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On the shock-induced ignition of explosive gases
ON THE SHOCK-INDUCED IGNITION OF EXPLOSIVE GASES* J. W. MEYER AND A. K. OPPENHEIM
University o) California, Berkeley, California The paper elucidates the distinction between two regimes of ignition, one strong and the other weak, that characterize the onset of combustion in homogeneous gaseous mixtures whose reaction mechanism is controlled by a chain-branching step, such as that associated with the H -[- 02 collision in the hydrogen-oxygen system. On the basis of experimental observations, made primarily by the use of a stroboscopic laser-schlieren system yielding a sequence of photographic records of the entire flow field behind a reflected shock near the closed end of the tube at a repetition rate of 2 microseconds between frames, it has been revealed that strong ignition is manifested by a practically instantaneous appearance of a relatively plane pressure front associated with the generation of a flow field across the whole cross section of the tube, while mild ignition starts in the form of distinct flame kernels whose growth is comparatively slow and essentially devoid of any gasdynamic effects. The demarcation line between the two regimes of ignition is then shown to be associated with a critical value of the gradient of the induction time with respect to temperature at constant initial pressure. Specifically, for a stoichiometric hydrogen-oxygen mixture, this turns out to be - 2 microseconds/~ Although basically controlled by the same elementary processes as those that establish the second explosion limit, this so-called strong igni'~ion limit differs from the locus of states obtained by direct extrapolation of the second limit. Moreover, it does not intersect with any of the explosion limits, encompassing a region that is fully contained within the classical explosion regime. Introduction One of the best known features of shockinduced ignition in gaseous hydrogen-oxygen mixtures is the fact that this process may occur in two distinct modes, depending on the thermodynamic state created by the shock wave. At lower temperatures the ignition is weak, or mild, being associated with a gradual development of the gasdynamic explosion; at higher temperatures it is strong or sharp, being manifested by a practically instantaneous appearance of a secondary shock induced by the explosive reaction. Most of the experimental observations of these phenomena have been performed by means of a reflected shock-tube techniquel"~; the same technique, in fact, as that used for the measurement of induction times yielding basic data for the determination of the critical kinetic rate constants governing the chain-reaction mechanism of the hydrogen-oxygen system.7-w I n the past, experi* This work was supported by the U.S. Air Force through the Air Force Office of Scientific Research under Grant AFOSR 129-67, by the National Aeronautics and Space Administration under Grant NsG-702/05-003-050, and by the National Science Foundation under Grant NSF GK-2156.
mental observations of the flow field generated by the ignition process were made primarily by the use of streak photography with just occasional snapshots of the whole flow field, 1 employing either schlieren or interferometer4 optics supplemented, in some case~% by pressure transducer records, 3 while the induction-time measurements were obtained from a photo-electric response to either absorption or emission due to hydroxyl radicals.7,s Since such techniques can provide only a limited insight into the flow field, there arose a certain amount of confusion concerning the exact nature of the two modes of ignition, especially as far as the dependence of the development of the flow field on the kinetic processes is concerned. The objective of the current study was then to clarify these aspects of the phenomenon.
Experiments Towards this aim, observations were made across the whole cross section of the tube, a rectangle 1.25 in. high and 1.75 in. deep, by means of a stroboscopic laser-schlieren system that could yield, from a single experiment, a set of up to one hundred photographic records at
1153
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DETONATION
intervals of 2 microseconds, n This was supplemented with pressure records obtained with the use of a piezo-electric "bar" transducer yielding a submicrosecond rise-time in the response signal, located at the back wall of the tube. In the course of our studies, records have been taken of a hundred experimental runs, all using only an undiluted stoichiometric hydrogen-oxygen mixture, with incident shocks of Mach numbers ranging from 2.3 to 2.9, producing, behind the reflected shock, pressures in the range of 0.23 to 1.96 atm and temperatures of 900 ~ to 1350~ Figure 1 represents a typical result obtained in the case of strong ignition. As it can be observed on the schlieren photographs and confirmed by
the pressure record, the first evidence of ignition is provided by the appearance of a steep and relatively flat pressure front, the reaction shock, very close to the end wall. The reaction shock was evidently formed by explosion in the gas layer adjacent to this wall and, in progressing through the unreacted mixture which was compressed by the reflected shock, it promoted the ignition of the gas practically at the same time throughout the whole cross section of the tube. Thus, except for the first layer of the gas that acts then, in effect, as a reaction center which undergoes the induction process without being influenced by any gasdynamic effects, the reacting gas mixture undergoes a gasdynamic compression near the
0
u ll)
~I0 9
E !--
20
I
I
l
I
I
I
I
I
15
10
5
0
15
10
5
0
Distance
(cm)
FIG. 1. Strong ignition. Initially behind reflected shock: 2 H2 + 02 at p = 0.89 atm and T = 1040~ first frame: 61 microseconds after shock reflection; vertical scale in pressure record: 2.1 atm/div; horizontal scale: 50 ~sec/div.
