An improved method for calculating near-field shock wave loads of underwater explosions
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摘要: 针对传统水下爆炸冲击波经验公式分段近似、近场预测精度不足且存在物理量不连续的局限,本文基于Chapman-Jouguet(CJ)爆轰模型、波后近似等熵流动假设及Kirkwood-Bethe(K-B)理论,建立了一种改进的近场冲击波载荷统一连续计算模型。通过引入二阶马赫精度形式的K-B方程和改进的压力衰减时间常数,将理论适用范围扩展至无量纲爆距2~20,避免了传统分段处理在分界处的不连续性。经多工况球形炸药试验、统一气泡动力学高保真理论、任意拉格朗日-欧拉(ALE)数值仿真及经典经验公式验证,峰值压力计算误差控制在10 %以内,冲量和能流密度精度显著优于Cole经验公式。基于该模型的计算结果表明:冲击波峰值压力与能流密度在近场呈强非线性快速衰减,中远场衰减速率显著降低;近场(2~10倍半径)峰值压力衰减中几何扩散贡献约89 %,能流密度衰减几乎完全由几何扩散主导;冲量随爆距缓慢衰减,衰减速率远小于峰值压力。Cole经验公式在中远场对冲量和能流密度的系统性高估,根源在于其恒定时间常数假设忽略了气泡膨胀的非定常过程。本文模型兼具解析效率与数值精度,为水中兵器战斗部设计及舰船抗爆防护提供了有效理论工具。
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关键词:
Abstract: To address the limitations of traditional segmented empirical formulas for underwater explosion shock wave loads, namely, insufficient near-field accuracy and physical discontinuities at partition boundaries, this paper establishes an improved unified continuous calculation model for near-field shock wave loads based on the Chapman-Jouguet (CJ) detonation model, post-shock approximate isentropic flow assumption, and Kirkwood-Bethe (K-B) theory. By introducing the K-B equation in the form of second-order Mach accuracy and an improved pressure attenuation time constant, the theoretical application range is extended to the dimensionless detonation distance of 2 to 20, eliminating the discontinuities inherent in conventional piecewise approximations. The model is validated against multi-scale spherical charge tests, unified bubble dynamics high-fidelity theory, Arbitrary Lagrangian-Eulerian (ALE) numerical simulation, and classical empirical formulas, with the peak pressure calculation error controlled within 10 % and the accuracy of impulse and energy flux significantly superior to Cole’s empirical formula. Calculation results show that the peak pressure and energy flux of the shock wave rapidly and nonlinearly decay in the near field, while the decay rate decreases markedly in the middle and far fields. In the near field (2-10 charge radii), geometric diffusion contributes approximately 89 % to the peak pressure attenuation, and the energy flux decay is almost entirely dominated by geometric diffusion. The impulse decays slowly with detonation distance at a rate much lower than that of the peak pressure. The systematic overestimation of impulse and energy flux by Cole’s formula in the middle and far fields stems from its constant time constant assumption, which neglects the unsteady nature of bubble expansion. The proposed model possesses both analytical efficiency and numerical accuracy, providing an effective theoretical tool for underwater weapon warhead design and ship anti-blast protection.-
Key words:
- underwater explosion (UNDEX) /
- shock wave /
- near field /
- CJ detonation model /
- K-B theory /
- geometric diffusion /
- dispersive effect
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