Calculation of pressure parameters at ignition moment of HMX-based aluminized pressed explosives during slow cook-off
-
摘要: 为了研究HMX基含铝压装炸药在慢烤过程中点火时刻的压力参量，设计了0.1和1.0 ℃/min升温速率下的慢烤试验，并对炸药内部进行了多点测温。在此基础上，基于炸药的通用烤燃模型，将HMX的多步分解机制与铝粉反应相结合，并考虑其分解中的相变过程，建立了HMX基含铝压装炸药慢烤反应速率与压力相关的计算模型并进行了数值模拟。试验结果表明，在0.1 ℃/min的升温速率下，端盖喷出，壳体沿轴向撕开裂缝，无药粉残留，判定炸药发生爆燃反应；在1.0 ℃/min的升温速率下，壳体发生轻微变形，有部分药粉残留，判定炸药发生燃烧反应。数值研究结果表明，随着热刺激强度的提高，炸药的点火温度呈对数上升趋势，而烤燃弹的反应进度和内部压力呈现指数下降趋势，且烤燃弹内部的反应压力在HMX相变前呈缓慢上升趋势，相变后呈快速上升趋势。Abstract: In order to study the pressure parameters of HMX-based aluminized pressed explosives at the ignition moment during slow cook-off, slow cook-off tests were designed at 0.1 and 1.0 ℃/min heating rates, and internal multi-point temperature measurements were taken inside explosives. On this foundation, based on the universal cook-off model of explosives, combining the multi-step decomposition reaction mechanism of HMX-based explosives with the reaction of aluminum powder, and considering the phase transition process in the decomposition of HMX-based explosives, a slow cook-off calculation model for pressure-department reaction rate of HMX-based aluminized pressed explosives is proposed. The calculation model is then written as a user defined function and imported into Ansys Fluent to perform calculations. Slow cook-off tests were conducted on large aspect ratio (5∶1) HMX-based aluminized pressed explosive charges with 4 mm shell thickness at heating rates of 0.1 and 1.0 ℃/min and compared with simulation results. And then the numerical simulations of the temperature field and internal pressure changes are performed before ignition of the cook-off bomb at heating rates of 0.055, 0.1, 0.2, 0.3, 0.5, and 1.0 ℃/min. It is found that at the heating rate of 0.1 ℃/min, after the test reaction, the end cover is ejected, the shell is axially cracked, and there is no powder left, so it is judged to be a deflagration reaction; while at the heating rate of 1.0 ℃/min, the shell is slightly deformed, with some powder left, indicating that a combustion reaction has occurred. The numerical calculations show that as the heat stimulus increases, the ignition temperature of the explosive tends to increase logarithmically, while the extent of reaction and internal pressure of the cook-off bomb tend to decrease exponentially. Before the HMX phase transition, the internal pressure inside the cook-off bomb grows slowly, after the HMX phase transition the pressure grow rapidly increases, and finally it rises sharply near the ignition moment.
