Visualization of High-Speed Impact of Projectile in Granular Sheet with Destructive Collision of Particles

The impact and penetration of a projectile in a particle-laden space, which are expected to have frequently occurred during the formation of the solar system and will occur in the case of an impact probe for future planetary exploration, were experimentally simulated by using the ballistic range. A two-dimensional sheet made from small glass beads or emery powder was formed by the free-falling device through a long slit in the test chamber evacuated down to about 35 Pa. A polycarbonate projectile of a hemisphere-cylinder or sphere shape with the mass and diameter about 4 g and 25 mm, respectively, was launched at the velocity up to 430 m/s, and the phenomena were observed by the high-speed camera at 20,000 fps. From a series of images, the bow-shock-wave-like laterally facing U-shaped pattern over the projectile and the absence of particles in the trail behind it were clearly seen. At the impact of the particles on the projectile surface, fine grains were formed due to the destructive collision and injected outward from the projectile. The images obtained by different lighting methods including the laser light sheet were compared. The effects of the particle diameter, its material and the impact velocity were also investigated.


Introduction
Impact in a particle-laden space in a vacuum is not an unusual event.For example, it is well known that the destruction and aggregation of objects at the impact played an important role during the formation of the solar system [1].An artifi-cial impact is expected to reveal the interior structure of a celestial object at the lunar and planetary exploration.In HAYABUSA 2 mission conducted by the Japan Aerospace Exploration Agency (JAXA), the impactor is planned to hit the surface of the asteroid Ryugu [2] for the in-situ observation of its interior structure.To reveal the mechanism of the phenomena in such cases, the fundamental understanding about the impact in a particle-laden space is essential.
When the particles are packed in the space, the dynamics of their motions has been intensively and extensively investigated in the field of the terra-dynamics.
The numerical method using virtual particles called DEM (Discrete Element Method) [1] [3] is known to appropriately simulate the behavior of the granular material both microscopically and meso-scopically.From a macroscopic viewpoint, the fluid-dynamics-like model is expected to work well.For example, the compressible and non-expanding fluid model successfully describes the nature of irreversible compression of granular materials [4].
When the particles at the undisturbed state are separately located at some distance, the situation seems similar to the rarefied gas dynamics with relatively large mean free path.In the presence of the atmosphere, various studies have been numerically and experimentally conducted in the framework of the two-phase flow.For example, the combination of the Eulerian description of the dynamics of the fluid and the Lagrangian description of the motion of the floating solid particles is known to reasonably simulate the dusty flow around a body at a supersonic speed [5].The phenomena around a circular cylinder in the stream of small spheres rolling down the slope of an inclined flat plate were experimentally observed, assuming that the aerodynamic force acting on the particles is negligible in comparison with the force due to collisions [6].In most of the studies made so far, the destructive collision, which may frequently occur at the high-speed impact, was not taken into account.Considering the application to the planetary science or planetary exploration engineering mentioned above, the impact velocity is expected to be high, and the fundamental understanding about the phenomena involving the destructive collision into finer grains is necessary based on the experimental study in the absence of the atmosphere.
In the present experimental study, a body was shot into a particle-laden space as seen in [3].For convenience of observation and simplicity of analysis, we experimentally simulated the two-dimensional on-plane impact and penetration of a projectile in a sheet of particles.A projectile with the diameter much larger than that of the particle was launched by the ballistic range in the direction on the plane of the granular sheet, which was formed by the free-falling device through a narrow slit [7] [8] in the low-pressure test chamber.The phenomena were observed by the high-speed camera in the direction normal to the particle sheet, as illustrated in Figure 1.It should be noted that the visualized image strongly depends on the lighting method.The images were obtained by various lighting methods including the laser light sheet.The effect of the experimental condition was investigated with respect to the impact velocity, the diameter of particles and the material of the particles.The major objectives in the present study are 1) to reveal the characteristic features of the granular flow around a projectile penetrating on the sheet of particles, 2) to clarify the presence of the destructive collision of particles at the projectile surface and its role in the granular flow field, and 3) to investigate the effect of the impact velocity, the diameter and the material of particles.

