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1. 中北大学 机电工程学院, 山西 太原 030051
2. 中国兵器装备集团自动化研究所有限公司 智能制造事业部, 四川 绵阳 621000
3. 湖北航天化学技术研究所 航天化学动力技术重点实验室, 湖北 襄阳 441003
Received:04 July 2022,
Published Online:25 July 2023,
Published:28 April 2023
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Kun ZHANG, Xiaoqi ZHI, You XIAO, et al. Theoretical Calculation of IgnitionLocation and Temperature for One-Dimensional Slow-Cook Model[J]. Acta Armamentarii, 2023, 44(4): 1139-1147.
Kun ZHANG, Xiaoqi ZHI, You XIAO, et al. Theoretical Calculation of IgnitionLocation and Temperature for One-Dimensional Slow-Cook Model[J]. Acta Armamentarii, 2023, 44(4): 1139-1147. DOI: 10.12382/bgxb.2022.0599.
为理论分析凝聚炸药慢速烤燃过程
及为烤燃研究奠定理论基础
根据炸药的热传导理论方程
利用叠加原理和分离变量法
将炸药非反应性热传导项与自热反应热传导项拆分
推导得到凝聚炸药一维慢速烤燃模型的温度分布解析解。计算并分析自热反应温度最高值所在位置随加热时间的变化规律以及自热反应温度最高值及温度梯度随厚度的变化规律。根据慢烤试验结果
对温度沿轴向的分布情况进行验证;利用数值计算方法对药柱烤燃的点火点位置、点火温度及时间进行验证。研究结果表明:理论确定的点火点位置与试验测量的点火点位置相符
理论确定的计算结果与数值计算结果吻合;对于一维RDX炸药
自热反应最高温度所在位置的变化从始至点火不足2%
即炸药自热反应的最高温度所在位置在烤燃过程中几乎不变;且当炸药厚度达到0.3m后
随着炸药厚度的增加
点火点位置至边界的距离趋于恒定值 0.015m
炸药内部温度梯度相似。
To theoretically analyze the slow-cook process of condensed explosives and lay a theoretical foundation for the study of cook-off
based on the theoretical equation for heat conduction of explosives
the non-reactive heat conduction and self-heating reaction heat conduction of explosives are separated by using the superposition principle and the method of separating variables. Therefore
an analytical solution of temperature distribution for one-dimensional slow-cook model of condensed explosives is derived. The variation of the location of the maximum temperature of the self-heating reaction with heating time is calculated and studied
along with the variation of maximum temperature of self-heating reaction and temperature gradient with thickness. According to the results of the slow-cook test
the temperature distribution along the axial direction is verified. The ignition position
ignition temperature and ignition time are verified by numerical calculation. The results show that the ignition position determined by theory is consistent with the measured result by experiment. The calculation results determined by theory are consistent with the numerical calculation results. As far as one-dimensional RDX explosives is concerned
the location change of the maximum temperature is less than 2% from beginning to ignition
which can be ignored. Therefore
the location of the maximum temperature of self-heating reaction of explosives is almost unchanged during the slow-cook process. When the thickness of explosive reaches 0.3m
with the increase of the explosive thickness
the distance from the ignition position to the boundary tends to be a constant value of 0.015m. The temperature gradients inside these explosives are similar.
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 http://doi.org/10.14077/j.issn.1007-7812.2019.01.010 为提高偏二甲肼(UDMH)废水的处理效率,采用活性炭-微波-Fenton联用技术对UDMH废水进行处理,考察了H<sub>2</sub>O<sub>2</sub>体积、微波功率、pH值、Fe<sup>2+</sup>与H<sub>2</sub>O<sub>2</sub>的摩尔比、活性炭质量等参数对UDMH废水处理效果的影响; 初步探讨了主要降解中间产物甲醛、氰根离子的变化规律; 在最佳反应条件下,对COD质量浓度与时间的关系进行线性拟合。结果表明,对于100mL质量浓度400mg/L的UDMH废水,在68.5g/L的H<sub>2</sub>O<sub>2</sub>体积4.0mL、微波功率460W、活性炭质量5.0g、pH值为3.5、n(Fe<sup>2+</sup>):n(H<sub>2</sub>O<sub>2</sub>)=1:10的条件下,废水中COD和UDMH的去除率最高,分别为98.0%和99.3%; 主要降解中间产物甲醛和氰根离子的浓度随着反应的进行达到峰值后迅速降低,最后基本可以实现完全降解; 线性拟合发现废水中的COD去除率遵循一级反应动力学特征,其动力学方程为:ln(C<sub>0</sub>/C)=0.00355t+0.1755; 活性炭-微波-Fenton联用技术处理UDMH废水,在反应开始6min内即可达到较为理想的效果,具有反应迅速的特点。该技术操作方便、成本低廉、无二次污染、装置简单且占地面积小、有机物矿化度高,是一种高效的UDMH废水处理技术。
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 . (in Chinese)
马欣 , 陈朗 . HMX基混合炸药烤燃特性及多步热反应计算 [J ] . 兵工学报 , 2015 , 36 ( 增刊1 ): 334 - 342 .