-
爆破振动强度的影响因素极其复杂，其衰减特征是在基于实践经验和对数据统计分析的基础上得到的，随着爆破技术在边坡工程中的广泛应用，萨道夫斯基公式计算值与实测数据的误差达到50%以上[1]，该公式对高差变化较大的地形已不再适用。许多学者采用现场实验、理论分析及数值模拟等手段对爆破振动的地形效应进行了深入研究。台阶地形的放大效应与高程、爆源距、坡面角以及结构面的产状有关[2-5]。吕淑然等[6]认为台阶正高差地形的高程越高放大效应越明显，而唐海等[1]认为台阶地形中振动速度的放大系数存在最大值。万鹏鹏等[7]通过实验观测分析得到台阶地形爆破振动放大效应是受鞭梢效应和坡面效应影响的结论。张伟康等[8]、胡光球等[9]、周同龄等[10]通过分析与爆破振动有关的物理量，运用量纲分析法推导了反映高程放大效应的爆破振动公式并在工程中应用。同时，动力有限元方法成功应用在了爆破动态模拟中，并被证明在边坡顶部质点振动速度都呈现出放大效应[11]，放大现象是一个局部的动力响应[12]，振动速度放大效应的实质是在台阶平台上产生波形转换及波形叠加[13]。
本文中利用数值模拟方法对台阶地形爆破地震波的放大与衰减规律进行研究，结合现场实验数据分析结果提出台阶地形爆破振动速度预测模型。
1. 数值模拟
1.1 参数选取
模型做如下假设：岩石视为各向同性的连续均匀介质，爆轰产物的膨胀是绝热过程；忽略重力影响。台阶模型的岩石材料参数如表 1所示，炸药材料及状态方程参数如表 2所示。
表 1 岩石材料参数Table 1. Material parameters of rock岩石 岩石密度/(g·cm-3) 弹性模量/GPa 泊松比 切线模量/GPa 抗压强度/MPa 抗拉强度/MPa 闪长玢岩 2.54 57.64 0.27 5.5 56 4.49 表 2 炸药的材料和状态方程参数Table 2. Material and equation of state parameters of explosive密度/(g·cm-3) 爆速/(km·s-1) 爆压/GPa A/GPa B/GPa R1 R2 ω E/GPa 1.0 3 3.43 321.9 0.18 4.2 0.8 0.15 3.51 采用高能炸药材料和JWL状态方程描述，爆轰压力计算：
p=A(1−ωR1V)e−R1V+B(1−ωR2V)e−R2V+ωEV (1) 式中:p为爆轰压力, E为炸药爆轰产物的内能, V为爆轰产物的相对体积, A、B、R1、R2、ω、为所选炸药的性质常数。
1.2 模型建立
利用LS-DYNA程序建立爆破模型，根据实验方案、岩石物理力学参数以及爆破参数，边坡爆破各模型尺寸：台阶高度H分别为12、15、18、21 m；台阶坡底面宽度W分别为10、15、20 m；坡面角为90°。图 1中给出了模型边界条件及炮孔主要参数。
1.3 台阶高度对振速的影响
模型计算时间0.03 s。爆炸后模型质点竖直方向振动速度随时间变化形态如图 2所示。
通过LS-PrePost后处理程序提取时间历程记录点处竖直方向的峰值质点振动速度，12组数值模型的计算结果如图 3所示。
图 3 质点峰值振动速度随高程变化曲线Figure 3. Variation of peak particle vibration velocity with elevation台阶表面质点振动速度总体上随距离的增加呈指数衰减规律；对于单个台阶，由于高差的存在质点振动速度在上级台阶坡顶处产生放大效应。由图 2中曲线分析可得：爆破振动速度的高程放大效应是在爆源距和高差达到一定值后产生。当W=10 m、H=12 m，振动速度的放大效应在第3级台阶出现，为研究产生放大效应后高程对振动速度的影响规律，改变第3级台阶的高度，建立16个台阶模型。
台阶坡顶质点振动速度的放大倍数n随高差的变化曲线如图 4所示，高差由1 m增加到18 m，放大倍数n呈现先增加后降低的变化规律，当高差为9 m时，放大倍数n达到最大值1.34。
质点振动速度的放大倍数并不随台阶高度的增加而单调增加，当台阶高度超过某一临界值时，放大倍数随台阶高度的增加而减小。这一现象表明，高程对地震波既有放大作用也存在衰减作用。
1.4 台阶坡底面宽度对振速的影响
当台阶高度一定，坡底面宽度分别为10、15、20 m时，建立12组数值模型，台阶坡顶、坡底处质点峰值振动速度与坡底面宽度的关系如图 5所示。
图 4中质点峰值振动速度衰减特征显示，坡底面宽度越大，相同高程处质点振动速度越低；坡底面宽度较大台阶的爆破振动速度衰减速率更快。振动速度随坡面宽度增大而减小。在有高差存在的台阶地形中，高程和爆源水平距离的共同作用影响爆破振动速度的大小。
2. 反应高程的数学模型
根据模拟实验数据的分析结果，结合对各参考文献中爆破振动速度计算经验公式的分析，认为用下式对台阶地形爆破振动速度计算更为准确：
v=K(3√QR)α(3√QH)β H≠0 (2) 式中：v为质点峰值振动速度，Q为装药量，R为距爆源的水平距离，H为高程差，K、α、β为与岩石、地形相关的系数。
如图 6所示，炸药爆炸后产生的爆破地震波传播至点A、B、C时，水平距离R对振动速度的衰减作用相同，A点振动速度为v，由于高程的影响B点振速为v+v′，高差h1对振动速度起到放大作用；当单个台阶高程增加为h1+h2时，C点速度降为v-v″，此时高程对振动速度起到衰减的作用。式(2)中R为距爆源水平距离，不影响高差对振速的作用。高差H值在一定范围内，产生振速放大效应，数据拟合得到的β为负值；高程增加到某一值后，此时速度v随着H的不断增加而降低，数据拟合得到的β为正值。
