\) mm and up to explosion pressures, by the joint deflection of the thin and thick membranes \(3\). At initial pressures of \(5—10\) atm our differential manograph records pressure changes down to \(5\) mm, as well as explosion pressures.

The photographic record in Fig. 7 was taken under the conditions of low-temperature self-ignition of a mixture of heptane with air. Here we are dealing with two-stage self-ignition, first studied by Townend[^12], Neumann[^21] and Kähne[^22]. The explosion proper in this case is preceded by the formation of a cool flame, giving products of incomplete oxidation of the hydrocarbon.

Fig. 7. Pressure diagram obtained with a differential indicator during self-ignition of heptane (experiments of Kravets and Yantovsky).
\(1\)—cool flame, \(2\)—hot flame

The sensitive membrane of the differential manograph shows no noticeable increase of pressure (and, probably, of temperature) during the induction period \(\tau_1\), up to the moment when the cool flame appears. Consequently, here we are dealing with an isothermal process in which the development of the preflame reaction is determined exclusively by the branching of reaction chains. The pressure rise in the cool flame characterizes its intensity and the depth of oxidation of the hydrocarbon.

After the cool flame, with an induction period \(\tau_2\), already at a relatively elevated temperature, a hot explosion occurs with the formation of the products of complete combustion, \(\mathrm{CO}_2\) and \(\mathrm{H}_2\mathrm{O}\).

The study of both stages of the pre-explosion process by this method, in conjunction with chemical analysis, represents a very promising path not only for understanding the mechanism of self-ignition, but also for

coverage of current technical questions connected with the kinetic characteristic of antiknock fuels.

The jet method. If a combustible mixture is passed through a tube heated to a certain temperature, then, at a sufficiently high jet velocity, self-ignition disappears; then, obviously, the residence time of the gas in the tube is less than the induction period corresponding to the given temperature. But precisely the necessity of using high velocities makes it difficult to use this method for the study of short delays.

Saxe \(^{23}\) made an attempt to get around this difficulty by establishing along the reaction tube the temperature distribution shown in Fig. 8. The passage of the gas through a section of tube with a gradual rise in temperature from 100 to 820°C is regarded by the author as

Fig. 8. Temperature distribution in the tube in Saxe’s experiments

a process of heating. And only the time of passage through the short section with maximum temperature (820–850°C) serves in Saxe’s experiments as a measure of the induction period corresponding to this temperature.

The conventionality of such a measurement of the induction period is obvious, since the time of preliminary heating of the mixture (during which its chemical changes are inevitable) is six times greater than the interval of time during which the mixture remains at the maximum temperature.

Here, therefore, one simply neglects the condition that underlies our method, i.e., that, when measuring short induction periods, the time of preliminary heating be less than the minimum value of the induction period (or comparable with it).

Measurements by Saxe’s method will therefore lead to a result all the more distorted, the more intensely the mixture reacts in the process of heating. For methane, for which appreciable reaction rates are possible only at relatively high temperatures (close to the maximum temperature of the tube), this method can give a value of the induction period relatively close to the true one. But

for higher hydrocarbons, which begin to oxidize at considerably lower temperatures, the Saxe method will give manifestly incorrect results—for example, the temperature coefficients corresponding to lower preheating temperatures will be arbitrarily assigned to the maximum temperature.

Method of heated particles. One of the possible ways in which mine gas may ignite is associated with its ignition by incandescent particles of various origin—for example, friction sparks (during the operation of cutting machines in some rocks) or particles of undecomposed explosive and cartridge casing during blasting operations. But the study of the self-ignition of combustible gas mixtures by heated particles carried through the gas at a definite velocity, besides being of purely practical interest, also acquires general interest as one of the methods for studying self-ignition under conditions of a very short delay.

Fig. 9. Schematic of the method for investigating gas ignition by heated particles

The scheme of such a method, in the form in which it was used by Silver \(^{24}\), is shown in Fig. 9.

• The bead (of quartz or platinum) is heated in the quartz tube \(PP\) to a definite temperature, measured by an optical pyrometer. By the pressure of compressed air the bead is ejected from the tube and carried at a definite velocity through a brass box filled with the combustible mixture under investigation. Opening the valve for admitting air into the tube \(PP\) is effected by releasing the clamp (schematically represented in \(TS\)), which simultaneously closes the current circuit in the solenoid. The iron core \(L\) then raises the shutter \(S\) so that its slot \(Sl\) brings the tube \(PP\) into communication with the box.

The latter is equipped with a screen \(T\), reflecting the ball, and a cellophane diaphragm \(CR\), the rupture of which serves as an indication of spontaneous ignition of the gas. Approximately the same apparatus was used in later experiments of the same laboratory (University of Glasgow) in the work of Paterson \(^{25}\), with the addition only of measurement of the velocity of the ball by means of a ballistic pendulum, as well as devices making it difficult for the jet of compressed air to penetrate, together with the ball, into the explosion vessel.

At a relatively constant velocity of the ball \((2\text{--}5\ \mathrm{m/sec})\), Silver measured the limiting temperature at which ignition of air mixtures of pentane, illuminating gas, and hydrogen is possible immediately after the ball penetrates into the explosion vessel. Silver’s method thus, in essence, gives a measurement of the temperatures of spontaneous ignition of a gas from a heated surface at a constant delay close to zero.

Under these conditions, as is seen from Fig. 10, spontaneous ignition of gases occurs at lower temperatures the larger the diameter of the heated ball.

The spontaneous-ignition temperature for methane is especially high at such a delay; for it, spontaneous ignition could be obtained only with a ball of diameter \(6.5\ \mathrm{mm}\) and at a temperature of about \(1200^\circ\mathrm{C}\).

Silver considers the process of spontaneous ignition of the gas shell surrounding the heated ball from the point of view of the thermal theory. For a gas layer of thickness \(dr\) surrounding a ball of diameter \(a = 2r\), the condition for spontaneous ignition will be equality of the heat losses to the surrounding medium with temperature \(T_0\) and the heat released in the same gas layer as a result of reaction. The heat losses are calculated as the difference between the heats: that carried away through the surface of the layer into the surrounding gas and that supplied to this layer from the ball, \(8\pi a\rho (T_p - T_0)\,dr\), where \(\rho\) is the heat-transfer coefficient.

The heat released as a result of reaction in this layer is equal to

\[ 4\pi a^2\,dr\,Q\beta e^{-\frac{A}{RT_p}}, \]

where \(\beta\) is a constant also including the pre-exponential factor in the Arrhenius equation.

Thus, the heat input increases more rapidly with increasing ball diameter (proportional to \(a^2\)) than the heat losses (proportional to \(a\)), which explains the facilitation of spontaneous ignition with increasing ball diameter.

Silver obtains the condition for spontaneous ignition in the form of the equation:

\[ 8\pi a\rho (T_p - T_0)\,dr = 4\pi a^2 dr Q\beta e^{-\frac{A}{RT_p}}, \]

which is reduced to the form:

\[ a = \frac{2\rho}{\beta Q}(T_p - T_0)e^{\frac{A}{RT_p}} \]

or

\[ \lg \frac{T_p - T_0}{a} = \lg \frac{\beta Q}{2\rho} - \frac{A}{RT_p}. \]

This equation describes well the experimental results shown in Fig. 10, but with several unusual consequences. Indeed, the values \(\lg \dfrac{T_p - T_0}{a}\), plotted against the values \(\dfrac{1}{T_p}\), give, as follows from the equation, a straight line. At the same time, however, for all the gases investigated Silver obtains exactly the same slope of the straight lines, i.e., the same value of the activation energy—from 20.5 to 22.5 cal.

In Silver’s opinion this means that, under the given conditions, self-ignition of the gas is the result of a heterogeneous reaction on the surface of the sphere, although this explanation is difficult to reconcile with the completely identical data obtained by him for quartz and platinum spheres.

