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The effect of slight confinement on the detonation waves in solid explosives
642
COMBUSTION OF EXPLOSIVES AND SOLID PROPELLANTS
84
THE EFFECT OF SLIGHT CONFINEMENT ON THE DETONATION WAVES IN SOLID EXPLOSIVES
By L. A. I n t r o d u c t i o n .
Statement
D E F F E T AND J. BOUCART
of the Problem
Confinement of solid explosives in rigid tubes has long been known to influence their velocity of detonation? In all cases, such confinement leads to an increase in the detonation velocity, a fact which has been explained by various authors, on the basis of the hydrodynamic theory of detonation. Two methods of calculation have been proposed, one based on the Jones expanding jet theory 2 and the other on the Eyring theory of a curved wave front? However, Eyring, Powell, Duffey and Parlin 3 were concerned mainly with the effect of the charge diameter on the detonation velocity; accordingly, in our study we will draw chiefly on the principles set forth by Jones. We need not go back to the development of this theory, with its quantitative explanation of earlier observations by other authors, who established an initial distinction between thin and thick confinements. Thus, a l-ram thick lead tube increases the velocity of detonation more than a steel one of the same thickness, whereas the opposite is true if the thickness of the tubes exceeds a few millimeters. Briefly, it can be said that the resistance of the confining material is not important, the important factors being density and inertia for thin confinement, and compressibility for a thick confinement, which explains the above observations. If the thickness of confinement attains and exceeds the thickness of the reaction zone of the explosive confined, that is to say, if the time required for the shock wave to traverse the tube is longer than the reaction time, we go from the first to the second state of confinement. Thus, the Jones equations governing the variations in the detonation velocity are necessarily different depending upon whether they apply to thin or to thick confinement. (1) For the former, the velocity of lateral expansion of the detonation products, of which the detonation velocity is a function, is determined by the velocity at which the tube is projected outwards. This velocity thus depends on the inertia of the tube which must have a fairly high density for it to act. The following formula, proposed by Jones, can be used to calculate the effect of such a
confinement: V~-
V
V
-
EsA
2mR
(1)
where Vm = maximum detonation velocity, corresponding to zero radial expansion at the reaction zone; V = detonation velocity under the experimental conditions; E = thickness of the reaction zone; A = loading density of the explosive; m = mass of the confining tube, per unit of surface, before expansion; and R = charge radius. (2) Equations governing the case of thick tubes also have been derived from Jones' theory, in particular by Copp and Ubbelohde? The latter authors have shown that when the thickness of confinement is such that the shock wave does not reach the outer wall of the tube within the reaction time, compressibility is the major factor in the action of this confinement. The formula corresponding to this effect is
(?)2
tgB
= 1 + 9E ~ -
(2)
where, in addition to the factors already known, B is the angle which the inner wall forms during expansion, with respect to its initial direction. In order to check this equation experimentally, Copp and Ubbelohde, who had no way of defining angle B, derived it from the values of the compressibility at high static pressures, which naturally involves considerable approximation. However, this check showed the validity of these hypotheses, which were further supported by Cybulski, Payman and Woodhead 5 in the course of other experiments. Belgian permissible explosives generally consist of an explosive core surrounded by an inert sheath. At the Fourth Symposium on Combustion we presented a study 6 on explosives of this type provided with active sheaths; i.e., which contained 10 to 15 per cent nitroglycerin. The present investigation is linfited to inert sheaths, more particularly to rigid sheaths. In point of fact, for about two years, Belgium has been developing a new type of sheath--a rigid sheath of compressed sodium chloride. In the
DETONATION WAVES IN SOLID EXPLOSIVES
course of a careful study of such sheaths, we were led to determine the various characteristics of explosives sheathed in this way, and in particular their velocities of detonation, the shape and thickness of the detonation waves (by the x-ray flash method), and the external shock waves (by the shadow method). This study showed first that explosives with rigid sheaths have considerably higher detonation velocities than explosives with unsheathed charges. This, in turn, led us to examine more closely the working of these sheaths, which we were able to compare with that of thick T A B L E 1. VELOCITIES OF DETONATION
IN M/SEC
Unsheathed Cartridges
Sheathed Cartridges
Difference
2.230 2.780 2.200 2.250 1.990 2.320
2.400 3.015 2.520 2.560 2.330 2.650 2.650 2.800 2.700 2.705 4.100 3.150 3.225 3.160 3.330 3.930 3.600
170 235 320 310 340 330 445 470 535 620 620 630 680 730 760 930 980
2.205
2.330 2.165 2.085 3.480 2.520 2.545 2.430 2.570 3.000 2.620
confinement. Observations on the detonation wave curve confirm this hypothesis which could be used to assess changes in the detonation reaction caused by rigid sheaths.