图 6 高程对振速的放大与衰减示意图Figure 6. Amplification and attenuation of vibration velocity based on elevation3. 工程实例
露天深孔爆破炮孔直径310 mm，孔深14~17.5 m，超深2~2.5 m，填塞长度7~8 m，孔网参数：矿石a×b=(7~8) m×(6~7) m，岩石a×b=(5~9) m×(4~8) m。露天台阶高度12~15 m。
爆破振动监测工作采用TC-4850爆破测振仪，如图 7所示。布置8个测点采集各台阶坡底和坡顶质点振动速度，测点位置如图 8所示。
从表 3数据可知，测点4、6和8均出现振动速度放大现象，根据公式(2)进行数据拟合处理得：
表 3 爆破振动观测结果Table 3. Blasting vibration measurements测点 最大单孔起爆药量/kg 水平距离/m 垂直距离/m 峰值振动速度/(cm·s-1) MP1 500 14.8 0.0 38.35 MP2 44.1 30.8 3.33 MP3 86.4 43.0 1.41 MP4 90.3 54.0 1.50 MP5 132.8 63.0 0.94 MP6 140.3 74.1 1.08 MP7 183.3 90.2 0.69 MP8 190.9 103.0 0.87 v=18.76(3√Q/R)1.757 (3√Q/H)−0.945 相关系数r2=0.995 3；撒道夫斯基公式拟合相关系数为0.945 3，相关性与公式(2)相比较低，且不能直观体现地形高差对爆破振动速度的影响。
4. 结论
(1) 台阶表面质点振动速度随着距离的增加整体上呈指数衰减规律；对于单个台阶，由于高差的存在坡顶质点产生振动速度放大效应，放大效应在距爆源一定距离、达到一定高差的条件下产生。
(2) 坡顶质点振动速度放大倍数并不随台阶高度的增加而单调增加，台阶高度超过某一临界值后，放大倍数随台阶高度的增加而减小。
(3) 坡底面宽度越大，爆破振动速度衰减速率越快，相同高程处质点振动速度越小。
(4) 台阶地形爆破振动速度预测模型为v=K(3√QR)α(3√QH)β(H≠0)，模型对类似工程的爆破地震波衰减规律研究具有一定的参考价值。
-
图 3 不同升温速率下炸药各测点温度-时间曲线
Figure 3. Temperature-time curves of explosives at various monitoring points under different heating rates
图 5 不同升温速率下监测点温度及弹体内部压力曲线
Figure 5. Curves of monitoring-point temperature and internal pressure of the bomb at different heating rates
图 8 不同升温速率下点火时刻温度梯度示意图
Figure 8. Temperature gradient diagram of ignition moment at different heating rates
图 9 点火时刻烤燃弹体中轴线上的温度分布
Figure 9. Temperature distribution on the central axis of the cook-off bomb at ignition moment
图 10 不同热刺激强度下烤燃弹点火时刻的温度及内部压力曲线
Figure 10. Temperature and internal pressure curves of the cook-off bomb at ignition moment under different thermal stimulation intensities
图 11 不同热刺激强度下烤燃弹点火时刻的温度分布
Figure 11. Temperature distribution in the cook-off bomb at ignition moment under different thermal stimulation intensities
图 12 不同热刺激强度下烤燃弹反应进度曲线
Figure 12. Extents of reaction of the cook-off bomb under different thermal stimulation intensities
表 1 点火时刻及点火时刻不同测点的温度
Table 1. Ignition moments as well as temperatures of different measuring pointsat ignition moments
升温速率/(℃·min−1) 点火时刻/s T1/℃ T2/℃ T3/℃ 0.1 43920 203.9 220.2 205.3 1.0 10740 209.0 221.9 230.4 注：T1、T2和T3分别为点火时刻测点1～3的温度。 
下载: 导出CSV
表 2 不同网格尺寸模型的数值计算结果
Table 2. Numerically-calculated results by the models with different grid sizes
网格尺寸/mm 网格数量 外壁温度/℃ 内部压力/MPa 0.3 2806242 215.26 10.65 0.4 1196698 215.27 10.96 0.5 734650 214.93 11.26