In Paterson’s work the influence of particle velocity on the self-ignition temperature of illuminating gas was investigated; moreover, Paterson regards the increase in the self-ignition temperature with increasing particle velocity as evidence that the process of self-ignition cannot be considered from the point of view of the “surface theory” alone, and that here a significant role is played by the “mechanism of energy transfer—thermal or chain.” But the state of the surface also has substantial importance (for example, that caused by the previous use of the spheres for explosive experiments).

Fig. 10. Influence of the diameter of particles on the self-ignition temperature of gases at \(\tau \sim 0\) (Silver)

Analyzing the process of self-ignition, similarly to Silver, from the point of view of thermal theory, Paterson considers heat transfer to be caused mainly by convection. Therefore into the formula for heat transfer

\[ \frac{dH_c}{dt} = Aa\mu c_p (T_s - T_\infty)\sqrt{Re}, \]

where the Reynolds number

\[ Re = \frac{2Va\rho}{\mu}, \]

the value of the velocity enters, so that the heat transfer is proportional to \(\sqrt{V}\).

In final form Paterson obtains a dependence of the form:

\[ D (T_s - T_\infty) V^{\frac{1}{2}} = \rho a^{\frac{3}{2}} e^{-\frac{A}{RT_s}}, \]

where \(D\) is a constant including the quantities of density, viscosity, and heat of reaction.

As is evident, the dependence of the self-ignition temperature on particle velocity obtained by Paterson by no means signifies any change in the self-ignition delay temperature, which here, as in Silver’s experiments, remains constant and close to zero. The increase in the self-ignition temperature with increasing particle velocity, as follows from the formula given, is directly connected with the increase in heat losses due to convection in proportion to \(\sqrt{V}\).

Paterson’s equation, moreover, presupposes a lowering of the self-ignition temperature at constant velocity \((V)\) and particle diameter \((d)\) with an increase in the temperature of the igniting gas \((T_\infty)\). But, as experiment has shown, raising the initial temperature even by \(200^\circ\mathrm{C}\) had no effect on the magnitude of the minimum particle temperature.

The investigations of Silver and Paterson do not provide direct experimental material on the dependence of short self-ignition delays on temperature and, consequently, cannot be used to check the independence of short delays from temperature established in our experiments (see § 2). However, certain results of the works considered, especially the independence of the temperature coefficient from the properties of the reacting gas, undoubtedly demonstrate the specific character of self-ignition under conditions of short delays and lend particular interest to further investigations in this direction.

4. Flame Propagation

Normal combustion. Non-detonative combustion is a complex phenomenon in which the motions of the gas itself are inevitably superimposed on the propagation of the reaction zone relative to the gas. This complexity lies in the very nature of “slow” combustion—in the fact that the velocity of propagation of the reaction zone relative to the gas (a process governed by thermal conduction and diffusion) is considerably smaller than the velocity of propagation of those compression waves that are produced in the process of ignition of each layer of gas and its subsequent expansion.

The propagation of these disturbances in the gas proceeds at the speed of sound, whereas the velocity of propagation of the reaction zone rarely exceeds several meters per second. This unavoidable separation of the mechanical effect of combustion from the combustion zone itself creates a mass flow of gas ahead of the flame front. The propagation of the reaction zone thus takes place in a moving gas, and it is necessary to take into account not only the motion of the gas along the axis of the tube (whose velocity is simply added to the velocity of propagation of the reaction zone relative to the stationary gas), but also the disorderly vortical motions that accelerate heat transfer from the combustion zone to the fresh gas.

The turbulence created ahead of the flame front during “slow” combustion is the principal factor causing an explosion

SELF-IGNITION AND COMBUSTION IN GASES

coal dust. Indeed, the ignition of mine gas (methane) in itself would not present a serious danger, in view of its relatively limited quantities, if it were not the principal cause of the explosion of coal dust. It is precisely the air currents arising ahead of the flame front that lift the coal dust from the ground, mix it with air, and create the medium in which the explosion propagates with an ever-increasing velocity (sometimes more than \(1\,000\ \text{m/sec}\)), developing in the process considerable pressures (above \(10\ \text{atm}\)). The formation of a dust cloud ahead of the flame front is visible in the photograph in Fig. 11, taken some time before the appearance of the flame at the mouth of the experimental gallery.

Fig. 11. Explosion of coal dust in an experimental gallery. At top—the ejection of the dust cloud; at bottom—the emergence of the flame front

The investigation of air currents ahead of the flame front is one of the most important tasks of experiments carried out in galleries under conditions that exactly reproduce the real conditions of a mine explosion1; and among the various measures for preventing explosions, not the least place is occupied by those whose aim is to make the formation of a dust cloud more difficult.

Coward’s investigations[^26] in recent years have revealed, moreover, one more important factor on which the velocity of flame propagation depends—namely, the change in the flame front itself under the influence of convective currents caused by the difference in density of the com-

hot and fresh gas.” Indeed, successive photographs of the flame front, obtained by Coward at various stages of its propagation through a tube, show that a plane flame front—or, as is usually assumed, a hemispherical front—is in most cases an arbitrary idealization. The flame front, as can be seen in the photographs in Fig. 12, is continuously distorted and stretched as the flame propagates, so that its surface considerably exceeds the cross-sectional area of the tube.

Coward, proceeding from the fact that the volume of gas burning per unit time is proportional to the area of the front, introduces the concept of the “fundamental velocity” of flame propagation (equivalent to the previously accepted term “normal velocity”), as the “linear velocity of propagation directed perpendicular to the surface

Fig. 12. Series of instantaneous photographs during flame propagation in tubes (Coward and Hartwell)

of the flame front and occurring in a stationary mixture at constant temperature and pressure ahead of the flame front.” The observed velocity of flame propagation, in accordance with this, will exceed the “fundamental velocity” in proportion to the increase in the surface of the flame front as a result of its distortion.

Indeed, measurements carried out by Coward and Hartwell for mixtures of methane with air showed that in a tube of diameter 5 cm (i.e., with a cross-sectional area of 20 cm²) the surface of the flame front varies within the limits of 60–117 cm² for different methane concentrations. Correspondingly, the flame propagation velocity varies from 30 to 90 cm/sec, while the fundamental velocity lies within the range 6–27 cm/sec.

The increase in the surface of the flame front has an especially strong effect in tubes of large diameter, where, correspondingly, considerable flame propagation velocities may arise. This, in particular, must be taken into account when calculating protective devices in ventilation systems that extract combustible gases.

Measurement of the normal flame velocity. Only the “fundamental” or “normal” flame velocity is directly connected with the physicochemical properties of the combustible mixture and does not depend on the hydrodynamic conditions under which the observation of flame propagation is carried out. The “fundamental” velocity

acquires, in this way, the significance of a certain physicochemical constant.

Coward and Payman \(^{27}\) give the following formula, taking into account the basic \(^{1)}\) factors determining the velocity of flame propagation:

\[ \begin{aligned} \text{Observed flame velocity} ={}& \\ ={}& \text{fundamental velocity} \times \frac{\text{surface of the flame front}}{\text{cross-sectional area of the tube}} +{}\\ &+ \text{velocity of motion of the combustible medium.} \end{aligned} \]

Measurement, in accordance with this formula, of the fundamental velocity under conditions of combustion in a tube is extremely complicated not only because of the need to measure the surface of the moving flame front (as shown in Fig. 12), but also because of the difficulty of estimating the velocity of motion of the gas. As Coward himself notes, the indicated method is therefore applicable only to such slowly burning mixtures as mixtures of methane with air, close to the limits of propagation, i.e., where the combustion velocity is relatively small and where, consequently, the mass flow of gas caused by combustion may be neglected.

