Theoretical Calculation of IgnitionLocation and Temperature for One-Dimensional Slow-Cook Model

doi:10.12382/bgxb.2022.0599

Abstract

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

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.

Figures/Tables 15

Fig.1 Location of temperature measuring points

Fig.2 Tested ammunition

Fig.3 Slow-cook test setup

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

Fig.4 Temperature history curves

Fig.5 Test results

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

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

Fig.6 Temperature distribution

Fig.7 Relative temperature distribution

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

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

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

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

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

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