SHOCK-INDUCED IGNITION OF EXPLOSIVE GASES
1155
0
u =L v
5 E p-
10
6 D is t a n c e
(cm)
FIG. 2. Close-up of strong ignition. Initially behind reflected shock: 2 H2 + 03 at p = 1.14 arm and T lll0~ first frame: 50 microseconds after shock reflection. end of its induction period, thus enhancing the explosive character of the phenomenon. Our experiments demonstrated that such reaction centers have a very small effective thickness, for fully formed shocks have been usually observed 1-4 mm from the end wall. A more detailed view of the reaction shock is provided by the record of Fig. 2, which was taken at a lower sweep speed of the rotating mirror camera to get a sharper photograph of the transverse wave structure that was somewhat smeared in Fig. 1. Of particular interest here is the appearance of a detonationlike, fine multiwave structure of the front in the frame at 10 ~sec. A typical record of mild ignition is represented by Fig. 3. In this case, instead of being initiated homogeneously across the whole cross section of the tube, the reaction starts at some distinct centers, usually in the stagnant regions at the corners. Combustion fronts propagate out of these centers in the form of flames, taki~g a relatively Iong period of time (on the order of 100 ~see in
contrast to the submicrosecond process of strong ignition) before the onset of an "explosion in the explosion," similar to that which triggers the transition to detonation ahead of accelerating flames) ~ During this interval practically no pressure rise is recorded, although the flame may eventually appear to fill an appreciable portion of the tube. The secondary "explosion in the explosion" is, on the contrary, associated with a sufficiently intense pressure pulse to promote the formation of a detonation wave. In Fig. 3, the front of the secondary explosion appears first in the frame at 66 #sec. I t s formation is evidently associated with the convergence of the flame around a pocket of unburned m i x t u r e - a phenomenon that has been observed in most of the records, indicating that the "explosion in the explosion" originates most likely from an imploding, flame-driven, pressure wave. The results of our experiments are shown on Fig. 4, the conventional Arrhenius plot of the induction time-initial density product (the latter
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DETONATION
Fro. 3. Mild ignition. Initially behind reflected shock: 2 H~ W O, at p -- 1.46 arm and T = 993~ first frame: 93 microseconds after shock reflection; vertical scale in pressure record: 1.2 atm/div; horizontal scale: 50 ~sec/div. expressed in terms of the initial oxygen concentration) versus the reciprocal of the temperature in the regime behind the reflected shock wave. As indicated there, the data cover a range of pressures in this regime from 0.23 to 1.96 atm. These points are in fair agreement with the constant pressure curves that have been obtained from the kinetic theory, as described here later in the section on Analysis. I t is quite apparent from this figure that mild ignition corresponds as a rule to large values of the induction time-initial density product.
Interpretation The occurrence of the two modes of ignition has been first noted by Saytzev and Soloukhin. 1 Later Voevodsky and Soloukhin 2 observed that the boundary between these modes, to which we will refer here as the "strong ignition limit," is associated with the same criterion as that governing the classical second explosion limit. On this basis they demonstrated that, in the domain of initial pressures and temperatures, the strong ignition limit can be determined to a good approxi-
SHOCK-INDUCED IGNITION OF EXPLOSIVE GASES marion by the second limit condition, that is, when the molecular concentration of the reactive mixture [-M] = 2kb/kt, kb being the rate constant of the H q- 02 chain branching, and kt that of the corresponding chain-terminating step. As exhibited by Fig. 4, the strong ignition limit lies in the vicinity of the change in the slope of the Arrhenius plot of the induction time-density product versus the temperature reciprocal. This change is due to the same reason as that establishing the criterion for the second limit, namely, the prevailing influence of the chain-terminating step at lower temperatures, being thus in essential agreement with the hypothesis of Voevodsky and Soloukhin. In our opinion, however, the most important consequence of this fact is the significant change in the sensitivity of the induction time to the temperature variation. This notion provides a more sophisticated approach to the hypothesis of Voevodsky and Soloukhin and it leads to a more refined method for the evaluation of the strong ignition limit than considering it just as an extrapolation of the second explosion limit as they did.
1157
Our approach emphasizes in effect the gasdynamic aspects of the process, being directly associated with the concept that, as it is well known, the thermodynamic state of the substance behind the reflected shock is, as a rule, nonuniform, in space as well as time. However, the nonuniformities are of lesser importance at higher temperatures where the induction time is, on one hand, less sensitive to temperature variation and, on the other, it is too short with respect to the characteristic time for transport phenomena to allow the latter to influence the development of the process. Under such circumstances then, the explosive ignition takes place practically at the same time throughout the whole cross section of the tube, giving rise to a pressure wave with a relatively plane front, as typical of the strong ignition mode. If, however, the gradient of the induction time with respect to temperature becomes larger, as it does when second limit conditions are approached, the dependence of the induction time on the temperature acquires a much more significant role. The spatial nonuniformity in the temperature of the shock-corn-
Legend:
i.. 9
o
mild i g n i t i o n
9
strong
ignition
-o-4- Q23 ~ p< G 5 6 a t m
U 9
o 9
0.61< p<- 1.59 a t m
{ Jt
1"61~p
:&.
Y
I
0
E
-0-
10
-0-
/
ld 2 0.6
/I 07
1
1
I
I
0.8
0.9
1.0
1.1
1000 T
(OK)q
Fro. 4. The Arrhenius plot of experimental data.
1.2
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DETONATION
pressed gas leads then to the formation of small reaction centers at some distinct points so that the rate of heat released across the whole cross section (or, in other words, the power density level of energy deposited in the medium) is too small to generate a significant pressure pulse. At the same time, as a consequence of the longer induction period, transport phenomena acquire greater influence and this leads, therefore, to the appearance of small flame kernels, as typical of mild ignition. Thus, the criterion proposed in this paper is based on a postulated limiting value for the gradient, at constant pressure, of the induction
time with respect to temperature. The details of evaluating the strong explosion limit on the basis of this postulate are described in the next section.
Analysis In order to evaluate (aria T)p with an acceptable accuracy, one has to have a consistent set of data giving a continuous functional relationship between the induction time and the temperature. The experimental data of Fig. 4, although providing a good indication for the range of such a relationship, especially with respect to its depend-
Z sl I
w
L,, lo-~
u') !
I1) 0
E
lo
Legend:
[]
p : 2,4 a r m 1.2
I
kinetic computations
0,6 0.3
10 -3 0,6
I
I
i
1
I
0.7
0.8
0.9
1.0
1.1
1000 T
1.2
(OK)q
FIG. 5. The Arrhenius plot of the induction time-initial density product corresponding to a set of initial pressures. The points represent the results of constant-temperature computations based on the kinetic scheme of Skinner and Ringrose (Ref. 8) for the hydrogen-oxygen system; the induction time having been defined as the time required for the hydrogen atom to reach maximum concentration; the curves represent plots of Eq. (1).