However limited the application of this method may be, Coward’s indisputable merit lies in the fact that he revealed the main source of errors in measurements of flame velocities by the classical Mallard and Le Chatelier method \(^{28}\). Indeed, in numerous investigations of flame propagation in a tube since the time of Le Chatelier, although special measures were taken to ensure that combustion proceeded under conditions of constant pressure (by connecting the end of the tube at ignition with the atmosphere or with a constant-pressure reservoir \(^{29,30}\)), no attention was ever paid to the possibility that the velocity of flame propagation might change because of an increase in the surface of the flame front. And only Coward’s experiments showed the fundamental possibility, in the complex phenomenon of flame propagation in a tube, of isolating that part of it—the normal combustion velocity—which has a fundamental physicochemical meaning. A remarkable confirmation of the correctness of Coward’s method is the agreement of the values of the normal flame propagation velocity obtained by measurements in tubes with their values for the same mixtures measured in the cone of a Bunsen flame \(^{31}\).

The normal flame velocity is most easily measured in the cone of the flame formed in a Bunsen burner. The method of measuring the velocity, developed independently by Gouy \(^{32}\) and by Michelson \(^{33}\), is based on the fact that in a stationary flame cone, whose surface is the surface of the combustion front (or, as Michelson calls it, the “surface of ignition”), the volume of gas flowing out of the burner per second must be equal to the product of the cone surface by the value of the normal propagation velocity. Thus, here too, in order to estimate the normal

\(^{1)}\) We say “basic” because here, as in the preceding exposition, the changes in gas pressure and temperature that occur during combustion in closed vessels and that lead to a continuous change in the “fundamental” velocity are not taken into account.

rate, to measure the surface of the flame front, but a stationary one, which is considerably simpler1.

The series of photographs from Khitrin’s work shown in Fig. 13 demonstrates how, at an unchanged gas-flow velocity, the surface of the cone decreases as the velocity of flame propagation increases, in accordance with the formula: \(Q = uS\), where \(u\) is the normal velocity of flame propagation and \(S\) is the surface of the cone.

Fig. 13. Increase of the surface of the flame cone when the “normal” burning velocity is lowered (Khitrin)

At very high flame-propagation velocities (for example, in the combustion of hydrogen or acetylene), it is accordingly necessary to increase the velocity of the gas flowing out of the burner in order to obtain a flame cone of sufficient height or to prevent its penetration into the burner.

Fig. 14. Soap bubble in which observation of flame propagation at constant pressure is carried out (Fiock and Marvin)

But the possibility of investigating flame propagation in a burner is also limited because of the penetration into the flame of “secondary” air from the surrounding atmosphere. It is precisely owing to this inevitable dilution of the mixture flowing out of the burner by the surrounding air that one can observe stable combustion in the burner of mixtures with such excesses of fuel that they lie far beyond the upper flammability limit—for example, mixtures containing up to 17% methane (with an upper limit of about 13.5%). Conversely, because of the same dilution by “secondary” air in the burner, combustion is impossible for mixtures with such an excess of air for which stable combustion in a tube is still possible, i.e., mixtures lying considerably above the lower flammability limit—for example, mixtures containing less than 7.3% methane (with a lower limit of 5.9%).

But if, in a Bunsen burner, the diffusion of air into the flame is only an attendant circumstance, somewhat altering

composition of the combustible mixture, then in some cases (the flame of a match, a candle, gas lamps) we are dealing with diffusion flames, in which the formation of the combustible mixture is entirely due to diffusion1.

Among the original methods for studying flame propagation, of interest is the method of the “constant-pressure bomb,” developed in 1926 by Stevens[^36] and subsequently improved by Fiock[^37] and others (at the U.S. Bureau of Standards).

As the vessel containing the combustible mixture, a soap bubble is used here, in the center of which a spark gap is placed (Fig. 14). Depending on the pressure at which the flame-speed measurement is carried out, the bomb in which the soap bubble is located is filled with an inert gas to a specified pressure (above or below atmospheric). Under these conditions the flame propagates with a continuously increasing volume, as is shown by the series of instantaneous photographs in Fig. 15, and, consequently, at constant pressure. The propagation velocity of the spherical flame front may be measured either from the photographs shown in Fig. 15, or by a time sweep of the flame trace, photographed through a narrow slit in the bomb, on a film fixed to a rotating drum. The flame speed $S_s$, correspond-

Fig. 15. Instantaneous photographs of a spherical flame front during combustion in a soap bubble (Fiock and Marvin)

Fig. 16. Sweep of flame propagation in a soap bubble on a moving film (Stevens)

the tangent of the angle of inclination of the flame trace to the direction of motion of the film (Fig. 16), is determined not only by the propagation of the reaction zone relative to the gas, but also by the motion of the gas itself as a result of its expansion during combustion. The degree of this expansion is determined by the relation:

\[ E=\frac{(mr')^3}{r^3}, \]

where \(r\) is the radius of the bubble at the instant of ignition, and \(mr'\) is the same radius at the end of combustion. Hence the normal flame velocity is

\[ S_t=\frac{S_{s'}}{E}. \]

The limitation in the application of this method is connected, chiefly, with the influence of the soap film itself (moisture) on combustion, which is especially significant for gases such as CO.

Flame propagation in an internal-combustion engine. The conditions of flame propagation in an internal-combustion engine are especially complex; here, alongside the general causes of curvature of the flame front (convection), there also act specific factors—swirling caused by the passage of the mixture through the intake valve and by the motion of the piston during compression, and the temperature nonuniformity of the combustion chamber. In addition, flame propagation here takes place under conditions of changing volume (owing to piston motion), changing cross sections of the combustion chamber, and changing gas pressure and temperature. As a result, the velocity of flame propagation in an engine depends to a lesser extent on the reaction properties of the mixture and on the normal burning velocity than on hydrodynamic factors associated with the engine operating regime (for example, with the number of revolutions), and with its design (especially with the shape of the combustion chamber). In this connection, prediction of the flame propagation velocity in an engine from data on the normal burning velocity obtained by any of the methods described should be regarded as practically impossible.

Fig. 17. Head of a single-cylinder engine with a quartz cover (Uttrow and Rassweiler).
\(1\) — spark electrodes, \(2\) — intake valve

Therefore, methods of direct observation and recording of flame propagation in an engine by means of ionization gaps placed at various points of the combustion chamber \(^{38, 39, 40}\), or photographic recording of the flame \(^{41, 42}\), acquire special importance.

In 1936 Rassweiler and Uttrow \(^{43, 44}\) (General Motors Co.) developed apparatus that made it possible to produce up to 2,000 successive instantaneous photographs of the flame per second through a quartz cover in the engine head (Fig. 17). A series of photographs for a single-

of the cycle under normal engine operation, shown in Fig. 18, makes it possible not only to estimate the speed of propagation of the flame—

Fig. 18. Series of instantaneous photographs of the flame front under normal engine operation (Withrow and Rassweiler)

—but also to trace in detail the change of the flame front during the combustion process. One of the effective applications of this method is the possibility of visual observation of the entire combustion process in the engine cylinder when such a film is projected slowly onto a screen.

Finally, simultaneous with photographing the flame, the recording of pressure changes led to the establishment of an important relation between the volume and the mass of the burned charge. This makes it possible, for example, to determine directly from the indicator diagram what part of the charge has burned at any stage of the cycle, as is shown in Fig. 19.

Fig. 19. Relation between the pressure rise due to combustion (○) and the mass of the burned charge (+); ВМТ — top dead center (Withrow and Rassweiler)

5. Afterglow of the Flame and the Temperature Gradient

The attention of researchers has more than once been drawn to the fact that, in explosions in closed vessels, a more or less intense afterglow is always observed, arising in the combustion products at the location

Fig. 20. Series of instantaneous photographs with afterglow during combustion of carbon monoxide (Ellis and Wheeler).

