Figure 1.
Schematic diagram of the Varas test device.
Figure 1.
Schematic diagram of the Varas test device.
Figure 2.
(a) Local magnification diagram of the simulation model. (b) The simulation model of the Varas test.
Figure 2.
(a) Local magnification diagram of the simulation model. (b) The simulation model of the Varas test.
Figure 3.
(
a) Pressure nephogram of the shock wave in water. (
b) Sectional view on the
xoz plane. (
c) Picture captured by a high-speed camera in Varas test [
9].
Figure 3.
(
a) Pressure nephogram of the shock wave in water. (
b) Sectional view on the
xoz plane. (
c) Picture captured by a high-speed camera in Varas test [
9].
Figure 4.
The simulation model of the debris impacting the satellite tank at the velocity of 7000 m/s; the right side is the model cut in half.
Figure 4.
The simulation model of the debris impacting the satellite tank at the velocity of 7000 m/s; the right side is the model cut in half.
Figure 5.
The velocities of debris at different times obtained by the simulation results.
Figure 5.
The velocities of debris at different times obtained by the simulation results.
Figure 6.
The pressure nephogram of the shock wave in the satellite tank at 53 μs, 125 μs, 160 μs, and 248 μs.
Figure 6.
The pressure nephogram of the shock wave in the satellite tank at 53 μs, 125 μs, 160 μs, and 248 μs.
Figure 7.
Pressure–time curves from element A to element G.
Figure 7.
Pressure–time curves from element A to element G.
Figure 8.
(a) Perforation and bulge on the front wall. (b) Perforation and bulge on the back wall.
Figure 8.
(a) Perforation and bulge on the front wall. (b) Perforation and bulge on the back wall.
Figure 9.
Curves of the bulge height varying with distance on the front and back walls.
Figure 9.
Curves of the bulge height varying with distance on the front and back walls.
Figure 10.
Simulation models of the satellite tanks with liquid-filling ratios of 70%, 80%, and 90%.
Figure 10.
Simulation models of the satellite tanks with liquid-filling ratios of 70%, 80%, and 90%.
Figure 11.
Stress–time curves of element H on the front wall with liquid-filling ratios of 70%, 80%, 90%, and 100%.
Figure 11.
Stress–time curves of element H on the front wall with liquid-filling ratios of 70%, 80%, 90%, and 100%.
Figure 12.
Stress–time curves of element I on the back wall with liquid-filling ratios of 70%, 80%, 90%, and 100%.
Figure 12.
Stress–time curves of element I on the back wall with liquid-filling ratios of 70%, 80%, 90%, and 100%.
Figure 13.
Front and back perforations caused by the debris impacting the satellite tank with angular velocities of wx = 5 rad/μs, wy = 5 rad/μs, and wz = 5 rad/μs.
Figure 13.
Front and back perforations caused by the debris impacting the satellite tank with angular velocities of wx = 5 rad/μs, wy = 5 rad/μs, and wz = 5 rad/μs.
Figure 14.
Debris trajectory when the debris penetrated the satellite tank with the angular velocities of wx = 5 rad/μs, wy = 5 rad/μs, and wz = 5 rad/μs.
Figure 14.
Debris trajectory when the debris penetrated the satellite tank with the angular velocities of wx = 5 rad/μs, wy = 5 rad/μs, and wz = 5 rad/μs.
Figure 15.
Flow patterns for liquid hydrazine past the debris without rotation (a) and the debris with rotation (b).
Figure 15.
Flow patterns for liquid hydrazine past the debris without rotation (a) and the debris with rotation (b).
Figure 16.
Front and back perforations caused by the impact of debris with angular velocities of wx = 0.01 rad/μs, 0.05 rad/μs, 0.1 rad/μs, 0.5 rad/μs, 1 rad/μs, 2 rad/μs, 3 rad/μs, and 4 rad/μs.
Figure 16.
Front and back perforations caused by the impact of debris with angular velocities of wx = 0.01 rad/μs, 0.05 rad/μs, 0.1 rad/μs, 0.5 rad/μs, 1 rad/μs, 2 rad/μs, 3 rad/μs, and 4 rad/μs.
