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This paper analyzes theoretically and numerically the refraction phenomenon of detonation wave at the explosive-metal interface, motivated by the problem that there exist large discrepancies between the experimental results and the classical shock polar theory. After pointing out the major defects of the classical shock polar theory based on CJ model of detonation, an improved shock polar theory based on ZND model of detonation is presented to give the styles of the refraction of detonation wave and the pressure values at the interaction point between the refracted shock wave and the incident shock wave, to show the pressure values at free-surface of copper remarkably lower than the ones at the shock interaction point due to the attenuation effects from the chemical reaction expansion and the following Taylor rarefaction. A second-order cell-centered Lagrangian hydrodynamics method with high resolution based on the subcharacteristics theory is develped to solve the reactive flow equations of detonation in condensed explosive, and then to numerically simulate a representative refraction experiment about T2 explosive interacting with copper. The simulated pressure values at the interaction point agree well with the ones from the improved shock polar theory, and the simulated pressure values at free-surface of copper agree well with the experimental values, meanwhile, the refraction styles predicted by the improved shock polar theory are confirmed by the numerically simulated flowfield images. From the theoretical and numerical results, there exist three kinds of refraction styles of detonation waves at explosive-metal interface:i) the regular refraction with reflecting shock wave, ii) the irregular refraction with Mach reflection, and iii) the regular refraction without any reflecting wave; in particular, the regular refraction with no reflecting wave is a kind of refraction style unable to be predicted by the classical shock polar theory, meanwhile, the pressure values at the free-surface and the interaction point inside the shocked metal both monotonically decrease with the increase of the incident angle.
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Keywords:
- detonation wave /
- refraction /
- shock polar theory /
- ZND model
[1] Sternberg H M, Piacesi D 1966 J. Phys. Fluids 9 1307
[2] Wang J H 1982 Explosion and Shock Wave 2 1 (in Chinese) [王继海 1982 爆炸与冲击 2 1]
[3] Cheret R, C. R. Acad. Sc. Paris, T. 303, Serie Ⅱ, No. 1, 1986
[4] Walsh J M, Shock Waves in Condensed Matter, 1987, Elsevier Science Publisher B. V., 3
[5] Aveille J 1989 9th Symposium (International) on Detonation, Portland, Oregon, 842-851
[6] Tarver C M, McGuire E M 2002 12th Symposium (International) on Detonation, San Diego, California, 641-649
[7] Zhao Y H, Liu H F 2007 Acta Phys. Sin. 56 4791 (in Chinese) [赵艳红, 刘海风 2007 56 4791]
[8] Sun Y T, Jia Z P, Yu M 2012 Chinese J. Comp. Phys. 29 45 (in Chinese) [孙宇涛, 贾祖朋, 于明 2012 计算物理 29 45]
[9] Sun C W 2000 Applied Detonation Physics (Beijing:Defense Industry Press) (in Chinese) [孙承纬 2000 应用爆轰物理(北京:国防工业出版社]
[10] Wilkins M L 1963 ADA395185, California University Livermore Radiation Laboratory
[11] Zhang B P, Jiang C L 1992 Trans. Beijing Institute of Technology 1 26 (in Chinese) [张宝坪, 姜春兰 1992 北京理工大学学报 1 26]
[12] Zhao F 2009 Physics 38 894 (in Chinese) [赵锋 2009 物理 38 894]
[13] Yu M, Zhang W H 2014 Explosion and Shock Wave 34 300 (in Chinese) [于明, 张文宏 2014 爆炸与冲击 34 300]
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[1] Sternberg H M, Piacesi D 1966 J. Phys. Fluids 9 1307
[2] Wang J H 1982 Explosion and Shock Wave 2 1 (in Chinese) [王继海 1982 爆炸与冲击 2 1]
[3] Cheret R, C. R. Acad. Sc. Paris, T. 303, Serie Ⅱ, No. 1, 1986
[4] Walsh J M, Shock Waves in Condensed Matter, 1987, Elsevier Science Publisher B. V., 3
[5] Aveille J 1989 9th Symposium (International) on Detonation, Portland, Oregon, 842-851
[6] Tarver C M, McGuire E M 2002 12th Symposium (International) on Detonation, San Diego, California, 641-649
[7] Zhao Y H, Liu H F 2007 Acta Phys. Sin. 56 4791 (in Chinese) [赵艳红, 刘海风 2007 56 4791]
[8] Sun Y T, Jia Z P, Yu M 2012 Chinese J. Comp. Phys. 29 45 (in Chinese) [孙宇涛, 贾祖朋, 于明 2012 计算物理 29 45]
[9] Sun C W 2000 Applied Detonation Physics (Beijing:Defense Industry Press) (in Chinese) [孙承纬 2000 应用爆轰物理(北京:国防工业出版社]
[10] Wilkins M L 1963 ADA395185, California University Livermore Radiation Laboratory
[11] Zhang B P, Jiang C L 1992 Trans. Beijing Institute of Technology 1 26 (in Chinese) [张宝坪, 姜春兰 1992 北京理工大学学报 1 26]
[12] Zhao F 2009 Physics 38 894 (in Chinese) [赵锋 2009 物理 38 894]
[13] Yu M, Zhang W H 2014 Explosion and Shock Wave 34 300 (in Chinese) [于明, 张文宏 2014 爆炸与冲击 34 300]
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