The numbers placed under each picture indicate the time, in milliseconds, elapsed from the moment of the flash.

of the ignition source. This phenomenon is vividly reproduced by consecutively taken instantaneous photographs during the combustion of CO in a spherical vessel with ignition by a spark at the center of the vessel (Fig. 20)45. Beginning with photograph 5, when the flame front has almost reached the walls of the vessel, an intense glow appears at its center,

gradually embracing the entire burned mixture. The afterglow not only arises near the spark, but also lasts longest there. Authors who have experimentally investigated the phenomenon of afterglow are inclined to attribute it to the afterburning of the unreacted part of the carbon, explaining the increased intensity of the afterglow by the occurrence of afterburning at relatively higher pressure and temperature.

A more correct explanation of the afterglow phenomenon was given by Lewis and Elbe (loc. cit., 166—176), who connected it with the formation of a temperature gradient in the combustion products, which was theoretically shown by Mache^46.

The origin of the temperature gradient becomes clear when one separately considers the combustion of a small initial part of the charge, located at the ignition point, and of the last part of the charge, adjacent to the vessel wall. The principal difference in the combustion of these parts of the charge is that combustion of the initial part proceeds with expansion at a pressure almost equal to the initial pressure (for example, at \(p_i = 1\ atm\)), and undergoes compression in the course of combustion at higher pressures, increasing from \(p_i\) to \(p_{\max}\) (for example, from 1 to \(8\ atm\)). The work of compression for this part of the charge, therefore, considerably exceeds the work of expansion.

Conversely, the last part of the charge is first compressed from \(p_i\) to \(p_{\max}\), and then burns with expansion at \(p_{\max}\). In this case the work of expansion is greater than the work of compression. As a result, the first part of the charge receives a certain excess of energy compared with the last part of the charge; with pressure completely equalized throughout the charge, the initial part of the charge proves to be at a higher temperature than the last part.

An idea of the possible magnitude of the temperature gradient may be obtained from the simplified calculation of Ribaud^47 using the example of combustion of the mixture:
\[ \mathrm{CO} + \frac{1}{2}\mathrm{O}_2 + 2\mathrm{N}_2 = \mathrm{CO}_2 + 2\mathrm{N}_2 + 68\ \mathrm{Cal}. \]
At an initial temperature \(T_i = 300^\circ K\), the temperature after combustion of the initial part of the charge (with simultaneous expansion, i.e. at \(p \sim \mathrm{const}\)) will be approximately (without allowance for dissociation):
\[ T_{\text{init}} = 300 + \frac{68\,000}{13.3 + 2\cdot 8.1} = \]
\[ = 2\,650^\circ K. \]
Subsequent compression from the initial pressure (\(1\ atm\)) to the final pressure (\(8\ atm\)) will raise the temperature of the initial part of the charge to
\[ T'_{\text{init}} = 2\,650 \cdot 8^{\frac{0.4}{1.4}} = 4\,900^\circ K, \]
taking
\[ \gamma = \frac{c_p}{c_v} = 1.4. \]
The temperature of the last part of the charge before combustion, as a result of the preceding compression, is:
\[ T_{\text{last}} = 300 \cdot 8^{\frac{0.4}{1.4}} = 560^\circ K, \]
and after combustion:
\[ T_{\text{last}} = 560 + \frac{68\,000}{13.7 + 2\cdot 8.3} = 2\,800^\circ K. \]

Thus, the temperature gradient between the initial and last parts of the charge is \(4\,900 - 2\,800 = 2\,100^\circ\).

In reality (owing to dissociation) the difference between these temperatures is considerably smaller. Thus, for the case of an ozone explosion, Lewis and Elbe (loc. cit., 175) obtained a temperature gradient of \(2552 - 1825 = 727^\circ\).

Fig. 21. Successive spectra showing the reversal of the sodium line with a gradual increase in the temperature of the light source (Uytrow and Rassweiler)

In any case it is sufficiently large to explain the intensification of the glow in the central part of the charge as it is compressed, and its propagation toward the periphery as the temperature becomes equalized.

The presence of a temperature gradient was shown by Uytrow and Rassweiler\(^{48}\) by direct measurement of the gas temperatures in an engine equipped with windows, using the sodium-line reversal method.

Light from a heated tungsten filament, whose temperature can be measured and varied over wide limits, is passed through the charge, to which traces of sodium have been added, into the slit of a spectrograph. A stroboscopic disk establishes the instant of the cycle for which the measurement is made. A series of successive photographs of the spectrum at a gradually increasing temperature of the light source shows, as is seen in Fig. 21, the temperature at which reversal of the line occurs (at which the temperature of the gas becomes equal to the temperature of the light source). In the present case it lies between \(3815\) and \(4015^\circ\)F (i.e., between \(2120\) and \(2230^\circ\)K).

Fig. 22. Temperature in different parts of the charge under normal and detonation operating conditions of the engine (Uytrow and Rassweiler).

1—\(10^\circ\) after ignition, 2—\(45^\circ\) after ignition, 3—\(10^\circ\) after ignition, 4—\(35^\circ\) after ignition

Finally, Fig. 22 gives temperature data for normal and detonation combustion in the initial and final parts of the charge. The temperature gradient reaches an especially significant magnitude during detonation (corresponding to the greater rise in pressure during combustion), so that the temperature of the burned gas at the spark plugs exceeds the temperature of the flame in the last part of the charge by \(390^\circ\)C. In Boyd’s apt expression, “the highest temperature proves to be here not in the flame, but in the ash.”

The temperature gradient in the gas leads to a more intense heating of the part of the combustion chamber adjacent to the spark plug. According to measurements by Pelletier\(^{49}\) (testing station at Delft), the temperature of the head walls here is \(50^\circ\) higher than at the opposite end of the combustion chamber. Heating of the spark-plug electrodes, caused by the temperature gra—

dient, creates a hazard, especially under aircraft-engine conditions, of premature self-ignition, which leads to a sharp decrease in power and even to engine stoppage. To prevent this it is necessary to intensify heat removal from the electrodes of the spark plug and the adjacent parts of the head, and also in every way to smooth out the temperature gradient by more intensive swirling of the charge.

6. Flame vibrations

As early as Mallard and Le Chatelier, during combustion in tubes, observed the transition from a smooth translational motion of the flame to vibrational burning, when the flame propagates in periodic bursts. Flame vibrations, as Kirkby and Wheeler showed \(^{50}\), are accompanied by pressure vibrations of the same frequency, and not only in closed tubes but also in open ones, despite the possibility of pressure equalization. In this respect the experiments of Coward \(^{51}\), carried out in tubes of various diameters—from 10 to 30 cm and with lengths from 5 to 30 m—are especially indicative. The photographic record of flame propagation shown in Fig. 23, with the corresponding pressure diagram, was obtained during combustion of a methane-air mixture (\(10\%\) methane) in a five-meter tube open at the ignition end.

The dependence of the vibration frequency and of the fact of their occurrence on the length of the tube, and the presence, along with the fundamental frequencies, of a series of harmonics—all this indicates that vibrational burning is associated with resonant oscillations of the gas column.

The experiments of Coward and Hartwell showed that the possibility of the occurrence of vibrations and their amplitude depend to the greatest degree also on the conditions for the release of explosion pressure. Thus, by gradually bringing a plate closer to the open end of the tube, the authors obtained a series of pressure records shown in Fig. 24. The diagrams show the location where vibrations arise, their frequency, and their amplitude (right-hand scale). The vertical line marks the moment of completion of combustion—the arrival of the flame front at the closed end of the tube (tube length 5 m, \(d = 10\) cm).