SHOCK-INDUCED IGNITION OF EXPLOSIVE GASES
1159
4
I0
103
U
9
~:~10=
10
0.6
0.7
0.8
0.9 1.0 1000. (oK)-1 T
1.1
1.2
FIG. 6. Plot of the functional relationship between the induction time and the temperature. According to Eq. (3). once on initial pressure, are clearly inadequate for this purpose. Moreover, there is a fundamental vagueness associated with the concept of the induction time that makes its value dependent on many extraneous factors as, for instance, the method of measurement. For this reason one has to approach the problem of evaluating (0r/0 T)p with caution, and we have adopted for this purpose the following procedure. First we have evaluated, for a stoichiometrie mixture, the induction time for a number of initial pressures, on the basis of the kinetic scheme for the hydrogen-oxygen system proposed by Skinner and Ringrose. 8 The computations were carried out using a code described recently by Zajac and Oppenheim. z2A constant-temperature process was assumed and the induction period was defined as the time required for the hydrogen atom to reach
maximum concentration, which, as we have found, corresponds closely to the peak in the specific power pulse of energy release. The results of these computations are represented by the points on Fig. 5. These were then fitted by a relationship of the form In (r[-O2]) = A + ( B / T ) + Cp '~exp (D/T). (1) The curves plotted on Fig. 5 correspond to the following constants in Eq. (1): A = -- 10.7 In (psee-mole/liter) B = 9130 (~ In (psec-mole/liter) n-2 C = 2 X 10-9 (aim) -2 in (psec-mole/liter) D = 19000 (~
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DETONATION
10 2
10 O
u O q) v
,.Q1 kcO
9 v
ld 1
10-2 0.6
0.7
0.8
0.9
1.0
1.1
1.2
1000 T Fie. 7. Plot of the gradient of the induction time with respect to temperature at constant pressure as a function of temperature. Based on Eq. (4).
From the comparison between these results with the data of Fig. 4 it appears that, although they give the correct trend, they do not quite coincide with most of the experimental points. Consequently, some additional computations were performed using the kinetic scheme proposed recently by Gardiner and Wakefieldt~ and it was found that the major modification they introduce is in the value of the constant C, namely, C' -- 3 X 10-9 (atm) -2 In (#sec-mole/liter). The curves of Fig. 4 represent thus Eq. (1) with all the constants equal to those listed there except for the use of C' instead of C. As demon-
strafed there, the agreement with our experimental data is quite good, especially in the most interesting, for practical applications, high initialpressure regime. Now, since
[0~] = Xo2p/R T,
(2)
it follows that l n r = A + (B/T) + Cp" exp (D/T) -- In (Ep/T), where
E = Xo~/R,
(3)
SHOCK-INDUCED IGNITION OF EXPLOSIVE GASES
1161
f~
o r
~J
o
5~
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DETONATION satisfactory. Represented by thick lines are the loci of constant gradients of induction time with respect to temperature at constant pressure crossplotted from Fig. 7. The shaded region denotes the location of the boundary between the experimentally observed weak and strong ignition regimes. It appears from the above that the strong explosion limit in the stoichiometric hydrogen-oxygen mixture corresponds to the criterion
2.5
,
4
2.0
-g .~
1,5
( Or /O T )~, = - 2 ttsec/~
~.c frl
For orientation, included on the diagram of Fig. 8 is the classical explosion limit of Lewis and yon Elba and a number of sehlieren records to illustrate the significant difference between the strong and mild ignition regimes.
0.~ / J I 900
30
I 1000
Temperature
I 1100
1200
(~
Conclusions
FIo. 9. Comparison between the various explosion limits on the pressure--temperature plane.
or, for the stoichiometric hydrogen-oxygen mixture, E = 4.06 (mole-~ Equation (3) is shown plotted on Fig. 6 for a set of initial pressures from 0.2 to 2 arm. Finally, by straight-forward differentiation one obtains the relation
(O~/OT)p = tiT--
B--
CDp ~ exp ( D / T ) V T 2,
(4)
which is graphically represented by Fig. 7, the value of v = T(p, T ) having been obtained from Eq. (3). Results
Our results are summarized on Fig. 8, representing, in effect, a portion of the classical pressure-temperature explosion diagram. Plotted there are experimental points with number,~ denoting the observed induction times in microseconds to which they correspond. The family of thin lines represents the loci of constant induction times evaluated from Eq. (3), or cross-plotted from Fig. 6. As it should be expected, the agreement between these curves and the data is quite
Our conclusions can be summarized most conveniently by reference to the diagram of Fig. 9. Represented there on the conventional pressure-temperature explosion plane are the following limit lines: Curve 1: the classical explosion limit of Lewis and yon Elbe. Curve 2: the second explosion limit corresponding to the criterion 2]vb/k~ = [M-] (i-M] representing the total concentration) based on the rate constants of Skinner and Ringrose. Curve 3: the second explosion limit replotted from the paper of Voevodsky and Soloukhin. Curve 4: the locus of (Or/O T)~ = - 2 gsec/~ replotted from Fig. 8. As on Fig. 8, the shaded region represents the strong explosion limit deduced from our experiments. As it is evident from the above, our criterion yields a somewhat better correlation with experimental observations than the curve of Voevodsky and Soloukhin. What is more important, however, is the fact that it provides also a secondary limit at lower pressures that, as it is conceptually desired, deviates significantly from the classical first as well as the second explosion limit. Finally, it should be noted, the experimental points indicate the existence of an interesting excursion from the boundary curve that, for the stoichiometric hydrogen-o~.xygen system, occurs in the vicinity of 1 atm, extending from 990 ~ to 1060~ This fact has been evidently overlooked by Voevodsky and Soloukhin, although it is in essential agreement with their observations, as
SHOCK-INDUCED IGNITION OF EXPLOSIVE GASES demonstrated by the chain-dotted line deduced from their data. So far, this observation has not been reflected in the theory of explosive ignition, but it m a y be of some significance in this respect, providing thus an interesting objective for future studies. REFERENCES 1. SAYTZEV, S. G. AND SOLOUKHIN, R. I. : Eighth
Symposium (International) on Combustion, p. 344, Williams and Wilkins, 1962. 2. SOLOUKHIN, R. I. : Shock Waves and Detonations
in Gases, pp. 89-10l, Mono Book Corp., Baltimore, Md., 1966. 3. VOI~VODSKY, V. V, AND SOLOUKHIN, R. I.:
Tenth Symposium (International) on Combustion, p. 279, The Combustion Institute, 1965. A. AND COHEN, A.: Phys. Fluids 5, 97 (1962). 5. GILBERT, R. B. AND STREHLOW, R. A. : AIAA J. ~, 10 (1966).
