基于压力-冲量曲线的水下爆炸压力-时间公式

徐庆涛; 马宏昊; 周章涛; 杨科; 沈兆武

doi:10.11883/bzycj-2023-0442

基于压力-冲量曲线的水下爆炸压力-时间公式

doi: 10.11883/bzycj-2023-0442

徐庆涛^1,,
马宏昊^{1, 2, ,},
周章涛³,
杨科¹,
沈兆武¹

1.
中国科学技术大学中国科学院材料力学行为和设计重点实验室，安徽合肥 230026
2.
中国科学技术大学火灾科学国家重点实验室，安徽合肥 230026
3.
中国船舶科学研究中心，江苏无锡 214082

基金项目: 国家自然科学基金（51874267）；中国科学技术大学基础研究基金（WK2480000008，WK2090000007， WK2320000049）

详细信息

作者简介:
徐庆涛（1999－　），男，博士研究生，SA21005087@mail.ustc.edu.cn

通讯作者:
马宏昊（1980－　），男，博士，副教授，hhma@ustc.edu.cn

中图分类号: O382; TJ011.1
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- 被引次数: 0
出版历程
- 收稿日期: 2023-12-14
- 修回日期: 2024-03-20
- 网络出版日期: 2024-04-07
- 刊出日期: 2024-08-05

Pressure-time formula for underwater explosion based on pressure-impulse curve

1.
CAS Key Laboratory of Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei 230026, Anhui, China
2.
State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230026, Anhui, China
3.
China Ship Scientific Research Center, Wuxi 214082, Jiangsu, China

摘要

摘要: 根据材料受冲击载荷时的压力-冲量函数，推导得到了适用于水下爆炸冲击载荷的压力时程公式。通过水下爆炸实验方法测量不同药量、不同距离的压力时程曲线，使用MATLAB软件对实验数据进行拟合，由此计算冲击波冲量和能量参数，并与通用的Cole与Орленко理论计算结果进行对比，验证拟合曲线的准确性。相较于Cole和Орленко理论，新方法得到的压力衰减曲线更接近实验值。计算水下爆炸冲击波的比冲量和比冲击波能时，新模型具有较高的计算精度，其中：比冲量与实验值的误差不超过4%，与Орленко理论相比，精度提高了5%~10%；比冲击波能与实验值的误差不超过1%，计算精度与通用理论相当。
- 水下爆炸 /
- 压力衰减 /
- 比冲量 /
- 比冲击波能 /
- 压力-冲量曲线
Abstract: Theoretical study on the attenuation law of underwater explosion shock waves plays a crucial role in predicting the underwater explosion power. The attenuation law of underwater explosion shock waves could be analyzed from the shock waves pressure-time curve. The pressure-impulse (p-I) model has usually been used to assess damage on material and structure. In this paper, the pressure-time formula is analytically derived according to the p-I model. To verify the accuracy of the formula, the pressure-time relation curve was obtained by experiments with various explosive charges and distances. The experimental data was fitted in accordance with the theoretical equations of Cole and Орленко, and also with the developed pressure-time formula. The parameters of the formula are thus obtained. The accuracy could be described by the fitting coefficient R-squared (R²) value. The R-squared value of the developed pressure-time formula exceeds 0.988, which is greater than the R-squared values calculated by the equations of Cole and Орленко. In order to further validate the formula, the impulse and energy of underwater explosion shock waves are derived from the developed pressure-time formula, experimental data, and the equations of Cole and Орленко, respectively. Compared with the experimental results, the error of impulse derived from the developed pressure-time remains below 4%, which is 5%−10% lower than the errors of impulse between the experimental results and the equations of Cole and Орленко. The energy of the shock waves is similarly analyzed. Compared with the experimental results, the error of energy derived from the developed pressure-time remains below 1%, approximately the same as the errors of energy between the experimental results and the equations of Cole and Орленко. Compared with the calculation by equations of Cole and Орленко, it is seen that there is better correlation between the developed pressure-time formula and the experimental results. The developed pressure-time formula can be used to calculate the impulse and energy of underwater explosion shock waves.
- underwater explosion /
- pressure decay /
- specific impulse /
- specific shock wave energy /
- pressure-impulse curve

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图 1 水下爆炸实验装置（单位：m）

Figure 1. Underwater explosion experiment device (unit: m)

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图 2 不同实验工况下水下爆炸压力时程曲线

Figure 2. Underwater explosion pressure-time curves under different experimental conditions

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图 3 9 g RDX实验的3种模拟结果

Figure 3. Three model fitting results of 9 g RDX experimental data

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图 4 12 g RDX实验的3种模拟结果

Figure 4. Three model fitting results of 12 g RDX experimental data

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图 5 19 g RDX实验的3种模拟结果

Figure 5. Three model fitting results of 19 g RDX experimental data

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表 1 3种拟合方法的精度

Table 1. Accuracy of three fitting methods

炸药	组号	R²			a/kPa	c/(kPa²·s)
炸药	组号	新模型	Cole理论	Орленко理论	a/kPa	c/(kPa²·s)
9 g RDX	1	0.9882	0.9282	0.9854	−0.097	0.053
9 g RDX	2	0.9923	0.9363	0.9881	−0.089	0.043
12 g RDX	1	0.9936	0.9327	0.9861	−0.210	0.135
12 g RDX	2	0.9963	0.9306	0.9861	−0.200	0.133
19 g RDX	1	0.9897	0.9274	0.9895	−0.180	0.131
19 g RDX	2	0.9908	0.9286	0.9900	−0.160	0.094

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表 2 冲量的理论值与实验值

Table 2. Theoretical and experimental values of impulse

炸药	组号	I/(Pa·s)			δ₁(I)/%	δ₂(I)/%
炸药	组号	实验	新模型	Cole-Орленко模型	δ₁(I)/%	δ₂(I)/%
9 g RDX	1	325.862	320.943	325.575	−1.510	−0.088
9 g RDX	2	282.572	279.108	325.575	−1.226	15.280
12 g RDX	1	376.875	375.155	326.037	−0.456	−13.490
12 g RDX	2	349.426	348.407	326.037	−0.292	−6.694
19 g RDX	1	439.536	439.484	431.403	−0.012	−1.850
19 g RDX	2	400.488	400.228	431.403	−0.065	7.719

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表 3 比冲击波能的理论值与实验值

Table 3. Theoretical and experimental values of specific shock wave energy

炸药	组号	E_s/(MJ·kg⁻¹)			δ₁(E_s)/%	δ₂(E_s)/%
炸药	组号	实验	新模型	Cole-Орленко模型	δ₁(E_s)/%	δ₂(E_s)/%
9 g RDX	1	1.057	1.051	0.929	−0.578	−12.110
9 g RDX	2	0.902	0.899	0.929	−0.370	2.993
12 g RDX	1	1.171	1.168	1.106	−0.256	−5.551
12 g RDX	2	1.087	1.082	1.106	−0.460	1.748
19 g RDX	1	0.840	0.836	0.772	−0.429	−8.095
19 g RDX	2	0.757	0.754	0.772	−0.396	1.982

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