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凝聚炸药爆轰波在高声速材料界面上的折射现象分析

于明 刘全

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凝聚炸药爆轰波在高声速材料界面上的折射现象分析

于明, 刘全

Refraction of detonation wave at interface between condensed explosives and high sound-speed material

Yu Ming, Liu Quan
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  • 凝聚炸药爆轰在边界高声速材料约束下传播时, 爆轰波会在约束材料界面上产生复杂的折射现象. 本文针对凝聚炸药爆轰波在高声速材料界面上的折射现象展开理论和数值模拟分析. 首先通过建立在爆轰ZND模型上的改进爆轰波极曲线理论给出爆轰波折射类型, 然后发展一种求解爆轰反应流动方程的基于特征理论的二阶单元中心型Lagrange计算方法来数值模拟典型的爆轰波折射过程. 从改进爆轰波极曲线理论和二阶Lagrange方法数值模拟给出的结果看出, 凝聚炸药爆轰波在高声速材料界面上的折射类型有四种: 反射冲击波的正规折射、带束缚前驱波的非正规折射、带双Mach反射的非正规折射、带 波结构的非正规折射.
    The denotation of condensed explosives is very vulnerable to be influenced by the character of its confinement material. Confinements of different materials on the condensed explosives can remarkably change the shock locus and propagation speed of the detonation wave. Especially, when the confinement material has a higher sound-speed than the CJ velocity of explosives, some highly complicated refraction phenomena of detonation waves would take place near the explosives-material interface. This paper aims at analyzing the refraction phenomena of detonation waves in condensed explosives in theoretical and numerical ways. Firstly, an improved shock polar theory based on ZND model of detonation is built to give the styles of the refraction in detonation waves in order to provide a leading-order prediction of the confinement interaction. The improved shock polar is established at the leading shock wave of explosives detonation, and the refraction interaction is determined by the polar curve of the leading shock waves within the unreacted explosives and the polar curve of the refraction shock waves within the confinement material. Secondly, a second-order cell-centered Lagrangian hydrodynamics method, based on the characteristics theory for two-dimensional hyperbolic partial differential equations, is developed to solve the chemically reactive flow equations by the three-term ignition-growth chemistry reaction law. The main character of this method is that the finite volume discretization is adopted and an instantaneous evolution solver from an approximate Galerkin evolution operator is applied to compute the velocity and pressure of a grid vertex in order to update the grid coordinates and evaluate the numerical flux across the cell interface. A representative experiment about the propagation of a slipping detonation wave is numerically simulated. From the theoretical and numerical results about the refraction of detonation waves while the PBX9502 explosives interacting with beryllium interface, there exist four kinds of refraction styles of the detonation wave at high sound-speed material interface: the regular refraction with reflecting shock wave, the irregular refraction with bound precursor wave, the irregular refraction with twin Mach reflection, and the irregular refraction with -wave structure. In the first style, the front of the leading shock wave is straight, the flows in the detonation reactive zone and beryllium are both supersonic, and a reflecting shock wave appears behind the leading shock wave and a refracting shock wave appears within beryllium. In the second style, the front of the leading shock wave is also straight, the flow in the detonation reactive zone is supersonic but the one in beryllium is subsonic, so a reflecting shock wave appears behind the leading shock wave and a refracting shock wave appears within beryllium too; moreover, the refracting shock wave is almost perpendicular to the material interface, that is a bound precursor wave. In the third style, the front of the leading shock wave becomes forward curve, and the flows in the detonation reactive zone and beryllium are both subsonic, i.e., a Mach item is produced at some distance above the material interface where there are two Mach reflection structures on the top and the bottom of the Mach item respectively. Obviously, the bottom Mach reflection is a free precursor wave from the refracting shock wave within beryllium. In the fourth style, the forward curve range of the front of the leading shock wave becomes very broad, and accordingly, the range of subsonic flows in the detonation reactive zone becomes very wide. This makes the top Mach reflection disappear but the bottom one still exist, so the whole structure of the reflection wave seems to be like the Greek alphabet ; meanwhile, the flow within beryllium may be all in a subsonic state.
      通信作者: 刘全, liuquan@iapcm.ac.cn.
    • 基金项目: 国家自然科学基金(批准号: 11272064)资助的课题.
      Corresponding author: Liu Quan, liuquan@iapcm.ac.cn.
    • Funds: Project supported by National Natural Science Foundation of China (Grant No. 11272064).
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    [2]

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    [3]

