Contribution to the study of spherical detonation waves

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LAMINAR COMBUSTION AND DETONATION WAVES 64

C O N T R I B U T I O N TO THE S T U D Y OF SPHERICAL DETONATION WAVES By N. MANSON AND F. FERRI]~ (Translated by Ruth F. Brinkley) INTRODUCTION

EXPERIMENTAL EQUIPMENT AND TECHNIQUE

Spherical detonation waves having the same velocity (independent of the initial conditions and at the limits) as plane detonation waves were observed by Laffitte (8) in mixtures of CS2 + 302 and 2H2 + 02. As these waves were initiated at the center of round glass flasks (20-26 cm diameter) by relatively powerful detonators (1 g mercury fulminate) and recorded over rather short distances (10 to 13 cm), there was some possible doubt as to their true nature. In particular, it was conceivable that the phenomenon might be a kind of pseudo-detonation supported by the shock wave from the priming explosive. [See Jost (6).] On the other hand, the hydrodynamic theory of shock waves and combustion waves led Jouguet (7) to the conclusion that a spherical detonation cannot propagate with a uniform velocity independent of the initial conditions (firing), and that these detonations will decrease and tend toward a state close to deflagration. Subsequently Taylor (13) on the one hand and Zeldovitch (14) on the other, examined solutions capable of representing the movement of the burned gas behind the combustion wave and showed that the hydrodynamic theory makes it possible to consider the existence of spherical detonation waves having the same velocity (as defined by the Chapman-Jouguet conditions) as plane waves. The only difference would be in the pressure and velocity gradients of the gases directly behind the waves. Accordingly, an experimental investigation of the problem seemed desirable to determine whether the technique used by Laffitte in 1923 could be improved, thus eliminating the above objections. For this purpose it was decided to operate with larger volumes of gas and to vary the ignition process. The present paper is a report of the first results obtained which, as we shall see, complete those of Laffitte and confirm the Taylor-Zeldovitch theory with respect to the velocity of spherical detonation waves.

Flasks Two series of transparent latex flasks were used. * The first series was oval, the largest diameter being 38-42 cm and the smallest (on which observations were based) 30-38 cm; the second series was virtually round and when inflated had a capacity of 113 liters (diameter, 60 cm). The inflating pressure was approximately the same for the two series and varied between 18 and 25 cm of water. T h ~ ignition device consisting of two electrically isolated coaxial copper tubes, and the inlet tubing were mounted in the rubber stopper that closed the mouth of the flask.

Type and preparation of combustible mixtures Mixtures of oxygen (technical) with the following gases were investigated: a) acetylene (tech~ nical) ; b) propane (about 98 per cent) ; c) ethylene (42 per cent) plus methane (35 per cent) with C2H6 (15 per cent), C2H2 (3 to 4 per cent) and CO2 (4 to 5 per cent); d) natural St. Marcet gas (93 per cent methane, 3.6 per cent ethane, 0.9 per cent propane, plus butane, plus CO2 and 2.5 per cent nitrogen). For the series of oval flasks, the mixtures were prepared by displacing water in a 50-liter tank graduated in 2 liters (fig. 1). The big flasks were filled either by measuring the volume of each component in the tank, or by determining the volume of the flask with calipers. In all cases the maximum estimated absolute error in the mixture composition should not exceed • per cent of the concentration (volume of combustible/total volume). However, it is possible that there may be an additional error due to permeability of the flasks. The flasks were found to be slightly permeable to the combustible gases investigated, especially to propane. The hourly measured loss over 5 to 6 hours for flasks of the second series inflated solely with these 1We wish to thank Mr. Duplessis of the Soci6t~ Franfaise du Latex, who designed and developed these flasks at our request.

STUDY OF SPHERICAL DETONATION WAVES gases to a diameter of 48 cm was the following: a) 2.1 per cent of the volume for C~H2; b) 3.5 per cent for C3H8; c) 0.6 per cent for the C~F[, + CH, gas; d) less than 0.5 per cent for St. Marcet gas. However, as only 10 to 15 minutes elapsed between filling the flask and running the test, the maximum error in composition due to this loss is certainly less than 0.5 to 1 per cent. Thus for a 30 per cent C3Hs mixture, the possible error due to loss of C3H~ during 15 minutes would be at most:

487

whole being englobed bv a ~etran[tropentaerithrite (1.5 g) and collodion paste. The setup fl~rms a ball 12-15 mm in diameter. Some of these devices--the spark and the electrically primed igniter--showed irregularities of operation; the first probably because of daintiness in the atmosphere where the tests were run.