Ballistic Range and Particle Sheet Generator
The ballistic range in the authors' laboratory [9] shown in Figure 2    projectile was launched and penetrating on the particle sheet in this period.The projectile was finally caught in a semi-hard-landing manner by the projectile catcher made from the sponge layer and the oil clay.
As discussed later, the obtained image strongly depends on the lighting method and the viewing area of the camera.We used three types of arrangement of the lighting and viewing area of the camera as shown in Figure 4.The arrangement (a) was selected as the nominal setting and was used to observe the phenomena both just after the impact of the projectile and during the penetration on the particle sheet.The back-lighting was selected for clearness of the obtained Journal of Flow Control, Measurement & Visualization image.After the penetration proceeded for some distance, the granular flow field around a projectile is expected to be in a steady state.The arrangement (b) was used for the observation after long penetration.We have to be careful to judge the presence of matter from a visualized image, because the dark image can be produced by not only the absence of matter but also the absence of light.To reduce the risk of misunderstanding, the arrangement (c) with the front-lighting was tested and compared with the arrangement (a).For the lighting, the high-intensity metal halide lamp MID-25 FC (Lighterrace Inc.) with the maximum power 250 W was used.To capture the images of the impact phenomena, the high-speed monochrome camera Phantom Miro 310 (Nobby Tech.Ltd.) was used.The sensitivity is 12 bit.The frame rate, exposure time and the spatial resolution were set to be 20,000 fps, 1 μs and 512 by 256 pixels, respectively, in the present experiment.

Particles and Projectiles
Three types of the glass beads (Types #40, 60 and 80) with different size were used for the particle sheet.They are originally supplied as the grinding powder with the particle size controlled under the industrial standard, that is, 355 -500 μm for Type #40, 250 -355 μm for #60 and 180 -250 μm for #80.The magnified image of the particles by the microscope showed that the shape of a glass bead was not a smooth sphere but a rugged irregular ball [7] [8].In addition to the glass beads, the emery powder with the particle size about 400 μm was used for the particle sheet.The emery powder is mainly made from the aluminum oxide Journal of Flow Control, Measurement & Visualization and iron oxide and is harder than the glass beads.The difference in the hardness of the particle is expected to change the nature of the destructive collision at the projectile surface and to affect the behavior of the granular flow around a body.
In the case of type #40 glass beads, the number density of the particles was estimated as 5 × 10 8 1/m 3 from the mass flow rate through the slit [7].The falling speed of the particles was estimated as about 3 m/s from two continuous snapshots and the frame rate [7].It was negligible in comparison with the flight velocity of the projectile.
Two types of the projectile shapes were tested, that is, the hemisphere cylinder and the sphere, as shown in Figure 5.Both types of the projectiles were made from the polycarbonate for its strength and low mass.The diameter of the body was 25.75 mm, which is the same as the inner diameter of the acceleration tube.
Consequently, the projectile was launched without the sabot by the ballistic range.Such launch method without the sabot enables us to avoid significant disturbance added to the trajectory and attitude of the projectile at the sabot separation [9].To obtain a high velocity from the ballistic range, the projectile mass was reduced by the hollow structure with the thickness 2 mm.The average mass of the hemisphere cylinder model and the spherical model is about 3.9 g and 4.3 g, respectively.

Uncertainty and Repeatability of Experimental Results
The projectile velocity was estimated from the frame rate and the difference in the projectile position between two continuous snapshots.The uncertainty in the estimated velocity was mainly caused by the blur of the projectile image in the exposure time [9], and it was less than 5%.
Thanks to the launching of the projectile without the sabot, the uncertainty in the flight condition was relatively small.The free flight of the projectile before reaching the edge of the particle sheet was stable.The fluctuation in the velocity and the path angle during the free flight was smaller than ±10 m/s and ±1.5 degrees, respectively [7].The repeatability of the particle sheet generator was good