4. STREHLOW, R.
1163
6. STREHLOW, R. A.: Fundamentals of Combustion, pp. 329-339, International Textbook Company, Scranton, Pa., 1968. 7. SCHOTT, G. L. AND I~INSEY, J. L.: J. Chem. Phys. 29, 1179 (1958). 8. SKINNER, G. B. AND RINGROSE, G. H. : J. Chem. Phys. 42, 2190 (1965). 9. WAKEFIELD, C. B., RIPLEY, D. L., AND GARDINER, W. C.: J. Chem. Phys. 50, 325 (1969). 10. GARDINER, W. C. AND WAKEFIELD, C. B.: "Influence of Gasdynamic Processes on the Chemical Kinetics of the Hydrogen-Oxygen Explosion at Temperatures Near 1000~ and Pressures of Several Atmospheres," Proceedings of the Second International Colloquium on Gasdynamics of Explosions and Reactive Systems, Astronautica Acta, 1970. 11. URTIEW, P. A. AND OPPENHEIM, A. K.: Proc. Roy. Soc. A295, 13 (1966). [2. ZAJAC, L. J. AND OPPENHEIM, A. K.: "Dynamics of an Explosive Reaction Center," AIAA Paper No. 70-147, to be published in the AIAA Journal.
COMMENTS R. I. Soloukhin, University of Novosibirsk, USSR. The new point of view on the hightemperature ignition process, presented in the paper, is very interesting. Determination of the strong explosion limit has been based this time on precise observations, performed with proper resolution in time and space, of the development of the flow field due to the gasdynamic effects of the exothermic reactions, permitting the establishment of a clear criterion for the distinction between the weak and strong explosion regimes. In particular, the former has been quite convincingly identified with what has been somewhat vaguely referred to in the literature as the "multi-spot mechanism." With reference to the proposed method of evaluating the strong explosion limit, I wonder whether a critical value of (1/r) (Or/OT)p, rather than just (Or/OT)~, would be more suitable. This supposition is based on the fact that, in a study recently conducted by myself and C. Brochet, as reported in a paper to be published shortly in Combustion and Flame, we found that, in evaluating the limits of irregular self-ignition behind a shock wave, the most appropriate criterion for the onset of chemical instability is the relative value of the change in the induction time as compared to its corresponding steady-state value.
Authors' Reply. The kind words expressed by Prof. So]oukhin about our work are appreciated. I t appears to us that the strong ignition limit
should depend on the variation in the induction time relative to the half-width of the power pulse of energy release, the characteristic time of the exothermic process, rather than of chemical induction that precedes its onset. Strong ignition occurs when this variation is relatively small throughout the medium, so that power pulses of most of the reaction centers overlap each other in time. Weak ignition corresponds to the case when the change in induction time between one point and another in the medium is so large that the power pulses occur at various reaction centers separately and are, therefore, unable to combine their effects in order to give rise to a significant gasdynamie phenomenon. Hence, in order to arrive at an absolute theory of strong ignition limit, it would be better to adopt as the basis the duration of the power pulse, rather than that of the induction process, as suggested by Soloukhin. Available information on the former is, however, still inadequate, thus suggesting a desirable direction for future studies in this field. In an effort to be more specific, we have determined the lines of constant (0 in r/OT)~ on the p - T plane corresponding to 1% and 2% change in the induction time per degree, and we found that they are much more shallow than those of constant (Or/OT)p, approaching closer the extrapolation of the second explosion limit. Thus, the strong explosion limit between 0.5 and 1.0 atm on Fig. 8, including the "excursion," could indeed be expressed in terms of (0 In r / 0 T ) p =
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DETONATION
--1.7% per ~ However, the direction of the experimentally determined upper branch of this limit, that is above 1.2 arm, coincides much better with a line of const. (Or/OT)~ than with one of const. (0 In r/OT)p.
H. Gg. Wagner, University of Gottingen. It would be of some interest to know what is the order of magnitude of the induction period at thermodynamic states corresponding to the third explosion limit on the pressure-temperature plane (p ~ 30 arm). What values are obtained on the basis of the theory presented in the paper?
Authors' Reply. In order to provide an answer to the question posed by Wagner, the authors used Eq. (3) to evaluate induction times corresponding to a number of points on the classical third explosion limit, as it is represented on Fig. 8, with due reservations, of course, as to the validity of such an extrapolation of this equation way beyond the scope for which it was intended in the paper. For the maximum temperature point of this limit that occurs at about 0.45 arm, one obtains the value of 8 msec, white at the point corresponding to 1 atm the induction time is 2.5 years. The remarkable difference between these two values is due to the effect of pressure in the third term of Eq. (3).