Photographic technique The flask was placed behind a vertical slit of adjustable width (0-10 ram) and the detonation

0.3 X 113 >( 0.035 15/60 = 0.3 liter so that the error on the C3H8 concentration of the mixture is less than: 0.3/(0.3 • 113) - 0.009

Note: To calculate the combustible content of the mixture the gases are assumed to be perfect,

FIG. 2. Ignition devices: A. hot wire; B. spark; C. electric primer; D. detonators.

FIG. 1. Setup used for preparation of test mixtures and for filling flasks. and no correction has been made with respect to the pressure (about 20 g / c m 2) and temperature (2~176

Ignition mechanism The following systems were used for ignition (fig. 2): a) A hot wire consisting of 15-20 m m of Ni-Cr resistance wire, lS~o0 mm in diameter, heated to white heat (in air) by an alternating electric current of 10-12 volts: b) A 12-joule discharge spark produced by means of two 3 # F capacitances in a series charged to 4000 volts; the distance between the electrodes is 4-5 m m : c) Commercial igniter with electric primer2; d) A detonator consisting of the above electric primer surrounded by mercury fulminate (0.5 g), the 2 Igniter P. 50 of the Soci~t~ Fran~aise de Munitions. This.igniter consists of a thin Ni-Cr wire forming a 2-ohm electric resistance covered with 10 mmg of an explosive organic paste.

Fie. 3. Filling a flask was recorded on 89-ram wide sensitive paper (thin Kodak recording paper) attached to a 20-cm diameter drum with a vertical axis of rotation (fig. 3). The rotational speed of the drum was regulated by a variable transformer (alternostat) on the feed potential of the electric motor. This speed was read on a gauge attached to the apparatus and measured immediately before and after each shot by means of a calibrated revolution indicator that was checked periodically. In general, for

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LAMINAR COMBUSTION AND DETONATION WAVES

speeds of the order of 6000 to 7500 rev/min (linear speed on paper of 63-78 m/sec) it may be assumed that the rotational velocity is affected by an error of less than 1-1.5 per cent. Several lenses were tested and the following two were adopted: Kodak F/7.7 anastigmatic (f = 170 ram) used especially for experiments

were run in the casemates of a dismantled fort that was placed at our disposal by the Direction of the Laboratory of the Commission on Explosive Materials) The photographs were developed on the spot after each test. It should be mentioned that certain recordings were repeated several times before a suitable adjustment of' the lens aperture could be obtained, due to the fact that the luminosity of the phenomenon varied appreciably from one mixture to another.

Accuracy of measurements As noted earlier, it was assumed that the composition of the mixtures investigated was known in terms of the combustible concentration to within an absolute error of 1-2 per cent. Thus precise values cannot be given for the lower detonation limits of the mixtures and their order of magnitude alone can be estimated. With respect to the velocity of the waves, the combined error in measurement due to enlargement and to rotational speed is less than 2.5-3.5 per cent. To this error must be added the error due to measurement of the slope which is hard to Fie.. 4a. Detonation 'wave in C~H~(50 per cent)-O2 estimate. We feel that in general this latter error mixture. Spark ignition. Oval flask, diam. 36 em. did not exceed 2 per cent and that in the least favorable cases (velocity of the order of 2900 m/sec for waves observed in the first type of flasks) it may amount to 5 per cent. It will be seen that these estimations are almost always high and that our measurements generally agree, to within less than 5 per cent, with those obtained by researchers working with tubes. RESULTS

Generalities

Fic. 4b. Detonation wave in C2H2(50 per cent)-O2 mixture. Ignition by electric primer. Oval flask, diam. 34.5 em. with oxi-acetylene mixtures that gave rise to violent explosions; and Boyer Topaz F/2.9 (f = 135 ram) for less violent mixtures. The enlargement generally was only 0.09--0.12 (4-1.5-2 per cent), but the distance between the recording instrument and the flask could not be less than 1..5-2 m for safety reasons. All tests

