A study on the behavior of underwater shock waves generated in a water container and its application to magnetic refrigeration material

Most of composite materials are made by sintering method. In this research, in order to make composite material for magnetic refrigeration, we carried out several experiments for the powder consolidation using the shock compaction method and numerical analysis for the behavior of underwater shock wave. The shock compaction method is to consolidate metal powder using underwater shock wave including an ultra-high pressure and high velocity generated by detonation of explosive. Generally, the magnitude of peak pressure and the pressure distribution of underwater shock wave depend on the inner shape of water container which is one of the parts of high pressure generating device. In this study, we have investigated several water containers using numerical analysis and observation experiments. Therefore, underwater shock wave is affected by the reflected wave generated from the wall of water container and the magnitude of reflected wave depends on the inner angle θ of water container. The pressure and velocity of reflected wave is gradually increased with increasing inner angle θ of water container.


INTRODUCTION
Recently, interest in magnetic material which exhibits a ferromagnetic property near room temperature has been increasing in order to realize the magnetic refrigeration.Most of magnetic materials are made by the sintering methods. [1,2]In this study, a shock compaction method which uses an underwater shock wave generated by the detonation of explosive is used.The shock compaction method has an advantage such as the grain size of metal powder can be minimized because of ultra-high pressure and high velocity.[5] Therefore, in order to consolidate the magnetic metal powder, we have carried out the consolidating experiments using ultra-high pressure generation devices.The ultra-high pressure generation device is composed of several parts; electric detonator, explosive lens, explosives, explosive container and water container.The most important part is the water container, because the pressure distribution and pressure magnitude of underwater shock wave absolutely depend on the inner shape of water container.Accordingly, the purpose of this research is to propose an optimal model of water container designed by numerical analysis.

ULTRA-HIGH PRESSURE GENERATION DEVICE
The ultra-high pressure generation device used in this study is shown in figure 1.The main parts are composed of an explosive container, water container and powder container.Explosive, water and magnetic powder are set in each container.The main explosive is SEP which made of PETN(65wt.%)and paraffin (35wt.%),detonation velocity of 6970m/s and C-J pressure of 15.9GPa produced by Asahi chemical Co. Ltd, Japan. [ 6]gure 1 The schematic of the ultra-high pressure generation device The explosive lens that is composed of SEP and HABW (detonation velocity; 4500m/s and density; 2200kg/m 3 produced by Asahi-Kasei Chemicals Corp) is set on the top of the main explosive to make a planar wave.Explosion is started from detonator and the detonation wave generated by explosive propagated into the water container which creates underwater shock wave of high pressure.High velocity occurs in the water container.

NUMERICAL ANALYSIS FOR THE WATER CONTAINER
In order to make a good consolidated bulk material, a planar wave on the top surface of powder is necessary.The pressure distribution and pressure magnitude of underwater shock wave depend on the inner shape of the water container.Therefore a series of phenomenon for the explosion and propagation of underwater shock wave is evaluated by means of LS-DYNA 3D (commercial program based on the explicit finite element code).The numerical simulation model is shown in figure 2. The simulation model is modeled as quarter of circle.In boundary condition, initial velocity is 1711m/s as particle velocity of explosive and we applied the constrained condition for the x, y, and z axis so that translational and rotational motions can not happen when explosion is occurring.The materials on the both sides of the surface are distinguished as master and slave, respectively.In the selection of the salve and master part, the material with greater density is chosen as the master.A null material model for water is applied and an elastic-plastic hydrodynamic material model for each container is used.In the case of powder material, it's modeled as a part of null material because we just need the distribution and magnitude of pressure of underwater shock wave impinged on the top surface of powder.The C-J detonation process of explosive is modeled using 'C-J volume burn' method.Water container models, straight type, convex type and concave type, for numerical simulation are shown in figure 3.

JONES-WILKINS-LEE EQUATION OF STATE
JWL equation of state is applied for the explosive.JWL coefficients and the main C-J characteristic values are given in Table 1.JWL equation of state is as follows; [7] (1) A, B, C, R 1 , R 2 and ω are the constants for a given explosive.P JWL is pressure, e is the specific internal energy, and V is ρ 0 /ρ g (Initial density of an explosive divided by the density of detonation gas).

C-J VOLUME BURN & MIE-GRUNEISEN EQUATION OF STATE
In order to resolve the reaction occurred in high explosive, 'C-J volume burn' model is applied. [23]When the volume of the cell of the original explosive in the calculation becomes equal to the volume of the detonation products at Chapman-Jouguet (C-J) state, the solidphase explosive is assumed to be completely decomposed into the gaseous products.If V 0 express the initial volume of explosive, V C J is the volume of the detonation products at the C-J state.The reaction rate of the explosive is simply expressed as follows; ( (3) Decomposition rate W of the explosive has values from 0 to 1. P JWL is the pressure of detonation products of the completely reacted explosive and can be obtained from JWL equation.P is assumed to be equal to that of the detonation products of the partly reacted explosive over the whole cell.Metal materials concerned with numerical simulation are applied to be elastic-plastic-hydrodynamic material comply with the von Mises yield criterion for the distinction of elastic and plastic phases.Accordingly, Mie-Gruneisen equation of state is applied and it's given as follows; (4)

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A study on the behavior of underwater shock waves generated in a water container and its application to magnetic refrigeration material η: 1 -ρ(Initial density of the medium) / ρ(Density of the medium) P: Pressure e: Specific internal energy C, s: Cons tant of material Γ : Grüeisen coefficient The parameters of water and SUS304 stainless steel for container are shown in table 2.

