一维慢速烤燃模型点火点位置及其温度的理论计算

doi:10.12382/bgxb.2022.0599

摘要/Abstract

摘要：

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。

关键词: 弹药, 慢速烤燃, 点火点位置, 热传导

Abstract:

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.

Key words: ammunition, slow-cook, ignition location, heat conduction

张坤, 智小琦, 肖游, 王帅. 一维慢速烤燃模型点火点位置及其温度的理论计算[J]. 兵工学报, 2023, 44(4): 1139-1147.

ZHANG Kun, ZHI Xiaoqi, XIAO You, WANG Shuai. Theoretical Calculation of IgnitionLocation and Temperature for One-Dimensional Slow-Cook Model[J]. Acta Armamentarii, 2023, 44(4): 1139-1147.

图/表 15

图1 温度测点的位置示意图

Fig.1 Location of temperature measuring points

图2 试验弹体

Fig.2 Tested ammunition

图3 慢速烤燃试验装置

Fig.3 Slow-cook test setup

表1 点火时刻热电偶的测量结果

Table 1 Measurement results of thermocouple

测点	外壁	1号	2号	3号	4号	5号
温度/K	468.9	461.7	460.9	460.7	460.8	461.7

图4 温度变化曲线

Fig.4 Temperature history curves

图5 试验结果

Fig.5 Test results

表2 RDX炸药物性参数和动力学参数

Table 2 Properties and kinetic parameters of RDX explosives

ρ/(kg·m^-3)	c/(J·kg^-1·K^-1)	λ/(W·m^-1·K^-1)	E/(J·mol^-1)	A/s^-1	Q/(J·kg^-1)
1610	1130	0.25	202730	5.8×10¹⁸	21010

表3 沿轴线方向的温度值

Table 3 Temperature value along the axis

位置/m	温度/K	位置/m	温度/K
-0.1425	480.6	0.0285	408.8
-0.1140	461.6	0.0570	418.8
-0.0855	436.4	0.0855	436.4
-0.0570	418.8	0.1140	461.6
-0.0285	408.5	0.1425	480.6
0	405.1

图6 温度分布

Fig.6 Temperature distribution

图7 相对温度分布

Fig.7 Relative temperature distribution

图8 点火点温度的理论解与数值解

Fig.8 Theoretical and numerical results of the temperature of ignition point

图9 炸药厚度L=0.285m时的理论计算结果与数值计算结果

Fig.9 Theoretical and numerical results with explosive thickness L=0.285m

图10 不同厚度炸药自热反应温度最高值所在的相对位置

Fig.10 Relative location of the maximum value point of self-heating reaction temperature of explosives with different thicknesses

图11 自热反应温度最高值所在位置至边界的距离

Fig.11 Distance from the maximum value point of self-heating reaction temperature to boundary

图12 炸药边界到中心的自热反应温度梯度

Fig.12 Temperature gradient of self-heating reaction from boundary to center of explosives

参考文献 23

[1]	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. (in Chinese)
[2]	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)
[3]	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 URL
[4]	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
	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)
[5]	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 URL
[6]	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.
[7]	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.
[8]	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
	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
[9]	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)
[10]	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 URL
[11]	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 pmid: 29780495
[12]	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
	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
[13]	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 URL
[14]	FRANK D A. Calculation of thermal explosion limits[J]. Acta Physicochim, 1939, 10: 365-370.
[15]	MYERS G E. Analytical methods in conduction heat transfer[M]. 2nd ed. Madison, WI, US: AMCHT Publications, 1998:141-148.
[16]	SUBANI N, JAMALUDDIN F, MOHAMED M. Analytical solution of homogeneous one-dimensional heat equation with neumann boundary conditions[C]//Proceedings of the 2nd International Conference on Recent Advancements in Science and Technology. Putrajaya, Malaysia: IOP Publishing Ltd., 2020, 1551: 012002.
[17]	LAMB G L. Introductory applications of partial differential equations (with emphasis on wave propagation and diffusion)Y[M]. New York,N, US: Wiley & Sons, 1995:1-59.
[18]	AGHILI A, SUKHORUKOVA N, UGON J. Bivariate rational approximations of the general temperature integral[J]. Journal of Mathematical Chemistry, 2021, 59(9): 2049-2062. doi: 10.1007/s10910-021-01273-z
[19]	杨世铭, 陶文铨. 传热学[M]. 第3版. 北京: 高等教育出版社, 1998.
	YANG S M, TAO W Q. Heat transfer[M]. 3rd ed. Beijing: Higher Education Press, 1998. (in Chinese)
[20]	NDLOVU P L, MOITSHEKI R J. Analysis of transient heat transfer in radial moving fins with temperature-dependent thermal properties[J]. Journal of Thermal Analysis and Calorimetry, 2019, 138(4):2913-2921. doi: 10.1007/s10973-019-08306-5
[21]	TREFETHEN L N. Exactness of quadrature formulas[J]. Siam Review, 2022, 64(1): 132-150. doi: 10.1137/20M1389522 URL
[22]	SUCESKA M. A computer program based on finite difference method for studying thermal initiation of explosives[J]. Journal of Thermal Analysis and Calorimetry, 2002, 65: 865-875. doi: 10.1023/A:1011940502316 URL
[23]	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 URL