- Email: [email protected]
Underwater explosion of spherical explosives
Journal of Materials Processing Technology 85 (1999) 64 – 68
Underwater explosion of spherical explosives Akio Kira a,*, Masahiro Fujita b, Shigeru Itoh b a
Cooperati6e Research Center, Kumamoto Uni6ersity, Kamimashiki-gun, Kumamoto 861 -22, Japan b Faculty of Engineering, Kumamoto Uni6ersity, Kurokami, Kumamoto 860, Japan
Abstract Underwater explosion of high explosive generates underwater shock waves. This phenomenon has been observed by optical measurement. Propagation histories of underwater shock waves in the range close to explosive have been obtained by processing photographs. In order to obtain pressure distributions of these shock waves, the non-linear curve fitting technique was applied to these histories. Underwater explosions have been simulated by an arbitrary Lagrangian – Eulerian (ALE) method and calculated results agree well with experimental results in both propagation histories and pressure distributions. Therefore, pressure histories can be determined by numerical simulation. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Optical measurement; Underwater shock wave; Numerical simulation; Pressure history; Spherical explosive
1. Introduction Metal processing techniques using underwater shock waves generated by the underwater explosion of high explosive have been studied for many years. For example, making holes on the wall of a metal pipe [1] and the shock compacting of difficult-to-consolidate powder [2] have been reported. It is necessary to control the underwater shock waves in order to adapt them to the processing taking place. In the underwater explosion of high explosive, the underwater shock waves are generated and they propagate in water. These waves have been investigated by many researchers [3]. The behavior of the underwater shock waves generated by spherical high explosives has been investigated by Sternberg et al. [4], who studied the strength of the underwater shock waves at a position far from the explosive using a numerical calculation. In their calculations, they used an equation of state of water suggested by Walker et al. [5], as well as an equation of state of Pentolite suggested by Wilkins et al. [6]. The numerical results have been compared with the experimental results obtained by Coleburn et al. [7]. Good agreement between the numerical and experimental results beyond 20 times the radius of the explosive was obtained. However, there is * Corresponding author. [email protected]
Fax:
+81
96
2861067;
e-mail:
no information concerning the strength and the attenuation process of the underwater shock waves close to the explosive. The purpose of this paper is to clarify the behavior of the underwater shock waves close to the spherical high explosives, using high speed photography and a numerical calculation.
2. Experimental and numerical procedure
2.1. Optical measurement The underwater explosion of spherical explosives was visualized by an optical measurement system using a shadow graph method. A schematic drawing of the optical measurement system is illustrated in Fig. 1. The explosions were carried out in an explosion room of 8× 8×5 m, in the High Energy Rate Laboratory of Kumamoto University. The thickness of the wall of the explosion room is about 0.8 m. Measurement instruments are set in the observation rooms outside the explosion room. Each explosion room has two observation windows. The explosive was placed in the PMMA tanks filled with water and a xenon flash light (Hadland Photonics, HL20/50) with a flash time of 50 ms was used as a light source. The beam emitted from the xenon flash light passes through a condenser lens and a pinhole and reflects on a concave mirror. The reflected
0924-0136/99/$ – see front matter © 1999 Elsevier Science S.A. All rights reserved. PII S0924-0136(98)00257-X
A. Kira et al. / Journal of Materials Processing Technology 85 (1999) 64–68
65
Fig. 1. Schematic drawing of the optical measurement system.
beam becomes parallel, passes through the PMMA tank and reflects again on another concave mirror. Both framing and streak photographs were taken with an image converter camera (Hadland Photonics, Imacon 790) with a maximum framing velocity of 20 million frames per second and a maximum streak speed of 1.0 ns mm − 1. A delay generator (Hadland Photonics, type JH-3CDG) was used to release the shutter corresponding with the phenomena. Streak speed was calibrated using a known pulse and distance was calibrated by taking a block gauge. The explosive called SEP (Asahi Chemical Industry) was used. It has a detonation wave velocity of 6970 m s − 1 and an initial density of 1310 kg m − 1. The explosives were formed spherically and were detonated with No. 6 electric detonator (Asahi Chemical Industry). The radii (R) of the explosives are 10, 18 and 29 mm, respectively.
