An inverse method for the equation of state of detonation products from underwater explosion tests
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摘要: 由于水下爆炸过程中爆轰产物的信息以水中压缩波形式向外传递，本文旨在探讨如何利用水下爆炸试验数据确定爆轰产物的状态方程。相较于常规圆筒试验，水下爆炸试验具有装置简单成本低、装药尺寸限制少、测定压力范围更广的特点，更适用于大药量或非理想炸药的现场测试。本文从水中冲击波轨迹和波后压力时程曲线出发，发展了由冲击波及其波后流场还原水气界面的逆特征线算法，以及根据水气界面确定爆轰产物状态方程的遗传算法。与水下爆炸正演结果对比，发现逆特征线法可以较准确地还原水气界面的位置和压力参数，有效压力下限可达2 MPa，远低于圆筒试验的测试下限0.1 GPa。根据水气界面的反演结果，遗传算法也能稳定地优化JWL方程参数，8种常用炸药的等熵衰减压力误差在爆压至0.01 GPa的区间内都小于3%。结果表明，利用本文的逆特征线算法和遗传算法，理论上可以反演出压力范围较宽、准确性较高的爆轰产物状态方程。Abstract: Since the information of detonation product is transmitted outward in the form of compression wave during underwater explosion, the purpose of this paper is to explore how to determine the equation of state (EOS) of detonation products using underwater explosion tests. Compared with conventional cylinder test, underwater explosion test has the advantages of simpler equipment, lower cost, less limited charge size, and wider range of calibration pressures, which makes it more suitable for the on-site testing of large or non-ideal explosives. Based on the measurable shock wave trajectory and post-shock pressure history in general underwater explosion test, an inverse method of characteristics (inverse MOC) is proposed to recover the gas-water interface from the shock and post-shock data, and a genetic algorithm is developed to determine the EOS of detonation products by the gas-water interface. Compared with virtual experimental data extracted from underwater explosion simulations, it is found that the inverse MOC can properly reproduce the position and pressure of gas-water interface. The lower limit of pressure range is close to 2 MPa, which is far lower than that of 0.1 GPa in cylinder test. Based on the inversed results of gas-water interface, it is also confirmed that the genetic algorithm can also stably optimize the parameters of JWL equation because the isentrope pressure error of eight commonly used explosives is less than 3% in the range of detonation pressure 0.01 GPa. The results show that it is by the inverse MOC and genetic algorithm that the EOS of detonation products can be properly and stably determined by the underwater explosion test data.
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图 1 球形与柱形装药水下爆炸模型
Figure 1. Model of an underwater explosion of a spherical or cylindrical geometry explosive
图 2 正特征线法求解的正演区与逆特征线法求解的反演区
Figure 2. A forward area calculated by MOC and an inverse area calculated by inverse MOC
图 3 水中流场的两类反演计算格式示意图
Figure 3. Schematic diagram of two types of numerical scheme for the inversion of the water field
图 4 从冲击波及其波后流场到水气界面的自适应特征线网格
Figure 4. An adaptive characteristic grid from known shock wave and after-shock flow to gas-water interface
图 5 本文优化问题的穷举搜索结果（30万数据点）
Figure 5. Exhaustive search results of this optimization problem (300 000 data points)
图 6 连续压导探针的测试结果示意图
Figure 6. Schematic diagram of test results of a continuous pressure-induced conduction probe
图 7 压电传感器的测试结果示意图
Figure 7. Schematic diagram of test results of a piezoelectric sensor
图 8 水下爆炸测试的数据节点示意图
Figure 8. Schematic diagram of data nodes of an underwater explosion test
图 9 水气界面的冲击波反演区域与波后流场反演区域
Figure 9. Inversed area of the shock wave and after-shock flow on the gas-water interface
图 10 水气界面的位置、压力的正演结果与反演结果的比较
Figure 10. Comparison between forward results and inversed results of position and pressure on gas-water interface
图 11 C4炸药的反演等熵线与JWL参考等熵线的比较
Figure 11. Comparison between inverse isentrope and JWL principle isentrope of C4 explosive
图 12 用球心的时程压力曲线验证所反演的JWL方程的有效性
Figure 12. Configuration of inverse JWL EOS by pressure-time history curve of sphere center
表 1 状态方程参数的二进制编码
Table 1. Binary encoding of JWL EOS parameters
参数 范围 网格数 分辨率 样本 R1 3.00～8.11 29 (512) 0.010 010010110 (4.5) R2 0.500～3.05 28 (256) 0.010 01011010 (1.4) ω 0.200～0.515 26 (64) 0.005 001010 (0.25) 
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表 2 交叉操作与突变操作的示意过程
Table 2. Schematic process of crossover operation and mutation operation
R1 交叉 突变 Samlpe 1 001010101×010101010→001101010+010010101 010(0)10101→010(1)10101 (3.85)×(4.70)→(4.06)+(4.49) (4.49)→(4.81) Samlpe 2 001111111×010000000→001000000+010111111 0101(1)111(1)→0101(0)111(0) (4.27)×(4.28)→(3.64)+(4.91) (4.91)→(4.74)
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表 3 几种炸药的爆轰参数
Table 3. Detonation parameters of several explosives
炸药 ρ0/(g·cm−3) D /(km·s−1) pJ/GPa E0/(GJ·m−3) ANFO 0.931 4.160 5.15 2.48 C4 1.601 8.193 28.0 9.0 Comp B 1.717 7.980 29.5 8.5 HNS 1.40 1.400 6.340 14.5 6.0 LX-01 1.230 6.840 15.5 6.1 PETN 1.50 1.500 7.450 22.0 8.56 Tetryl 1.730 7.910 28.5 8.2 TNT 1.630 6.930 21.0 6.0
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表 4 JWL方程参数的反演结果与标准数据对比
Table 4. Comparison between inversed results and reference parameters of JWL EOS
实验 A/GPa B/GPa C/GPa R1 R1 ω 最大误差(p＞0.01 GPa)/% ANFO (1) 49.46 1.89 0.474 3.90 1.10 0.333 3 − ANFO (2) 50.82 2.101 0.437 3.96 1.11 0.32 2.8 C4 (1) 609.77 12.95 1.043 4.50 1.40 0.25 − C4 (2) 610.64 12.71 1.033 4.50 1.38 0.25 1.3 Comp B (1) 524.23 7.678 1.082 4.20 1.10 0.34 − Comp B (2) 528.29 8.021 1.087 4.22 1.10 0.35 2.9 HNS 1.40 (1) 366.5 6.75 1.163 4.80 1.40 0.32 − HNS 1.40 (2) 365.60 6.482 1.157 4.79 1.37 0.32 1.0 LX-01 (1) 311.04 4.761 1.042 4.50 1.00 0.35 − LX-01 (2) 305.98 4.244 1.007 4.45 0.95 0.34 2.0 PETN 1.50 (1) 625.3 23.29 1.149 5.25 1.60 0.28 − PETN 1.50 (2) 630.48 23.52 1.111 5.27 1.59 0.275 1.3 Tetryl (1) 586.83 10.67 0.774 4.40 1.20 0.275 − Tetryl (2) 584.47 10.51 0.768 4.39 1.20 0.27 1.1 TNT (1) 373.77 3.7471 0.735 4.15 0.90 0.35 − TNT (2) 376.61 4.011 0.769 4.17 0.92 0.36 1.7 注：(1) Reference parameters；(2) Inversed results
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