SPH simulation on the behaviors of projectile water entry
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摘要: 应用SPH方法研究弹丸入水过程中的动力学特征。利用拉格朗日形式的N-S方程自编SPH程序，建立弹丸入水的计算模型，赋予相应的材料参数及状态方程，研究弹丸外形、入水速度和角度等因素对入水过程的影响。模拟结果表明：空化泡的形态及发展规律主要由弹丸的运动姿态决定；弹道越稳定，阻力因数就越小，弹丸的存速就越大。SPH方法具有较强的自适应性，适用于研究弹丸入水的流固耦合问题。Abstract: In this work we investigated the dynamic behaviors of the projectile water entry using the SPH method. We developed our own SPH program based on the N-S equation of the Lagrange form and established a calculation model for the projectile water entry and, with corresponding material parameters and equation of state given, studied the influence of such factors as projectile shape, velocity and angle into the water on the process of the projectile water entry. The simulation results show that the formation and the development of the cavitation bubble are mainly determined by the projectile's state of motion: the more stable the projectile's trajectory, the smaller its drag coefficient, and the greater its sustained velocity. It is found that the SPH method has a high self-adaptability, for which it is applicable for studying the problems related with fluid-structure interaction occurring during the process of the projectile water entry.
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Key words:
- fluid mechanics /
- underwater trajectory /
- SPH /
- drag coefficient
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图 1 弹丸外形及入水示意图
Figure 1. Schematic diagram of the projectile shape and projectile entry into the water
2a 尖头弹丸入水的空化泡形状发展(θ=90°)
2a. Shape formation of cavitation bubble during the cuspidal projectile entry into the water (θ=90°)
2b 尖头弹丸入水的空化泡形状发展(θ=60°)
2b. Shape formation of cavitation bubble during the cuspidal projectile entry into the water (θ=60°)
2c 尖头弹丸入水的空化泡形状发展(θ=30°)
2c. Shape formation of cavitation bubble during the cuspidal projectile entry into the water (θ=30°)
图 3 尖头弹丸的入水轨迹(v0=1200m/s，θ=60°)
Figure 3. Trajectory of cuspidal projectile entry into the water (v0=1200m/s, θ=60°)
图 4 平头弹入水运动轨迹(v0=1200m/s，θ=90°)
Figure 4. Trajectory of blunt projectile entry into the water (v0=1200m/s, θ=90°)
5a 弹丸入水过程中的弹道轨迹(θ=90°)
5a. Ballistic trajectory of projectile during the process of entry into the water (θ=90°)
5b 弹丸入水过程中的弹道轨迹(θ=60°)
5b. Ballistic trajectory of projectile during the process of entry into the water (θ=60°)
5c 弹丸入水过程中的弹道轨迹(θ=30°)
5c. Ballistic trajectory of projectile during the process of entry into the water (θ=30°)
图 6 弹丸入水的速度变化规律
Figure 6. Profile of the velocity variation during the projectile entry into the water
表 1 Mie-Grüneisen状态方程的材料参数
Table 1. Material parameters of Mie-Grüneisen equation of state
ρ0/(kg·m-3) c/(m·s-1) γ0 S1 S2 S3 a 1000 1480 0.5 2.56 1.986 1.227 0 
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