Two-Dimensionality of Phenomena
The present experimental setup was designed under the assumption that the motion of the particles mainly occurs on the plane of the particle sheet, because the plane of symmetry of a projectile coincides with that of the sheet.To confirm that, the setup of the lighting and the camera shown in Figure 6(a) was additionally tested.Thanks to the mirror put in front of the projectile catcher, the oblique frontal view of the projectile was obtained.The cloud seems to expand more in the vertical direction than in the horizontal direction.These pictures imply that the granular motion on the particles sheet was more significant than the out-of-plane motion.The fine grains were produced by the destructive collision of the particle sheet at the projectile surface.
Though the flight velocity cannot be estimated from the oblique view, it was expected to be about 370 -380 m/s from the experimental data of the spherical projectile at the same pressure of 0.6 MPa charged at the breech of the ballistic range.
To check the two-dimensionality of the phenomena, the visualization using the laser light sheet was also conducted.Two types of the laser light sheets, that is, the horizontal sheet and the vertical sheet, were tested as shown in Figure 7(a) and   contrast.In both pictures, the projectile moved from left to right, and the cross section curve of the projectile surface was clearly seen.Though the projectile velocity could not be estimated because of unclear images, it was expected to be about 400 m/s from the experiments in the similar condition.This fact indicated that the out-of-plane granular flow was not so significant to fully cover the projectile surface.
Consequently, the two-dimensional behavior of the particles and fine grains around a projectile was expected to be visualized in the present experimental setup as illustrated in Figure 1.

Formation of Granular Flow Field around a Projectile
The typical pattern of a snapshot taken by the back-lighting arrangement (a) in The above features were commonly observed in both cases of the sphere model and the hemisphere cylinder model.However, the diffusion of the fine grains into the trail was much weaker in the case of the hemisphere cylinder model as shown in Figure 9.This was expected to be caused by the presence of the sharp corner at the rear end of the body as pointed out in [8].This fact indicates that the properties of the fine grains produced from the glass beads at the collision with the projectile surface depend on the initial particle size.

Effect of Particle Size, Material and Impact Velocity
The effect of the material of the particle sheet on the granular flow field around a hemisphere cylinder model is shown in Figure 12, where the images taken at 0.15 ms after the impact with the sheet of the glass beads #40 and that of the emery powder are compared.The images were intensified by 20% in the brightness and contrast.The impact velocity is almost the same for both cases at about 440 m/s.The formation of the laterally facing U-shaped fine grain zone and the zone of absence of the particles or fine grains behind projectile was clearly seen in both cases.The dark zone in the laterally facing U-shaped structure becomes narrower for the emery powder than for the glass beads.This fact indicates that the properties of the fine grains formed at the particle collision at the projectile surface also depend on the particle material.
Finally, the effect of the impact velocity was shown in Figure 13  ing U-shaped layer of the fine grains was seen in front of the projectile than at the velocity 330 m/s.In addition, the luminous zone of the fine grain layer in front of the projectile becomes wider in the case of higher impact velocity.The mass flux of the colliding glass beads increases with the impact velocity and the destruction of the colliding glass beads becomes more significant at higher impact velocity.The velocity of the fine grains injected in the forward direction at the projectile surface is expected to increase with the impact velocity.As a result, higher production rate and higher injection velocity of the fine grains are obtained at higher impact velocity.Consequently, the zone of the fine grains spreads more quickly in front of the projectile at higher velocity.

Conclusions
The impact and penetration of a projectile in a particle-laden space were experimentally investigated by using the ballistic range.A thin sheet made from small glass particles or emery powder was formed by the free-falling device through a long slit over the trajectory of a projectile in the test chamber.A polycarbonate projectile of a hemisphere cylinder or sphere shape with the mass and diameter about 4 g and 25 mm, respectively, was launched at the velocity from 310 m/s to 430 m/s.The phenomena were observed by the high-speed camera at 20,000 fps.To reduce the effect of the flow of the residual air in the test chamber, it was evacuated beforehand.From the obtained images using various lighting and camera arrangement including the laser light sheet, the two-dimensionality of the phenomena was discussed.The bow-shock-wave-like laterally facing U-shaped pattern in front of the projectile and the zone of absence of the particles or fine grains in the trail behind it were clearly observed in the pictures.The process of the formation of the granular flow field around a projectile was characterized by the destructive collision of the glass beads into fine grains at the projectile surface, the removal of the particles or fine grains behind the projectile by the sweeping effect, the shock-wave-like propagation of the laterally facing U-shaped zone of the fine grains in front of the projectile, and the diffusion of the fine grains into the trail of the projectile.The similar pattern was observed irrespectively to the projectile velocity, the size and material of the particles.However, the production rate and the spread speed of the fine grains depend on these conditions.The above results suggest that the present phenomena can be numerically simulated by the model including the appropriate description for the motion of the original particles, the formation of the fine grains at the projectile surface and the flow of the fine grains.The numerical analysis using such model is expected to be quite useful for understanding of the formation of the celestial objects in the solar system, designing the impact probe for planetary exploration in the future and so on.