MA X , CHEN L . Research on cook-off characteristics and multistep thermal decomposition calculation of HMX-based explosive [J ] . Acta Armamentarii , 2015 , 36 ( S1 ): 334 - 342 . (in Chinese)
TRINGE J W , GLASCOE E A , MCCLELLAND M A , et al. Pre-ignition confinement and deflagration violence in LX-10 and PBX 9501 [J ] . Journal of Applied Physics , 2014 , 116 ( 5 ): 054903 . DOI: 10.1063/1.4891994 http://doi.org/10.1063/1.4891994 https://pubs.aip.org/jap/article/116/5/054903/363827/Pre-ignition-confinement-and-deflagration-violence https://pubs.aip.org/jap/article/116/5/054903/363827/Pre-ignition-confinement-and-deflagration-violence In thermal explosions of the nitramine octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX)-based explosives LX-10 and PBX-9501, the pre-ignition spatial and temporal heating profile defines the ignition location. The ignition location then determines the extent of inertial confinement and the violence of the resulting deflagration. In this work, we present results of experiments in which ∼23 g cylinders of LX-10 and PBX 9501 in thin-walled aluminum confinement vessels were subjected to identical heating profiles but which presented starkly different energy release signatures. Post-explosion LX-10 containment vessels were completely fragmented, while the PBX 9501 vessels were merely ruptured. Flash x-ray radiography images show that the initiation location for the LX-10 is a few mm farther from the end caps of the vessel relative to the initiation location of PBX 9501. This difference increases deflagration confinement for LX-10 at the time of ignition and extends the pressurization time during which the deflagration front propagates in the explosive. The variation in the initiation location, in turn, is determined by the thermal boundary conditions, which differ for these two explosives because of the larger coefficient of thermal expansion and greater thermal stability of the Viton binder in LX-10 relative to the estane and bis(2,2-dinitropropyl) acetal/formal binder of the PBX 9501. The thermal profile and initiation location were modeled for LX-10 using the hydrodynamics and structures code ALE3D; results indicate temperatures in the vicinity of the ignition location in excess of 274 °C near the time of ignition. The conductive burn rates for these two explosives, as determined by flash x-ray radiography, are comparable in the range 0.1–0.2 mm/μs, somewhat faster than rates observed by strand burner experiments for explosives in the temperature range 150–180 °C and pressures up to 100 MPa. The thinnest-wall aluminum containment vessels presented here rupture at lower pressures, in the range 10 MPa, suggesting that moderately higher temperatures and pressures are present near the deflagration front. For these explosives, however the most important property for determining deflagration violence is the degree of inertial confinement.
