一种改进的Euler方法模拟凝聚炸药的爆轰过程
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摘要
在爆轰的数值模拟中,采用合适的计算方法及相应的计算程序,在计算机上数值求解流体力学和化学反应动力学方程组,以正确反映爆轰过程,对于爆轰理论以及工程应用研究,都是十分重要的。
本文使用一种改进的Euler方法,把无波动、不含自由参数的NND格式应用到凝聚炸药的爆轰问题,实现了高分辨格式对复杂物态方程爆轰问题的数值模拟计算。化学反应率使用Lee-Tarver的点火成长模型,未反应的固体炸药和化学反应气体产物都使用JWL(Jones-Wilkins-Lee)状态方程。首先研究了一维平面爆轰波结构与网格尺寸的关系,然后研究了柱面散心爆轰波结构及其正规反射、Mach反射问题。
文中数值模拟了非均质固体炸药PBX-9404的爆轰传播过程。从典型爆轰算例来看,该方法正确预测了凝聚炸药爆轰的起爆及传播过程中的关键特征,如Von Neumann尖峰和化学反应区等。通过数值模拟值与理论结果和试验结果的比较,各物理量均达到了满意的准确程度。
Numerical simulation of detonation is to apply appropriate numerical methods to calculate the complicated detonation process of fluid dynamics coupled with chemical reaction. The study of numerical scheme is always concerned in the numerical simulation of detonation.In this paper, we applied NND scheme, a non-oscillatory, no free parameters and dissipative scheme, to numerical simulation of detonation in heterogeneous explosives with an improved Eulerian method. The ignition and growth model by Lee-Tarver is used to the chemistry reaction law of explosives, then a practical method for detonation simulation is constructed. First, The relation between one dimension plane detonation wave configuration and mesh size was investigated, then, regular reflection and Mach reflection was studied too.Simulations of detonation problem in heterogeneous explosives of PBX-9404 have been performed. From some representative examples about unsteady detonation, this method can correctly predict the key characters of initiation and propagation of detonation course, such as Von Neumann spike pressure and reaction zone width. Comparisons between the exact and numerical results, show that all parameters are approached very well.
本文使用一种改进的Euler方法,把无波动、不含自由参数的NND格式应用到凝聚炸药的爆轰问题,实现了高分辨格式对复杂物态方程爆轰问题的数值模拟计算。化学反应率使用Lee-Tarver的点火成长模型,未反应的固体炸药和化学反应气体产物都使用JWL(Jones-Wilkins-Lee)状态方程。首先研究了一维平面爆轰波结构与网格尺寸的关系,然后研究了柱面散心爆轰波结构及其正规反射、Mach反射问题。
文中数值模拟了非均质固体炸药PBX-9404的爆轰传播过程。从典型爆轰算例来看,该方法正确预测了凝聚炸药爆轰的起爆及传播过程中的关键特征,如Von Neumann尖峰和化学反应区等。通过数值模拟值与理论结果和试验结果的比较,各物理量均达到了满意的准确程度。
Numerical simulation of detonation is to apply appropriate numerical methods to calculate the complicated detonation process of fluid dynamics coupled with chemical reaction. The study of numerical scheme is always concerned in the numerical simulation of detonation.In this paper, we applied NND scheme, a non-oscillatory, no free parameters and dissipative scheme, to numerical simulation of detonation in heterogeneous explosives with an improved Eulerian method. The ignition and growth model by Lee-Tarver is used to the chemistry reaction law of explosives, then a practical method for detonation simulation is constructed. First, The relation between one dimension plane detonation wave configuration and mesh size was investigated, then, regular reflection and Mach reflection was studied too.Simulations of detonation problem in heterogeneous explosives of PBX-9404 have been performed. From some representative examples about unsteady detonation, this method can correctly predict the key characters of initiation and propagation of detonation course, such as Von Neumann spike pressure and reaction zone width. Comparisons between the exact and numerical results, show that all parameters are approached very well.