The first diagram was obtained under conditions corresponding to Fig. 23, i.e., with the end of the tube at the ignition side completely open. The vibrations weaken and, finally, disappear completely when a plate with a small clearance (about 15 mm) or a piece of glass wool is placed in front of the open end of the tube. But when the tube is completely closed, vibrations again arise with a considerably increased amplitude and an increased burning rate. The same change of conditions at the ignition end—a gradual reduction of the clearance—in a tube 30 cm in diameter did not lead to suppression of the vibrations, but only to their earlier occurrence and to such an increase in amplitude that, in the closed tube, the explosion invariably led to its destruction.

The practical significance of these experiments is connected precisely with the shattering effect of a vibrational explosion, and on the basis of the results obtained in tubes of small diameter (about 10 cm), the authors recommend installing safety dampers with a certain clearance that ensures suppression of the vibrations.

Many investigators tried to relate vibrational combustion to “knocking” in the engine1. This, however, was refuted by direct study of detonation combustion in the engine, as well as by further study of vibrational combustion itself.

Köchling[^52], comparing the amplitudes of pressure vibrations that arise during combustion in a bomb of various fuels, came to the conclusion that “the chemical structure of fuels, and also the physical properties associated with it, for example the autoignition temperature (and, if we add, the detonation properties), contrary to every expectation have only a quite insignificant influence on the appearance of vibrations (or, as the author calls them, the ‘knock phenomenon’ in the bomb).”

It is enough to point out that the amplitude of the vibrations for benzene, toluene

Fig. 23. Photographic recording of vibrational combustion with a pressure diagram during the combustion of methane in an open tube (Coward and Hartwell)

or ethyl alcohol (fuels with maximum detonation resistance) proved to be approximately the same as for heptane.

Köchling notes, in addition, that partial replacement of nitrogen by oxygen leads to suppression of the vibrations while simultaneously increasing the rate of combustion. The necessity, for the occurrence of vibrations, of a certain, quite definite combustion rate corresponding

Fig. 24. Change in the amplitude of pressure vibration at various degrees of pipe opening (Coward and Hartwell). \(\Delta p\) is the change in pressure in pounds per square inch.

conditions of resonance, points to the fact that for hydrogen the maximum amplitudes of vibrations were observed both for the mixture with the maximum rate of combustion (36% H₂; flame velocity 35 m/sec), and at the limit of propagation (10% H₂; flame velocity about 1 m/sec).

Lewis and Elbe (loc. cit., 317) deny the connection of vibrational combustion with the phenomenon of resonance, asserting, for example (on unknown grounds), that “the appearance of vibrations does not depend on the size and shape of the vessel”—this is simply incorrect. Their own, very few experiments with hydrogen–air mixtures led them to the conclusion that the occurrence of vibrations is associated with the presence of an excess of oxygen or nitrogen, especially the former (let us recall that Kuchling observed vibrations with maximum amplitude also in mixtures with a deficiency of oxygen).

Lewis and Elbe propose an original explanation of vibrational combustion, which in their opinion arises as a result of an “excitation delay”—a delay in the establishment of an equilibrium distribution of energy between the kinetic and internal (vibrational) energy of the O₂ and N₂ molecules.

This delay and, consequently, the abnormal excess of kinetic energy is the greater, the lower the combustion temperature; and therefore, in the authors’ opinion, it should manifest itself especially sharply in mixtures strongly diluted with oxygen and nitrogen.

“Excitation delay” means a certain change of heat capacity with time—namely, its gradual increase as the equilibrium distribution of energy is established. In this case the transition of the excess kinetic energy into vibrational energy must also be accompanied by a decrease in pressure according to the equation:

\[ \frac{3}{2}pv = N \cdot \frac{1}{2}mV^2. \]

The heating of the inner layers of the gas, owing to compression in the process of combustion, promotes the rapid establishment of an equilibrium distribution of energy and a reduction in the volume of this part of the burned gas. Hence—the formation of an inward-directed mass flow of gas and the occurrence of pressure waves.

In evaluating the proposed hypothesis it should be taken into account that it proceeds from the necessary existence of those conditions which create a temperature gradient in the combustion products and which occur, naturally, only in closed vessels. Meanwhile, vibrational explosions, as follows from the experiments of Coward and many other investigators, up to Mallard and Le Chatelier, are also observed in open tubes, where these conditions do not exist, where there is no adiabatic compression of the gas increasing as combustion proceeds and, correspondingly, no rise in the temperature of the “core,” where, on the contrary, the temperature of the combustion products is continuously lowered owing to heat transfer. Therefore the hypothesis of Lewis and Elbe can at best have only limited application to the case of combustion of “poor” mixtures in closed vessels.

7. Detonation

Structure of an explosive wave. According to the classical conceptions[^53] underlying the theory of a detonation or explosive wave, the latter is the combined propagation, at the same speed (exceeding the speed of sound), of a shock wave (i.e., a wave with an instantaneous and appreciable increase in pressure) and a combustion wave. In this, it was usually assumed that the fronts of the two waves coincide exactly, as is shown schematically in Fig. 25, A. This means that the instantaneous compression produced by the shock wave must cause equally instantaneous (i.e., with zero delay) self-ignition of the gas mixture.

The propagation of the combustion wave at the same speed as the shock wave leads to the following fundamental differences between a detonation wave and normal combustion:

1. In a detonation wave, self-ignition of the gas occurs not from its being heated by thermal conductivity (as occurs in “normal” combustion), but from the adiabatic compression of the gas by the shock wave along the dynamic Hugoniot adiabat, which differs from the ordinary Poisson adiabat, as is seen from Fig. 26, by a higher rise in pressure for the same reduction in volume.

2. In detonation combustion, the state of the mixture ahead of the front of the explosive wave remains unchanged, and the conditions for self-ignition of each layer of gas also remain unchanged; the explosive wave is thus, by its very nature, a stationary type of combustion propagation.

3. Finally, in a detonation explosion, the continuous equalization of pressure throughout the entire volume of gas, occurring simultaneously with the propagation of the flame (as in normal combustion), becomes impossible, since the pressure wave propagates together with the flame front and with the same speed as it.

Fig. 25. Diagram of an explosive wave: A — with exact coincidence of the flame front (F) with the shock-wave front (C); B — with lag of the combustion wave

Fig. 26. Hugoniot adiabat (H) and Poisson adiabat (P)

Research in recent years has introduced a substantial correction into the classical conceptions of the structure of the explosive wave. Various authors, almost simultaneously and independently of one another, came to the conclusion that in a detonation wave there is always, except in isolated cases, a certain discontinuity between the front of the shock wave and the combustion wave, as is shown schematically in Fig. 25, B.

Bohn and co-workers[^54] in 1935 published a major investigation of the structure of the detonation wave, carried out with the aid of Fraser’s new ultra-high-speed photographic camera, shown in Fig. 27.

Fig. 27. Diagram of Fraser’s high-speed mirror photographic camera

Here the photographic streaking of the flame is carried out on a stationary film by means of a rotating double-sided mirror in a chamber evacuated to vacuum (to reduce resistance at high rotational speeds of the mirror). The apparatus gives a streak record corresponding to a linear velocity of displacement of the image on the film of up to 1,000 m/sec. The photograph shown in Fig. 28 gives a detailed analysis of the process of formation of an explosive wave in a mixture \(2CO + O_2\), despite the fact that the entire process lasts about \(10^{-4}\) sec.

Fig. 28. Photographic recording of the occurrence of an explosive wave in a mixture \(2CO + O_2\) (Bohn, Fraser, and Wheeler)

Self-ignition in the shock wave initiating the detonation occurs at a distance of 64 mm from the flame front. From Bohn’s point of view this is the maximum distance at which “radiation from the flame front, absorbed by the compressed gas in the shock wave, can lead to such a rise in temperature and intense activation of the molecules that it will produce self-ignition in the shock wave” (loc. cit., 39). Although the separation between the flame front and the place where the detonation wave arises was observed by Bohn with sufficient clarity only for carbon monoxide, nevertheless this gives him grounds for formulating the conclusion in general form that “the detonation wave should now be represented as a more or less stable combination of two separate and separable components—namely, an intensely luminous flame front and an invisible shock wave immediately ahead of it” (loc. cit., 31).