邓海 , 赵小锋 , 任新联 , 等 . 不同约束条件下硝酸酯类PBX炸药装药慢烤响应特性 [J ] . 火炸药学报 , 2021 , 44 ( 5 ): 652 - 657 . DOI: 10.14077/j.issn.1007-7812.202106003 http://doi.org/10.14077/j.issn.1007-7812.202106003 为了探究具有短程有序、长程无序的非晶态纳米氧化物对含能材料的催化分解性能,以乙酰丙酮镍为原料,通过高温煅烧制备出了非晶态纳米NiO; 采用X射线衍射(XRD)、X射线光电子能谱(XPS)、扫描电子显微镜(SEM)、高分辨率透射电子显微镜(HRTEM)、N<sub>2</sub>吸附-脱附法(BET)和差示扫描量热法(DSC)等研究了其组成、结构及其对高氯酸铵(AP)和GAP基推进剂的催化分解性能。结果表明, 非晶态纳米NiO可使AP的热分解峰温由406.4℃降至309.5℃,表观分解活化能由158.17kJ/mol降至129.82kJ/mol,放热量由747.7J/g增至1780J/g; 与晶态纳米NiO相比,非晶态纳米NiO使GAP基推进剂的燃速提高了约10%,压力指数降低了约9.7%。
DENG H , ZHAO X F , REN X L , et al. Slow cook-off response characteristics of nitrate explosive PBX charge under different constraint conditions [J ] . Chinese Journal of Explosives and Propellants , 2021 , 44 ( 5 ): 652 - 657 . (in Chinese)
HOBBS M L , KANESHIGE M J . Ignition experiments and models of a plastic bonded explosive (PBX9502) [J ] . Journal of Chemical Physics , 2014 , 140 ( 12 ): 124203 . DOI: 10.1063/1.4869351 http://doi.org/10.1063/1.4869351 https://pubs.aip.org/jcp/article/140/12/124203/211881/Ignition-experiments-and-models-of-a-plastic https://pubs.aip.org/jcp/article/140/12/124203/211881/Ignition-experiments-and-models-of-a-plastic Ignition experiments from various sources, including our own laboratory, have been used to develop a simple four-step, pressure-dependent ignition model for PBX 9502, which is composed of 95% by mass triaminotrinitrobenzene (TATB) and a 5% by mass chlorotrifluoroethylene/vinylidine fluoride binder. The four-steps include drying, mono-furazan formation, and decomposition of mono-furazan and TATB into equilibrium products. Our experiments were both sealed and vented and included various ullage percentages ranging from 18% to 75% of unfilled confinement volume. Our sample densities ranged from 38% of the theoretical maximum density (TMD) to 98% TMD. We observed a decrease in ignition times with the higher density samples, an increase in ignition times with increased venting, and an increase in ignition times with increased ullage. From our experiments, we conclude that decomposition of PBX 9502 is pressure dependent, open pore decomposition occurs in low-density experiments, and that closed pore decomposition occurs when the samples are pressed to near full density. In some of our confined high-density experiments we have observed for the first time, multiple temperature excursions prior to ignition caused by internal pressure generation.
ZHI X Q , HU S Q . RDX-based energetic material cook-off characters in different clearances [J ] . Applied Mechanics and Materials , 2011 , 29 ( 2 ) : 75 - 87 .
ESSEL J T , NELSON A P , SMILOWITZ L B , et al. Investigating the effect of chemical ingredient modifications on the slow cook-off violence of ammonium perchlorate solid propellants on the laboratory scale [J ] . Journal of Energetic Materials , 2020 , 32 ( 8 ): 127 - 141 .
周捷 , 智小琦 , 刘子德 , 等 . 2, 4-二硝基苯甲醚基熔铸炸药慢速烤燃过程传热特征分析 [J ] . 兵工学报 , 2019 , 40 ( 6 ): 1154 - 1160 . DOI: 10.3969/j.issn.1000-1093.2019.06.005 http://doi.org/10.3969/j.issn.1000-1093.2019.06.005 为探究2,4-二硝基苯甲醚基熔铸炸药慢速烤燃过程的内部传热特征,设计了3组试验装置并进行烤燃试验。通过试验获得了炸药内部各测点在1 K/min热刺激下的温度变化曲线,其相变温度为73 ℃,响应温度为205 ℃,响应后均表现为不完全燃烧反应;结合响应结果判断出点火点位于弹体上部;系统地描述了炸药从固相到液相再到响应的内部温度变化过程。通过数值模拟观察了炸药相变的整个过程,对炸药受热时内部温度场变化进一步分析后发现:固相时炸药内部温度场为同心类椭圆状分布,液相时内部温度场为类层状分布;炸药相变后内部存在自然对流,对流是影响炸药点火点位置分布的主要因素。
ZHOU J , ZHI X Q , LIU Z D , et al. Analysis of the heat transfer characteristics of DNAN-based melt-cast explosive in slow cook-off test [J ] . Acta Armamentarii , 2019 , 40 ( 6 ): 1154 - 1160 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2019.06.005 http://doi.org/10.3969/j.issn.1000-1093.2019.06.005 3 experimental devices were designed to investigate the internal heat transfer characteristics of 2,4-dinitroanisole(DNAN)-based melt-cast explosive in slow cook-off test, and tested by scaled thermal explosion experiment. The temperature curves of internal monitoring points in the explosive under a thermal stimulus with the rate of 1 K/min were obtained. It is found that the phase-transition temperature is 73 ℃, the ignition temperature is 205 ℃, and the incomplete combustion reaction occurs after ignition. The ignition location is estimated to be on the upper half of bomb body. The changing process of internal temperature of DNAN-based melt-cast explosive is described. The internal temperature field was analyzed by numerical simulation, and the whole process of phase transition was observed. The results show that the internal temperature field of explosive in solid phase is elliptical, and its internal temperature field in liquid phase is layered. A natural convection arises inside the explosive after phase transition, which is a major factor to affect the ignition location distribution of the explosive. Key
王琦 , 智小琦 , 肖游 , 等 . 基于UCM模型的B炸药慢烤泄压结构的作用分析 [J ] . 爆炸与冲击 , 2022 , 42 ( 4 ): 36 - 44 .