2.2. Numerical calculation
useful. Although many Lagrangian methods have been developed in the course of the last decade, in application of this method to the simulation of an underwater explosion, there are many problems to be resolved. For example, the pressure of the shock wave is extremely high, so that the Courant number is very high. In this case, it is very easy to destroy the solution. Furthermore, the simulation of the detonating processes of the explosives is very difficult using the Lagrangian method. These authors used an arbitrary Lagrangian– Eulerian (ALE) method [8] in the basic calculations. The detonation process of the explosives is very complex, so that suitable assumptions are necessary for the simulation. In this paper, it is supposed that the explosives are homogeneous. In addition, it is assumed that the detonation is stationary, that the part of the explosive at which the detonation wave arrives changes perfectly into product gas and that the rear region of the detonation wave has the pressure, density and energy which satisfies the Chapman–Jouget condition.
In the underwater explosion, a moving boundary exists between the water and the product gas. In calculations involving the moving boundary, a method such as the Lagrangian method, which considers movement of the lattice point of the calculating field, is very
Fig. 2. An example of a streak photograph where R =18 mm.
Fig. 3. x– t wave diagram obtained by processing three streak photographs.
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A. Kira et al. / Journal of Materials Processing Technology 85 (1999) 64–68
Fig. 6. Relationship between distance r and the time constant u.
Fig. 4. Comparison of shock attenuation between experimental and numerical results.
We must investigate whether these assumptions are acceptable in the explosion of high explosive. In practical applications to simulate these detonation processes of the explosives, there are many difficulties, such as determining the detonation wave velocity. In the Lagrangian grid, it is very difficult to obtain a steady state detonation due to the fact that the grid moves at the detonation wave velocity. In this region, we used a perfect Euler grid system with a rezoning technique. However, when this time increment is used, the Courant number exceeds unity, so that the solution of the calculations breaks very easily. To avoid this, an
Fig. 5. Pressure histories obtained by numerical calculation where R = 10 mm at intervals of 20 mm from the surface of the explosive.
implicit technique is used; the full description of the ALE method is refered to the original paper. In simulation of the flow field, it is necessary to apply equation of states of the materials [9]. The Jones–Wilkins–Lee (JWL) equation of state was used for the product gas of explosive, while the Mie–Gruneisen equation of state was used for water.
3. Results and discussion An example of the streak photographs is shown in Fig. 2. This was obtained in the case of explosive having a radius of 10 mm. The vertical line in this figure corresponds to the real distance (x) of 50 mm. The horizontal line corresponds to the real time (t) of 20 s. The straight line EX indicates explosive. The white line SL corresponds to the light due to the detonation. The edge of the curve SW indicates the propagation of the underwater shock wave. Fig. 3 shows the x– t wave
Fig. 7. Value of coefficients k and h for radii R.
A. Kira et al. / Journal of Materials Processing Technology 85 (1999) 64–68
67
diagram obtained by processing the photographs of three different radii of explosive. In this figure, symbols indicate the results obtained by processing photograph in the case of each radii. The solid line indicates the numerical results, which are equivalent to the experimental results. The numerical results are in good agreement with the experimental results. The experimental data were approximated by the following equation, using a nonlinear curve fitting method [10].
distance r from the surface of the explosive is expressed by the next equation.