Bohr gives a number of proofs of the instability of the blast wave and of the “separability” of both its components, using the example of the same mixture.

Thus, when the tube diameter is reduced to 3.6 mm (close to the limiting diameter at which propagation of the blast wave is still possible), a periodic attenuation of the detonation wave is observed “as a result of the cooling action of the walls.” The same temporary attenuation of the detonation wave occurs when it passes through a narrow (about 6 mm) layer of nitrogen, the wave velocity falling from 1,800 to 700 m/sec, or when a section of the blast tube is placed in the field of a powerful electromagnet directed along the axis of the tube (a decrease in velocity by 90 m/sec), or, finally, when the wave passes through an electric field (a decrease in the wave velocity by almost a factor of two, especially when the wave propagates from cathode to anode, which Bohr explains by the “pulling back” of \( \mathrm{C}^{+}\mathrm{O} \) ions from the wave front). All these experiments, in Bohr’s opinion, indicate that even a slight slowing of the flame front (as a result of one of the factors cited) leads to a complete disruption of the unstable connection between the combustion zone and the shock wave, to a complete separation of the shock wave that has gone ahead from the flame front. In his conclusions Bohr in no way notes a possible connection between the structure of the blast wave and the reaction-kinetic properties of the mixture, although his own experiments give some indications of this. We note that neither the characteristic “rupture” when a detonation wave arises (self-ignition ahead of the flame front), nor the extinction of the wave during propagation in an electric field, could be obtained for many other oxygen mixtures investigated by Bohr—hydrogen, methane, and others.

The connection between the structure of the detonation wave and the kinetic properties of the mixture is revealed most clearly at the detonation limits, i.e. in mixtures of limiting concentration at which propagation of a detonation wave is possible. A systematic study of detonation limits in our laboratory \(^{55,56}\) has provided numerous examples of how closely the unstable character of the detonation wave is connected with the chemical characteristics of the mixture—as, for example, in mixtures of CO with oxygen the detonation wave at the limit acquires the character of a stationary wave as small additions of hydrogen are introduced into the mixture (which is connected with the sharply accelerating action of hydrogen on the oxidation of carbon monoxide); conversely, in mixtures of methane with oxygen the detonation wave becomes less and less stable as the mixture is diluted with nitrogen.

In accordance with the scheme of Fig. 25, \(B\), stable propagation of a detonation wave is possible provided that the self-ignition delay at the pressure and temperature of compression in the shock wave does not exceed some limiting value; otherwise the gas layer will find itself, after compression (in the shock wave), in the zone of rarefaction and will cool before self-ignition has time to occur. Thus, despite the extremely short time during which the gas remains in the shock wave, the possibility of its self-ignition (and this is the basic condition for the existence of a detonation wave) will be determined by the kinetics of the oxidation reactions, by their self-acceleration during

compression by the shock wave. From this point of view, some discontinuity between the front of the shock wave and the combustion wave must occur in every explosive wave, being especially sharply expressed near the detonation limits.

The most direct confirmation of these ideas was provided by experiments in which, by means of a small addition of H$_2$ or C$_2$H$_2$ (up to 0.3%) to a non-detonating mixture of CO with air, it first proved possible to obtain in it a stable propagation of an explosive wave. In this case the combustion energy of the mixture remained unchanged, but its reactivity was sharply increased.

An effect on the kinetics in a detonation wave is also possible from the other side: by changing, for example, the strength of the shock wave, i.e. the increase in pressure and temperature which it creates in the combustible mixture. It is precisely in this sense that Payman’s experiments$^{57}$ are of interest; in them, for the first time, the propagation of an explosive wave in a methane–air mixture was achieved when it was ignited by a shock wave from the explosion of a powerful charge of mercury fulminate (50 g).

In this connection, it would be of interest to carry out a detonation explosion in the same methane–air mixture with the addition of small amounts of NO$_2$, whose catalytic action on the oxidation and autoignition of methane is widely known$^{58,59}$.

Detonation spin. Connected with the structure of the detonation wave, although by a relation that is still unclear, is the phenomenon of “detonation spin,” which gives a characteristic “striped” structure in photographic records of an explosive wave (Fig. 29).

As early as 1926, Campbell and co-workers$^{60}$, on the basis of their experiments, came to the conclusion that this character of the photographic record is caused by the advance of the front of the detonation wave along a spiral path. This is, incidentally, also confirmed by the fact that the detonation wave leaves on the walls of tubes coated with a layer of silver or lead dust a spiral-shaped trace, the “pitch” of which exactly coincides with the pitch measured from the photographic records$^{1}$.

It seemed natural to suppose that the “spin” is connected not only with the screw-like motion of the combustion zone, but also with a similar motion of the gas. However, the high-speed method of photographic analysis, by means of Fraser’s remarkable apparatus, showed the incorrectness of this assumption and led to a new interpretation of the phenomenon of “detonation spin.” The photographic record of a detonation wave in a mixture 2CO + O$_2$ shown in Fig. 30 demonstrates that the “striped” structure which we saw in Fig. 29 in reality represents, as the authors write, “a secondary effect produced by the intersection of two series of lines; one of them is due to luminous particles moving forward behind the wave front with a velocity of 780 m/sec (this is the mass velocity $u$, constituting one of the components of the velocity of the detonation wave: $D = u + c$, where $c$ is the speed of sound at the corresponding temperature); the other is the luminous trace of the compression wave propagating through the heated medium with a resultant velo-

$^{1}$ For a review of these works see my monograph Combustion and Detonation in Gases, pp. 43–49, 1934.

at a speed of 320 m/sec (this speed is equal to 1100–780 m/sec, i.e., to the difference between the true velocity of the compression wave and the oppositely directed velocity of the gas)... This means that during each complete revolution of the “head” of the detonation wave, a sudden ignition of a portion of the gas occurs here at the moment when the shock-wave front passes, or immediately behind it” (loc. cit., 38).

On the basis of these experiments, the detonation wave should be regarded not as a continuous process of propagation of the combustion wave together with the shock wave, but as periodically occurring self-ignition of the gas caused by the shock wave.

Fig. 29. Photographic record of a detonation spin in a mixture \(2\mathrm{CO} + \mathrm{O}_2\)
(Bone and Fraser)

Observations by various investigators indicate a direct connection between the “periodic” character of detonation combustion and such a structure of the wave, when one may assume a more or less significant lag of self-ignition behind the shock-wave front.

Thus, in the experiments of Bone and Fraser\(^{61}\), a “spin” is always observed near the onset of the detonation wave, whereas in the established wave it is absent in some mixtures (or, at any rate, is not observed). The extinction of a detonation wave when it passes through a layer of inert gas, or through an electric or magnetic field, likewise applies only to a wave with a “spin” structure.

In Breton’s investigations\(^{62}\), and in ours\(^{55}\), a “spin” was almost always observed in mixtures close to the detonation limits (including hydrogen mixtures), i.e., where self-ignition in the detonation wave occurs with the greatest possible delay and disappears as this delay is shortened, for example with an increase in the addition of hydrogen to carbon monoxide mixtures.

Fig. 30. Photographic record of a detonation spin in a mixture \(2\mathrm{CO} + \mathrm{O}_2\), obtained with high-speed scanning
(Bone, Fraser, and Wheeler)

Attempts at a theoretical analysis of the phenomenon of “detonation spin”\(^{63,64}\) are so far only qualitative in character and amount in practice to the statement of periodic self-ignition in the shock ...

wave with a finite delay, while in no way explaining the occurrence of rotation of the detonation-wave front.