WANG Q , ZHI X Q , XIAO Y , et al. Analysis of the effect of a venting structure on slow cookoff of Comp-B based on a universal cookoff model [J ] . Explosion and Shock Waves , 2022 , 42 ( 4 ): 36 - 44 . (in Chinese)
HOBBS M L , KANESHIGE M J , ERIKSON W W , et al. Cookoff modeling of a melt cast explosive (Comp-B) [J ] . Combustion and Flame , 2020 , 215 : 36 - 50 . DOI: 10.1016/j.combustflame.2020.01.022 http://doi.org/10.1016/j.combustflame.2020.01.022 https://linkinghub.elsevier.com/retrieve/pii/S0010218020300341 https://linkinghub.elsevier.com/retrieve/pii/S0010218020300341
MANNER V W , CAWKWELL M J , KOBER E M , et al. Examining the chemical and structural properties that influence the sensitivity of energetic nitrate esters [J ] . Chemical Science , 2018 , 9 ( 15 ): 3649 - 3663 . DOI: 10.1039/c8sc00903a http://doi.org/10.1039/c8sc00903a The sensitivity of explosives is controlled by factors that span from intrinsic chemical reactivity and chemical intramolecular effects to mesoscale structure and defects, and has been a topic of extensive study for over 50 years. Due to these complex competing chemical and physical elements, a unifying relationship between molecular framework, crystal structure, and sensitivity has yet to be developed. In order to move towards this goal, ideally experimental studies should be performed on systems with small, systematic structural modifications, with modeling utilized to interpret experimental results. Pentaerythritol tetranitrate (PETN) is a common nitrate ester explosive that has been widely studied due to its use in military and commercial explosives. We have synthesized PETN derivatives with modified sensitivity characteristics by substituting one -CCHONO moiety with other substituents, including -CH, -CNH, -CNHX, -CCH, and -PO. We relate the handling sensitivity properties of each PETN derivative to its structural properties, and discuss the potential roles of thermodynamic properties such as heat capacity and heat of formation, thermal stability, crystal structure, compressibility, and inter- and intramolecular hydrogen bonding on impact sensitivity. Reactive molecular dynamics (MD) simulations of the C/H/N/O-based PETN-derivatives have been performed under cook-off conditions that mimic those accessed in impact tests. These simulations infer how changes in chemistry affect the subsequent decomposition pathways.