The recordings reproduced in figures 4a and 4b may be considered as typical for spherical detonation waves. Both recordings were made in the course of experiments with flasks of the first type filled with oxygen-acetylene mixtures containing 50 per cent C2H2. One of these flasks (fig. 4a) was ignited by spark and the other (fig. 4b) by the electrically primed igniter. Figure 4b shows a rather long predetonation period (about 0.25 of the total path) which is not always as clearly visible and usually must be guessed at. The walls of the flask are brilliantly illuminated by the flame and sometimes by the ignition source (especially the spark); they show up dearly on We wish to thank Chief Engineer Medard, Director of the Laboratory, and Commandant Cessat for their help, particularly in preparing the detonators.

STUDY OF SPHERICAL DETONATION WAVES virtually all the recordings, thus making it possible to check their immobility up to the time when the wave reaches them. Rupture of the walls generally is very regular and instantaneous as shown by line AA' (fig. 5). The average rate at which the burned gas escapes can be determined approximately from the slope of the AE and A ' E ' curves (fig. 5). As far as we can tell, this rate depends principally on the composition of the mixture; the ignition process has no effect on the velocity (provided that it produces a detonation wave), but perceptible differences were observed from one flask to the other.

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known to form in tubes when deflagration changes to detonation.

O.D,gen-acelylelte mixtures Spherical detonation waves were observed in oxygen-acetylene mixtures for COM._,concentrations between 5.3 and 60 per cent. ttowever this result depends on the ignition source. Wilh hot-wire ignition, none of the mixtures tested (25 50 per cent Cell.,) ignited in either of the two series of flasks. This type of ignition produces a deIlagration (fig. 6) having a non-uniform propagatio~ velocity, whose acceleration is first posilive, lhen negative and finally becomes positive again over the last few centimeters. It will be seen from figure 6 that the flask dilates at)t)rcciably before

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FIG..5. Diagram of photographic recordings: I = ignition; ID, ID' = flame (predetonation frequently absent); DA, D'A' = detonation wave; AP, A ' P ' = wall of flask; AA' = rupture of flask; a, a', a " = path of gas escaping through slit. The cross-shaped trace at M (fig. 5) which can be seen on the photographs of figures 7, 9, etc., appears to correspond to a centripetal wave formed at the moment when the walls of the flask rupture. Its average velocity (from A to M) is of the same order (at least for 50 per eenr C2H2 mixtures in 02) as the calculated velocity of sound in the burned gas immediately behind the wave (1600 m/sec, measured, as compared with 1585 m / s e e calculated (10) for the 50 per cent C~H2 mixture). In addition it should be mentioned that another influx is sometimes observed (diagrammed as F F J, fig. 5) caused by the gas following its impact with the floor. Finally it should be noted that no clear case was observed of retrograde waves such as are

FIG. 6. Deflagration in C._,H2(50 per cent)-O_~ mixture. Ignition by hot wire. Oval flask, diam. 33 cm. rupturing and that the rupture is much less regular than in the case of propagation by detonation wave. Initiation of detonation waves by electrically primed igniters was obtained in mixtures containing from 25 to 50 per cont C2H~, but the results were less reproducible than with sparks. With this latter type of ignition, waves were observed in mixtures containing from 14 to 60 per cent C~_H> Finally with tetranitropentaerythrite detonators, a wave was still visible in a 5.3 per cent C._,H._, mixture. However, the wave trace is very faint and its propagation velocity decreases perceptibly

(fig. 7). The graph in figure 8 summarizes the results of our wave velocity measurements. I t includes the results of various workers who studied the propa-

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LAMINAR COMBUSTION AND DETONATION WAVES

gation of detonation waves in the same mixtures in tubes. There are no appreciable divergences. I t should be noted that immediately following the rupture of the flask, the speed of the

lated speed (10) of the burned gas immediately behind the wave front (1375 m/sec). Note: In obtaining the above results, flasks of both series were used without any perceptible difference in the appearance of the waves. Howev.er, as was to be expected, mechanical effects were much more pronounced with the second series of flasks.