B. Experimental Study 1. VELOCITIES OF DETONATION
The variations in the detonation velocities of unsheathed and sheathed explosives arc always positive and sufficiently well-defined to show that, independent of other findings, rigid sheaths are responsible for these variations. The tests coyered different types of industrial.explosive, the compositions of which varied little and always included nitroglycerin, nitroglycol, trinitrotoluene, ammonium nitrate, sodium chloride, wood meal, and sometimes small amounts of nitrocotton. These constituents separate them from the explosives used ordinarily in theoretical studies and make comparisons of a physico-chemical
643
nature on the effect of confinement more difficult. Accordingly, we have limited ourselves to physieal data, which are quite sufficient. Detonation velocities of unconfined explosives were determined in thin cardboard tubes, which offer virtually no obstacle to radial expansion of the products. The inner diameter of the tubes was 26 ram. The confined explosives were studied in their industrial forin; i.e., a diameter of 26 mm and a 5 ram-thick compressed sodium chloride sheath, making the external diameter 36 mm. Table 1 gives detonation velocities of various explosives cartridged in the two manners. It will be noted that the velocities of detonation undergo increases that range fronl 170 m/see to 980 m/see. Such an increase in detonation velocity at first may seem inconsistent with the effect that a slight confinement can produce. However, the following observations indicate that these increases in detonation velocity must be attributed solely to this confinement. 2. S~OCK WAVES We have already shown that shock waves cnfitted laterally by the detonation wave of sheathed cartridges are very different in form from those emitted by unsheathed cartridges. 7 We shall not linger over this point, but will simply recall that, for a few microseconds, the shock waves of sheathed cartridges form a rather slight angle and that they form a connection cone between their starting point and their intersection with the shock waves preceding the expanding detonation gases (Fig. 1). Shadow photographs of this type also show that the rigid sheaths do not burst upon passage of the detonation wave, which in itself is qualitative evidence of their confining action. We shall see, moreover, that the angles formed by these expanding sheaths can be used in the equation which links this parameter with the detonation velocities of unconfined charges (Equation (2). 3. DETONATION WAVES
The structure of detonation waves can be studled by the x-ray flash method which gives direct indications as to their curvature and thickness. In addition to the usual difficulties of this type of recording, x-ray photography of sheathed cartridges offers considerable complications due to the fact that sodium chloride sheaths absorb x-rays strongly which makes it difficult to obtain clear records of the detonation waves and the reaction zone. However, Figures 2 and 3 show
644
COMBUSTION OF EXPLOSIVES AND SOLID PROPELLANTS
that these difficulties can be overcome, and that the great difference in convexity between the detonation waves of unsheathed and s~eathed cartridges can be observed. The detonation waves of sheathed cartridges are more nearly plane, showing that radial expansion is slight and inhibited by the sheath. The difference in curvature of the waves can be used to calculate the changes in the detonation velocity. This would also be proof of the confining
I t is noted that the compressibitities of steel lead, and sodium chloride at 30,000 kg/em 2 are 1:3.5 and 1:5.5, respectively. The order of magnitude of the compressibilities is thus the same,
FIG. 2.
FIG. 1.
action of the sheaths, but it seemed more interesting to apply the equations of Jones, and of Copp and Ubbelohde directly to sodium chloride sheaths in order to confirm their action.
C. Preliminary Calculations We have seen that, in first approximation, compressed sodium chloride sheaths can be likened to thick confinements, the classical examples of which are lead or steel tubes. Copp and Ubbelohde have shown that calculations based on eompressibilities determined by Bridgman 8 up to 12,000 kg/cm 2 roughly confirm theoretical predictions. To avoid any basic error, we began by comparing the compressibilities of different materials in accordance with new experimental data by Bridgman given in Table 2.
FIG. 3.
DETONATION WAVES IN SOLID EXPLOSIVES
and the remarks made previously on the difference in the behavior of steel and lead tubes apply to the case of sodium chloride tubes. Just as a lead tube has a less satisfactory confining action than a steel tube of the same thickness, so the action of a sodium chloride tube is somewhat less favorable with respect to lead than that of lead with respect to steel. This comparison would be really exact if the sodium chloride tubes were formed of a single crystal without any interposition of air. I t is evident that the air located between the sodium chloride crystals decreases the action of the sheath by diminishing its cornTABLE 2
vIvox Substance
Pressures kg/cm 2
(x)
V/Vo steel V/Vo
(taking the steel values as 30,000 kg/cm~ = 0.1)
Stainless steel H26..
30,000 0.0167 20,000 0.0113 Stainless steel H29.. 30,000 0.0175 20,000 0.0119 Iron . . . . . . . . . . . . . . . . 30,000 0.0167( 20,000 0.0113~ Lead . . . . . . . . . . . . . . . . 100,000 0.145 50,000 0.0892 30,000 0.0587 20,000 0.041 NaC1 . . . . . . . . . . . . . . 100,000 0.210 50,000 0.135 30,000 0.093 20,000 0.068
0.01 0.01 0.01
0.0351
0.0556
pressibility. Correspondingly, sheaths of similar, less compressed substances or pulverulent sheaths have an even slighter effect on the confinement of the explosive. However, the x-ray photographs show that even the pulverulent sheaths remain intact for a certain length of time and are compressed by the passage of the shock wave. Thus, it appears that confinement due to sodium chloride sheaths can be considered a thick confinement. D. Applications
of the ExperimentaI
Results
Having established that the equations for thick confinement can be applied accurately to inert sheaths of permissible explosives regardless of their rigidity, i.e., their resistance, we used the experimental results obtained by our three methods of study to check these equations, in particu-
645
lar the following:
I n making this check, rather than determine the maximum velocity, Vm, experimentally, we calculated it from the other quantities which are all accessible to experiment. I n fact, V, E, B and R can be determined experimentally with sufficient precision to calculate the maximum speed with good approximation, as shown by the estimated error. The two quantifies that can be defined by photographic and x-ray methods can be determined with the following maximum errors: E (thickness of the reaction zone): 0.5 mm; B (angle of expansion): 1 ° . The following calculation shows the effect of these errors on the final result: Let V = 3,000m/ sec, E = 2.5 ram, B = 10°; then Vm = 3,427.5 m/see. For E = 3.0 mm, Vm = 3,507 m/see, i.e., a difference of 80 m/see. For B = 11°, Vm = 3,478.5 m/see, i.e., a difference of 51 m/see. I t will be seen that we remain within the acceptable limits of precision, assuming experimental errors that are certainly larger than in reality. Moreover, these errors are of the same order as the initial errors in the detonation velocity, V, and of those due to the lack of precision in the measurement of the charge radius. Starting from the maximum velocity thus obtained, which is the same for a given explosive no matter how it is cartridged, we can calculate, in accordance with other experimental data, the detonation velocities of explosives sheathed in various manners. Thus we have a method of determining whether the calculated detonation velocities agree with the observed velocities. An initial series of approximate calculations was performed taking 2.5 mm as the reaction zone thickness, and measuring the angles, B, on photographic recordings by the shadow method. Table 3 gives the results of these measurements. Taking the average values of the angle formed by the sheath (21° for pulverulent sheaths and 13° for rigid sheaths), the difference in the average detonation velocities of explosives with different sheaths can be determined. This difference is of the order of 300 m/sec, which agrees with the experimental results. However it is rather hazardous to base calculations of the maximum velocity on observations for sheathed industrial explosives because it is often difficult to measure the thickness of the reaction zone. The results would have
646
COMBUSTION OF EXPLOSIVES AND SOLID PROPELLANTS
to be confirmed by calculations on explosives of different diameters. The diffieulty in measuring the thickness of the reaction zone arises from the fact that the sodium chloride sheath is not very transparent to x-rays. Moreover, the increase in the density of the sheath, due to compression by the shock wave precisely at the point of the detonation wave, diminishes this transparency still further. We have tried to circumvent this difficulty by using polyethylene (polythene) sheaths of two different diameters. These plastic sheaths are less opaque to x-rays and make it possible to measure more exaetly the thickness of the reaction zone, and also give a better value for the angle formed
sidered reliable and to supply new evidence of the action of rigid compressed sheaths. This discussion has been limited to the application of the Jones equation, and the Copp and
T A B L E 3. ANGLES FORMED BY THE SHEATH ~ H A D O W PHOTOGRAPHS) Type of Explosive
Type of Sodium Chloride Sheath
Mean Angle
A B B B C
Pulverulent Pulverulent Semi-rigid Semi -rigid Pulverulent
19° 21 o 20 °
B B B C C
Average: Rigid Compressed Compressed Compressed Compressed
21 ° 13° 14°30 , 12° 12°30 , 13°
Average:
23 ° 22 °
13°
FIG. 4. TABLE 4 Detonation Velocities in m/see Diameter
Unsheathed
NaCI Sheath
1,805 1,965 2,200 2,250
-2,305 ---
Polythene Sheath
mr)~
by the sheath upon passage of the detonation wave (Fig. 4). The results of these tests are given in Table 4. The Jones formula (Equation (2)) can be applied to sheathed explosives to calculate the maximum velocity, Vm, by using the experimental values in Table 5 measured on x-ray photographs. These results as a whole indicate that the compressed sodium chloride sheath exerts a confining action comparable to a thick confinement as defined by Jones, since the increases in the detonation velocity for the 26-mm explosive diameter are greater than those observed for confinement by a polythene tube which is certainly not as compressible as the sodium chloride tube. Moreover, the maximum detonation velocities obtained for these few experimental values by the Jones formula are in good enough agreement to be con-
20 26 30 36
1,885 2,170
---
TABLE 5 E
B
Vm
mm
Explosive with NaC1 sheath Explosive with polythene sheath, 20 mm. 26 ram.
4.6
13°
3.7 4
28°4 ~ 3,110 3,185 23 °
3,070
Ubbelohde equation to confinement by inert sheaths. In the course of this study, we recorded a large number of detonation speeds, shock waves and reaction zones of unsheathed explosives, with a view to studying the influence of the cartridge
DETONATION WAVES IN SOLID EXPLOSIVES
diameter for cases that are easier to observe experimentally. Moreover, it seemed interesting to us to test against actual experience the accuracy of another theoretical equation proposed by Eyring, Powell, Duffey and Parlin a, for calculating the maximum speed as a function of the reaction zone thickness V
E
--=1-0.5-V~ R
This equation offers the advantage that Dr. R. Schall--the only other investigator besides us to have studied detonation waves by instantaneous x-rays--employed it to check the influence of the particle size on the thickness of the reaction zone. In addition, it is interesting to see to what extent the Eyring and Jones equations lead to similar results for the maximum detonation velocity. Table 6 has been drawn up for the same TABLE 6 Cartridge Diameter
Detonation Velocity
E
20 26 30 36
1,805 1,965 2,200 2,250
4 3.7 -2.5
Maximum Velocity
2,260 2,315 -2,410
standard industrial explosive as was used for the confinement tests. The reaction zone thicknesses determined for this explosive were confirmed by a large number of experiments bearing on other explosives. A cheek was made on a square cartridge (20 minD. By treating such a cartridge as a cylindrical cartridge, we obtain 2,305 m/see as the maximum velocity, the real speed being 1,800 m/see and the thickness of the reaction zone, 4.4 mm. We must take into account the lack of precision of the measurements, and the fact that the difference in the particle size of the explosive has a certain effect on the thickness of the reaction zone. In spite of this lack of precision, we get an average maximum velocity of 2,315 m/see, with divergences of 55 and 100 m. The agreement between these values and those obtained by applying Jones' formula to sheathed explosives is far from good. The average maximum speed determined from experiments on sheathed explosives is 3,120 m/see, with divergences of about 50 and 65 m/see. The difference of the average values is 800 m/see, which is obviously higher
647
than the experimental error. Thus, the Eyring and Jones equations appear to lead to aberrant results, although it is not possible for us to decide which of the equations is the more exact. Taylor 1° had already pointed out this discordance between the values of the reaction zone thickness calcutated by these two equations, without however indicating which he believes to be the more accurate. There is a direct method of determining the maximum velocity based on graphic extrapolation for infinite diameters of the curves established as functions of the detonation velocities and the cartridge diameters. This method is applicable separately to unsheathed and to sheathed explosives, as the maximum velocities must be identical in both cases. It is not possible for us to effect these extrapolations for sheathed explosives as we have studied only two diameters (20 and 26 ram). I n the case of unsheathed explosives, we have studied the explosive for four diameters, which allows a certain evaluation. However, as the maximum diameters are eertainly over 100 mm, extrapolation from diameters which do not exceed 36 mm also runs the risk of being somewhat inaccurate. The chart shows that extrapolation leads to values of the order of 2,400 m/see, which agrees much better with values obtained by Eyring's equation than by Jones'.