戴湘晖 , 段建 , 沈子楷 , 等 . 侵彻弹体慢速烤燃响应特性实验研究 [J ] . 兵工学报 , 2020 , 41 ( 2 ): 291 - 297 . DOI: 10.3969/j.issn.1000-1093.2020.02.010 http://doi.org/10.3969/j.issn.1000-1093.2020.02.010 为考核全尺寸侵彻弹体的慢速烤燃响应特性,利用自行研制的慢速烤燃装置开展了实验。将质量为290 kg的侵彻弹体平放在慢烤箱中以3.3 ℃/h的升温速率缓慢加热,实时采集弹体表面温度曲线并拍摄整个实验过程,测量距弹体质心水平7 m处的反射冲击波峰值超压。实验结果表明:全尺寸侵彻弹体在加热42 h45 min23 s、温度达到约190 ℃时发生燃烧,41 s后发生了更为剧烈的反应,弹体和慢烤箱被炸裂成大块破片;通过反射冲击波超压峰值反推弹体剧烈反应时对应的等效裸露装药当量为4.153 kg,远小于实际装药当量和完全爆轰时的等效裸露装药当量;从加热时间、弹体表面温度、实验现场破坏情况、反射冲击波峰值超压、反应机理等方面综合判断该侵彻弹体的慢速烤燃响应类型为燃烧转爆炸。
DAI X H , DUAN J , SHEN Z K , et al. Experiment of slow cook-off response characteristics of penetrator [J ] . Acta Armamentarii , 2020 , 41 ( 2 ): 291 - 297 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2020.02.010 http://doi.org/10.3969/j.issn.1000-1093.2020.02.010 An experimental device was designed for evaluating the slow cook-off response characteristic of full-scale penetrator. The penetrator with a mass of 290 kg was placed in the slow cook-off oven and slowly heated at a heating rate of 3.3 ℃/h. The surface temperature of penetrator was collected in real time, and the whole experimental process was recorded. The peak value of reflected shock wave overpressure at a distance of 7 m from the mass center of penetrator was measured. The full-scale penetrator burns when it is heated for 42 hours, 45 minutes and 23 seconds and the temperature reaches 190 ℃, a more intense reaction occurs after 41 seconds, and the slow cook-off oven and the penetrator are exploded to form large fragments. The exposed explosive equivalent is deduced to be 4.153 kg from peak value of the reflected shock wave overpressure, which is far less than the actual charge equivalent and the exposed explosive equivalent during full detonation. Based on the analysis of the heating time, the surface temperature of penetrator, the damage on experimental site, the fragments of penetrator, the peak value of reflected shock wave overpressure and the reaction mechanism, the slow cook-off response type of penetrator is judged to be combustion-to-explosion transition.Key
GAMBINO J R , TARVER C M , SPRINGER H K . Numerical parameter optimizations of the Ignition and Growth model for a HMX plastic bonded explosive [J ] . Journal of Applied Physics , 2018 , 124 ( 19 ): 195901 . DOI: 10.1063/1.5052339 http://doi.org/10.1063/1.5052339 https://pubs.aip.org/jap/article/124/19/195901/286661/Numerical-parameter-optimizations-of-the-Ignition https://pubs.aip.org/jap/article/124/19/195901/286661/Numerical-parameter-optimizations-of-the-Ignition We present a novel method for optimizing parameters of the Ignition and Growth (I&amp;G) reactive flow model for high explosives. The I&amp;G model predicts the shock initiation response of explosives subjected to dynamic loading. However, calibrating the model is a time-consuming process because it has several parameters, typically requires multiple data sets, and there are no direct correlations between parameters and data. In this study, we couple a scalable optimization algorithm to simulations of shock initiation experiments in the multi-physics code ALE3D. We develop four I&amp;G model parameter sets for the HMX (1,3,5,7-tetranitro-1,3,5,7-tetrazocane)-based explosive LX-07 [90 wt. % HMX, 10 wt. % Viton A] based on minimizing the difference between calculations and measurements at the embedded pressure gauges in 1D gun shock experiments. Our study shows that a cost function based on both shock time of arrival and pressure pulse shape demonstrates the best agreement with experimental data.
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KALIS H , KANGRO I . Simple algorithm’s for the calculation of heat transport problem in plate [J ] . Mathematical Modelling and Analysis , 2001 , 6 ( 1 ): 85 - 96 . DOI: 10.3846/13926292.2001.9637148 http://doi.org/10.3846/13926292.2001.9637148 https://journals.vilniustech.lt/index.php/MMA/article/view/9887 https://journals.vilniustech.lt/index.php/MMA/article/view/9887 The approximations of some heat transport problem in a thin plate are based on the finite volume and conservative averaging methods [1,2]. These procedures allow one to reduce the two dimensional heat transport problem described by a partial differential equation to an initial‐value problem for a system of two ordinary differential equations (ODEs) of the first order or to an initial‐value problem for one ordinary differential equations of the first order with one algebraic equation. Solution of the corresponding problems is obtained by using MAPLE routines “gear”, “mgear” and “lsode”.
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