NUMERICAL SIMULATION RESULTS
We have analyzed several water containers to obtain a good pressure distribution and proper pressure magnitude of underwater shock wave impinging on the top surface of powder.The underwater shock wave propagation on the top surface of the powder for each water container is shown in figure 4. When a detonation wave occurred due to the explosion by explosive enters the water, the underwater shock wave is created and then a reflected wave occurs from the wall of the container and converges at the middle point, creating ultra high pressure.
Figure 4 The propagation phenomenon of underwater shock wave for each water container   The peak pressure profiles of underwater shock wave impinged on the top surface of powder obtained at the central position (A), middle position (B), near wall position (C) are shown in figure 5.In the straight type case, the reflected wave is small compared to the detonation wave, and the duration time of pressure acting on the top surface of the powder is longer than other models.Whereas, the pressure magnitude is lower.In case of convex type, the distribution of peak pressures for each position is better than that of other models, and we found that it has the proper pressure magnitude to consolidate the magnetic powder.In the case of concave type, it has a large volume in comparison with convex type.Although the inner angle θ of water container is small, the pressure magnitude is higher than that of convex type.Accordingly, it can be confirmed that the pressure magnitude of underwater shock wave is related to the shape of water container.Figure 6 shows pressure distribution diagrams for each water container.The detonation of the explosive generates a shock wave in the water.This underwater shock wave is modified by the shape of the water container. The reflected wave continues through the center line decreasing from ultra high pressure.Finally, the reflected wave and underwater shock wave are united and impinge on the top surface of the powder at about t=12µs.The pressure magnitude of reflected wave at the central portion of the water container is increased with   19.4GPa at the middle position (B) and 15.1GPa at the wall (C). Figure 7 is represented the pressure magnitude and velocity change at the central position along with axis direction in the water container in the convex type.It's considered that the gathering of reflected wave in the middle position of water container occurred between 8 and 9 µs.At 9 µs, the peak pressure of reflected wave is decreased whereas, the velocity of reflected wave is gradually increased after 10 µs.We confirmed that the velocity of underwater shock wave is not affected by reflected wave until the moment the reflected wave is converged in the middle position.

OBSERVATION EXPERIMENT OF UNDERWATER SHOCK WAVE
The observation experiment is carried out to observe the behavior of underwater shock wave and the reflected wave in the water to verify numerical analysis results.The test device is a planar symmetric setup to allow viewing the shock wave.The test device is set in the explosion chamber and a high-speed camera system, IMACON 468(Hadland Photonics), is equipped with Xenon Flash for observation.The start of the photography is controlled by ionization wire probes inserting into the test device which can be connected with trigger.The schematic of observation experiment system is shown in figure 8. [10] Figure 9 shows the comparison between result of numerical analysis and framing photograph of underwater shock wave in the case of convex type.Based on validation of simulation by the experiment of 2D type, the 3D model should also be sufficient to simulate the shock wave in the axisymmetric water container.

MEAN PEAK PRESSURE MEASUREMENT
In order to check the peak pressure of underwater shock wave, we carried out the pressure measurement experiment using manganin gauge as designed by Mashimo et al. [11] Figure 10 shows the mean peak pressure of underwater shock wave obtained from the experiment and numerical analysis.The mean peak pressure for the experiment and numerical analysis is 16.8GPa and 17.9GPa, respectively.The difference is similar to the measurement error of 1GPa, confirming the ability of the numerical analysis to predict the pressure in the water container.
Figure 10 Comparison between mean peak pressure of numerical analysis and real experiment for the underwater shock wave impinged on the top surface of powder

APPLICATION TO CONSOLIDATING EXPERIMENT
We have carried out the experiment for the metal powder consolidation based on the results of numerical analysis.The metal powders used in this study are MnSi 4 Fe 3 and La Co 0.7 Si 1.1 Fe 11.2. Figure 11 shows the cross sectional photographs of the consolidated bulk materials.We found that the consolidation using underwater shock wave is good and also confirmed that the grain size is similar to the starting powder.

CONCLUSION
We have analyzed several water containers, one of the parts of the ultra-high pressure generation device, using numerical analysis and verified it through the experiment.We found that the velocity and pressure of underwater shock wave is affected by the reflected wave generated from wall and the magnitude of reflected wave is increased with increasing inner angle θ of water container.Also, the pressure magnitude of underwater shock wave is related to the shape of the water container.We confirmed that the grain size of the initial powder is maintained in the consolidated bulk material.In case of convex type, the distribution of peak pressures for each position is better than that of other models.Lastly, the experimental and numerical mean peak pressure is 16.11GPa and 16.07GPa, respectively.

Figure 2 Figure 3
Figure 2 Numerical simulation model

Figure 5
Figure 5 Peak pressure of underwater shock wave impinged on the top surface of powder for each water container

Figure 6
Figure 6 Pressure distribution diagrams of underwater shock wave impinged on the top surface of powder for each water container

Figure 7
Figure 7 Pressure magnitude and velocity change of reflected wave at the central position along with axis direction in the water container in the convex type

Figure 8 Figure 9
Figure 8 Schematic of observation measurement system Framing photographs of underwater shock wave 10 µs 11 µs (a) Pressure diagram of underwater shock wave

Figure 11
Figure 11 Consolidated bulk materials using shock compaction method

Table 1
JWL coefficients and C-J values of SEP

Table 2
Mie-Gruneisen parameter of water and SUS304