r = A1{1.0− exp(− B1t)} + A2{1.0 − exp( − B2t)}
u= kr+h
+ A3{1.0− exp(− B3t)} + C0t
(1)
where r is the distance to the radial direction from the surface of the explosive, C is the sound velocity of water (1490 m s − 1) and A1, A2, A3, B1, B2, B3 are coefficients obtained by using a nonlinear curve fitting method. Differentiating Eq. (1) with t, the propagation velocity of the underwater shock wave U =dr/dt is obtained. The relationships between the propagating velocity and the particle velocity u are described next equation. (2) Us = C0 +suP where s= 1.79. Using Eq. (2), the pressure P of the underwater shock wave is P− P0 = r0UsuP
(3)
where P0 is atmospheric pressure and r0 is the density of water (1000 kg m − 3). The comparison of the shock attenuation between the experimental results is obtained by using the above equations and the numerical results is shown in Fig. 4. A horizontal axis indicates the ratio of the distance R + r to the radius of the explosives R. The vertical axis indicates the pressure ratio P/P0. In this figure, circles, triangles and squares indicate the experimental results, while solid, broken and dash-dotted lines indicate the numerical results. Each result corresponds to R =10, 18 and 29 mm, respectively. As is obvious from this figure, the agreement between the experimental and the numerical results is very good. Therefore, taking streak photographs and carrying out numerical calculations is a suitable method to investigate the properties of underwater shock waves. The strength of the pressure decreases almost linearly as distance increases. This relationship is expressed by the next equation. P/P0 =a{(R+ r)/R} − b
P= Pr × e − t/u
(5)
where Pr is the maximum pressure at each distance r and u is a time constant and indicates inclination on the graph. Fig. 6 indicates the relationship between r and u. For every radius, the increases in u are nearly linear as r increases. (6)
where k and h are coefficients. The values k and h for R are plotted in Fig. 7, k and h increasing almost linearly as R increases. In this case, the following equation is obtained. k= 0.0041R+ 0.058
(7)
h= 0.093R+2.9 (8) It was found that using Eqs. (4)–(8), the pressure history at any position when the explosive was detonated is known.
4. Conclusions Underwater explosions of the spherical high explosives were investigated via optical measurements and numerical calculations. It has been concluded that taking streak photographs and carrying out numerical calculations are suitable methods of investigating the properties of underwater shock waves. It is also concluded that the strength of the underwater shock waves decreases exponentially with the increase of the distance from the explosives and the pressure histories, when the explosive were detonated in water, are known at any position.
Acknowledgements We wish to thank Y. Ishitani in the High Energy Rate Laboratory of Kumamoto University for his able assistance in obtaining the high speed photographs.
References
(4)
where a and b are coefficients; a =1.1 ×105, b = 1.8. Fig. 5 shows the pressure histories obtained by numerical calculation in the case of R =10 mm at intervals of 20 mm from the surface of the explosive. A horizontal axis indicates time t after completing the detonation and a vertical axis indicates the pressure P. The attenuation process of the pressure for the
[1] S. Itoh, M. Fujita, S. Nagano and K. Kamohara, Converging Underwater Shock Waves for Metal Processing, Shock Waves @ Marseille, vol.3, Springer, Berlin, 1993, pp. 289 – 294. [2] S. Itoh, S. Kubota, S. Nagano, K. Hokamoto, M. Fujita, A. Chiba, Characteristics of shock compaction assembly using converged underwater shock waves, first report, Trans. Jpn. Soc. Mech. Eng. 61 (588B) (1995) 217 – 222. [3] R.H. Cole, Underwater Explosions, Princeton University Press, Princeton, NJ, 1948.
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A. Kira et al. / Journal of Materials Processing Technology 85 (1999) 64–68
[4] H.M. Sternberg, W.A. Walker, Calculate flows and energy distribution following underwater detonating of a pentolite sphere, Phys. Fluid 14 (9) (1971) 1869–1878. [5] W.A. Walker, H.M. Sternberg, Proc. 4th Symp. on Detonation, White Oak, 1965, pp. 27. [6] M.L. Wilkins, B. Squire, B. Halperin, The equation of state of PBX 9404 and LX04-01, UCRL-7797, Lawrence Radiation Laboratory, Berkeley, CA, 1964. [7] N.L. Coleburn, L.A. Roshlund, Proc. 5th Symp. on Detonation, Pasadena, CA, 1970.
.
[8] A.A. Amsden, H.M. Ruppel, C.W. Hirt, Sale: A Simplified ALE Computer Program for Fluid Flow at All Speeds, LA-8095, UC-32, 1980. [9] M. Lee, M. Finger and W. Collins, JWL equation of state coefficients for high explosive, UCID-16189, Lawrence Livermore Laboratory, 1973. [10] P.R. Bervington, Data Reduction and Error Analysis for the Physical Sciences, Ch. 11, McGraw-Hill, New York, 1969.