University o) California, Berkeley, California The paper elucidates the distinction between two regimes of ignition, one strong and the other weak, that characterize the onset of combustion in homogeneous gaseous mixtures whose reaction mechanism is controlled by a chain-branching step, such as that associated with the H -[- 02 collision in the hydrogen-oxygen system. On the basis of experimental observations, made primarily by the use of a stroboscopic laser-schlieren system yielding a sequence of photographic records of the entire flow field behind a reflected shock near the closed end of the tube at a repetition rate of 2 microseconds between frames, it has been revealed that strong ignition is manifested by a practically instantaneous appearance of a relatively plane pressure front associated with the generation of a flow field across the whole cross section of the tube, while mild ignition starts in the form of distinct flame kernels whose growth is comparatively slow and essentially devoid of any gasdynamic effects. The demarcation line between the two regimes of ignition is then shown to be associated with a critical value of the gradient of the induction time with respect to temperature at constant initial pressure. Specifically, for a stoichiometric hydrogen-oxygen mixture, this turns out to be - 2 microseconds/~ Although basically controlled by the same elementary processes as those that establish the second explosion limit, this so-called strong igni'~ion limit differs from the locus of states obtained by direct extrapolation of the second limit. Moreover, it does not intersect with any of the explosion limits, encompassing a region that is fully contained within the classical explosion regime. Introduction One of the best known features of shockinduced ignition in gaseous hydrogen-oxygen mixtures is the fact that this process may occur in two distinct modes, depending on the thermodynamic state created by the shock wave. At lower temperatures the ignition is weak, or mild, being associated with a gradual development of the gasdynamic explosion; at higher temperatures it is strong or sharp, being manifested by a practically instantaneous appearance of a secondary shock induced by the explosive reaction. Most of the experimental observations of these phenomena have been performed by means of a reflected shock-tube techniquel"~; the same technique, in fact, as that used for the measurement of induction times yielding basic data for the determination of the critical kinetic rate constants governing the chain-reaction mechanism of the hydrogen-oxygen system.7-w I n the past, experi* This work was supported by the U.S. Air Force through the Air Force Office of Scientific Research under Grant AFOSR 129-67, by the National Aeronautics and Space Administration under Grant NsG-702/05-003-050, and by the National Science Foundation under Grant NSF GK-2156.
mental observations of the flow field generated by the ignition process were made primarily by the use of streak photography with just occasional snapshots of the whole flow field, 1 employing either schlieren or interferometer4 optics supplemented, in some case~% by pressure transducer records, 3 while the induction-time measurements were obtained from a photo-electric response to either absorption or emission due to hydroxyl radicals.7,s Since such techniques can provide only a limited insight into the flow field, there arose a certain amount of confusion concerning the exact nature of the two modes of ignition, especially as far as the dependence of the development of the flow field on the kinetic processes is concerned. The objective of the current study was then to clarify these aspects of the phenomenon.
Experiments Towards this aim, observations were made across the whole cross section of the tube, a rectangle 1.25 in. high and 1.75 in. deep, by means of a stroboscopic laser-schlieren system that could yield, from a single experiment, a set of up to one hundred photographic records at
1153
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DETONATION
intervals of 2 microseconds, n This was supplemented with pressure records obtained with the use of a piezo-electric "bar" transducer yielding a submicrosecond rise-time in the response signal, located at the back wall of the tube. In the course of our studies, records have been taken of a hundred experimental runs, all using only an undiluted stoichiometric hydrogen-oxygen mixture, with incident shocks of Mach numbers ranging from 2.3 to 2.9, producing, behind the reflected shock, pressures in the range of 0.23 to 1.96 atm and temperatures of 900 ~ to 1350~ Figure 1 represents a typical result obtained in the case of strong ignition. As it can be observed on the schlieren photographs and confirmed by
the pressure record, the first evidence of ignition is provided by the appearance of a steep and relatively flat pressure front, the reaction shock, very close to the end wall. The reaction shock was evidently formed by explosion in the gas layer adjacent to this wall and, in progressing through the unreacted mixture which was compressed by the reflected shock, it promoted the ignition of the gas practically at the same time throughout the whole cross section of the tube. Thus, except for the first layer of the gas that acts then, in effect, as a reaction center which undergoes the induction process without being influenced by any gasdynamic effects, the reacting gas mixture undergoes a gasdynamic compression near the
0
u ll)
~I0 9
E !--
20
I
I
l
I
I
I
I
I
15
10
5
0
15
10
5
0
Distance
(cm)
FIG. 1. Strong ignition. Initially behind reflected shock: 2 H2 + 02 at p = 0.89 atm and T = 1040~ first frame: 61 microseconds after shock reflection; vertical scale in pressure record: 2.1 atm/div; horizontal scale: 50 ~sec/div.