Let us note, finally, that the propagation of detonation in solid explosives also gives a spiral trace^65, which Mowrer^66 explains by the occurrence in the gas, at supersonic velocities, of a periodic alternation of compression and rarefaction.

Fig. 31. Series of instantaneous photographs of detonation combustion in an engine (Uytrow and Rassweiler)

Detonation in an internal-combustion engine. The use in our laboratory of high-speed photographic recording for the study of combustion in an engine led to the discovery of a fact of fundamental importance—the formation in the engine during “knock” of an explosive wave with all its characteristic features^42. This completed a certain stage in the many-year investigation of the nature of detonation in an engine and posed anew the question of the mechanism of its occurrence. At the same time, our experiments prompted a number of new attempts at such an interpretation of detonation combustion in an engine in which it would be possible not to resort to identifying it with an explosive wave. In describing detonation combustion, the point of departure is to a considerable extent the experiments of Uytrow and Rassweiler, carried out by the method of accelerated cinematographic filming^43.

In Fig. 31 six series of instantaneous photographs are shown, obtained on a detonating experimental engine (see Fig. 17), beginning with the moment immediately preceding the detonation explosion. Up to this moment the propagation of the flame does not differ in any way from the normal operating regime of the engine. The authors note, as a characteristic feature of detonation combustion, the appearance of a focus (or foci) of flame ahead of the primary flame front, indicating self-ignition in the last part of the charge.

Fig. 32. Photographic recordings of detonation combustion in an engine (Sokolik and Voinov). \(H\) — self-ignition ahead of the primary flame front

On this basis it is asserted that “knock is, of course, not the result of a sudden increase in the velocity of the flame propagating forward,” but represents an almost instantaneous propagation of flame from the focus of self-ignition. Finally, it is noted that “detonation self-ignition” of the last part of the charge causes a sharply accelerated motion of the gas in the main part of the combustion chamber, directed toward the spark plug.

What new information did these observations provide? First of all, they show that the flame during “knock” embraces the last part of the charge in a time shorter than the interval between two successive exposures (2 degrees of crankshaft rotation, which at 900 rpm corresponds to \(1/2700\) sec.). This can give only a lower limit for the velocity of flame propagation during “knock,” namely, an indication that it is higher than \(180\ \mathrm{m/sec}\); at the same time, our measurements, carried out at a considerably greater sweep speed (with an accuracy down to 0.1 degree of shaft rotation), give the true value of this velocity — \(2000\ \mathrm{m/sec}\).

As for the place of origin of detonation, our photographic recordings, shown in Fig. 32, also demonstrate with great clarity that self-ignition is often accompanied by the appearance of a detonation wave, but gives a flame that propagates with a low velocity. In this case the detonation wave may arise simultaneously both from the primary flame front and from the secondary one created by self-ignition (see Fig. 32, C). Finally, our observation that with relatively early self-ignition the occurrence of detonation becomes altogether impossible is of exceptional importance.

Fig. 33. Photographic record of the “ejection” of a flame in a mixture of butane with oxygen (Laffitte)

In 1938 Laffitte^67 proposed a new description of detonation combustion in an engine (intended to explain the wave velocities obtained by us) on the basis of its analogy with the phenomenon of “flame ejection.”

Exploding detonating mixtures of butane or acetylene with oxygen in a glass tube separated from another open tube by a thin cellophane diaphragm, Laffitte obtained photographic records analogous to that shown in Fig. 33.

In essence, these are ordinary photographic records of a detonation wave arising as a result of predetonation self-acceleration of the flame (see below) and sharply different from photographic records of detonation combustion in an engine, for which the sudden formation of a detonation wave is precisely characteristic.

Fig. 34.

a — a “possible explanation of the observations of Sokolik and Voinov; lateral centers of ignition”; b — diagram of high-speed photographic recording of a detonation wave in an engine (Sokolik and Voinov). F — primary flame front, D — detonation, R — redetonation, C — reflected shock wave

But Laffitte draws attention to the fact that here, at the place where the cellophane ruptures, self-ignition occurs (which, as we have seen, indicates a special structure of the blast wave) and that the propagation of the flame with detonation velocity (1,700–1,900 m/sec) takes place in the second, open tube (in a small part of it), in the gas expelled after the rupture of the diaphragm. An analogous ejection of flame with increased velocity, in Laffitte’s opinion, also occurs in the engine from centers of self-ignition, thus forming so-called “dissociated detonation” (Jouguet’s term, identical with the concept of a finite gap between the front of the shock wave and the combustion wave)^67a.

Laffitte’s “theory,” vigorously advertised in France1, by no means represents any new interpretation of the nature of a detonation explosion in an engine, as was announced by the author, but merely repeats the conclusions of Uytrow and Rassweiler concerning the place of origin of detonation, proceeding from a completely arbitrary analogy between combustion in an engine and experiments in tubes.

Finally, Breze[^68] (director of the testing station in Delft) proposes still another explanation of our experiments, schematically presented in Fig. 34, a. Breze writes: “When the secondary flame (from self-ignition in foci 4–5) propagates from the side of the chamber, its front may intersect the narrow field of view in the window at some angle, so that the velocity measurement made by Sokolik and Voinov is then already incorrect.”

This curious interpretation of our photographic records is based partly on an insufficiently careful study of them, since then the author would have seen, at the place where detonation arises, a retonation wave (see Fig. 34, b), which can no longer be explained by any optical illusion, and partly on the strange assumption that in all experiments the secondary flame front accidentally passes through the field of view always at the same angle, corresponding precisely to the detonation velocity. Finally, Breze’s explanation delicately keeps silent about the source of formation of the reflected shock waves, which, as we have shown, are produced by detonation and retonation waves and, for a long time after the end of combustion, propagate in the cylinder at supersonic speeds.

Fig. 35. Photographic records of flame (upper images) and shock waves (lower images) during the formation of a detonation wave in mixtures of ethylene with oxygen (Payman and Titman)

Thus, our experiments, which showed the formation in the engine, during “knock,” of an explosive wave, are in no way shaken by subsequent

studies and must still form the basis of modern ideas about the nature of detonation in an engine.

How, then, should one conceive the mechanism by which detonation arises in an engine?—First of all, one must especially note the fundamental difference between the processes of formation of a detonation wave in oxygen mixtures in a tube and in an engine. In the first case, a shock wave is born as a result of the accumulation of successively formed compression waves. This process, theoretically described by Jouguet^53 and Becker^69, was reproduced experimentally by Payman^70 with the aid of the Toepler method, which makes it possible to observe the propagation of compression waves in a gas (using the change in the optical density of the medium).

The photographic records presented in Fig. 35 show that the detonation wave in tubes arises at the point where a series of compression waves unite and as a result of self-acceleration of the flame in the predetonation period. That in an engine one must assume a different source for the formation of the shock wave follows from the fact that the propagation of the flame before the onset of detonation here does not differ in any way from combustion under normal engine operation and, as our photographic records and the instantaneous photographs of Withrow and Rassweiler show, proceeds at a low velocity (15–20 m/sec). This, as well as a number of other considerations^1), compels one to accept that the formation of the shock wave in an engine is entirely due to a preflame oxidative process occurring in the last part of the charge.

Fig. 36. Antidetonation combustion chamber (Serbius)

Without going into an analysis of the chemistry of this process, we shall note only that it is analogous to those preflame processes which occur in the first stage of the induction period during the autoignition of hydrocarbons in the low-temperature zone (see Fig. 7), and whose essence consists in the accumulation of a critical concentration of active products of intermediate oxidation (peroxides). It should be assumed that these products are not distributed uniformly throughout the entire volume of the last part of the charge, but, as is always the case in preflame oxidation, are localized in separate portions of it. The ignition of these foci with a critical concentration of peroxides by tongues of the flame front must occur with an extremely short delay and with the formation of a local sharp pressure discontinuity. This is the shock wave that initiates the explosive wave in the remaining part of the charge.