Underwater explosion of spherical explosives Akio Kira a,*, Masahiro Fujita b, Shigeru Itoh b a
Cooperati6e Research Center, Kumamoto Uni6ersity, Kamimashiki-gun, Kumamoto 861 -22, Japan b Faculty of Engineering, Kumamoto Uni6ersity, Kurokami, Kumamoto 860, Japan
Abstract Underwater explosion of high explosive generates underwater shock waves. This phenomenon has been observed by optical measurement. Propagation histories of underwater shock waves in the range close to explosive have been obtained by processing photographs. In order to obtain pressure distributions of these shock waves, the non-linear curve fitting technique was applied to these histories. Underwater explosions have been simulated by an arbitrary Lagrangian – Eulerian (ALE) method and calculated results agree well with experimental results in both propagation histories and pressure distributions. Therefore, pressure histories can be determined by numerical simulation. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Optical measurement; Underwater shock wave; Numerical simulation; Pressure history; Spherical explosive
1. Introduction Metal processing techniques using underwater shock waves generated by the underwater explosion of high explosive have been studied for many years. For example, making holes on the wall of a metal pipe [1] and the shock compacting of difficult-to-consolidate powder [2] have been reported. It is necessary to control the underwater shock waves in order to adapt them to the processing taking place. In the underwater explosion of high explosive, the underwater shock waves are generated and they propagate in water. These waves have been investigated by many researchers [3]. The behavior of the underwater shock waves generated by spherical high explosives has been investigated by Sternberg et al. [4], who studied the strength of the underwater shock waves at a position far from the explosive using a numerical calculation. In their calculations, they used an equation of state of water suggested by Walker et al. [5], as well as an equation of state of Pentolite suggested by Wilkins et al. [6]. The numerical results have been compared with the experimental results obtained by Coleburn et al. [7]. Good agreement between the numerical and experimental results beyond 20 times the radius of the explosive was obtained. However, there is * Corresponding author. [email protected]
Fax:
+81
96
2861067;
e-mail:
no information concerning the strength and the attenuation process of the underwater shock waves close to the explosive. The purpose of this paper is to clarify the behavior of the underwater shock waves close to the spherical high explosives, using high speed photography and a numerical calculation.
2. Experimental and numerical procedure
2.1. Optical measurement The underwater explosion of spherical explosives was visualized by an optical measurement system using a shadow graph method. A schematic drawing of the optical measurement system is illustrated in Fig. 1. The explosions were carried out in an explosion room of 8× 8×5 m, in the High Energy Rate Laboratory of Kumamoto University. The thickness of the wall of the explosion room is about 0.8 m. Measurement instruments are set in the observation rooms outside the explosion room. Each explosion room has two observation windows. The explosive was placed in the PMMA tanks filled with water and a xenon flash light (Hadland Photonics, HL20/50) with a flash time of 50 ms was used as a light source. The beam emitted from the xenon flash light passes through a condenser lens and a pinhole and reflects on a concave mirror. The reflected
0924-0136/99/$ – see front matter © 1999 Elsevier Science S.A. All rights reserved. PII S0924-0136(98)00257-X
A. Kira et al. / Journal of Materials Processing Technology 85 (1999) 64–68
65
Fig. 1. Schematic drawing of the optical measurement system.
beam becomes parallel, passes through the PMMA tank and reflects again on another concave mirror. Both framing and streak photographs were taken with an image converter camera (Hadland Photonics, Imacon 790) with a maximum framing velocity of 20 million frames per second and a maximum streak speed of 1.0 ns mm − 1. A delay generator (Hadland Photonics, type JH-3CDG) was used to release the shutter corresponding with the phenomena. Streak speed was calibrated using a known pulse and distance was calibrated by taking a block gauge. The explosive called SEP (Asahi Chemical Industry) was used. It has a detonation wave velocity of 6970 m s − 1 and an initial density of 1310 kg m − 1. The explosives were formed spherically and were detonated with No. 6 electric detonator (Asahi Chemical Industry). The radii (R) of the explosives are 10, 18 and 29 mm, respectively.
