Modeling on the reflection and focusing process of the underwater explosion shock waves by an ellipsoidal reflector
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摘要: 基于冲击波传播、非线性反射和聚焦理论，建立水下爆炸冲击波在椭球罩作用下的反射聚焦模型。讨论自由传播、壁面反射和定向聚焦阶段的冲击波特性和压力计算方法，利用波前和波法线的近似方程构建压力场的数值计算域，进而模拟聚焦过程，并与现有实验结果进行对比，结果表明：所建模型可为正聚焦压力提供满足工程精度的预测，并能描述水下冲击波及产生的拉伸波聚焦过程中的一些细节；椭球罩能有效地聚焦水下冲击波，在动力学焦点附近获得有效增益区，在近轴方向上明显削弱冲击波压力衰减；理想条件下的动力学焦点一般位于几何焦点之前，但实际的反射罩变形和背向位移将使其发生后迁，甚至能越过几何焦点。Abstract: In the present study, based on the theories of shock wave propagation and nonlinear reflection and focusing, we modelled the reflection and focusing of the underwater explosion shock waves by an ellipsoidal reflector, where the shock wave characteristics in three stages, those of the free propagation, the reflection on the wall and the directional focusing, were discussed respectively, and the corresponding methods on the pressure calculation were introduced. It was found that the discretized calculation domain of the pressure field is determined by employing the approximate geometric equations of the wave fronts and normal lines. Further, the focusing process was simulated and verification was performed by comparison with experimental data, with explanations given. The results indicate that this model can predict the positive focusing pressure with a precision that satisfies engineering requirements, keeping most errors below 10% and draw the focusing process of the shock waves and induced tensile waves in some detail; that the ellipsoidal reflector can focus underwater shock waves efficiently, generating an efficient gain region near the dynamic focus and weakening the attenuation along the closely axial direction; and that the dynamic focus appear ideally in front of the geometric focus, but it is also possible to move backward and even pass the geometric focus, due to actual deformation and backward displacement of the reflector.
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Key words:
- underwater explosion /
- ellipsoidal reflector /
- pressure distribution /
- focusing /
- gain
1) “第十一届全国爆炸力学学术会议”推荐论文 -
图 1 冲击波在椭球罩作用下的非线性聚焦
Figure 1. Nonlinear focusing of shock waves by an ellipsoidal reflector
图 2 非线性规则反射中反射角与入射角关系
Figure 2. Incident angle versus reflection angle in nonlinear regular reflection
图 3 非线性和线性反射波面变化过程
Figure 3. Variation process of wave surface in nonlinear reflection against linear case
图 4 反射聚焦过程的波前与波法线几何形状
Figure 4. Normal lines and fronts of shock waves in the focusing process
图 5 直达波压力与距离关系的双对数曲线
Figure 5. Double logarithmic curve of direct peak pressure vs. distance
图 7 外聚焦的初始波前压力数值解与近似分布
Figure 7. Numerical solutions of pressures on initial wave front in outside focusing process and associated approximate distribution
图 9 压力场随时间的变化过程
Figure 9. Pressure field of underwater shock waves vs. propagation time
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