Energy Conversion Prediction Model of Expansion Tube under Near-Field Blast Loading
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摘要: 爆炸近场是弹药爆炸毁伤的核心区域，涉及强冲击波与爆轰产物的耦合载荷作用。目前，扩胀管结构（expansion tube structure, ETS）在此类极端载荷下的力学响应及能量转化机制尚不明确。为此，将ETS作为典型吸能结构，研究其在近场强冲击波与爆轰产物耦合作用下的能量转化机制。在试验验证的基础上，通过数值模拟方法研究近场爆炸载荷特性及ETS的动态响应特性，建立了近场爆炸载荷的理论预测公式，并在强冲击假设的基础上构建了能量转化效率的理论预测模型。结果表明：能量转化效率随着比例距离的增加而显著下降，当比例距离超过0.80 m/kg1/3时，能量转化效率低于10%；能量转化效率与反射波比冲量呈显著正相关，说明比冲量是决定能量传递的关键因素。研究结果揭示了ETS在近场爆炸载荷作用下能量转化的内在机制，所建立的理论模型为近场防护结构设计与性能评估提供了有力的理论支撑。Abstract: The explosion near-field is the core zone of munition-induced damage, involving the coupled load effect of intense shock waves and detonation products. Currently, the mechanical response and energy conversion mechanisms of expansion tube structures (ETS) under such extreme loading conditions remain unclear. In this study, ETS is adopted as a representative energy-absorbing structure to investigate its energy conversion behavior under the coupled action of near-field shock waves and detonation products. Based on the experimental verification, numerical simulation methods were employed to analyze the characteristics of near-field blast loading and the dynamic response of ETS. Furthermore, a theoretical prediction formula for near-field blast loading was established, and a theoretical model for predicting energy conversion efficiency was developed based on the strong-shock assumption. The results show that the energy conversion efficiency decreases significantly with increasing scaled distance. The energy conversion efficiency drops to below 10% when the scaled distance exceeds 0.80 m/kg1/3. Moreover, the energy conversion efficiency exhibits a strong positive correlation with the specific impulse of the reflected wave, indicating that specific impulse is a key factor determining energy transfer. This work elucidates the intrinsic mechanism of energy conversion in ETS under near-field coupled loading. The proposed theoretical model provides a robust foundation for the design and performance evaluation of near-field protective structures.
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Key words:
- near-field blast /
- detonation products /
- energy conversion /
- overpressure /
- specific impulse
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图 2 近场爆炸载荷作用下ETS示意图
Figure 2. Schematic diagram of the expansion tube structure under near-field blast loading
图 6 不同比例距离下反射波的压力时程曲线
Figure 6. Pressure history curves for reflected waves at various scaled distances
图 8 ETS的嵌入位移随比例距离的变化
Figure 8. Variations of ETS embedding displacement with scaled distance
图 10 近场爆炸载荷的经验公式拟合
Figure 10. Fitting of empirical formula for near-field blast loading
图 12 近场爆炸载荷作用下ETS响应历程示意图
Figure 12. Schematic diagram of ETS response history under near-field blast loading
图 13 Z=0.60 m/kg1/3处ETS的响应过程及能量吸收理论预测结果
Figure 13. Theoretical prediction results of the response process and energy absorption of ETS at Z=0.60 m/kg1/3
图 14 不同比例距离处的能量转化效率及其对应的反射超压峰值（pr）和比冲量（Ir）
Figure 14. Energy conversion efficiency at different scaled distances and the corresponding peak reflected overpressure (pr) and specific impulse (Ir)