E. Conclusions The results show that sodium chloride sheaths act as thick confinements. Direct comparison of the x-ray photographs of explosives with polythene and sodium chloride sheaths confirms the hypothesis proposed by us on the basis of observed detonation velocities. Consequently, sodium chloride sheaths, and more particularly rigid sheaths of that substance, give the detonation wave and the reaction zone special qualities and make the explosive safer with respect to fire-damp and dust, quite apart from that safety which it acquires as a result of materially better sheathing. Detailed discussion of this problem would exceed the scope of this symposium. However, it seems well to mention it as a reminder that the research which we have undertaken and are continuing in this field bears on the improvement of permissible explosives.
Acknowledgment This research work was carried out with the support of the Association of Belgian Explosive
648
COMBUSTION OF EXPLOSIVES AND SOLID PROPELLANTS
5. CYBULSKI, W. B., PAYMAN, W., AND WOOD-
Manufacturers and the Institute for the Promotion of Scientific Research in Industry and Agriculture (I. R. S. I. A.), to whom we tender our sincere thanks.
HEAD, ~). W.: Proc. Royal Soc., A197, 51 (1949). 6. DEFFET, L., DE COSTER, M., AND VANDE
WOUWER, P. J.: Fourth Symposium on Combustion, p. 481. Baltimore, The Williams & Wilkins Co., 1953. 7. DEFFET, L., AND BOUCART, J.: Explosifs, 8, 83 (1955).
REFERENCES 1. BERTHELOT, M.: Ann. Chim. Phys., 6, 556 (1885); BERTHELOT, M., AND VIEILLE, P.: Memorial des Poudres, 4, 7 (1891). 2. JONES, H.: Proc. Royal Soc., A189, 415, (1947). 3. EYRING, H., POWELL, R. E., DUFFEY, G. H.,
8. BRIDGMAN,P. W.: The Physics of High Pressure. London, Bell & Sons, 1931; Proc. Am.
Acad. Sci., 76, 1 (1945); Proc. Am. Acad. Sci., 77, 187 (1949). 9. SCHALL,R. : Nobel Hefte, 20, 75 (1954). 10. TAYLOR, J.: Detonation in Condensed Explosives. Oxford, Clarendon Press, 1952.
AND PARLIN, R. B.: Chem. Rev., 45, 69
(1949). 4. COPP, J. L., AND UBELOHDE, A. R.: Trans. Faraday Soc., 44, 658 (1948).
85 POST-DETONATION PRESSURE AND THERMAL STUDIES OF SOLID HIGH
EXPLOSIVES IN A CLOSED CHAMBER By WILLIAM S. F I L L E R Introduction Current methods and principles involved in determining the heat energy released by high explosives have been very well presented by Lothrop and Handriek. 1 Measurements of heat of detonation usually involve small quantities of explosive initiated in a small space within a strong container filled with inert gas. s, 3.4 The quantity of explosive used has been limited by practical considerations of calorimetric technique. Since many explosives will not detonate in small quantities, this limits the type of explosives that may be used. Also, many explosives, although they apparently detonate, do not undergo the same chemical transformation as they do in larger quantities. If an explosive booster is used even in small amounts, its interaction chemically with the test explosive must introduce uncertainties in the measured heat of detonation values. Values for heat of detonation of organic explosives can also be computed if products of detonation are known. The chief drawback of this method is the lack of exact knowledge regarding the products formed on detonation of many explosives. Due to these difficulties of measurement and
computation, heat of detonation for many explosives is not well established, and few published measurements exist. Yet, the energy which can be released by detonation is one of the most fundamental properties of explosives. This paper describes studies of pressures that develop shortly after the detonation of high explosives in a closed chamber and how these pressures may be used to measure heat of detonation of high explosives. I t was found that a hydrostatic pressure developed within the enclosure a few msee after the initial shock wave traversed the chamber space and that the maximum value of this pressure (before decay due to heat conduetion) was in good agreement with simple theory for adiabatic heating of a perfect gas in a fixed volume. If a quantity of heat, H, is added to a gas with a ratio of specific heats, Cp/C~ = % contained in a volume, V, the pressure rise, P, is given by the relation H(~ - 1) P -- - V
(1)
This relationship applies to the ambient gas initially present in the chamber. The correction
COMBUSTION OF EXPLOSIVES AND SOLID PROPELLANTS
84
THE EFFECT OF SLIGHT CONFINEMENT ON THE DETONATION WAVES IN SOLID EXPLOSIVES
By L. A. I n t r o d u c t i o n .