下载: 导出CSV
表 3 2种升温速率下点火时间及监测点温度计算值与试验值的对比
Table 3. Comparison of calculated and experimental values of ignition time and temperatureat monitoring points under two different heating rates
升温速率/
(℃·min−1)点火时间 T1 T2 T3 试验值/s 计算值/s 误差/% 试验值/℃ 计算值/℃ 误差/% 试验值/℃ 计算值/℃ 误差/% 试验值/℃ 计算值/℃ 误差/% 0.1 43920 42100 4.14 203.9 200.39 1.72 220.2 218.97 0.56 205.3 213.34 −3.92 1.0 10740 11160 −3.91 209.0 214.93 −2.84 221.9 227.26 −2.42 230.4 228.40 0.87
下载: 导出CSV
-
[1] 曾稼, 智小琦, 于永利, 等. 热刺激强度对DNAN基熔铸炸药烤燃响应特性的影响 [J]. 火炸药学报, 2018, 41(2): 131–136. DOI: 10.14077/j.issn.1007-7812.2018.02.005.ZENG J, ZHI X Q, YU Y L, et al. Effect of thermal stimulation intensity on cook-off response characteristics of DNAN based casting explosives [J]. Chinese Journal of Explosives and Propellants, 2018, 41(2): 131–136. DOI: 10.14077/j.issn.1007-7812.2018.02.005. [2] 李凌峰, 韩秀凤, 沈飞, 等. 典型约束环境下HMX基温压炸药内爆释能特性 [J]. 火工品, 2022(2): 48–53. DOI: 10.3969/j.issn.1003-1480.2022.02.011.LI L F, HAN X F, SHEN F, et al. Internal explosion energy release characteristics of HMX-based thermos-baric explosive in typical confined environment [J]. Initiators and Pyrotechnics, 2022(2): 48–53. DOI: 10.3969/j.issn.1003-1480.2022.02.011. [3] 智小琦, 胡双启, 李娟娟, 等. 不同约束条件下钝化RDX的烤燃响应特性 [J]. 火炸药学报, 2009, 32(3): 22–24, 34. DOI: 10.3969/j.issn.1007-7812.2009.03.007.ZHI X Q, HU S Q, LI J J, et al. Cook-off response characteristics of desensitizing RDX explosive under different restriction conditions [J]. Chinese Journal of Explosives and Propellants, 2009, 32(3): 22–24, 34. DOI: 10.3969/j.issn.1007-7812.2009.03.007. [4] 董泽霖, 屈可朋, 胡雪垚, 等. 约束方式和强度对HMX基压装含铝炸药慢烤响应特性的影响 [J]. 火炸药学报, 2023, 46(10): 897–904. DOI: 10.14077/j.issn.1007-7812.202212010.DONG Z L, QU K P, HU X Y, et al. Effect of restraint mode and strength on slow cook-off response characteristics of HMX-based pressed aluminized explosives [J]. Chinese Journal of Explosives and Propellants., 2023, 46(10): 897–904. DOI: 10.14077/j.issn.1007-7812.202212010. [5] 沈飞, 王胜强, 王辉. 不同约束条件下HMX基含铝炸药的慢烤响应特性 [J]. 火炸药学报, 2019, 42(4): 385–390. DOI: 10.14077/7812.2019.04.012.SHEN F, WANG S Q, WANG H. Slow cook-off response characteristics of HMX-based aluminized explosives under different constraint conditions [J]. Chinese Journal of Explosives and Propellants, 2019, 42(4): 385–390. DOI: 10.14077/7812.2019.04.012. [6] 智小琦, 胡双启. 