Influences of adiabatic index γ on the parameters of different complex wave zones in a planar detonation
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摘要: 爆炸气体产物冲击膨胀过程中会形成多种复合波区，当爆炸气体绝热指数γ不同时其波区衰减特性差异较大。为研究不同γ条件下（γ＞3，γ=3，γ＜3）复合波区的特性差异，基于特征线法，对一平面爆轰过程中不同复合波区的波系相交特性进行了规律分析，并利用MATLAB对该平面爆轰过程进行流场模拟，验证并分析了不同复合波区流场内的参数变化特性。对比发现，γ不同时复合波区衰减特性的差异主要体现在与质点速度和气体声速相关的u-c平面特性上，其中在两中心稀疏波相交的复合波区，其差异还体现当γ≠3时相交的中心稀疏波不再具有中心发散特性。对爆炸过程中各波区特性的分析可为全面了解各特征参数的衰减规律提供参考。Abstract: A variety of complex wave zones are formed during the impact and expansion of explosive gas products. When the adiabatic index γ of explosive gas is different, the attenuation characteristics of the wave zones are quite different. In order to understand the characteristics of the complex wave zone under the different γ conditions (γ＞3, γ=3, γ＜3), the intersection characteristics of different complex wave zones in a planar detonation were analyzed based on the characteristic line method. The flow field in the planar detonation was simulated by MATLAB to verify and analyze the parameter change characteristics of the flow fields in the different complex wave zones. Comparisons display that the differences in the attenuation characteristics of the wave zones are mainly reflected in the differences in the u-c plane characteristics related to the particle velocity and the gas sound velocity. Among them, in the complex wave zone where two rarefaction waves intersect, the difference is also reflected in that when γ≠3, the rarefaction wave no longer has the characteristic of central divergence. The analysis result on the characteristics of each wave zone in the explosion process provides a reference for comprehensively understanding the attenuation of each characteristic parameter.
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图 1 平面爆轰过程中复合波区的形成及相对位置（+右行，−左行）
Figure 1. Formation and relative positions of complex wave zones in plane detonation (+ showing a going-right wave, − showing a going-left wave)
图 2 两稀疏波在原点相遇时流场内的特征参数分布
Figure 2. Distribution of characteristic parameters when two rarefaction waves meet at the origin
图 3 两中心稀疏波相交的x-t平面
Figure 3. x-t plane of intersection of two central rarefaction waves
图 4 应用c值均布特性后系统流场特性变化
Figure 4. Changes of flow field characteristics after the application of c-value uniform distribution
图 6 两同等强度稀疏波相交的平面特性
Figure 6. Plane characteristics of the intersection of two rarefaction waves with equal intensity
图 7 两同等强度压缩波相交的平面特性
Figure 7. Plane characteristics of the intersection of two compression waves with equal intensity
图 8 不同强度压缩波和稀疏波相交的平面特性
Figure 8. Plane characteristics of the intersection of a compression wave and a rarefaction wave with different intensities
图 9 γ≠3时两同等强度稀疏波相交的平面特性示意图
Figure 9. Plane characteristics of intersection of two rarefaction waves with equal intensity at γ≠3
图 11 MATLAB计算生成的特征线流场
Figure 11. Characteristic line flow field generated by MATLAB calculation
图 12 T2、T3、Tn时刻的流场参数分布
Figure 12. Distribution of flow field parameters at times T2, T3 and Tn
图 13 爆轰流场中复合波⑤区的u-c特性
Figure 13. u-c characteristics of complex wave zone ⑤ in the post-detonation flow field
图 14 爆轰流场中复合波⑦区的u-c特性
Figure 14. u-c characteristics of complex wave zone ⑦ in the post-detonation flow field
表 1 阶段1各区域的状态参量
Table 1. Characteristic parameters of each region in stage 1
区域 压力p/
MPa密度ρ/
（kg·m−3）质点速度u/
（m·s−1）气体声速c/
（m·s−1）绝热指数γ ③区 9130.8 1630 0 3 620.500 2.34 ④区 介于③区和②区之间，参数按中心稀疏波规律衰减 2.34 ②区 28.29 138.05 4 730.127 692.510 2.34 ①区 28.29 7.20 4 730.127 2 345.567 1.40 ⓪区 0.101 1.225 0 340.294 1.40 
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