Shock Velocity Measurement in Water by Sulfur Probes

150 Propellants, Explosives, Pyrotechnics 11, 150-154 (1986)

Shock Velocity Measurement in Water by Sulfur Probes

H. S. Yadav and P. V. Kamath

Explosives Research and Development Laboratory, Pashan, Pune - 411 021 (India)

Geschwindigkeitsmessung von StoRwellen in Wasser mit schwefelbe- schichteten Sonden

Die oszillografische Signalauswertung schwefelbeschichteter Son- den (SPOT) ist als ein neues MeRverfahren fur die StoRwellenge- schwindigkeit in Wasser entwickelt worden. Im Gegensatz zu anderen Verfahren, die allgemein piezoelektrische Umwandler oder Kurzzcit- aufnahmen benutzen, ist seine Anwendung nicht auf die Messung von StoRwellendriicken in einem begrenzten Bereich beschrankt. Um seine Einsatzfahigkeit und Genauigkeit zu uberprufen, wurden die Detonationsdrucke von einigen typischen Sprengstoffen nach dieser Methode gemessen und mit den Werten anderer Verfahren vergli- chen. Das neue Verfahren liefert MeBwerte fur die StoRwellenge- schwindigkeit in Wasser mit einer Genauigkeit von 2%.

Mesure de la vitesse de propagation das ondes de choc dans I’eau a I’aide de sondes a cnuche de soufre

L‘enregistrement oscillographique de signaux fournis par des sondes B couche de soufre (SPOT) est une nouvelle mtthode mise au point pour determiner la vitesse de propagation des ondes de choc dans I’eau. Contrairement ?I d‘autres prockdts qui utilisent en gtntral des capteurs pitzo-Clectriques ou la photographie ultrarapide, cette mtthode n’est pas limitte dans son application B la mesure de la pression des ondes de choc dans un domaine restreint. Afin de vtrifier ses conditions d’application et sa prtcision, on a mesurt la pression engendree par la detonation de divers explosifs et on a compare les resultats obtenus avec ceux fournis par d’autres mkthodes. Na nouvelle mtthode permet de mesurer la vitesse de propagation des ondes de choc dans l’eau avec une incertitude de 2%.

Summary

Sulfur-coated pin oscillographic technique (SPOT) has been developed as a new technique for measurement of shock velocity in water. Unlike other techniques, generally employing piezo-electric transducer or high speed photography, the application of this technique is not restricted to the measurement of shock wave pressures over a limited range. To illustrate the application and accuracy of the technique the detonation pressures of a few typical explosives have been measured with this technique and compared with those determined elsewhere by using other techniques. The new technique has yielded measurement of shock velocity in water within an accuracy of 2%.

1. Introduction

Measurement of shock velocity in water is of prime impor- tance for determining scaling laws of underwater explosions, the shock wave attenuation in water, equation of state of water under dynamic loading and yield of both nuclear as well as chemical explosions. So far, the shock wave propagation in water has been studied experimentally either by usin

measured shock pressures at long distances from point of explosion upto a maximum of about 1 kbar with piezoelectric transducers, while Cook(’) and Rice et al.(3) employed high speed photography to determine shock velocity in water and its Hugoniot. Recently Yadav et al.(4) have measured refractive index of water at high dynamic pressures and determined there from the shock wave pressures in the vicinity of the explosive charges by use of Kerr-cell photographic technique.

In this paper an electrical method for measuring shock wave velocity in water is presented. The sensing element for shock detection in this method is a sulfur coated electrical probe. Earlier it has been reported(5) that a large increase in the electrical conductivity of sulfur occurs when it is subjected to a high dynamic pressure. Hauver@) has used this property for studying the Von-Neumann spikes associated with the detonation wave of a high explosive charge. Duvall and F ~ w l e ( ~ ) have

piezoelectric gauges or streak photographic technique. Cole (3

also used sulfur probes to study shock wave propagation in non-conducting solids. In the present work we have developed sulfur-coated electrical probes which are suitable to shock velocity measurement in water in very close vicinity of the explosive charge. These probes are particularly useful when such measurements are required to be made in-situ experiments.