SHOCK-INDUCED IGNITION OF EXPLOSIVE GASES
1155
0
u =L v
5 E p-
10
6 D is t a n c e
(cm)
FIG. 2. Close-up of strong ignition. Initially behind reflected shock: 2 H2 + 03 at p = 1.14 arm and T lll0~ first frame: 50 microseconds after shock reflection. end of its induction period, thus enhancing the explosive character of the phenomenon. Our experiments demonstrated that such reaction centers have a very small effective thickness, for fully formed shocks have been usually observed 1-4 mm from the end wall. A more detailed view of the reaction shock is provided by the record of Fig. 2, which was taken at a lower sweep speed of the rotating mirror camera to get a sharper photograph of the transverse wave structure that was somewhat smeared in Fig. 1. Of particular interest here is the appearance of a detonationlike, fine multiwave structure of the front in the frame at 10 ~sec. A typical record of mild ignition is represented by Fig. 3. In this case, instead of being initiated homogeneously across the whole cross section of the tube, the reaction starts at some distinct centers, usually in the stagnant regions at the corners. Combustion fronts propagate out of these centers in the form of flames, taki~g a relatively Iong period of time (on the order of 100 ~see in
contrast to the submicrosecond process of strong ignition) before the onset of an "explosion in the explosion," similar to that which triggers the transition to detonation ahead of accelerating flames) ~ During this interval practically no pressure rise is recorded, although the flame may eventually appear to fill an appreciable portion of the tube. The secondary "explosion in the explosion" is, on the contrary, associated with a sufficiently intense pressure pulse to promote the formation of a detonation wave. In Fig. 3, the front of the secondary explosion appears first in the frame at 66 #sec. I t s formation is evidently associated with the convergence of the flame around a pocket of unburned m i x t u r e - a phenomenon that has been observed in most of the records, indicating that the "explosion in the explosion" originates most likely from an imploding, flame-driven, pressure wave. The results of our experiments are shown on Fig. 4, the conventional Arrhenius plot of the induction time-initial density product (the latter
1156
DETONATION
Fro. 3. Mild ignition. Initially behind reflected shock: 2 H~ W O, at p -- 1.46 arm and T = 993~ first frame: 93 microseconds after shock reflection; vertical scale in pressure record: 1.2 atm/div; horizontal scale: 50 ~sec/div. expressed in terms of the initial oxygen concentration) versus the reciprocal of the temperature in the regime behind the reflected shock wave. As indicated there, the data cover a range of pressures in this regime from 0.23 to 1.96 atm. These points are in fair agreement with the constant pressure curves that have been obtained from the kinetic theory, as described here later in the section on Analysis. I t is quite apparent from this figure that mild ignition corresponds as a rule to large values of the induction time-initial density product.
Interpretation The occurrence of the two modes of ignition has been first noted by Saytzev and Soloukhin. 1 Later Voevodsky and Soloukhin 2 observed that the boundary between these modes, to which we will refer here as the "strong ignition limit," is associated with the same criterion as that governing the classical second explosion limit. On this basis they demonstrated that, in the domain of initial pressures and temperatures, the strong ignition limit can be determined to a good approxi-
SHOCK-INDUCED IGNITION OF EXPLOSIVE GASES marion by the second limit condition, that is, when the molecular concentration of the reactive mixture [-M] = 2kb/kt, kb being the rate constant of the H q- 02 chain branching, and kt that of the corresponding chain-terminating step. As exhibited by Fig. 4, the strong ignition limit lies in the vicinity of the change in the slope of the Arrhenius plot of the induction time-density product versus the temperature reciprocal. This change is due to the same reason as that establishing the criterion for the second limit, namely, the prevailing influence of the chain-terminating step at lower temperatures, being thus in essential agreement with the hypothesis of Voevodsky and Soloukhin. In our opinion, however, the most important consequence of this fact is the significant change in the sensitivity of the induction time to the temperature variation. This notion provides a more sophisticated approach to the hypothesis of Voevodsky and Soloukhin and it leads to a more refined method for the evaluation of the strong ignition limit than considering it just as an extrapolation of the second explosion limit as they did.
1157
Our approach emphasizes in effect the gasdynamic aspects of the process, being directly associated with the concept that, as it is well known, the thermodynamic state of the substance behind the reflected shock is, as a rule, nonuniform, in space as well as time. However, the nonuniformities are of lesser importance at higher temperatures where the induction time is, on one hand, less sensitive to temperature variation and, on the other, it is too short with respect to the characteristic time for transport phenomena to allow the latter to influence the development of the process. Under such circumstances then, the explosive ignition takes place practically at the same time throughout the whole cross section of the tube, giving rise to a pressure wave with a relatively plane front, as typical of the strong ignition mode. If, however, the gradient of the induction time with respect to temperature becomes larger, as it does when second limit conditions are approached, the dependence of the induction time on the temperature acquires a much more significant role. The spatial nonuniformity in the temperature of the shock-corn-
Legend:
i.. 9
o
mild i g n i t i o n
9
strong
ignition
-o-4- Q23 ~ p< G 5 6 a t m
U 9
o 9
0.61< p<- 1.59 a t m
{ Jt
1"61~p
:&.
Y
I
0
E
-0-
10
-0-
/
ld 2 0.6
/I 07
1
1
I
I
0.8
0.9
1.0
1.1
1000 T
(OK)q
Fro. 4. The Arrhenius plot of experimental data.
1.2
1158
DETONATION
pressed gas leads then to the formation of small reaction centers at some distinct points so that the rate of heat released across the whole cross section (or, in other words, the power density level of energy deposited in the medium) is too small to generate a significant pressure pulse. At the same time, as a consequence of the longer induction period, transport phenomena acquire greater influence and this leads, therefore, to the appearance of small flame kernels, as typical of mild ignition. Thus, the criterion proposed in this paper is based on a postulated limiting value for the gradient, at constant pressure, of the induction
time with respect to temperature. The details of evaluating the strong explosion limit on the basis of this postulate are described in the next section.
Analysis In order to evaluate (aria T)p with an acceptable accuracy, one has to have a consistent set of data giving a continuous functional relationship between the induction time and the temperature. The experimental data of Fig. 4, although providing a good indication for the range of such a relationship, especially with respect to its depend-
Z sl I
w
L,, lo-~
u') !
I1) 0
E
lo
Legend:
[]
p : 2,4 a r m 1.2
I
kinetic computations
0,6 0.3
10 -3 0,6
I
I
i
1
I
0.7
0.8
0.9
1.0
1.1
1000 T
1.2
(OK)q
FIG. 5. The Arrhenius plot of the induction time-initial density product corresponding to a set of initial pressures. The points represent the results of constant-temperature computations based on the kinetic scheme of Skinner and Ringrose (Ref. 8) for the hydrogen-oxygen system; the induction time having been defined as the time required for the hydrogen atom to reach maximum concentration; the curves represent plots of Eq. (1).
