Similarity relations of underwater explosion in centrifuge and pressurizing vessels
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摘要: 水下爆炸冲击波和气泡脉动的共同作用不能仅依据几何相似条件进行模型试验，相关的尺寸缩比模型试验可以借助密闭加压罐或离心机进行。通过量纲分析和π定理对模型试验的相似理论进行了推导，分别探讨了密闭加压容器和离心机中水下爆炸的相似关系及其适用范围，并对原型工况和尺寸缩比为1/20和1/30的模型工况基于LS-DYNA进行了数值模拟。结果表明：加压模型试验中水下爆炸冲击波、气泡脉动半径和周期可以满足相似关系，但是气泡迁移和射流不符合相似关系；离心模型试验中水下爆炸冲击波和气泡脉动基本完全相似。Abstract: The collective effect of underwater explosion shock wave and bubble pulsation does not meet the traditional geometric similarity relation, and the scaled model test must be carried out in a closed pressurized tank or centrifuge apparatus. Through the dimensional analysis and π theorem, the similarity theory of the model tests was deduced. The prototype condition and model conditions with the scaled ratio of 1/20 and 1/30 were simulated based on LS-DYNA, which shows the similarity relations and application scope of the pressurized model and centrifugal model. The shock wave, bubble radius and bubble period can meet the similarity relations but the bubble motion and jet can not meet the similarity relations in the pressurized model; and the shock wave and bubble pulsation almost meet the similarity relations in the centrifugal model.
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Key words:
- underwater explosion /
- model test /
- centrifugal model /
- pressurized model /
- LS-DYNA
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图 4 离心模型工况2和工况3的气泡半径数值结果
Figure 4. Numerical bubble radius histories under working conditions 2 and 3 of the centrifugal model
图 5 离心模型换算到原型的气泡半径数值结果
Figure 5. Numerical bubble radius histories for converting the centrifugal model into the prototype
图 6 离心模型工况2和工况3的冲击波数值结果
Figure 6. Numerical shock wave pressure-time curves under working conditions 2 and 3 of the centrifugal model
图 7 离心模型换算到原型的冲击波数值结果
Figure 7. Numerical shock wave pressure-time curves for converting the centrifugal model into the prototype
图 8 150 mg药量在0.170 8 MPa气压、37.5 cm水深下爆炸气泡脉动过程数值模拟结果(工况5)
Figure 8. The numerical simulated process of bubble pulsation of 150 mg charge in the water depth of 37.5 cm under the atmospheric pressure of 0.170 8 MPa (condition 5)
图 9 加压模型工况4和工况5的气泡半径数值结果
Figure 9. Numerical bubble radius histories under working conditions 4 and 5 of the pressurized model
图 10 加压模型换算到原型的气泡半径数值结果
Figure 10. Numerical bubble radius histories for converting the pressurized model into the prototype
图 11 加压模型工况4和工况5的冲击波数值结果
Figure 11. Numerical shock wave pressure-time curves under working conditions 4 and 5 of the pressurized model
图 12 加压模型换算到原型的冲击波数值结果
Figure 12. Numerical shock wave pressure-time curves for converting the pressurized model into the prototype
图 13 加压模型气泡垂直方向迁移运动的数值结果
Figure 13. Numerical vertical motion of the bubble for the pressurized model
图 14 加压模型换算到原型气泡垂直方向迁移运动的数值结果
Figure 14. Numerical vertical motion of the bubble for converting the pressurized model into the prototype
表 1 相似关系
Table 1. The similarity relations
参量分类 参数名称 原型参量 离心模型 加压模型 模型参量 参量缩比 模型参量 参量缩比 长度参数 装药半径 r λr λ λr λ 爆距 d λd λ λd λ 装药沉深 h λh λ λh λ 特征长度 l λl λ λl λ 速度参数 流速 v v 1 v 1 重力参数 加速度 ag ag/λ 1/λ ag 1 压力参数 大气压强 p0 p0 1 p0+ρ0agh(1-λ) 装药参数 装药质量 m λ3m λ3 λ3m λ3 冲击波参数 峰值压力 ps ps 1 ps 1 时间常数 τ λτ λ λτ λ 冲量 I λI λ λI λ 气泡参数 气泡半径 R λR λ λR λ 脉动周期 T λT λ λT λ 
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表 2 工况设置
Table 2. The working conditions
模型 工况 m h/cm ag/g p0/MPa 长度缩比 mp/g hp/cm 原型 1 1 200 g 750.0 1 0.101 0 1 1 200 750.0 离心模型 2 50 mg 25.0 30 0.101 0 1/30 1 350 750.0 3 150 mg 37.5 20 0.101 0 1/20 1 200 750.0 加压模型 4 50 mg 25.0 1 0.172 1 1/30 1 350 750.0 5 150 mg 37.5 1 0.170 8 1/20 1 200 750.0
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表 3 模型和原型数值计算结果对比
Table 3. Comparison of the numerical calculation results between the models and prototype
工况 工况参数 d/cm 模型 原型 m ag/g h/cm p/kPa ps/MPa Rmax/cm T/ms ps/MPa Rmax/cm T/ms 1 1 200 g 1 750.0 0.101 0 150.0 28.84 144.2 221.3 2 50 mg 30 25.0 0.101 0 5.0 25.80 4.95 6.82 25.80 148.5 204.6 3 150 mg 20 37.5 0.101 0 7.5 27.03 7.02 10.84 27.03 140.4 216.8 4 50 mg 1 25.0 0.172 1 5.0 25.80 4.69 6.85 25.80 140.7 205.5 5 150 mg 1 37.5 0.170 8 7.5 27.03 7.02 10.82 27.03 140.4 216.4
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