Figure 17.
Attenuation curves of the translation velocity when the debris impacted the satellite tank with angular velocities of wx = 0.01 rad/μs, wx = 0.05 rad/μs, wx = 0.1 rad/μs, wx = 0.5 rad/μs, and wx = 1 rad/μs.
Figure 17.
Attenuation curves of the translation velocity when the debris impacted the satellite tank with angular velocities of wx = 0.01 rad/μs, wx = 0.05 rad/μs, wx = 0.1 rad/μs, wx = 0.5 rad/μs, and wx = 1 rad/μs.
Figure 18.
Front and back perforations caused by the impact of debris with angular velocities of wy = 1 rad/μs, wy = 2 rad/μs, wy = 3 rad/μs, wy = 4 rad/μs, and wy = 5 rad/μs.
Figure 18.
Front and back perforations caused by the impact of debris with angular velocities of wy = 1 rad/μs, wy = 2 rad/μs, wy = 3 rad/μs, wy = 4 rad/μs, and wy = 5 rad/μs.
Figure 19.
Attenuation curves of the translation velocity when the debris impacted the satellite tank with angular velocities of wy = 1 rad/μs, wy = 2 rad/μs, wy = 3 rad/μs, wy = 4 rad/μs, and wy = 5 rad/μs.
Figure 19.
Attenuation curves of the translation velocity when the debris impacted the satellite tank with angular velocities of wy = 1 rad/μs, wy = 2 rad/μs, wy = 3 rad/μs, wy = 4 rad/μs, and wy = 5 rad/μs.
Table 1.
Material parameters of the water and air.
Table 1.
Material parameters of the water and air.
Material | ρ (kg/m3) | S1 | S2 | S3 | γ0 | C4 | C5 |
---|
Water | 1000 | 1.979 | 0 | 0 | 0.11 | — | — |
Air | 1.29 | — | — | — | — | 0.4 | 0.4 |
Table 2.
Material parameters of the aluminum and steel.
Table 2.
Material parameters of the aluminum and steel.
Material | ρ (kg/m3) | A (MPa) | B (MPa) | n | C | m |
---|
Aluminum | 2700 | 200 | 144 | 0.62 | 0.01 | 1.00 |
Steel | 7830 | 496 | 434 | 0.307 | 0.008 | 0.804 |
Table 3.
Cavity diameter in the simulation results and test results.
Table 3.
Cavity diameter in the simulation results and test results.
t (μs) | x (cm) | ds (mm) | de (mm) | ε/% |
---|
84 | 1.5 | 35.1 | 33.12 | 5.9 |
5.0 | 20.3 | 19.4 | 4.6 |
140 | 2.0 | 43.5 | 41.9 | 3.8 |
7.5 | 28.9 | 28.2 | 2.5 |
Table 4.
Materials parameters of liquid hydrazine.
Table 4.
Materials parameters of liquid hydrazine.
Material | ρ (kg/m3) | Cl (m/s) | S1 | S2 | S3 | γ0 |
---|
Liquid hydrazine | 1008 | 1500 | 1.979 | — | — | 0.11 |
Table 5.
Material parameters of titanium.
Table 5.
Material parameters of titanium.
Material | ρ (kg/m3) | E (GPa) | υ | σs (MPa) | σb (MPa) |
---|
Titanium | 4500 | 118 | 0.34 | 820 | 890 |
Table 6.
Perforation diameters and bulge heights at different liquid-filling ratios.
Table 6.
Perforation diameters and bulge heights at different liquid-filling ratios.
Deformation (cm) | 100% | 90% | 80% | 70% |
---|
Diameter of front perforation | 10.23 | 9.46 | 9.20 | 9.08 |
Diameter of back perforation | 6.90 | 6.24 | 5.51 | 5.05 |
Bulge height on front wall | 1.12 | 0.99 | 0.79 | 0.71 |
Bulge height on back wall | 1.58 | 1.45 | 1.33 | 1.29 |