SHOCK-INDUCED IGNITION OF EXPLOSIVE GASES
1159
4
I0
103
U
9
~:~10=
10
0.6
0.7
0.8
0.9 1.0 1000. (oK)-1 T
1.1
1.2
FIG. 6. Plot of the functional relationship between the induction time and the temperature. According to Eq. (3). once on initial pressure, are clearly inadequate for this purpose. Moreover, there is a fundamental vagueness associated with the concept of the induction time that makes its value dependent on many extraneous factors as, for instance, the method of measurement. For this reason one has to approach the problem of evaluating (0r/0 T)p with caution, and we have adopted for this purpose the following procedure. First we have evaluated, for a stoichiometrie mixture, the induction time for a number of initial pressures, on the basis of the kinetic scheme for the hydrogen-oxygen system proposed by Skinner and Ringrose. 8 The computations were carried out using a code described recently by Zajac and Oppenheim. z2A constant-temperature process was assumed and the induction period was defined as the time required for the hydrogen atom to reach
maximum concentration, which, as we have found, corresponds closely to the peak in the specific power pulse of energy release. The results of these computations are represented by the points on Fig. 5. These were then fitted by a relationship of the form In (r[-O2]) = A + ( B / T ) + Cp '~exp (D/T). (1) The curves plotted on Fig. 5 correspond to the following constants in Eq. (1): A = -- 10.7 In (psee-mole/liter) B = 9130 (~ In (psec-mole/liter) n-2 C = 2 X 10-9 (aim) -2 in (psec-mole/liter) D = 19000 (~
1160
DETONATION
10 2
10 O
u O q) v
,.Q1 kcO
9 v
ld 1
10-2 0.6
0.7
0.8
0.9
1.0
1.1
1.2
1000 T Fie. 7. Plot of the gradient of the induction time with respect to temperature at constant pressure as a function of temperature. Based on Eq. (4).
From the comparison between these results with the data of Fig. 4 it appears that, although they give the correct trend, they do not quite coincide with most of the experimental points. Consequently, some additional computations were performed using the kinetic scheme proposed recently by Gardiner and Wakefieldt~ and it was found that the major modification they introduce is in the value of the constant C, namely, C' -- 3 X 10-9 (atm) -2 In (#sec-mole/liter). The curves of Fig. 4 represent thus Eq. (1) with all the constants equal to those listed there except for the use of C' instead of C. As demon-
strafed there, the agreement with our experimental data is quite good, especially in the most interesting, for practical applications, high initialpressure regime. Now, since
[0~] = Xo2p/R T,
(2)
it follows that l n r = A + (B/T) + Cp" exp (D/T) -- In (Ep/T), where
E = Xo~/R,
(3)
SHOCK-INDUCED IGNITION OF EXPLOSIVE GASES
1161
f~
o r
~J
o
5~
1162
DETONATION satisfactory. Represented by thick lines are the loci of constant gradients of induction time with respect to temperature at constant pressure crossplotted from Fig. 7. The shaded region denotes the location of the boundary between the experimentally observed weak and strong ignition regimes. It appears from the above that the strong explosion limit in the stoichiometric hydrogen-oxygen mixture corresponds to the criterion
2.5
,
4
2.0
-g .~
1,5
( Or /O T )~, = - 2 ttsec/~
~.c frl
For orientation, included on the diagram of Fig. 8 is the classical explosion limit of Lewis and yon Elba and a number of sehlieren records to illustrate the significant difference between the strong and mild ignition regimes.
0.~ / J I 900
30
I 1000
Temperature
I 1100
1200
(~
Conclusions
FIo. 9. Comparison between the various explosion limits on the pressure--temperature plane.
or, for the stoichiometric hydrogen-oxygen mixture, E = 4.06 (mole-~ Equation (3) is shown plotted on Fig. 6 for a set of initial pressures from 0.2 to 2 arm. Finally, by straight-forward differentiation one obtains the relation
(O~/OT)p = tiT--
B--
CDp ~ exp ( D / T ) V T 2,
(4)
which is graphically represented by Fig. 7, the value of v = T(p, T ) having been obtained from Eq. (3). Results
Our results are summarized on Fig. 8, representing, in effect, a portion of the classical pressure-temperature explosion diagram. Plotted there are experimental points with number,~ denoting the observed induction times in microseconds to which they correspond. The family of thin lines represents the loci of constant induction times evaluated from Eq. (3), or cross-plotted from Fig. 6. As it should be expected, the agreement between these curves and the data is quite
Our conclusions can be summarized most conveniently by reference to the diagram of Fig. 9. Represented there on the conventional pressure-temperature explosion plane are the following limit lines: Curve 1: the classical explosion limit of Lewis and yon Elbe. Curve 2: the second explosion limit corresponding to the criterion 2]vb/k~ = [M-] (i-M] representing the total concentration) based on the rate constants of Skinner and Ringrose. Curve 3: the second explosion limit replotted from the paper of Voevodsky and Soloukhin. Curve 4: the locus of (Or/O T)~ = - 2 gsec/~ replotted from Fig. 8. As on Fig. 8, the shaded region represents the strong explosion limit deduced from our experiments. As it is evident from the above, our criterion yields a somewhat better correlation with experimental observations than the curve of Voevodsky and Soloukhin. What is more important, however, is the fact that it provides also a secondary limit at lower pressures that, as it is conceptually desired, deviates significantly from the classical first as well as the second explosion limit. Finally, it should be noted, the experimental points indicate the existence of an interesting excursion from the boundary curve that, for the stoichiometric hydrogen-o~.xygen system, occurs in the vicinity of 1 atm, extending from 990 ~ to 1060~ This fact has been evidently overlooked by Voevodsky and Soloukhin, although it is in essential agreement with their observations, as
SHOCK-INDUCED IGNITION OF EXPLOSIVE GASES demonstrated by the chain-dotted line deduced from their data. So far, this observation has not been reflected in the theory of explosive ignition, but it m a y be of some significance in this respect, providing thus an interesting objective for future studies. REFERENCES 1. SAYTZEV, S. G. AND SOLOUKHIN, R. I. : Eighth
Symposium (International) on Combustion, p. 344, Williams and Wilkins, 1962. 2. SOLOUKHIN, R. I. : Shock Waves and Detonations
in Gases, pp. 89-10l, Mono Book Corp., Baltimore, Md., 1966. 3. VOI~VODSKY, V. V, AND SOLOUKHIN, R. I.:
Tenth Symposium (International) on Combustion, p. 279, The Combustion Institute, 1965. A. AND COHEN, A.: Phys. Fluids 5, 97 (1962). 5. GILBERT, R. B. AND STREHLOW, R. A. : AIAA J. ~, 10 (1966).
