Space Conversion Model of Peak Overpressure in Near-Earth Air Blast Shockwave with Cylindrical Charge
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摘要: 为研究近地空爆冲击波峰值超压空间数值关系，基于镜像法、角等分和超压归一化思想，确定了冲击波空间传播界线，建立了混合流场中超压的理论计算方法。首先，利用三波点轨迹与爆高水平线交点、虚拟爆源、真实爆心三者连线构成的几何约束以及马赫反射终点条件，确定了冲击波流场分布界限。其次，等分测点角度，并基于超压归一化值分段线性假设构建归一化值方程。然后将归一化值方程扩展为圆柱装药长径比、爆高、当量、测点角度和比例距离的函数。最后，基于控制变量法，利用符合经验公式和实爆结果的圆柱装药近地空爆AUTODYN-2D数值模型的计算结果代入上述函数求解。结果表明：以长径比、比例爆高、比例距离和测点角度为输入参数的峰值超压空间转换模型可描述圆柱装药近地空爆峰值超压的空间数值关系，转换效果良好。Abstract: The shockwave overpressure is one of the main damage elements of the high energy warhead, and many researchers have paid great attention on it. The spatial propagation boundary of shockwave is determined based on the method of image, division angle and overpressure normalization, and the theoretical calculation method of overpressure in mixed flow field is also established. Firstly, the boundary of shockwave flow field distribution is determined by using the terminal condition of Mach reflection and the geometric constraints formed by connecting three points, including the intersection of triple point trajectory and the horizontal line of height of burst (HOB), the imaginary burst point and real blast center. Secondly, the angle of measuring point (AMP) is equalized and the normalized value equation is constructed based on the piecewise linear assumption of the normalized value of overpressure. Then, the normalized value equation is extended to the functions of the length diameter ratio (k) of cylindrical charge, HOB, equivalent, AMP and scaled distance. Finally, based on the control variable method, the above function is solved by using the calculated results of AUTODYN-2D numerical model of near-earth air blast with cylindrical charge in accordance with the empirical equations and the real explosion results. The results show that the spatial conversion model of peak overpressure with k, scaled HOB, scaled distance and AMP as input parameters can describe the spatial numerical relation of peak overpressure of cylindrical charge in near-earth air blast, and the conversion effect is well.
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图 1 近地爆炸冲击波近距离传播流场示意图
Figure 1. Near-earth blast shockwave propagation flow field at close range
图 2 近地爆炸冲击波远距离传播流场示意图
Figure 2. Near-earth blast shockwave propagation flow field over long distance
图 6 不同比例爆高时峰值超压的归一化值
Figure 6. Normalized value of peak overpressure under different scaled height of burst (HOB)
图 7 相对于长径比（k）1.0的变量
Figure 7. Variables that relative to the length diameter ratio (k) of 1.0
A/GPa B/GPa R1 R2 $\omega $ E/(GJ·m−3) 371.2 3.231 4.15 0.95 0.3 7 
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表 2 实爆及数值模拟结果对比
Table 2. Real blast and numerical simulation results
Case No. Scaled distance/(m·kg−1/3) Peak overpressure/kPa Error/% Real blast Numerical simulation 1 3.2 111.8 102.017 −8.75 2 4.2 69.8 64.177 −8.06 3 5.1 47.6 44.663 −6.17 4 6.0 39.3 33.311 −15.24
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表 3 系数汇总表
Table 3. Summary of coefficients
No. $\theta $/(°) A1 A2 A3 1 0 70.08 764.30 −69.75 2 15 175.40 −38.19 677.70 3 30 137.30 −161.10 1177.00 4 45 67.84 317.10 370.50 5 60 68.28 330.50 315.00 6 75 75.65 315.50 216.10 7 90 99.50 123.10 503.60
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表 4 模型计算结果对比
Table 4. Comparison of model calculation results
m/kg k HOB/m Scaled distance/
(kg·m−1/3)Peak overpressure/kPa Error/% Test value (90°) Test value (0°) Predicted value 20 1.0 1.5 2.58 143.8 221.1 191.3 13.5 3.32 90.3 110.6 92.7 16.2
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