Propane-oxygen mixtures No detonation waves were observed-in oxygenpropane mixtures when the ignition source was a hot wire, spark or electrically primed igniter. In

FIG. 7. Acetylene-oxygen mixtures. Flask diameters, 60 cm. Ignition by detonator (1.5 g tetranitropentaerythrite).

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FIG. 8. Velocity of detonation waves in the C2H2oxygen mixture. Arrows indicate probable limits of detonation waves. burned gas is of the order of 1000 to 1300 m/sec for mixtures containing 14 to 60 per cent C2H~; it drops to 475-500 m/sec for the 5.3 per cent C2H2 mixture. In the case of 50 per cent C2H2 mixtures, this speed is comparable to the calcu-

FIG. 9a. Detonation wave in C3Hs(19.5 per cent)02 mixture. our experiments, only the 2 gram fulminate-tetranitropentaerythrite paste detonator produced detonation waves in mixtures containing 11 to 13 and 27 to 29 per cent propane. The recordings have the same general appearance as those obtained for oxygen-acetylene mixtures except that the wave trace (line DA of fig. 5) tends to be somewhat less well defined (figs. 9a and 9b); we do not believe that this tendency is due to improper focusing, as this was checked before each test. The graph in figure 10 summarizes results of our wave-velocity measurements in 60 cm diameter flasks and 10 mm diameter tubes, together with results of other workers. As in the case of C2H2-O2 mixtures, there were no divergences.

Mixtures of oxygen with a gas containing principally ethylene and methane Figure 11 shows a series of recordings of detonation ~v~ves in flasks of:the second series (diameter,

STUDY OF SPHERICAL DETONATION WAVES 60 cm) filled with mixtures of oxygen and C2H,CH4 gas. For waves to form in these mixtures, the ignition source must be a detonator; deflagration was observed with spark ignition or ignition by an electrically primed igniter. The graph in figure 12

FIG. 9b. Detonation wave in C3H8(26 per cent)-O2 mixture.

491

agree with those indicated by Bone and Townend (1) and Campbell (3) 4 in oxygen-methane mixtures. Generally speaking, the recordings (fig. 14) of waves in oxygen-St. Marcet gas mixtures have the same character as in the case of the previous mixtures with a single exception, figure 15, where

FI6. l l. Ethylene-methane-oxygen mixtures. Flask diameter, 60 cm. Ignition: 1.5 g tetranitropentaerythrite.

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FIG. 10. Velocity of detonation waves in C~H,-O2 mixtures. Arrows indicate probable limits of spherical detonation waves. summarizes our measurements of the propagation velocity of waves in flasks and tubes (diameter, 10 ram). Oxygen-natural St. Marcet gas mixtures

As before, spherical detonation waves were observed only when the mixture was ignited by the 2-gram detonator. The velocities of the detonation waves measured in the course of experiments with flasks and tubes (diameter, 10 mm) are shown in figure 13. Except for rich mixtures, our values

FIG. 12. Velocity of detonation waves in ethylenemethane-oxygen mixtures. Arrows indicate probable limits of detonation waves. unsymmetrical wave initiation occurred for some unknown reason (perhaps due to an irregularity in the construction of the detonator). Remarks on mixtures with air

In no case were spherical detonation waves observed for mixtures of any of the above gases in air. The various ignition sources were all tested (hot wire, spark, etc.) as were the detonators 4See also Jost (6) and Laffitte (9).

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LAMINAR COMBUSTION AND DETONATION WAVES

whose tetranitropentaerythrite charge was increased to about 3.5 to 4 grams. The recordings have the same general aspect as in figure 6 except when ignition is produced by detonator (fig. I6). Moreover, in some cases the flask ruptures before the flame reaches the wall.

phase during which the flask is not dilated, or to observe the dilation phenomenon as carefully as the progress of the f a m e front, the two phenomena being interdependent. ~

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9a6 F16. 13. Velocity of detonation waves in mixtures of St. Marcet gas and oxygen. Arrows indicate probable limits of detonation w~ves.

FIG. 15. Unsymmetrical ignition with formation of detonation wave in mixture of St. Marcet gas (36 per cent) and oxygen.