引文
1 朱建士.关于爆轰数值模拟的建模.含能材料增刊,2004:483
2 李维新.一维不定常流与冲击波.北京:国防工业出版社,2003:394
3 孙锦山,朱建士.理论爆轰物理.北京:国防工业出版社,1995:144
4 水鸿寿.一维流体力学差分方法.北京:国防工业出版社,1998
5 蔚喜军,周铁.流体力学方程的间断有限元方法.计算物理,2005:Vol.22,No.2
6 章冠人,陈大年编著.凝聚炸药起爆动力学.北京:国防工业出版社,1991
7 王继海.二维非定常流和激波,北京:科学出版社,1994
8 张涵信,沈孟育.计算流体力学-差分方法的原理和应用.北京:国防工业出版社,2003:134
9 Charles L. Mader. Numerical Modeling of Explosives and Propellants. CRC press. 1998
10 E. L. Lee and C. M. Tarver. Phenomenological model of shock initiation in heterogeneous explosives. Physics of Fluids, 1980
11 Ami Harten. High Resolution Schemes for Hyperbolic Conservation Laws. Journal of Computational Physics, 1983, 49:357-393
12 Gilbert Strange. ON THE CONSTRUCTION AND COMPARISON OF DIFFERENCE SCHEMES. SIAM J. Number. Anal. Vol. 5, No. 3, September 1968 : 507
13 J. K. Clutter and D. Belk. Simulation of detonation wave interaction using an ignition and growth model. SHOCK WAVE(12), 2002
14 Mader C L. Numerical Modeling of Detonation. London, 1979
15 李智伟,刘邦弟.散心爆轰的数值模拟.计算物理,1985,2(1):55-66
16 李德元,徐国荣,水鸿寿著.二维非定常流体力学数值方法.北京:科学出版社,1987
17 R.柯朗K.O.弗里德里克斯.超声速流与冲击波.北京:科学出版社,1986
18 忻孝康,刘儒勋,蒋伯诚.计算流体动力学.长沙:国防科技大学出版社,1989
19 傅德薰,流体力学数值模拟.北京:国防工业出版社,1993.1
20 彭国伦.Fortran95程序设计.北京:中国电力出版社,2002
21 刘卫国.Fortran90程序设计教程.北京:中国邮电大学出版社,2003
22 吴子牛.计算流体力学基本原理.北京:科学出版社,2001.2
23 李德元.爆轰的数值模拟.北京:应用物理与计算数学研究所,1983
24 李宏.高分辨率间断有限元方法.计算物理,2004:Vol.21,No.4
25 陆金甫,关治.偏微分方程数值解法.第二版.北京:清华大学出版社,2004
26 李宏.高分辨率间断有限元方法.计算物理,2004:Vol.21,No.4
27 Ton Vinh T. Improved shock-capturing methods for multicomponent and reacting flows. Journal of Computational Physics, 128(2), 1996:237-253
28 LeVeque Randall J. Wave propagation algorithms for multidimensions hyperbolic systems. Journal of Computational Physics, 131 (1), 1997: 327-353
29 朱建士,孙锦山.爆轰波讲义.北京:应用物理与计算数学研究所
30 P. Colella, A.J. Majda and V. Roytburd, Theoretical and numerical structure of reacting shock waves. SIAM J. Sci. Stat. Comp. 1986, 7:1059
31 忻孝康,刘儒勋,蒋伯诚编著.计算流体动力学.长沙:国防科技大学出版社,1989
32 张宝铼,张庆明,黄风雷.爆轰物理学.北京:兵器工业出版社,2001.8
33 曹菊珍,PBX-9404和TATB的散心临界冲击引爆问题.爆炸与冲击.1986,6(4):350-353
34 Von Neumann J. theory of Detonation Waves. John Von Neumann Collected works, Ed. A J Tanb, New York: 1942
35 董海山,周芬芬.高能炸药及相关物性能.北京:科学出版社,1989
36 姜礼尚,庞之垣.有限元方法及其理论.北京:人民出版社,1979
37 楼建锋.非定常问题的高分辨CTVD格式数值模拟.硕士学位论文.北京:应用物理与计算数学研究所
38 柏劲松.godunov方法和随机选取方法(RCM)及其对反应流爆轰模型的数值研究.硕士学位论文.北京:应用物理与计算数学研究所
