Property and Uncertainty Quantification of Detonation Pressure Based on Shock Hugoniot Relationship

doi:10.12382/bgxb.2022.1207

Abstract

Abstract:

The confidential interval of explosive shock Hugoniot parameters is exactly assessed and the uncertainties associated with shock ignition and equation of state are efficiently quantified to improve the robustness and reliability of the model and enormously reduce the calibration cost of detonation pressure. The linear regression method is utilized to calibrate the shock Hugoniot parameters, and the confidential interval of Hugoniot parameters are also deduced from parameter estimation. Moreover, the availability of Hugoniot model is validated through domestic experiment data. On the basis of reasonable assumptions, Chapman-Jouguet theory and shock Hugoniot relationship are combined to the functional relationships among detonation pressure. sample thickness, shock passing time, initial density, Hugoniot slope and 0-presure sound speed are deduced. The input uncertainty is characterized by log-normal distribution and Beta distribution, and it is transformed into independent standard normal random variables by Rosenblatt transformation. Polynomial chaos with basis adaptation is applied to implement uncertainty propagation, and the probability density function and confidential interval of detonation pressure is obtained. The results show that the detonation pressure satisfies the quasi-monotonicity with respect to sample thickness, passing time and detonation speed. The assertion of previous studies is confirmed in specific conditions. The confidence interval is much wider when it is used in PBX9502, which coincides with the prior judgment given by experimental expert. This study develops an efficient uncertainty quantification and propagation method. The result can provide technique support for developing highly predictable and confidential software.

Key words: shock Hugoniot relationship, uncertainty quantification, detonation pressure, Chapman-Jouguet theory, polynomial chaos with basis adaptation, quasi-monotonicity

CLC Number:

O381

LIANG Xiao, WANG Ruili. Property and Uncertainty Quantification of Detonation Pressure Based on Shock Hugoniot Relationship[J]. Acta Armamentarii, 2024, 45(5): 1673-1680.

Figures/Tables 7

Table 1 Data of shock Hugoniot experiment[21]

编号	u_p/(mm·μs^-1)	D_s/(mm·μs^-1)
1	0.618	3.788
2	0.779	4.028
3	0.48	3.433
4	0.963	4.502