炸药装药密度对慢速烤燃响应特性的影响 [J]. 爆炸与冲击, 2013, 33(2): 221–224. DOI: 10.11883/1001-1455(2013)02-0221-04.ZHI X Q, HU S Q. Influences of charge densities on responses of explosives to slow cook-off [J]. Explosion and Shock Waves, 2013, 33(2): 221–224. DOI: 10.11883/1001-1455(2013)02-0221-04. [7] 赵亮. 尺寸效应对炸药烤燃响应特性影响的研究[D]. 太原: 中北大学, 2018.ZHAO L. Research on the effect of size effect on the flaming characteristics of explosives [D]. Taiyuan: North University of China, 2018. [8] 刘子德, 智小琦, 王帅, 等. 几何尺寸对DNAN基熔铸炸药慢烤响应特性的影响 [J]. 火炸药学报, 2019, 42(1): 63–68. DOI: 10.14077/j.issn.1007-7812.2019.01.010.LIU Z D, ZHI X Q, WANG S, et al. Effect of geometric dimensions on slow cook-off response characteristics of DNAN-based melt-casting explosive [J]. Chinese Journal of Explosives and Propellants, 2019, 42(1): 63–68. DOI: 10.14077/j.issn.1007-7812.2019.01.010. [9] 马欣, 陈朗, 鲁峰, 等. 烤燃条件下HMX/TATB基混合炸药多步热分解反应计算 [J]. 爆炸与冲击, 2014, 34(1): 67–74. DOI: 10.11883/1001-1455(2014)01-0067-08.MA X, CHEN L, LU F, et al. Calculation on multi-step thermal decomposition of HMX- and TATB-based composite explosives under cook-off conditions [J]. Explosion and Shock Waves, 2014, 34(1): 67–74. DOI: 10.11883/1001-1455(2014)01-0067-08. [10] DICKSON P M, ASAY B W, HENSON B F, et al. Measurement of phase change and thermal decomposition kinetics during cookoff of PBX9501 [J]. AIP Conference Proceedings, 2000, 505(1): 837–840. [11] PERRY W L , GUNDERSON J A , DICKSON P M . Application of a four-step HMX kinetic model to an impact-induced fraction ignition problems[C]//14th International Detonation Symposium. Coeur d'Alene, Idaho, United States, 2010. [12] HOBBS M L, KANESHIGE M J, ERIKSON W W. A universal cookoff model for explosives[C]//50th International Annual Conference of the Fraunhofer ICT. Karlsruhe, Germany, 2019. [13] 范士锋, 董平, 李鑫, 等. 国外海军弹药安全性研究进展 [J]. 火炸药学报, 2017, 40(2): 101–106. DOI: 10.14077/j.issn.1007-7812.2017.02.019.FAN S F, DONG P, LI X, et al. Research progress in the safety of foreign naval ammunition [J]. Chinese Journal of Explosives and Propellants, 2017, 40(2): 101–106. DOI: 10.14077/j.issn.1007-7812.2017.02.019. [14] 董泽霖, 屈可朋, 胡雪垚, 等. 升温速率对HMX基大长径比压装装药烤燃特性的影响研究 [J]. 火工品, 2023(4): 56–60. DOI: 10.3969/j.issn.1003-1480.2023.04.011.DONG Z L, QU K P, HU X Y, et al. Study on the effect of heating rate on the cook-off characteristics of HMX-based pressure charge with large aspect ratio [J]. Initiators and Pyrotechnics, 2023(4): 56–60. DOI: 10.3969/j.issn.1003-1480.2023.04.011. [15] 封雪松, 冯晓军, 赵娟, 等. 