2.2. Numerical calculation
useful. Although many Lagrangian methods have been developed in the course of the last decade, in application of this method to the simulation of an underwater explosion, there are many problems to be resolved. For example, the pressure of the shock wave is extremely high, so that the Courant number is very high. In this case, it is very easy to destroy the solution. Furthermore, the simulation of the detonating processes of the explosives is very difficult using the Lagrangian method. These authors used an arbitrary Lagrangian– Eulerian (ALE) method [8] in the basic calculations. The detonation process of the explosives is very complex, so that suitable assumptions are necessary for the simulation. In this paper, it is supposed that the explosives are homogeneous. In addition, it is assumed that the detonation is stationary, that the part of the explosive at which the detonation wave arrives changes perfectly into product gas and that the rear region of the detonation wave has the pressure, density and energy which satisfies the Chapman–Jouget condition.
In the underwater explosion, a moving boundary exists between the water and the product gas. In calculations involving the moving boundary, a method such as the Lagrangian method, which considers movement of the lattice point of the calculating field, is very
Fig. 2. An example of a streak photograph where R =18 mm.
Fig. 3. x– t wave diagram obtained by processing three streak photographs.
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A. Kira et al. / Journal of Materials Processing Technology 85 (1999) 64–68
Fig. 6. Relationship between distance r and the time constant u.
Fig. 4. Comparison of shock attenuation between experimental and numerical results.
We must investigate whether these assumptions are acceptable in the explosion of high explosive. In practical applications to simulate these detonation processes of the explosives, there are many difficulties, such as determining the detonation wave velocity. In the Lagrangian grid, it is very difficult to obtain a steady state detonation due to the fact that the grid moves at the detonation wave velocity. In this region, we used a perfect Euler grid system with a rezoning technique. However, when this time increment is used, the Courant number exceeds unity, so that the solution of the calculations breaks very easily. To avoid this, an
Fig. 5. Pressure histories obtained by numerical calculation where R = 10 mm at intervals of 20 mm from the surface of the explosive.
implicit technique is used; the full description of the ALE method is refered to the original paper. In simulation of the flow field, it is necessary to apply equation of states of the materials [9]. The Jones–Wilkins–Lee (JWL) equation of state was used for the product gas of explosive, while the Mie–Gruneisen equation of state was used for water.
3. Results and discussion An example of the streak photographs is shown in Fig. 2. This was obtained in the case of explosive having a radius of 10 mm. The vertical line in this figure corresponds to the real distance (x) of 50 mm. The horizontal line corresponds to the real time (t) of 20 s. The straight line EX indicates explosive. The white line SL corresponds to the light due to the detonation. The edge of the curve SW indicates the propagation of the underwater shock wave. Fig. 3 shows the x– t wave
Fig. 7. Value of coefficients k and h for radii R.
A. Kira et al. / Journal of Materials Processing Technology 85 (1999) 64–68
67
diagram obtained by processing the photographs of three different radii of explosive. In this figure, symbols indicate the results obtained by processing photograph in the case of each radii. The solid line indicates the numerical results, which are equivalent to the experimental results. The numerical results are in good agreement with the experimental results. The experimental data were approximated by the following equation, using a nonlinear curve fitting method [10].
distance r from the surface of the explosive is expressed by the next equation.