4. STREHLOW, R.
1163
6. STREHLOW, R. A.: Fundamentals of Combustion, pp. 329-339, International Textbook Company, Scranton, Pa., 1968. 7. SCHOTT, G. L. AND I~INSEY, J. L.: J. Chem. Phys. 29, 1179 (1958). 8. SKINNER, G. B. AND RINGROSE, G. H. : J. Chem. Phys. 42, 2190 (1965). 9. WAKEFIELD, C. B., RIPLEY, D. L., AND GARDINER, W. C.: J. Chem. Phys. 50, 325 (1969). 10. GARDINER, W. C. AND WAKEFIELD, C. B.: "Influence of Gasdynamic Processes on the Chemical Kinetics of the Hydrogen-Oxygen Explosion at Temperatures Near 1000~ and Pressures of Several Atmospheres," Proceedings of the Second International Colloquium on Gasdynamics of Explosions and Reactive Systems, Astronautica Acta, 1970. 11. URTIEW, P. A. AND OPPENHEIM, A. K.: Proc. Roy. Soc. A295, 13 (1966). [2. ZAJAC, L. J. AND OPPENHEIM, A. K.: "Dynamics of an Explosive Reaction Center," AIAA Paper No. 70-147, to be published in the AIAA Journal.
COMMENTS R. I. Soloukhin, University of Novosibirsk, USSR. The new point of view on the hightemperature ignition process, presented in the paper, is very interesting. Determination of the strong explosion limit has been based this time on precise observations, performed with proper resolution in time and space, of the development of the flow field due to the gasdynamic effects of the exothermic reactions, permitting the establishment of a clear criterion for the distinction between the weak and strong explosion regimes. In particular, the former has been quite convincingly identified with what has been somewhat vaguely referred to in the literature as the "multi-spot mechanism." With reference to the proposed method of evaluating the strong explosion limit, I wonder whether a critical value of (1/r) (Or/OT)p, rather than just (Or/OT)~, would be more suitable. This supposition is based on the fact that, in a study recently conducted by myself and C. Brochet, as reported in a paper to be published shortly in Combustion and Flame, we found that, in evaluating the limits of irregular self-ignition behind a shock wave, the most appropriate criterion for the onset of chemical instability is the relative value of the change in the induction time as compared to its corresponding steady-state value.
Authors' Reply. The kind words expressed by Prof. So]oukhin about our work are appreciated. I t appears to us that the strong ignition limit
should depend on the variation in the induction time relative to the half-width of the power pulse of energy release, the characteristic time of the exothermic process, rather than of chemical induction that precedes its onset. Strong ignition occurs when this variation is relatively small throughout the medium, so that power pulses of most of the reaction centers overlap each other in time. Weak ignition corresponds to the case when the change in induction time between one point and another in the medium is so large that the power pulses occur at various reaction centers separately and are, therefore, unable to combine their effects in order to give rise to a significant gasdynamie phenomenon. Hence, in order to arrive at an absolute theory of strong ignition limit, it would be better to adopt as the basis the duration of the power pulse, rather than that of the induction process, as suggested by Soloukhin. Available information on the former is, however, still inadequate, thus suggesting a desirable direction for future studies in this field. In an effort to be more specific, we have determined the lines of constant (0 in r/OT)~ on the p - T plane corresponding to 1% and 2% change in the induction time per degree, and we found that they are much more shallow than those of constant (Or/OT)p, approaching closer the extrapolation of the second explosion limit. Thus, the strong explosion limit between 0.5 and 1.0 atm on Fig. 8, including the "excursion," could indeed be expressed in terms of (0 In r / 0 T ) p =
1164
DETONATION
--1.7% per ~ However, the direction of the experimentally determined upper branch of this limit, that is above 1.2 arm, coincides much better with a line of const. (Or/OT)~ than with one of const. (0 In r/OT)p.
H. Gg. Wagner, University of Gottingen. It would be of some interest to know what is the order of magnitude of the induction period at thermodynamic states corresponding to the third explosion limit on the pressure-temperature plane (p ~ 30 arm). What values are obtained on the basis of the theory presented in the paper?
Authors' Reply. In order to provide an answer to the question posed by Wagner, the authors used Eq. (3) to evaluate induction times corresponding to a number of points on the classical third explosion limit, as it is represented on Fig. 8, with due reservations, of course, as to the validity of such an extrapolation of this equation way beyond the scope for which it was intended in the paper. For the maximum temperature point of this limit that occurs at about 0.45 arm, one obtains the value of 8 msec, white at the point corresponding to 1 atm the induction time is 2.5 years. The remarkable difference between these two values is due to the effect of pressure in the third term of Eq. (3).