2 李维新.一维不定常流与冲击波.北京:国防工业出版社,2003:394
3 孙锦山,朱建士.理论爆轰物理.北京:国防工业出版社,1995:144
4 水鸿寿.一维流体力学差分方法.北京:国防工业出版社,1998
5 蔚喜军,周铁.流体力学方程的间断有限元方法.计算物理,2005:Vol.22,No.2
6 章冠人,陈大年编著.凝聚炸药起爆动力学.北京:国防工业出版社,1991
7 王继海.二维非定常流和激波,北京:科学出版社,1994
8 张涵信,沈孟育.计算流体力学-差分方法的原理和应用.北京:国防工业出版社,2003:134
9 Charles L. Mader. Numerical Modeling of Explosives and Propellants. CRC press. 1998
10 E. L. Lee and C. M. Tarver. Phenomenological model of shock initiation in heterogeneous explosives. Physics of Fluids, 1980
11 Ami Harten. High Resolution Schemes for Hyperbolic Conservation Laws. Journal of Computational Physics, 1983, 49:357-393
12 Gilbert Strange. ON THE CONSTRUCTION AND COMPARISON OF DIFFERENCE SCHEMES. SIAM J. Number. Anal. Vol. 5, No. 3, September 1968 : 507
13 J. K. Clutter and D. Belk. Simulation of detonation wave interaction using an ignition and growth model. SHOCK WAVE(12), 2002
14 Mader C L. Numerical Modeling of Detonation. London, 1979
15 李智伟,刘邦弟.散心爆轰的数值模拟.计算物理,1985,2(1):55-66
16 李德元,徐国荣,水鸿寿著.二维非定常流体力学数值方法.北京:科学出版社,1987
17 R.柯朗K.O.弗里德里克斯.超声速流与冲击波.北京:科学出版社,1986
18 忻孝康,刘儒勋,蒋伯诚.计算流体动力学.长沙:国防科技大学出版社,1989
19 傅德薰,流体力学数值模拟.北京:国防工业出版社,1993.1
20 彭国伦.Fortran95程序设计.北京:中国电力出版社,2002
21 刘卫国.Fortran90程序设计教程.北京:中国邮电大学出版社,2003
22 吴子牛.计算流体力学基本原理.北京:科学出版社,2001.2
23 李德元.爆轰的数值模拟.北京:应用物理与计算数学研究所,1983
24 李宏.高分辨率间断有限元方法.计算物理,2004:Vol.21,No.4
25 陆金甫,关治.偏微分方程数值解法.第二版.北京:清华大学出版社,2004
26 李宏.高分辨率间断有限元方法.计算物理,2004:Vol.21,No.4
27 Ton Vinh T. Improved shock-capturing methods for multicomponent and reacting flows. Journal of Computational Physics, 128(2), 1996:237-253
28 LeVeque Randall J. Wave propagation algorithms for multidimensions hyperbolic systems. Journal of Computational Physics, 131 (1), 1997: 327-353
29 朱建士,孙锦山.爆轰波讲义.北京:应用物理与计算数学研究所
30 P. Colella, A.J. Majda and V. Roytburd, Theoretical and numerical structure of reacting shock waves. SIAM J. Sci. Stat. Comp. 1986, 7:1059
31 忻孝康,刘儒勋,蒋伯诚编著.计算流体动力学.长沙:国防科技大学出版社,1989
32 张宝铼,张庆明,黄风雷.爆轰物理学.北京:兵器工业出版社,2001.8
33 曹菊珍,PBX-9404和TATB的散心临界冲击引爆问题.爆炸与冲击.1986,6(4):350-353
34 Von Neumann J. theory of Detonation Waves. John Von Neumann Collected works, Ed. A J Tanb, New York: 1942
35 董海山,周芬芬.高能炸药及相关物性能.北京:科学出版社,1989
36 姜礼尚,庞之垣.有限元方法及其理论.北京:人民出版社,1979
37 楼建锋.非定常问题的高分辨CTVD格式数值模拟.硕士学位论文.北京:应用物理与计算数学研究所
38 柏劲松.godunov方法和随机选取方法(RCM)及其对反应流爆轰模型的数值研究.硕士学位论文.北京:应用物理与计算数学研究所