r = A1{1.0− exp(− B1t)} + A2{1.0 − exp( − B2t)}
u= kr+h
+ A3{1.0− exp(− B3t)} + C0t
(1)
where r is the distance to the radial direction from the surface of the explosive, C is the sound velocity of water (1490 m s − 1) and A1, A2, A3, B1, B2, B3 are coefficients obtained by using a nonlinear curve fitting method. Differentiating Eq. (1) with t, the propagation velocity of the underwater shock wave U =dr/dt is obtained. The relationships between the propagating velocity and the particle velocity u are described next equation. (2) Us = C0 +suP where s= 1.79. Using Eq. (2), the pressure P of the underwater shock wave is P− P0 = r0UsuP
(3)
where P0 is atmospheric pressure and r0 is the density of water (1000 kg m − 3). The comparison of the shock attenuation between the experimental results is obtained by using the above equations and the numerical results is shown in Fig. 4. A horizontal axis indicates the ratio of the distance R + r to the radius of the explosives R. The vertical axis indicates the pressure ratio P/P0. In this figure, circles, triangles and squares indicate the experimental results, while solid, broken and dash-dotted lines indicate the numerical results. Each result corresponds to R =10, 18 and 29 mm, respectively. As is obvious from this figure, the agreement between the experimental and the numerical results is very good. Therefore, taking streak photographs and carrying out numerical calculations is a suitable method to investigate the properties of underwater shock waves. The strength of the pressure decreases almost linearly as distance increases. This relationship is expressed by the next equation. P/P0 =a{(R+ r)/R} − b
P= Pr × e − t/u
(5)
where Pr is the maximum pressure at each distance r and u is a time constant and indicates inclination on the graph. Fig. 6 indicates the relationship between r and u. For every radius, the increases in u are nearly linear as r increases. (6)
where k and h are coefficients. The values k and h for R are plotted in Fig. 7, k and h increasing almost linearly as R increases. In this case, the following equation is obtained. k= 0.0041R+ 0.058
(7)
h= 0.093R+2.9 (8) It was found that using Eqs. (4)–(8), the pressure history at any position when the explosive was detonated is known.
4. Conclusions Underwater explosions of the spherical high explosives were investigated via optical measurements and numerical calculations. It has been concluded that taking streak photographs and carrying out numerical calculations are suitable methods of investigating the properties of underwater shock waves. It is also concluded that the strength of the underwater shock waves decreases exponentially with the increase of the distance from the explosives and the pressure histories, when the explosive were detonated in water, are known at any position.
Acknowledgements We wish to thank Y. Ishitani in the High Energy Rate Laboratory of Kumamoto University for his able assistance in obtaining the high speed photographs.
References
(4)
where a and b are coefficients; a =1.1 ×105, b = 1.8. Fig. 5 shows the pressure histories obtained by numerical calculation in the case of R =10 mm at intervals of 20 mm from the surface of the explosive. A horizontal axis indicates time t after completing the detonation and a vertical axis indicates the pressure P. The attenuation process of the pressure for the
[1] S. Itoh, M. Fujita, S. Nagano and K. Kamohara, Converging Underwater Shock Waves for Metal Processing, Shock Waves @ Marseille, vol.3, Springer, Berlin, 1993, pp. 289 – 294. [2] S. Itoh, S. Kubota, S. Nagano, K. Hokamoto, M. Fujita, A. Chiba, Characteristics of shock compaction assembly using converged underwater shock waves, first report, Trans. Jpn. Soc. Mech. Eng. 61 (588B) (1995) 217 – 222. [3] R.H. Cole, Underwater Explosions, Princeton University Press, Princeton, NJ, 1948.
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A. Kira et al. / Journal of Materials Processing Technology 85 (1999) 64–68
[4] H.M. Sternberg, W.A. Walker, Calculate flows and energy distribution following underwater detonating of a pentolite sphere, Phys. Fluid 14 (9) (1971) 1869–1878. [5] W.A. Walker, H.M. Sternberg, Proc. 4th Symp. on Detonation, White Oak, 1965, pp. 27. [6] M.L. Wilkins, B. Squire, B. Halperin, The equation of state of PBX 9404 and LX04-01, UCRL-7797, Lawrence Radiation Laboratory, Berkeley, CA, 1964. [7] N.L. Coleburn, L.A. Roshlund, Proc. 5th Symp. on Detonation, Pasadena, CA, 1970.
.
[8] A.A. Amsden, H.M. Ruppel, C.W. Hirt, Sale: A Simplified ALE Computer Program for Fluid Flow at All Speeds, LA-8095, UC-32, 1980. [9] M. Lee, M. Finger and W. Collins, JWL equation of state coefficients for high explosive, UCID-16189, Lawrence Livermore Laboratory, 1973. [10] P.R. Bervington, Data Reduction and Error Analysis for the Physical Sciences, Ch. 11, McGraw-Hill, New York, 1969.