Figure 1 .
Figure 1.Schematic view of experimental setup.
was used for the present experiments.It can launch a projectile with the mass about 5 g at a speed up to about 500 m/s, depending on the charged pressure in the high-pressure chamber (breech) at 0.4 MPa to 0.8 MPa[7].Before the shot, the projectile was inserted at the rear end of the acceleration tube with the length 6 m.The muzzle of the acceleration tube was open to the test chamber without the diaphragm.The test chamber and the acceleration tube were evacuated down to about 35 Pa to reduce the effect of the residual air as much as possible.The photo of the test chamber interior is shown in the inset of Figure2.The particle sheet generator was set above the trajectory of the projectile launched from the muzzle.The particle sheet generator was composed of the particle reservoir having the triangular cross section and the narrow slit with the width and length 2 mm and 600 mm, respectively, at the bottom of the reservoir.The long lid was set at the exit of the slit.It opened by receiving the electric signal from the outside of the test chamber.As shown in Figure3, almost the uniform particle sheet was generated before the impact of the projectile by the present device except the local clustering of the particles, which became more evident for the case of smaller particles.The sheet of free falling particles continued for about 10 s.The

Figure 2 .
Figure 2. Photos of ballistic range facility and test chamber interior.

Figure 3 .
Figure 3.Snapshot of particle sheet before impact of a sphere model with exposure time 1 μs.

Figure 4 .
Figure 4. Arrangement of lighting and viewing area of camera (top view of test chamber).

Figure 5 .
Figure 5. Hemisphere cylinder model and sphere model used for a projectile.

Figure 6 (
Figure 6(c) were intensified by enhancing the brightness and contrast by 20% using the image processing function of Microsoft  Power Point  2008 for Mac.

Figure 7 (
b), respectively.For the light source, Kentech model LDB2W blue laser was used.The maximum power, the wave length and the width of the laser sheet were 2 W, 450 nm and 2 -3 mm, respectively.If the granular flow around the projectile had a significant three-dimensional out-of-plane structure, the laser light sheet would be scattered by the presence of the thick cloud of the particles and fine grains, and the cross section curve of the projectile surface could not be visualized by the laser light sheet.Figure8(a) and Figure 8(b) show the snapshots of the sphere model in the horizontal and vertical laser light sheets, respectively.These images were intensified by 20% in the brightness and Journal of Flow Control, Measurement & Visualization

Figure 6 .
Figure 6.Oblique frontal view of motion of a sphere model and granular flow around it.(a) Setup of lighting and camera view; (b) Snapshot just after impact of projectile at edge of particle sheet; (c) Snapshot at 0.1 ms after impact.

Figure 4 Figure 9 .
Figure 4 is shown in Figure 9(a).The particle sheet was made from the grass beads #40.The hemisphere cylinder model was used for the projectile, moving from left to right in the picture.The projectile velocity was estimated as 436 m/s.The snapshot was taken at 0.2 ms after the impact at the edge of the particle sheet.The bow-shock-wave-like laterally facing U-shaped structure over the projectile and the dark zone in its trail are clearly seen.The motion of the particles in the other area seems undisturbed in the picture.The dark zone behind the body indicates the absence of the particles due to the sweeping effect of the

Figure 11
Figure11shows the effect of the particle size on the granular flow field around a sphere model.The images were intensified by 20% in the brightness and contrast.The images obtained in the particle sheet of the grass beads #40 (coarse), #60 (medium) and #80 (fine) are compared.The picture of the glass beads #80 is the same as the snapshot 4 in Figure10.Qualitatively, these patterns seem almost the same.However, the region behind the projectile was more significantly . The hemisphere cylinder model and the glass beads #40 were used for the projectile and the Journal of Flow Control, Measurement & Visualization

Figure 12 .Figure 13 .
Figure 12.Effect of particle material on formation of granular flow field around a hemisphere cylinder model.(a) Glass beads #40; (b) Emery powder.