2. Experimental

In present method, the propagation of shock wave is essen- tially monitored by electrically charged pin type of probes placed at pre-determined positions in the path of the shock wave. Each probe consists of two insulated copper wires twisted together and cut at the end to make their tips conducting. The other ends of these probes are connected to an ener- gised resistance-capacitance (R-C) network as shown in Fig. 1. On arrival of shock wave at the location of the probe, the open end of the probe is shorted by the conducting medium associated with the shock front. This results in discharging of the capacitor, C, and generation of a sharp electrical pulse, across resistance R4 which is recorded on a high speed time base of a Tektronix oscilloscope,

The electrical probes in this form however, are not suitable for recording shock wave propagation in water. Water, being a good conductor of electricity, discharges the capacitors of the R-C network before the arrival of the shock wave. This has been the main difficulty in adopting the electrical probe method for shock wave propagation studies in water. To over- come this difficulty the conducting tips of these electrical probes have been coated with sulfur in the present work. Since sulfur behaves as an insulator (resistivity = 2 x loz3 pohmkm) at ordinary pressures, it prevents the discharge of capacitors when such probes are immersed in water. At shock waves pressure, however, sulfur becomes conducting and allows R-C network to generate the electrical pulse at the time of arrival of shock wave, and thus makes measurement of shock wave propagation in water possible by electrical method.

0721-31 15/86/051@015U$02.50/0 0 VCH Verlagsgesellschaft mbH, D-6940 Weinheim, 1986

Propellants, Explosives, Pyrotechnics 11, 150-154 (1986)

, 1 7 FLEXIBLE WIRE PERSPEX PROBE CARRIER

I

SULFUR COATED PROBE

SHOCK FRONT _ -

DETONATOR x-- Figure 1. Experimental set-up for measurement of shock velocity in water by sulfur-coated pin oscillographic technique (SPOT).

2.1 Design of sulfur-coated probes

To fabricate the probes for underwater shock wave measurements, two insulated copper wires of diameter 0.8 mm are twisted together and cut at the end to make their tips conducting. These ends are now separated from each other to intro- duce an air gap of about 0.01 mm between them so that two ends of the twisted probe can withstand an electrical voltage of about 50 volt. A number of such probes of small length (-2.5 cm) are inserted into holes made in a perspex strip at predetermined distances. Each probe, protruding about 2 cm from the plane surface of the perspex probe carrier, is adjusted such that the tips of all the probes fall in one line. Fixing the probes in perspex holes with araldite, the ends of these probes are dipped into a bath of molten sulfur. The sulfur whose bulk density is 2.00 g/cm3, MP = 115°C sticks to the tip of each probe and gets solidified immediately after removal of the probes from the sulfur bath. Uncoated end of each probe is connected to an R-C network, charged to 30 V, to make these probes ready for recording shock wave propagation in water.

2.2 Experimental set-up

As shown in Fig. 1, the experimental set-up used for measuring shock velocity in water by electrical pin method consists of a cylindrical explosive charge, long enough for making its detonation wave stable, and a perspex probe carrier assembled together are placed inside a water tank whose dimensions are such that rarefaction waves from lateral sides do not reach the probes before the arrival of shock wave. A number of specially designed sulfur coated electrical probes are mounted on the probe carrier such that the tip of each probe is colinear with the axis of the charge. These probes are connected to a R-C network which is charged to an electrical voltage of about 30 volt. The out put of these probes is fed to a high velocity oscilloscope through low noise cable terminated with its characteristic impedance. When explosive charge is detonated, a shock wave is produced in water. This shock

Shock Velocity Measurement in Water by Sulfur Probes 151

Figure 2. Typical oscillographic record for shock wave propagation in water obtained with sulfur probes. Time base = 1 Wcm. Vertical deflection = 2 volticm.

wave on interaction with sulfur, placed on the tip of the probe, reduces its resistance and actuates R-C network to generate electrical pulses of amplitude which depends on the pressure of the shock wave. A typical oscillograph obtained with such an experimental set-up is shown in Fig. 2.

As the first probe is kept in contact with the explosive charge itself and successive probes are kept at 5 mm-10 mm apart, one can measure the velocity of shock wave upto 2.5 mm from the end of the charge. This distance is sufficiently small to extrapolate the shock velocity measurements even upto zero distance from the end of the explosive provided, it is assumed that shock wave corresponding to Neumann spikes in explosive is attenuated within very short distance in water and causes a negligible error in recording of shock travel time between initial probes.

3. Analysis

If we assume that shock wave reaches first probe at time t = 0, and the distance of each probe x is measured from an arbitrary reference, then distance and time of shock travel, obtained experimentally, can be fitted into a polynomial@),

x = + alt + azt2 -F . . . (1)

which, on differentiation, yields the expression for shock velocity at time t as

dx - _ - a t + 2 a 2 t + ... dt

Eliminating t between Eqs. 1 and 2, the shock velocity Us at different distances is readily obtained. Extrapolating this velocity to interface of explosive and water, and obtaining corresponding particle velocity Up from the relation

Us = a + bU, (3)

where a (= 3.09), and b (= 1.164), are constants for water, determined elsewhere(3), one then computes shock pressure P, in water from the hydrodynamic relation