This mechanism of formation of the shock and detonation waves in an engine differs from the “nuclear” theory of detonation, recently proposed—

^1) See my article in Uspekhi khimii, 7, 976, 1938.

from that proposed by Serruys^71, in the essential respect that the latter considers the formation of a shock wave as the direct result of the spontaneous self-ignition of individual centers (“nuclei”) as a result of their overheating, which, as we have seen, contradicts direct observations.

The proposed scheme leads to the interesting conclusion that one of the effective methods of suppressing detonation in an engine may be intensive mixing of the last part of the charge, preventing the formation of local centers with an increased concentration of peroxides. It is possible that this is precisely the source of the remarkable antiknock properties of the combustion chamber of Serruys’ design, shown in Fig. 36. From this point of view, the concentric grooves do not so much intensify the cooling of the last part of the charge (to which Serruys himself attributes the antiknock effect), as promote the swirling and mixing of the charge, making difficult the formation in the chamber of centers of “detonation ignition.”

REFERENCES

1. N. N. Semenov, Chain Reactions, Goskhimtekhizdat, Leningrad, 1934.
2. R. G. W. Norrish, Proc. Roy. Soc., 150, 36, 1935; 157, 503, 1936.
3. Saks, Uspekhi khimii, 7, 436, 1938.
4. Van’t Hoff, Essays on Chemical Dynamics, ONTI, 1936.
5. Dixon and Bradshaw, J. Chem. Soc., 105, 2027, 1914.
6. Norrish, Proc. Roy. Soc., 135, 334, 1932; Sow. Phys., 3, 225, 1933; Proc. Roy. Soc., 167, 292, 1938.
7. O. M. Todes, Zhurnal fizich. khimii, 13, 868, 1939.
8. D. A. Frank-Kamenetskii, DAN, 18, 411, 1938.
9. Zel’dovich and Yakovlev, DAN, 19, 699, 1938.
10. A. V. Zagulin, Zhurnal fizich. khimii, 4, 92, 1933.
11. Naylor and Wheeler, J. Chem. Soc., 1426, 1935.
12. D. T. A. Townend, Chem. Rev., 21, 259, 1937.
13. Kravets, Yantovskii and Sokolik, Zhurnal fizich. khimii, 13, 1742, 1939.
14. Tizard and Pye, Phil. Mag., 44, (6), 79, 1922.
15. Neiman and Egorov, Zhurnal fizich. khimii, 3, 61, 1932.
16. Shtern, Kravets and Sokolik, Zhurnal fizich. khimii, 11, 706; 12, 69, 1938.
17. Kaulin, Neiman and Serbikov, Zhurnal tekhnich. fiziki, 6, 183, 1936.
18. Kaulin, Mikhailova and Neiman, Dizelestroenie, No. 6, 4, 1936.
19. Morozov and Smirnov, Dizelestroenie, No. 10, 3, 1938.
20. A. S. Sokolik, Acta Physicochimica URSS, 11, 381, 1939.
21. M. B. Neiman, Uspekhi khimii, 7, 341, 1938.
22. G. P. Kane, Proc. Roy. Soc., 167, 62, 1938.
23. Sachsse, Z. physik. Chem., B 33, 229, 1936.
24. R. S. Silver, Phil. Mag., (7), 23, 633, 1937.
25. S. Paterson, Phil. Mag., (7), 28, 1, 1939.
26. Coward and Hartwell, J. Chem. Soc., 2676, 1932, 546, 1933.
27. Coward and Payman, Chem. Rev., 21, No. 3, 359, 1937.
28. Mallard et Le-Chatelier, Ann. d. Mines, 8, 274, 1883.
29. Voronkov and Sokolik, Zhurnal fizich. khimii, 6, 1385, 1935.
30. Ribaud et Gaudry, XVIII Congr. de Chim. Ind., Nancy, 1, 18-C, 1938.
31. L. Khitrin, Techn. Physics URSS, 4, 110, 121, 1937.
32. Gouy, Ann. d. Chim. et Phys., 18, 1, 1879.
33. V. A. Mikhel’son, Collected Works, Part 1, Moscow, 1930.

1. F. A. Smith, Chem. Rev., 21, 389, 1937.
2. Lews and Elbe, Combustion, Flames and Explosions of Gases, Cambridge, 1938.
3. F. W. Stevens, J. Am. Chem. Soc., 48, 1896, 1926; 50, 3244, 1928; NACA Rep., 372, 1930.
4. Fiock and Marvin, Chem. Rev., 21, 367, 1937.
5. K. Schnauffer, VDI, 75, 455, 1931; SAEJ, 34, 17, 1934.
6. Abugov and Sokolik, ZhETF, 3, 438, 1933.
7. Rabezzana, Kalmar. Automob. Engin., 29, 347, 1934.
8. Withrow and Boyd, Ind. Eng. Chem., 23, 539, 1931.
9. Sokolik and Voinov, Izvestiya AN SSSR, OMEN, 123, 1937.
10. Rassweiler and Withrow, SAEJ, 31, 297, 1936.
11. Rassweiler and Withrow, SAEJ, 42, 185, 1938.
12. Ellis and Wheeler, J. Chem. Soc., 310, 1927.
13. Mache, Die Physik der Verbrennungserscheinungen, Leipzig, 1918.
14. Ribaud, Chaleur et Industrie, 20, 15, 1939.
15. Rassweiler and Withrow, SAEJ, 30, 125, 1935.
16. Peletier, Chaleur et Industrie, 20, 1939, Discussion.
17. Kirkby and Wheeler, J. Chem. Soc., 847, 1931.
18. Coward, Hartwell and Georgeson, J. Chem. Soc., 1482, 1937.
19. A. Kúchling, VDI, 82, 1126, 1938.
20. E. Jouguet, Mécanique des explosifs, Paris, 1917.
21. Bone, Fraser and Wheeler, Phil. Trans., 235, 29, 1935.
22. Rivin and Sokolik, Journal of Physical Chemistry, 7, 571; 8, 767, 1936; 10, 688, 692, 1938.
23. A. Sokolik, Journal of Physical Chemistry, 13, 1031, 1939.
24. Payman and Shepherd, Proc. Roy. Soc., 158, 348, 1937.
25. Norrish and Wallace, Proc. Roy. Soc., 145, 307, 1934.
26. H. F. Coward, J. Chem. Soc., 1382, 1934.
27. Campbell, Finch and Woodhead, J. Chem. Soc., 3010, 1925; 1572, 1927; 2094, 1928.
28. Bone and Fraser, Phil. Trans., 230, 363, 1931.
29. Bréton J., Thèses, Nancy, 1936.
30. R. Becker, Z. Elektrochem., 42, 457, 1936.
31. W. Jost, Z. physik. Chem., B 42, 136, 1939.
32. Urbanski, Z. Ges. Schiess.-u. Sprengst., 22, 270, 1927.
33. Muraour, Chimie et Industrie, 42, 604, 1939.
34. P. Laffitte, La propagation des flammes dans les mélanges gazeux, Paris, 1939; C. R., 206, 603, 1648, 1938.
    67a. E. Jouguet, La science aérienne, 3, 138, 1934.
35. Broeze, v. Driel, Peletiez, Schriften der Deutsch. Akad. d. Luftfahrtforsch. H. 9, 1939.
36. R. Becker, Z. Physik, 8, 321, 1922.
37. Payman and Titman, Proc. Roy. Soc., 152, 418, 1935.
38. M. Sérruys, La combustion détonante dans les moteurs à explosions, Paris, 1937. (See my abstract in “Tekhn. vozd. flota” No. 5, 1938.)

1. See the article in Nouvelles de la chimie, Mars, 1939, No. 51. ↩↩↩↩↩↩