FIG. 14. Detonation wave in mixture of-St. Marcet gas (31 per cent) and oxygen.

FIG. 16. Deflagration in C2H~(8 per cent)-air mixture. Ignition by detonator. Round flask, diam. 60 cm.

Deflagration is highly accelerated (fig. 17) without, however, changing to detonation. To date we have not made systematic measurements of deflagration velocities, but it is already apparent that latex flasks can be substituted for soap bubbles in studying such waves. However it will be necessary (especially in the case of rapid deflagrations) either to limit measurements to the

DISCUSSION A N D CONCLUSIONS The recordings described above confirm previous observations by Laflitte to the effect that an established spherical detonation wave propagates throughout the entire combustible charge at the 5 This question will be discussed in greater detail in a subsequent publication.

STUDY OF SPHERICAL DETONATION WAVES same velocity as a plane wave. 6 As the ignition source does not affect this velocity, for a given mixture there is no difference between spherical a n d plane detonation waves with respect to this characteristic. W e obtained no evidence in support of the opinion expressed by C o u r a n t a n d Friedrichs (4) to the effect t h a t the spherical detonation wave m u s t be diminished by events behind the wave (expansion wave in the burned gas). Once a steady state is attained, we have seen t h a t as in the case of plane waves, the velocity of the wave is determined only by the physical-chemical

FIG. 17. Deflagration in C~H2(15 per cent)-air mixture. Ignition by hot wire. Oval flask, diam. 30 cm. characteristics of the mixture in which it propagates. I t is only for mixtures with a very low combustible content t h a t we observed a decrease in the wave velocity, indicating t h a t the energy liberated b y the reaction was no longer sufficient to support propagation in the form of a detonation wave. I n all other cases, provided t h a t the ignition source is powerful enough, propagation b y detonation wave was observed. However we c a n n o t affirm t h a t a suitable choice of ignition source (sufficiently powerful detonator) necessarily makes it possible to observe a spherical detonation wave in all cases. Experiments with air mixtures h a v e shown t h a t increasing the power of the ignition source does not constitute a necessary a n d sufficient condition for the initiation of a spherical detonation wave in a given gas mixture. We apply this term to waves propagating in tubes simply as a matter of convenience, it being understood that such waves probably are not really plane.

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The intensity of the shock wave produced by the ignition source u n d o u h t e d l y is a primordial factor, but the mixture must be capable of a chcnfica! reaction t h a t is b o t h rapid enough and generates enough energy to support the wave. This is well known and has frequently been formulated in connection with plane explosive waves. In the case of spherical waves, lhc condi tions are more rigorous because, as our observations show, the detonation limits are narrower than for plane waves. The greater severity of these conditions can be explained perhap~ in terms of the differences in the laws of motion of gases t)ehind these waves which result from the TaylorZeldovitch theory. According to this theory the gradients of pressure, velocity, etc., arc necessarily infinite at the spherical wave on the side of the burned gas, whereas in the case of plane waves this additional discontinuity m a y not exist. H a v i n g no direct influence on the velocity of the established wave, the structure of the motion of the burned gas would be more difficult to develop perhaps in the case of a spherical wave than in the case of a plane wave, thus requiring more specific conditions with respect to the association of chemical (reactions) and mechanical p h e n o m e n a in the wave. In every case, however, we feel t h a t a t the present time the Taylor-Zeldovitch theory offers a very satisfactory i n t e r p r e t a t i o n of the concept of spherical detonation waves. To explain why ignition by a h o t wire does not lead to the formation of a spherical detonation wave r under the conditions described above even in the case of mixtures t h a t detonate as readily as C=H2-O2, it should be noted t h a t there is no opportunity whatsoever for a powerful enough shock wave to form. s W e know t h a t a n y spherical centrifugal disturbance decreases continuously as it propagates; in other words, the formation of a shock wave appears very improbable. This, of course, is true only if the walls of the flask are elastic and can be destroyed by the burned gas or by sufficient compression of the gas in front of the We do not think that Rakipova, Trochkine, and Schtchelkine (12) observed the formation of a detona tion in their experiments with CeH2--O._, mixtures in soap bubbles. However, the authors themselves make a number of reservations, and comparison of figures 9 and 16 of their work with figures 17 and 6 of the present paper clearly shows that the observed phenomenon is either the rupture of the bubble itself or an acceleration of the flame immediately following this rupture. *The concept of the formation of such a wave for the plane case has heen discussed elsewhere (11).