152 H. S . Yadav and P. V. Kamath Propellants, Explosives, Pyrotechnics 11, 150-154 (1986)

pw = e w w - J p (4)

where, ew is density of unshocked water. Further assuming adiabatic expansion of detonation products and continuity of pressure and particle velocity at the interface of water and explosive, one can derive the relation("),

( 5 )

where subscript j indicates detonation parameters at C-J plane and y is the adiabatic exponent for detonation products. An approximate value of C-J pressure can easily be obtained from shock impedance mismatch equation("),

pi = f P, (1 + 5) where Z, and Z, denote the shock impedances in water and explosive. Further if D denotes the velocity of detonation in an explosive of density eo, then, hydrodynamic theory of detonation wave provides a relation,

(7)

which can be used to eliminate y from relation ( 5 ) . Equations (1-7) offer the computation of C-J pressure from

the measurement of shock velocity in water. Results of such calculations for some typical explosives have been enlisted in Tables 1 and 2 along with those obtained elsewhere for comparison. The detonation pressures, reported in the literature, have been corrected for the present density of the explosive by modifying the relation (7) for two densities as,

4. Results and Discussion

It is evident from the typical oscillograph, shown in Fig. 2 that sulfur-coated electrical probes generated sharp pulses on interaction with shock wave and are capable of indicating arrival of shock wave with some nanosecond order of resolution in time. The amplitude of the electrical pulse, generated from those probes, decreases with increasing distance of the probe. This leads us to conclude that the pressure of the shock wave, which decreases with increasing distance of its propagation, affects the amplitude of the pulse or in other words, the greater the pressure, the larger the decrease in resistance of the probe. A definite relationship between decrease in resistance of the probe and pressure of shock wave, however, can not be derived from such records as the pulse amplitude depends also on other factors like voltage on capacitor and variation in design of the probe etc.

As all the probes located up to a distance of 35 mm responded to the arrival of shock wave, it can be concluded that sulfur type probes are sensitive to pressures as low as about 1 kbar. The quantity of sulfur coating on each probe, also does not seem to be affecting the response time of the probe. It is probably due to the fact that the portion of the sulfur which exists between the leads of the probe only is

30

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0 EXPERIMENTAL POINTS

0 1 2 3 4 5 6 TIME [ p s ] -

Figure 3. Attenuation of shock wave generated by RDXiTNT (60 : 40) cylindrical charge (32 mm dia and 1.50 mm length) in water.

important for conduction of current in the probe and that width of sulfur is not changed with its quantity on the probe.

Only a small quantity of sulfur, however, has been used to avoid generation of an irregularity in the shape of the shock front in water.

It is important to note that the cylindrical explosive charges, used in the present study, were initiated at single point. The shape of the shock wave, emerged out of this charge therefore, is not plane over entire cross-section of the charge. The shock velocity-attenuation curve for water, presented in Fig. 3, therefore, corresponds to this typical shock wave in the direc- tion of probes and not to a perfectly plane or a perfectly spher- ical shock wave. Not much error is, however, expected in the determination of the initial shock velocity as the central velocity of the detonation wave obtained from point initiation in cylindrical charges remains very close to that of a plane detonation wave and reflection of curved shock from perspex probe carrier does not affect the part of the wave front which faces the sensing portion of the probe as their projection above the perspex is greater than the inter distance of the probes. However ideal situation for such measurements exists when plane shock wave moves parallel to the surface of the probe carrier.

Smooth attenuation curve, depicted in Fig. 3, for shock velocity in water further indicates that natural water, used in our experiments, does not undergo a phase transformation, as was observed by other investigators('") for double shock structure in water. Table 1 shows that shock velocities in water determined with the present probe system lie within 2% experimental variation while C-J pressures are found within 7% in agree- ment with other reported

5. Conclusion

Sulfur-coated electrical probes are suitable and accurate for oscillographic measurement of shock velocity in water for


Table 1. Expeimental Values of Shock Wave Parameters in Water and Detonation Pressures obtained from them

Shock Velocity Measurement in Water by Sulfur Probes 153

Sr. No. Explosives Probe No. Distance [mm] ‘Time [FS] Interface Detonation Shock velocity Pressure pressure lmm4sl [kbar] calculated from

mismatch equation [kbar]

RDWTNT 1 0 0 60 : 40 2 10 1.79 eo = 1.68 g/cm3 3 15 2.77 5.9837 149 238 D = 7.8 m d p s 4 20 3.95