铝粉含量和粒度对HMX基炸药空爆性能的影响 [J]. 爆破器材, 2018, 47(4): 10–15. DOI: 10.3969/j.issn.1001-8352.2018.04.002.FENG X S, FENG X J, ZHAO J, et al. Effect of content and particle size of aluminum powder on the air blast property of HMX-based explosive [J]. Explosive Materials, 2018, 47(4): 10–15. DOI: 10.3969/j.issn.1001-8352.2018.04.002. [16] HOBBS M L, KANESHIGE M J. Ignition experiments and models of a plastic bonded explosive (PBX 9502) [J]. The Journal of Chemical Physics, 2014, 140(12): 124203. DOI: 10.1063/1.4869351. [17] HENSON B F, SMILOWITZ L, ASAY B W, et al. The β-δ phase transition in the energetic nitramine octahydro-1, 3, 5, 7-tetranitro-1, 3, 5, 7-tetrazocine: thermodynamics [J]. The Journal of Chemical Physics, 2002, 117(8): 3780–3788. DOI: 10.1063/1.1495398. [18] 周建兴, 刘瑞祥, 陈立亮, 等. 凝固过程数值模拟中的潜热处理方法 [J]. 铸造, 2001, 50(7): 404–407. DOI: 10.3321/j.issn:1001-4977.2001.07.010.ZHOU J X, LIU R X, CHEN L L, et al. The approaches of latent heat treatment [J]. Foundry, 2001, 50(7): 404–407. DOI: 10.3321/j.issn:1001-4977.2001.07.010. [19] HOBBS M L, KANESHIGE M J, ERIKSON W W. Modeling the measured effect of a nitroplasticizer (BDNPA/F) on cookoff of a plastic bonded explosive (PBX 9501) [J]. Combustion and Flame, 2016, 173: 132–150. DOI: 10.1016/j.combustflame.2016.08.014. [20] TARVER C M, TRAN T D. Thermal decomposition models for HMX-based plastic bonded explosives [J]. Combustion and Flame, 2004, 137(1/2): 50–62. DOI: 10.1016/j.combustflame.2004.01.002. [21] BAO Q, FANG Q, ZHANG Y D, et al. Effects of gas concentration and venting pressure on overpressure transients during vented explosion of methane-air mixtures [J]. Fuel, 2016, 175: 40–48. DOI: 10.1016/j.fuel.2016.01.084. [22] 韦世豪, 杜扬, 王世茂, 等. 不同形状受限空间内油气爆燃特性的实验研究 [J]. 中国安全生产科学技术, 2017, 13(5): 41–47. DOI: 10.11731/j.issn.1673-193x.2017.05.007.WEI S H, DU Y, WANG S M, et al. Experimental study on deflagration characteristics of gasoline-air mixture in confined space with different shapes [J]. Journal of Safety Science and Technology, 2017, 13(5): 41–47. DOI: 10.11731/j.issn.1673-193x.2017.05.007. [23] 傅献彩, 沈文霞, 姚天扬, 等. 物理化学(上) [M]. 5版. 北京: 高等教育出版社, 2005: 99–103. -
下载:
计量
- 文章访问数: 166
- HTML全文浏览量: 65
- PDF下载量: 76
- 被引次数: 0