Statement
D E F F E T AND J. BOUCART
of the Problem
Confinement of solid explosives in rigid tubes has long been known to influence their velocity of detonation? In all cases, such confinement leads to an increase in the detonation velocity, a fact which has been explained by various authors, on the basis of the hydrodynamic theory of detonation. Two methods of calculation have been proposed, one based on the Jones expanding jet theory 2 and the other on the Eyring theory of a curved wave front? However, Eyring, Powell, Duffey and Parlin 3 were concerned mainly with the effect of the charge diameter on the detonation velocity; accordingly, in our study we will draw chiefly on the principles set forth by Jones. We need not go back to the development of this theory, with its quantitative explanation of earlier observations by other authors, who established an initial distinction between thin and thick confinements. Thus, a l-ram thick lead tube increases the velocity of detonation more than a steel one of the same thickness, whereas the opposite is true if the thickness of the tubes exceeds a few millimeters. Briefly, it can be said that the resistance of the confining material is not important, the important factors being density and inertia for thin confinement, and compressibility for a thick confinement, which explains the above observations. If the thickness of confinement attains and exceeds the thickness of the reaction zone of the explosive confined, that is to say, if the time required for the shock wave to traverse the tube is longer than the reaction time, we go from the first to the second state of confinement. Thus, the Jones equations governing the variations in the detonation velocity are necessarily different depending upon whether they apply to thin or to thick confinement. (1) For the former, the velocity of lateral expansion of the detonation products, of which the detonation velocity is a function, is determined by the velocity at which the tube is projected outwards. This velocity thus depends on the inertia of the tube which must have a fairly high density for it to act. The following formula, proposed by Jones, can be used to calculate the effect of such a
confinement: V~-
V
V
-
EsA
2mR
(1)
where Vm = maximum detonation velocity, corresponding to zero radial expansion at the reaction zone; V = detonation velocity under the experimental conditions; E = thickness of the reaction zone; A = loading density of the explosive; m = mass of the confining tube, per unit of surface, before expansion; and R = charge radius. (2) Equations governing the case of thick tubes also have been derived from Jones' theory, in particular by Copp and Ubbelohde? The latter authors have shown that when the thickness of confinement is such that the shock wave does not reach the outer wall of the tube within the reaction time, compressibility is the major factor in the action of this confinement. The formula corresponding to this effect is
(?)2
tgB
= 1 + 9E ~ -
(2)
where, in addition to the factors already known, B is the angle which the inner wall forms during expansion, with respect to its initial direction. In order to check this equation experimentally, Copp and Ubbelohde, who had no way of defining angle B, derived it from the values of the compressibility at high static pressures, which naturally involves considerable approximation. However, this check showed the validity of these hypotheses, which were further supported by Cybulski, Payman and Woodhead 5 in the course of other experiments. Belgian permissible explosives generally consist of an explosive core surrounded by an inert sheath. At the Fourth Symposium on Combustion we presented a study 6 on explosives of this type provided with active sheaths; i.e., which contained 10 to 15 per cent nitroglycerin. The present investigation is linfited to inert sheaths, more particularly to rigid sheaths. In point of fact, for about two years, Belgium has been developing a new type of sheath--a rigid sheath of compressed sodium chloride. In the
DETONATION WAVES IN SOLID EXPLOSIVES
course of a careful study of such sheaths, we were led to determine the various characteristics of explosives sheathed in this way, and in particular their velocities of detonation, the shape and thickness of the detonation waves (by the x-ray flash method), and the external shock waves (by the shadow method). This study showed first that explosives with rigid sheaths have considerably higher detonation velocities than explosives with unsheathed charges. This, in turn, led us to examine more closely the working of these sheaths, which we were able to compare with that of thick T A B L E 1. VELOCITIES OF DETONATION
IN M/SEC
Unsheathed Cartridges
Sheathed Cartridges
Difference
2.230 2.780 2.200 2.250 1.990 2.320
2.400 3.015 2.520 2.560 2.330 2.650 2.650 2.800 2.700 2.705 4.100 3.150 3.225 3.160 3.330 3.930 3.600
170 235 320 310 340 330 445 470 535 620 620 630 680 730 760 930 980
2.205
2.330 2.165 2.085 3.480 2.520 2.545 2.430 2.570 3.000 2.620
confinement. Observations on the detonation wave curve confirm this hypothesis which could be used to assess changes in the detonation reaction caused by rigid sheaths.