表 1 ETS各部件的几何尺寸
Table 1. Geometric parameters of each component in ETS
Thin-wall tube Cone piston Material LT/mm r0/mm h/mm Material rdie/mm lD/mm lC/mm α/(°) mC/g 1060/H12 aluminum 48.0 13.0 1.0 304 steel 13.5 2.0 5.0 5.71 16.8 Supporting rod Slider Material DR/mm lR/mm mR/g Material DS/mm lS/mm lE/mm mS/g 304 steel 10.0 27.0 14.98 304 steel 40.0 37.0 5.0 149.8 
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W/kg Case R/m Z/(m·kg−1/3) L/mm W/kg Case R/m Z/(m·kg−1/3) L/mm 2.00 W2-E1 0.60 0.48 13.35 5.00 W5-E1 0.63 0.37 33.88 W2-E2 0.63 0.50 17.40 W5-E2 0.72 0.42 27.54 W2-E3 0.72 0.57 13.05 W5-E3 0.77 0.45 30.89 W2-E4 0.77 0.61 21.75 W5-E4 0.87 0.51 22.80 W2-E5 0.80 0.63 7.68 W5-E5 1.05 0.61 21.91 W2-E6 1.05 0.83 5.52 W5-E6 1.08 0.63 15.64 W2-E7 1.08 0.86 3.12 W5-E7 1.14 0.67 11.44 W2-E8 1.31 1.04 2.24 W5-E8 1.31 0.77 6.69 W2-E9 1.31 1.04 2.56 W5-E9 1.31 0.77 7.48 W2-E10 1.40 1.11 2.08 W5-E10 1.35 0.79 4.66 W2-E11 1.42 1.13 1.44 W5-E11 1.40 0.82 5.98 W2-E12 1.46 1.16 0.64 W5-E12 1.46 0.85 9.68 4.01 W4-E1 0.63 0.40 29.57 3.01 W3-E1 0.60 0.42 25.14 W4-E2 0.72 0.45 15.93 W3-E2 0.63 0.44 25.72 W4-E3 0.77 0.49 19.18 W3-E3 0.72 0.50 9.02 W4-E4 0.80 0.50 12.72 W3-E4 0.77 0.53 6.34 W4-E5 0.87 0.55 11.97 W3-E5 0.80 0.55 8.52 W4-E6 1.05 0.66 6.69 W3-E6 0.87 0.60 11.32 W4-E7 1.08 0.68 10.21 W3-E7 1.05 0.73 2.52 W4-E8 1.14 0.72 7.92 W3-E8 1.08 0.75 4.56 W4-E9 1.31 0.83 4.22 W3-E9 1.14 0.79 2.60 W4-E10 1.31 0.83 5.72 W4-E11 1.35 0.85 3.52 W4-E12 1.40 0.88 3.08 W4-E13 1.42 0.89 4.22 W4-E14 1.46 0.92 6.69
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表 3 近场爆炸载荷下反射峰值超压和比冲量的数值模拟结果
Table 3. Simulation results of reflected peak overpressure and specific impulse of the near-field blast loading
Z/(m·kg−1/3) W/kg pr2/MPa Ir2/(Pa·s) Z/(m·kg−1/3) W/kg pr2/MPa Ir2/(Pa·s) 0.30 2 61.66 3770.76 0.30 10 75.99 6044.95 0.35 57.72 3152.27 0.35 63.56 5663.29 0.40 48.93 2636.03 0.40 57.11 4531.02 0.45 36.94 2240.10 0.45 41.89 4476.01 0.50 27.89 2107.74 0.50 34.63 4442.93 0.60 20.28 1682.53 0.60 18.39 3088.02 0.70 14.66 1281.50 0.70 14.23 2436.08 0.80 8.19 1070.14 0.80 13.46 2107.83 0.30 3 61.13 4094.75 0.30 30 71.06 8429.43 0.35 53.59 3309.89 0.35 55.22 6430.83 0.40 45.44 2389.84 0.40 44.78 5125.89 0.45 39.12 2184.19 0.45 35.74 4656.37 0.50 34.39 2109.40 0.50 27.21 3985.79 0.60 18.21 1732.51 0.60 19.63 3735.01 0.70 12.01 1276.29 0.70 13.15 3043.11 0.80 8.56 950.22 0.80 9.54 2498.36 0.30 5 72.08 5006.16 0.30 50 77.94 9821.96 0.35 44.64 3729.77 0.35 64.93 7193.28 0.40 37.13 2908.95 0.40 55.93 5515.95 0.45 32.90 2989.50 0.45 38.42 5887.95 0.50 24.99 2201.57 0.50 31.44 4784.21 0.60 17.87 1958.20 0.60 19.37 3877.84 0.70 14.34 1537.50 0.70 12.56 2869.21 0.80 10.36 1066.83 0.80 9.71 2526.05
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表 4 10 kg 炸药当量下不同比例距离处ETS的能量吸收
Table 4. Energy absorption of ETS at different distances under a 10 kg TNT equivalent charge
R/m Z/(m·kg−1/3) Ee Simulation/J Theory/J Error/% 0.862 0.40 119.12 140.57 18.01 1.077 0.50 114.81 101.29 −11.77 1.293 0.60 55.18 59.42 7.68 1.508 0.70 34.11 39.59 16.07 1.724 0.80 25.28 26.06 3.09
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