5 25 5.18

RDXiTNT 1 0 0 60 : 40 2 10 1.70 en = 1.68 gkm3 3 15 2.80 D = 7.8 mmips 4 20 4.10

5 25 5.40

RDX 1 0 0

D = 6.394 m n d p 3 15 3.51 4 20 4.75 5 25 6.45

RDX 1 0 0 eo = 1.1 g/cm3 2 10 1.96 D = 6.394 mmiys 3 15 3.24

4 20 - 5 25 5.53

TNT 1 0 0 en = 1.62 g/cm3 2 1.5 0.36

4 16.5 3.35 5 21.5 4.66 6 26.5 5.97

(1)

(2)

eo = 1.1 g/cm3 2 10 1.82 (3)

(4)

(5 )

D = 7.00 mmips 3 11.5 2.22 5.5785 119 180

6.1036

5.122

5.038

158 249

89.4 108

84.3 103

Table 2. Comparison of Detonation Pressures ~

Detonation Parameters Present work Cook’s data Coleburn’s data Kamlet-Jacob data

(Ref. 9) (Ref. 11) (Ref. 12) eo D P ea D P eo D P 90 D P [gicm’] [mm/pss] [kbar] [gicm’] [mmips] [kbar] [g/cm3] [mmlys] [kbar] [gkm’] [mmips] [kbar]

~~ ~

282.5 (255.6) RDX 1.13 6.394 106 1.10 6.4 112 (115) 1.63 8.34 283 (112) 1.806 8.805 344.6 (113.7) TNT 1.62 7.00 180 1.58 6.88 176 (187) 1.622 6.79 187 (198) 1.654 7.002 206.4 (202)

eo = Initial density of the explosive D = Detonation velocity P = Detonation Pressure Values within brackets are the corrected ones for present density of the explosives with the help of Equation 8.

R D m 1.68 7.8 244 1.68 7.8 2 3 0 i 10 1.668 7.86 264 (261) 1.73 -

laboratory as well as in-situ measurements, and can be used for measurement of detonation pressures of explosives. Since the time resolution of oscillographic technique is about an order higher than that of streak-photographic method, therefore the shock velocity measurements, reported here, are rela- tively more accurate. Further, this sulfur-coated pin oscillographic technique (SPOT) is less cumbersome and more con- venient for underwater shock velocity measurements particularly when such measurements are to be undertaken in-situ.

5. References

(1) R. H. Cole, “Underwater Explosions”, Princeton University,

(2) M. K. Cook, R. T. Keyes, and W . 0. Ursenback, J . Appl. Phys.

(3) M. H. Rice and J. M. Walsh, J. Chem. Phys. 26, 824 (1957). (4) H. S. Yadav, D. S. Murty, S. N. Verma, and N. H. C. Sinha,

“Measurement of Refractive Index of Water under High Dynamic Pressures”, J. Appl. Phys. 44 (9, 2197 (1973).

New Jersey, USA 194& p. 145.

33, 3413 (1962).

154 H. S. Yadav and P. V. Kamath

(5) S. Joigneau and J. Thuvenin, “Electrical Conductivity of Sulfur under the Action of Shock Wave”, C.R. Hebd. Seances Acad. Sci. 246,3422-25 (1958).

(6) G. E. Hauver, “Pressure Profile in Detonating Solid Explosive”, 3rd ONR Symposium on Detonation, 1960, pp. 241-52.

(7) G. E. Duvall and G. R. Fowles, in “High Pressure Physics and Chemistry”, Ed. R. S . Bradley, Academic Press Ltd., London 1963.

(8) G. E. Duvall, in “Physics of High Energy Density”, Eds. P. Caldirola and H. Knoefel, Academic Press, New York 1971,

(9) M. A. Cook, “The Science ofHigh Explosives”, Reinhold Pub-

(10) S . B. Kormer, K. B. Yushko, and G. V. Krishkevish, Suv. Phys.-

pp. 7-59.

lishing Corporation, New York 1963, p. 111.

JETP (Engl. Transl.) 6, 879-881 (1968).


(11) M. L. Coleburn, “Chapman-Jouguet Pressure of Several Pure and Mixed Explosive”, NOL Tech Report No. 64-58, National Technical Information Service, Springfield, USA 1964.

(12) M. J. Kamlet and S. J. Jacobs, J . Chem. Phys. 48, 23 (1968). Also cited in the paper of H. Dean Mallory, Combust. Flame 59, 217-224 (1985), p. 219.

Acknowledgement

Authors feel grateful to Dr. K. R. K. Rao, Director, Explosives Research and Development Laboratory, for granting permission to publish this paper and giving inspiration and valuable suggestions throughout this work.

(Received March 4, 1986; Ms 7/86)

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Shock Velocity Measurement in Water by Sulfur Probes