B. Experimental Study 1. VELOCITIES OF DETONATION
The variations in the detonation velocities of unsheathed and sheathed explosives arc always positive and sufficiently well-defined to show that, independent of other findings, rigid sheaths are responsible for these variations. The tests coyered different types of industrial.explosive, the compositions of which varied little and always included nitroglycerin, nitroglycol, trinitrotoluene, ammonium nitrate, sodium chloride, wood meal, and sometimes small amounts of nitrocotton. These constituents separate them from the explosives used ordinarily in theoretical studies and make comparisons of a physico-chemical
643
nature on the effect of confinement more difficult. Accordingly, we have limited ourselves to physieal data, which are quite sufficient. Detonation velocities of unconfined explosives were determined in thin cardboard tubes, which offer virtually no obstacle to radial expansion of the products. The inner diameter of the tubes was 26 ram. The confined explosives were studied in their industrial forin; i.e., a diameter of 26 mm and a 5 ram-thick compressed sodium chloride sheath, making the external diameter 36 mm. Table 1 gives detonation velocities of various explosives cartridged in the two manners. It will be noted that the velocities of detonation undergo increases that range fronl 170 m/see to 980 m/see. Such an increase in detonation velocity at first may seem inconsistent with the effect that a slight confinement can produce. However, the following observations indicate that these increases in detonation velocity must be attributed solely to this confinement. 2. S~OCK WAVES We have already shown that shock waves cnfitted laterally by the detonation wave of sheathed cartridges are very different in form from those emitted by unsheathed cartridges. 7 We shall not linger over this point, but will simply recall that, for a few microseconds, the shock waves of sheathed cartridges form a rather slight angle and that they form a connection cone between their starting point and their intersection with the shock waves preceding the expanding detonation gases (Fig. 1). Shadow photographs of this type also show that the rigid sheaths do not burst upon passage of the detonation wave, which in itself is qualitative evidence of their confining action. We shall see, moreover, that the angles formed by these expanding sheaths can be used in the equation which links this parameter with the detonation velocities of unconfined charges (Equation (2). 3. DETONATION WAVES
The structure of detonation waves can be studled by the x-ray flash method which gives direct indications as to their curvature and thickness. In addition to the usual difficulties of this type of recording, x-ray photography of sheathed cartridges offers considerable complications due to the fact that sodium chloride sheaths absorb x-rays strongly which makes it difficult to obtain clear records of the detonation waves and the reaction zone. However, Figures 2 and 3 show
644
COMBUSTION OF EXPLOSIVES AND SOLID PROPELLANTS
that these difficulties can be overcome, and that the great difference in convexity between the detonation waves of unsheathed and s~eathed cartridges can be observed. The detonation waves of sheathed cartridges are more nearly plane, showing that radial expansion is slight and inhibited by the sheath. The difference in curvature of the waves can be used to calculate the changes in the detonation velocity. This would also be proof of the confining
I t is noted that the compressibitities of steel lead, and sodium chloride at 30,000 kg/em 2 are 1:3.5 and 1:5.5, respectively. The order of magnitude of the compressibilities is thus the same,
FIG. 2.
FIG. 1.
action of the sheaths, but it seemed more interesting to apply the equations of Jones, and of Copp and Ubbelohde directly to sodium chloride sheaths in order to confirm their action.
C. Preliminary Calculations We have seen that, in first approximation, compressed sodium chloride sheaths can be likened to thick confinements, the classical examples of which are lead or steel tubes. Copp and Ubbelohde have shown that calculations based on eompressibilities determined by Bridgman 8 up to 12,000 kg/cm 2 roughly confirm theoretical predictions. To avoid any basic error, we began by comparing the compressibilities of different materials in accordance with new experimental data by Bridgman given in Table 2.
FIG. 3.
DETONATION WAVES IN SOLID EXPLOSIVES
and the remarks made previously on the difference in the behavior of steel and lead tubes apply to the case of sodium chloride tubes. Just as a lead tube has a less satisfactory confining action than a steel tube of the same thickness, so the action of a sodium chloride tube is somewhat less favorable with respect to lead than that of lead with respect to steel. This comparison would be really exact if the sodium chloride tubes were formed of a single crystal without any interposition of air. I t is evident that the air located between the sodium chloride crystals decreases the action of the sheath by diminishing its cornTABLE 2
vIvox Substance
Pressures kg/cm 2
(x)
V/Vo steel V/Vo
(taking the steel values as 30,000 kg/cm~ = 0.1)
Stainless steel H26..
30,000 0.0167 20,000 0.0113 Stainless steel H29.. 30,000 0.0175 20,000 0.0119 Iron . . . . . . . . . . . . . . . . 30,000 0.0167( 20,000 0.0113~ Lead . . . . . . . . . . . . . . . . 100,000 0.145 50,000 0.0892 30,000 0.0587 20,000 0.041 NaC1 . . . . . . . . . . . . . . 100,000 0.210 50,000 0.135 30,000 0.093 20,000 0.068
0.01 0.01 0.01
0.0351
0.0556
pressibility. Correspondingly, sheaths of similar, less compressed substances or pulverulent sheaths have an even slighter effect on the confinement of the explosive. However, the x-ray photographs show that even the pulverulent sheaths remain intact for a certain length of time and are compressed by the passage of the shock wave. Thus, it appears that confinement due to sodium chloride sheaths can be considered a thick confinement. D. Applications
of the ExperimentaI
Results
Having established that the equations for thick confinement can be applied accurately to inert sheaths of permissible explosives regardless of their rigidity, i.e., their resistance, we used the experimental results obtained by our three methods of study to check these equations, in particu-
645
lar the following:
I n making this check, rather than determine the maximum velocity, Vm, experimentally, we calculated it from the other quantities which are all accessible to experiment. I n fact, V, E, B and R can be determined experimentally with sufficient precision to calculate the maximum speed with good approximation, as shown by the estimated error. The two quantifies that can be defined by photographic and x-ray methods can be determined with the following maximum errors: E (thickness of the reaction zone): 0.5 mm; B (angle of expansion): 1 ° . The following calculation shows the effect of these errors on the final result: Let V = 3,000m/ sec, E = 2.5 ram, B = 10°; then Vm = 3,427.5 m/see. For E = 3.0 mm, Vm = 3,507 m/see, i.e., a difference of 80 m/see. For B = 11°, Vm = 3,478.5 m/see, i.e., a difference of 51 m/see. I t will be seen that we remain within the acceptable limits of precision, assuming experimental errors that are certainly larger than in reality. Moreover, these errors are of the same order as the initial errors in the detonation velocity, V, and of those due to the lack of precision in the measurement of the charge radius. Starting from the maximum velocity thus obtained, which is the same for a given explosive no matter how it is cartridged, we can calculate, in accordance with other experimental data, the detonation velocities of explosives sheathed in various manners. Thus we have a method of determining whether the calculated detonation velocities agree with the observed velocities. An initial series of approximate calculations was performed taking 2.5 mm as the reaction zone thickness, and measuring the angles, B, on photographic recordings by the shadow method. Table 3 gives the results of these measurements. Taking the average values of the angle formed by the sheath (21° for pulverulent sheaths and 13° for rigid sheaths), the difference in the average detonation velocities of explosives with different sheaths can be determined. This difference is of the order of 300 m/sec, which agrees with the experimental results. However it is rather hazardous to base calculations of the maximum velocity on observations for sheathed industrial explosives because it is often difficult to measure the thickness of the reaction zone. The results would have
646
COMBUSTION OF EXPLOSIVES AND SOLID PROPELLANTS
to be confirmed by calculations on explosives of different diameters. The diffieulty in measuring the thickness of the reaction zone arises from the fact that the sodium chloride sheath is not very transparent to x-rays. Moreover, the increase in the density of the sheath, due to compression by the shock wave precisely at the point of the detonation wave, diminishes this transparency still further. We have tried to circumvent this difficulty by using polyethylene (polythene) sheaths of two different diameters. These plastic sheaths are less opaque to x-rays and make it possible to measure more exaetly the thickness of the reaction zone, and also give a better value for the angle formed
sidered reliable and to supply new evidence of the action of rigid compressed sheaths. This discussion has been limited to the application of the Jones equation, and the Copp and
T A B L E 3. ANGLES FORMED BY THE SHEATH ~ H A D O W PHOTOGRAPHS) Type of Explosive
Type of Sodium Chloride Sheath
Mean Angle
A B B B C
Pulverulent Pulverulent Semi-rigid Semi -rigid Pulverulent
19° 21 o 20 °
B B B C C
Average: Rigid Compressed Compressed Compressed Compressed
21 ° 13° 14°30 , 12° 12°30 , 13°
Average:
23 ° 22 °
13°
FIG. 4. TABLE 4 Detonation Velocities in m/see Diameter
Unsheathed
NaCI Sheath
1,805 1,965 2,200 2,250
-2,305 ---
Polythene Sheath
mr)~
by the sheath upon passage of the detonation wave (Fig. 4). The results of these tests are given in Table 4. The Jones formula (Equation (2)) can be applied to sheathed explosives to calculate the maximum velocity, Vm, by using the experimental values in Table 5 measured on x-ray photographs. These results as a whole indicate that the compressed sodium chloride sheath exerts a confining action comparable to a thick confinement as defined by Jones, since the increases in the detonation velocity for the 26-mm explosive diameter are greater than those observed for confinement by a polythene tube which is certainly not as compressible as the sodium chloride tube. Moreover, the maximum detonation velocities obtained for these few experimental values by the Jones formula are in good enough agreement to be con-
20 26 30 36
1,885 2,170
---
TABLE 5 E
B
Vm
mm
Explosive with NaC1 sheath Explosive with polythene sheath, 20 mm. 26 ram.
4.6
13°
3.7 4
28°4 ~ 3,110 3,185 23 °
3,070
Ubbelohde equation to confinement by inert sheaths. In the course of this study, we recorded a large number of detonation speeds, shock waves and reaction zones of unsheathed explosives, with a view to studying the influence of the cartridge
DETONATION WAVES IN SOLID EXPLOSIVES
diameter for cases that are easier to observe experimentally. Moreover, it seemed interesting to us to test against actual experience the accuracy of another theoretical equation proposed by Eyring, Powell, Duffey and Parlin a, for calculating the maximum speed as a function of the reaction zone thickness V
E
--=1-0.5-V~ R
This equation offers the advantage that Dr. R. Schall--the only other investigator besides us to have studied detonation waves by instantaneous x-rays--employed it to check the influence of the particle size on the thickness of the reaction zone. In addition, it is interesting to see to what extent the Eyring and Jones equations lead to similar results for the maximum detonation velocity. Table 6 has been drawn up for the same TABLE 6 Cartridge Diameter
Detonation Velocity
E
20 26 30 36
1,805 1,965 2,200 2,250
4 3.7 -2.5
Maximum Velocity
2,260 2,315 -2,410
standard industrial explosive as was used for the confinement tests. The reaction zone thicknesses determined for this explosive were confirmed by a large number of experiments bearing on other explosives. A cheek was made on a square cartridge (20 minD. By treating such a cartridge as a cylindrical cartridge, we obtain 2,305 m/see as the maximum velocity, the real speed being 1,800 m/see and the thickness of the reaction zone, 4.4 mm. We must take into account the lack of precision of the measurements, and the fact that the difference in the particle size of the explosive has a certain effect on the thickness of the reaction zone. In spite of this lack of precision, we get an average maximum velocity of 2,315 m/see, with divergences of 55 and 100 m. The agreement between these values and those obtained by applying Jones' formula to sheathed explosives is far from good. The average maximum speed determined from experiments on sheathed explosives is 3,120 m/see, with divergences of about 50 and 65 m/see. The difference of the average values is 800 m/see, which is obviously higher
647
than the experimental error. Thus, the Eyring and Jones equations appear to lead to aberrant results, although it is not possible for us to decide which of the equations is the more exact. Taylor 1° had already pointed out this discordance between the values of the reaction zone thickness calcutated by these two equations, without however indicating which he believes to be the more accurate. There is a direct method of determining the maximum velocity based on graphic extrapolation for infinite diameters of the curves established as functions of the detonation velocities and the cartridge diameters. This method is applicable separately to unsheathed and to sheathed explosives, as the maximum velocities must be identical in both cases. It is not possible for us to effect these extrapolations for sheathed explosives as we have studied only two diameters (20 and 26 ram). I n the case of unsheathed explosives, we have studied the explosive for four diameters, which allows a certain evaluation. However, as the maximum diameters are eertainly over 100 mm, extrapolation from diameters which do not exceed 36 mm also runs the risk of being somewhat inaccurate. The chart shows that extrapolation leads to values of the order of 2,400 m/see, which agrees much better with values obtained by Eyring's equation than by Jones'.