    Eden J, Belcher R A 1989 The 9th Symposium (International) on Detonation, Portland, Oregon, 830-841

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    Aveille J 1989 The 9th Symposium (International) on Detonation, Portland, Oregon, 842-851

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    Balagansky I A, Hokamoto K, Manikandan P 2011 Journal of Applied Physics 110 123516

    [6]

    Aslam T D, Bdzil J B 2002 The 12th Symposium (International) on Detonation, San Diego, California, 483-488

    [7]

    Aslam T D, Bdzil J B 2006 The 13th Symposium (International) on Detonation, Norfolk, VA, 761-770

    [8]

    Jing F Q 1999 Introduction to Experimental Equation of State (2nd Ed.), (Beijing: Science Press) (in Chinese) [经福谦 1999 实验状态方程导引 (北京: 科学出版社)]

    [9]

    Bdzil J B, Stewart D S 1981 Journal of Fluid Mechanics 108 195

    [10]

    Tarver C M, McGuire E M 2002 The 12th Symposium (International) on Detonation, San Diego, California, 641-649

    [11]

    Lukčov-Medvid'ov M, Saibertov J, Warnecke G 2002 J. Comp. Phys. 183 533

    [12]

    Godunov S 1959 Math. Sb. 47 271

    [13]

    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)]

    [14]

    Schoch S, Nikolaos N, Lee B J 2013 Physics of Fluids 25 086102

  • [1]

    Walsh J M 1987 Shock Waves in Condensed Matter (Elsevier Science Publisher) BV.3-10

    [2]

    Yu M, Sun Y T, Liu Q 2015 Acta Phys. Sin. 64 114702 (in Chinese) [于明, 孙宇涛, 刘全 2015 物理学报 64 114702]

    [3]

    Eden J, Belcher R A 1989 The 9th Symposium (International) on Detonation, Portland, Oregon, 830-841

    [4]

    Aveille J 1989 The 9th Symposium (International) on Detonation, Portland, Oregon, 842-851

    [5]

    Balagansky I A, Hokamoto K, Manikandan P 2011 Journal of Applied Physics 110 123516

    [6]

    Aslam T D, Bdzil J B 2002 The 12th Symposium (International) on Detonation, San Diego, California, 483-488

    [7]

    Aslam T D, Bdzil J B 2006 The 13th Symposium (International) on Detonation, Norfolk, VA, 761-770

    [8]

    Jing F Q 1999 Introduction to Experimental Equation of State (2nd Ed.), (Beijing: Science Press) (in Chinese) [经福谦 1999 实验状态方程导引 (北京: 科学出版社)]

    [9]

    Bdzil J B, Stewart D S 1981 Journal of Fluid Mechanics 108 195

    [10]

    Tarver C M, McGuire E M 2002 The 12th Symposium (International) on Detonation, San Diego, California, 641-649

    [11]

    Lukčov-Medvid'ov M, Saibertov J, Warnecke G 2002 J. Comp. Phys. 183 533

    [12]

    Godunov S 1959 Math. Sb. 47 271

    [13]

    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)]

    [14]

    Schoch S, Nikolaos N, Lee B J 2013 Physics of Fluids 25 086102

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出版历程
  • 收稿日期:  2015-07-11
  • 修回日期:  2015-10-10
  • 刊出日期:  2016-01-20

凝聚炸药爆轰波在高声速材料界面上的折射现象分析

  • 1. 北京应用物理与计算数学研究所, 计算物理重点实验室, 北京 100094
  • 通信作者: 刘全, liuquan@iapcm.ac.cn.
    基金项目: 国家自然科学基金(批准号: 11272064)资助的课题.

摘要: 凝聚炸药爆轰在边界高声速材料约束下传播时, 爆轰波会在约束材料界面上产生复杂的折射现象. 本文针对凝聚炸药爆轰波在高声速材料界面上的折射现象展开理论和数值模拟分析. 首先通过建立在爆轰ZND模型上的改进爆轰波极曲线理论给出爆轰波折射类型, 然后发展一种求解爆轰反应流动方程的基于特征理论的二阶单元中心型Lagrange计算方法来数值模拟典型的爆轰波折射过程. 从改进爆轰波极曲线理论和二阶Lagrange方法数值模拟给出的结果看出, 凝聚炸药爆轰波在高声速材料界面上的折射类型有四种: 反射冲击波的正规折射、带束缚前驱波的非正规折射、带双Mach反射的非正规折射、带 波结构的非正规折射.

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