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LAMINAR COMBUSTION AND DETONATION WAVES

deflagration; in the case of rigid bombs, events may be different although at present we see no reason why this should be so. In dosing we wish to thank our collaborator, R. Eddi, for his help in carrying out the above experiments. REFERENCES 1. BONE, W. A., AND TOWNEN~, D. T. A. : Flame and Combustion in Gases. London, Longman, Green & Co. (1927). 2. Bm~TON, J.: Ann. des Comb. Liq., 11, 487 (1936). 3. CAMPBELL,C., LITTLER, W. B., AND WHITWORTH, C.: Proc. Roy. Soc., A 137, 380 (1932). CAMPBELL, C., KINO, A., ANn WHITWORTH, C.: Trans. Faraday Soc., 20~ 681 (1932). 4. COURAI~T,R., AND FRIEDRmHS, K. O.: Supersonic Flow and Shock Waves. Interscience Publ. No. 4, 430 (1950). 5. GU~NOCHE,H.: Th~se Paris (1948), Revue I.F.P., Jam-Feb. (1949).

6. JOST, W.: Explosion u. Verbr. Vorgg.nge in Gasen, pp. 185-186. Berlin, J. Springer (1938). 7. JOU6tYET, E.: La M6canique des Explosifs, pp. 359-366. Paris, Ed. Doin (1917). 8. LAFFITTE, P.: C. R. Acad. Sc:, Paris, 177, 178 (1923); Ann. de Phys., 10b ser. 4, 587 (1925). 9. LAPFITTE, P.: Comb. et d6tonat, des gaz. Tabl. ann. de Constantes. Paris, Hermann (1937). 10. MANSON, N.: Propagation des d6tonat, et des d6flag, dans les m61anges gaseux. I.F.P. et O.N.E.R.A., 105, Paris (1947). 11. MANSON, N.: Comm. au 7~ Congr~s Intern. de M6eanique, London (1948). 12. RAKIPOVA, H. A., TROCHKINE, J. K., AND SCHTCHELKINE, K. I.: J. Phys. Techn. URSS, 17, 1397 (1947). 13. TAYLOR, G. I.: Min. of Home Sec., G. B., Jan. (1941); Proc. Roy. Soc. A 200, 235 (1950). 14. ZELDOVlTCH,J. B.: J. Phys. Exp. et Th6or., URSS, 112, 389 (1942).

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DETONATION AND SHOCK IN A HOLLOW EXPLOSIVE CYLINDER By MORTON SULTANOFF INTRODUCTION The effects of axial cavities in cylindrical explosive charges have been of considerable interest in the study of detonation and shock (1). In the past, most of the studies of hollow cylinders have been confined to the investigation of these effects as functions of varying charge parameters. This report presents an analysis of the detonation and shock associated with a hollow pentolite cylinder 6 inches long, with inside and outside diameters of 1 and 11/~ inches respectively. The results presented are essentially experimental in nature and include both quantitative and qualitative data. The experimental methods did not require that the charges be modified to include viewing holes or slits to obtain internal details. Simultaneous streak-camera (2, 3) " r a t e " recording of both side and end views of the detonating charge, plus ultra-high-speed camera records (4), Faraday shutter (5) pictures, and "profile" streak camera photographs have been utilized to map

the shock and detonation configurations at one microsecond interVals. INSTRUMENTATION The Bowen RC-3 rotating-mirror streak-camera (2), modified as reported earlier (3), was used with the slit in the rate position to obtain time-distance data for the detonation and shock fronts. A mirror, positioned as shown in figure 1, was used to obtain end view records simultaneously on the film with the rate records. Since the charges were semi-transparent to the internal shock, this instrumentation produced records of the internal and external luminosity in both views (fig. 2). By "profile" position recording with the streakcamera, the profile of the internal and external luminous phenomena was obtained on emergence from the end of the charge as shown in figure 3. Since the profiles at various times can only be obtained in this manner by firing charges of various length across the camera slit, the ultra-high-speed