E. Conclusions The results show that sodium chloride sheaths act as thick confinements. Direct comparison of the x-ray photographs of explosives with polythene and sodium chloride sheaths confirms the hypothesis proposed by us on the basis of observed detonation velocities. Consequently, sodium chloride sheaths, and more particularly rigid sheaths of that substance, give the detonation wave and the reaction zone special qualities and make the explosive safer with respect to fire-damp and dust, quite apart from that safety which it acquires as a result of materially better sheathing. Detailed discussion of this problem would exceed the scope of this symposium. However, it seems well to mention it as a reminder that the research which we have undertaken and are continuing in this field bears on the improvement of permissible explosives.
Acknowledgment This research work was carried out with the support of the Association of Belgian Explosive
648
COMBUSTION OF EXPLOSIVES AND SOLID PROPELLANTS
5. CYBULSKI, W. B., PAYMAN, W., AND WOOD-
Manufacturers and the Institute for the Promotion of Scientific Research in Industry and Agriculture (I. R. S. I. A.), to whom we tender our sincere thanks.
HEAD, ~). W.: Proc. Royal Soc., A197, 51 (1949). 6. DEFFET, L., DE COSTER, M., AND VANDE
WOUWER, P. J.: Fourth Symposium on Combustion, p. 481. Baltimore, The Williams & Wilkins Co., 1953. 7. DEFFET, L., AND BOUCART, J.: Explosifs, 8, 83 (1955).
REFERENCES 1. BERTHELOT, M.: Ann. Chim. Phys., 6, 556 (1885); BERTHELOT, M., AND VIEILLE, P.: Memorial des Poudres, 4, 7 (1891). 2. JONES, H.: Proc. Royal Soc., A189, 415, (1947). 3. EYRING, H., POWELL, R. E., DUFFEY, G. H.,
8. BRIDGMAN,P. W.: The Physics of High Pressure. London, Bell & Sons, 1931; Proc. Am.
Acad. Sci., 76, 1 (1945); Proc. Am. Acad. Sci., 77, 187 (1949). 9. SCHALL,R. : Nobel Hefte, 20, 75 (1954). 10. TAYLOR, J.: Detonation in Condensed Explosives. Oxford, Clarendon Press, 1952.
AND PARLIN, R. B.: Chem. Rev., 45, 69
(1949). 4. COPP, J. L., AND UBELOHDE, A. R.: Trans. Faraday Soc., 44, 658 (1948).
85 POST-DETONATION PRESSURE AND THERMAL STUDIES OF SOLID HIGH
EXPLOSIVES IN A CLOSED CHAMBER By WILLIAM S. F I L L E R Introduction Current methods and principles involved in determining the heat energy released by high explosives have been very well presented by Lothrop and Handriek. 1 Measurements of heat of detonation usually involve small quantities of explosive initiated in a small space within a strong container filled with inert gas. s, 3.4 The quantity of explosive used has been limited by practical considerations of calorimetric technique. Since many explosives will not detonate in small quantities, this limits the type of explosives that may be used. Also, many explosives, although they apparently detonate, do not undergo the same chemical transformation as they do in larger quantities. If an explosive booster is used even in small amounts, its interaction chemically with the test explosive must introduce uncertainties in the measured heat of detonation values. Values for heat of detonation of organic explosives can also be computed if products of detonation are known. The chief drawback of this method is the lack of exact knowledge regarding the products formed on detonation of many explosives. Due to these difficulties of measurement and
computation, heat of detonation for many explosives is not well established, and few published measurements exist. Yet, the energy which can be released by detonation is one of the most fundamental properties of explosives. This paper describes studies of pressures that develop shortly after the detonation of high explosives in a closed chamber and how these pressures may be used to measure heat of detonation of high explosives. I t was found that a hydrostatic pressure developed within the enclosure a few msee after the initial shock wave traversed the chamber space and that the maximum value of this pressure (before decay due to heat conduetion) was in good agreement with simple theory for adiabatic heating of a perfect gas in a fixed volume. If a quantity of heat, H, is added to a gas with a ratio of specific heats, Cp/C~ = % contained in a volume, V, the pressure rise, P, is given by the relation H(~ - 1) P -- - V
(1)
This relationship applies to the ambient gas initially present in the chamber. The correction