Fig.1 Experimental data and shock Hugoniot curve of PBX9502

Fig.2 Histogram and PDF of initial density of PBX9502

Fig.3 Histogram and PDF of thickness of PBX9502

Fig.4 Histogram and PDF of passing time of shock wave

Fig.5 PDF of shock Hugoniot parameters

Fig.6 PDF of detonation pressure

References 27

[1]	孙承纬, 卫玉章, 周之奎. 应用爆轰物理[M]. 北京: 国防工业出版社, 2000.
	SUN C W, WEI Y Z, ZHOU Z K. Applied detonation physics[M]. Beijing: National Defense Industry Press, 2000.
[2]	舒俊翔, 裴红波, 黄文斌, 等. 几种常用炸药的爆压与爆轰反应区精密测量[J]. 爆炸与冲击, 2022, 42(5): 052301.
	SHU J X, PEI H B, HUANG W B, et al. Accurate measurement of detonation reaction zones of several commonly-used explosives[J]. Explosion and Shock Waves, 2022, 42(5): 052301. (in Chinese)
[3]	MADER C. Numerical modeling of detonation[M]. Berkeley,CA, US: University of California Press, 1979.
[4]	PERRY W, DUQUE A, MANG J, et al. Computing continuum-level explosive shock and detonation response over a wide pressure range from microstructural details[J]. Combustion and Flame, 2021, 231:111470.
[5]	LIANG X, WANG R L. Verification and validation of detonation modeling[J]. Defence Technology, 2019, 15(1):398-408.
[6]	LIANG X, WANG R L, GHANEM R. Uncertainty quantification of detonation through adapted polynomial chaos[J]. International Journal for Uncertainty Quantification, 2020, 10(1):83-100.
[7]	梁霄, 陈江涛, 王瑞利. 高维参数不确定爆轰的不确定度量化[J]. 兵工学报, 2020, 41(4):723-734.
	LIANG X, CHEN J T, WANG R L. Uncertainty quantification of detonation with high-dimensional parameter uncertainty[J]. Acta Armamentarii, 2020, 41(4):723-734. (in Chinese)
[8]	COLEMAN H, STEELE W. Experimentation and uncertainty: experimentation uncertainty analysis for engineers[M]. New York,NY, US: John Wiley & Sons, 1999.
[9]	戴诚达, 王翔, 谭华. Hugoniot实验的粒子速度测量不确定度分析[J]. 高压物理学报, 2005, 19(2):113-119.
	DAI C D, WANG X, TAN H. Equation for uncertainty of particle velocity in Hugoniot measurements[J]. Chinese Journal of High Pressure Physics, 2005, 19(2):113-119. (in Chinese)
[10]	DAVIS W. Complete equation of state for unreacted solid explosive[J]. Combustion & Flame, 2000, 120:399-403.
[11]	刘俊明, 张旭, 裴红波, 等. JB-9014钝感炸药冲击Hugoniot关系测量[J]. 高压物理学报, 2018, 32(3):033202.
	LIU J M, ZHANG X, PEI H B, et al. Measurement of Hugoniot relation for JB-9014 insensitive explosive[J]. Chinese Journal of High Pressure Physics, 2018, 32(3):033202. (in Chinese)
[12]	WESCOTT B, STEWART D, DAVIS W. Equation of state and reaction rate for condensed-phase explosive[J]. Journal of Applied Physics, 2005, 98: 053514.
[13]	HU J Q, CHEN Z. Atomistic study of shock Hugoniot in columnar nano-crystalline copper[J]. Computational Materials Science, 2021, 197:110635.
[14]	周霖, 王昭元, 张向荣, 等. DNP炸药冲击Hugoniot关系实验研究[J]. 含能材料, 2021, 29(9): 833-839.
	ZHOU L, WANG Z Y, ZHANG X R, et al. Experimental measurement on Hugoniot relationship of DNP explosive[J]. Chinese Journal of Energetic Materials, 2021, 29(9): 833-839. (in Chinese)
[15]	LI X, ZHAI J Y, SHEN Z J. Elastic Hugoniot curve of one-dimensional Wilkins model with general Grüneisen-type equation of state[J]. Journal of Computational Physics, 2022, 464:111337.
[16]	SVINGALA F, HARGATHER M, SETTLES G. Optical techniques for measuring the shock Hugoniot using ballistic projectile and high-explosive shock initiation[J]. International Journal of Impact Engineering, 2012, 50:76-82.
[17]	TSILIFIS P, GAHNEM R. Bayesian adaptation of chaos representations using variationalinference and sampling on geodesics[J]. Proceedings of the Royal Society, A:Mathematical, Physicaland Engineering Sciences, 2018,474:11350.
[18]	JACKSON S. A pressure- or velocity-dependent acceleration rate law for the shock to detonation transition process in PBX 9502 high explosive[J]. Combustion and Flame, 2020, 213:98-106.
[19]	孙海权, 洪滔. PBX-9502炸药超压爆轰条件下的状态方程[J]. 含能材料, 2007, 15(5):455-459.
	SUN H Q, HONG T. Equations of state for PBX-9502 in the condition of strong detonation[J]. Chinese Journal of Energetic Materials, 2007, 15(5): 455-459. (in Chinese)
[20]	GUSTAVSEN R, SHEFFIELD S, ALCON R. Measurements of shock initiation in the tri-amino-tri-nitro-benzene based explosive PBX-9502:Wave forms from embedded gauges and comparison of four different material lots[J]. Journal of Applied Physics, 2006, 99(6):114907.
[21]	刘俊明. JB-9014炸药未反应状态方程研究[D]. 绵阳: 中国工程物理研究院, 2019.
	LIU J M. Equation of state of un-reacted explosive JB-9014[D]. Mianyang: China Academy of Engineering Physics, 2019. (in Chinese)
[22]	ANDERSON E, CHIQUETE C, JACKSON S. Experimental measurement of energy release from an initiating layer in an insensitive explosive[J]. Proceedings of Combustion Institute, 2021, 38:3733-3840.
[23]	PENG K F, ZHENG Z J, PAN H, et al. Quasi-static and dynamic compaction of granular materials: astrain-activated statistical compaction model and its evaluation[J]. Mechanics of Materials, 2022, 167:104250.
[24]	ANDERSON T, DARLING D. A test of goodness of fit[J]. Journal of the American Statistical Association, 1954, 49:765-769.
[25]	ROSENBLATT W. Remarks on a multivariate transformation[J]. Annals of Mathematical Statistics, 1952, 23(1): 470-472.
[26]	CHIDESTER S, VANDERSALL K, TARVER C. Shock initiation of damaged explosives[R]. LLNL-CONF-418560, 2009.
[27]	CRAIG B G. Measurements of the detonation-front structure in condensed phase explosives[C]// Proceeding of the 10th Symposium(International) on Combustion. Amsterdam, the Netherlands: Elsevier, 1965, 10(1):863-867.