固体炸药冲击起爆的物质点法研究
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摘要
开展起爆动力学方面的研究对军事科学领域的发展具有非常重要的意义,由于问题的复杂性,其实验和理论的研究进展非常缓慢。随着计算机技术的迅速发展,数值模拟技术逐渐成为解决此类问题的重要手段。
对于冲击起爆问题,涉及大变形、化学动力学、多相介质耦合等问题,这给传统的基于网格算法带来了极大地困难。对于拉格朗日型网格,网格畸变导致时间步的急剧减小,大大降低了计算效率,并增加累计误差;对于欧拉型网格,由于对流项的存在,计算也有一定的困难。针对传统网格算法的缺陷,无网格法逐渐发展成为当今计算力学的热点。物质点法就是一种无网格算法,它由质点网格法(Particle-in-Cell, PIC)和流体代码FLIP的基础上发展而来。物质点法集合了拉格朗日法和欧拉法两者的优点,避免了网格畸变和对流误差。物质点法最大的特点是它自动满足无滑移边界条件,在计算碰撞接触问题时,无需设置主从接触面,在求解本文所研究课题时具有较大的优势。
建立了冲击动力学的物质点法计算模型,采用集中质量法,给出了控制方程的显式求解格式。物质点法采用固定的背景网格,为方便本质边界条件的处理,采用有限元形函数进行位移函数近似;为保证大变形分析时材料标架的客观性,采用焦曼应力率进行应力的更新;在处理冲击波波阵面的强间断性时,引入了人工粘性;为满足显式时间积分算法的条件稳定性,对时间步控制和声速计算等进行了讨论。采用不同的强度模型对冲击碰撞问题进行了研究,结果表明在高速撞击条件下,强度模型对压力的计算结果影响不大。分别采用物质点法、有限元法、光滑粒子流体动力学方法对高速冲击问题进行了数值模拟,从计算效率来看,采用物质点法来求解本文所研究的问题是相对较优的。对超高速碰撞下碎片云的形状进行了数值模拟,计算得到的碎片云形状与实验结果基本一致。
进一步发展了物质点法,提出了多物质物质点计算格式并将其成功应用到固体炸药冲击起爆问题。在本文的计算中,未反应炸药和爆轰产物的状态方程均采用JWL状态方程,炸药的反应速率方程采用点火增长方程。通过物质点内两相介质的热力学平衡假设等给出了合理的两相混合准则,并在此基础上提出了多物质物质点法计算格式。由于爆轰过程燃烧速率过快,采用传统时间步控制方法求解时,计算精度较低,本文提出了通过控制燃烧质量分数增量修正时间步的方法来提高计算精度。对冲击起爆问题进行了数值模拟,通过升降法得到了破片冲击下固体炸药起爆的临界速度,并与实验结果吻合较好。与传统算法进行了比较,物质点法计算的结果与实验结果相比更为接近,并且物质点算法简单,计算方便,物质点法在冲击起爆领域中具有较大的发展潜力和应用前景。
采用冲击波理论推导了在破片冲击下炸药内部冲击波的强度和宽度,对冲击起爆的工程计算方法进行了研究,并用数值模拟结果验证了工程计算方法的有效性,此工程计算方法可与数值模拟方法互为补充。
目前物质点法还处于研究阶段,没有可用的商业软件,本文开发了相应的计算程序,为计算冲击动力学和冲击起爆问题提供了一个全新的数值模拟平台。该程序包括前处理(可划分背景网格和物质点)和主体计算模块,并编制了相应接口导出数据,可采用Tecplot或Origin等科学绘图软件进行后处理分析。
Study on initiation kinetics is very important for military science. Due to its complexity, progress of experimental and theoretical study is very slow. With the rapid development of computer technology, more and more attention was paid on numerical simulation.
The main work of this paper focused on Shock to Detonation Transition (SDT). SDT problems, involving large deformation, chemical kinetics, multiphase coupling and so on, is solved difficultly by traditional grid-based algorithms, such as the finite element method (FEM) and the finite difference method (FDM). For the Lagrangian grids, large deformation will lead to large distortion, it made the time steps became smaller and smaller, which made the whole calculation time extended. And mesh distortion made the accumulated error increscent. For the Eulerian grids,there are advection errors. To overcome these disadvantages of traditional grid-based algorithms, meshfree methods were developed rapidly and became hotspot in Computational Mechanics. The material point method (MPM) is an extension to solid mechanics problems of a hydrodynamics code called FLIP which, in turn, evolved from the particle-in-cell method. MPM, which is a new meshfree method, takes advantage of both Eurlerian and Lagrangian methods and avoids the mesh distortion and tangling issues associated with Lagrangian methods and the advection errors associated with Eulerian methods. The key feature of the MPM is the use of the same set of nodal basis functions for both the mapping from material points to cell nodes, and the mapping from cell nodes to material points. As a result, the use of the single-valued mapping functions yields a natural no-slip contact/impact scheme so that no interpenetration would occur for penetration problems.
Impact dynamics model with material point method was established, and explicit calculation format of MPM was deduced. Fixed background mesh was used, and finite element shape function was used for function approximation. Stress for large deformation material which exhibit elastic-plastic behavior was integrated by Jaumann stress rate. Artificial bulk viscosity was used to treat shock wave. For the stability of explicit time integration, the time step and sound speed was studied. Several impacting problems were computed. Several impacting problems with different strength models were computed, and it shows that Strength model has little effect on the calculation results. MPM method, FEM method, SPH method were used to simulate impact engineering problems, and the comparison of results proved the advantage of MPM from the aspect of precision and cost. At last, a hypervelocity impact problem was study. The shapes of debris cloud obtained by MPM are in agreement with the experimental result.
Material point method was first proposed for SDT problems. JWL Equation of state was used for unreacted explosive and reacted product, and ignition and growth model of explosive initiation was used. According to thermodynamic equilibrium assumption in material points, a two-phase mixture of unreacted explosive and reacted product was proposed. And multi-material material point, which contains unreacted explosive and reacted product in the same time, design procedure was first proposed on that basis. Because of rapid process of explosive detonation, the mass fraction incremental of combustion was controlled to promote accuracy. Simulating some SDT problems, the critical detonating velocities were gained by means of the‘up-down’method. Compared with the traditional algorithm, the superiority of material point method in the calculation of shock initiation problems is obvious.
Duration and value of shock wave in explosive generated due to impact was deduced with shock wave theory. And a method in engineering calculation, which was validated by numerical results, was proposed in this paper. Engineering calculation method and numerical simulation methods complement each other.
Currently, the material point method is still in the research stage, and there is no commercial software. A Computer code was developed, which provide a new numerical simulation platform for impact problem and SDT problem. It contains pre-processing, main calculation and data interface modules, and Tecplot, Origin software can be used for Post-processing.
对于冲击起爆问题,涉及大变形、化学动力学、多相介质耦合等问题,这给传统的基于网格算法带来了极大地困难。对于拉格朗日型网格,网格畸变导致时间步的急剧减小,大大降低了计算效率,并增加累计误差;对于欧拉型网格,由于对流项的存在,计算也有一定的困难。针对传统网格算法的缺陷,无网格法逐渐发展成为当今计算力学的热点。物质点法就是一种无网格算法,它由质点网格法(Particle-in-Cell, PIC)和流体代码FLIP的基础上发展而来。物质点法集合了拉格朗日法和欧拉法两者的优点,避免了网格畸变和对流误差。物质点法最大的特点是它自动满足无滑移边界条件,在计算碰撞接触问题时,无需设置主从接触面,在求解本文所研究课题时具有较大的优势。
建立了冲击动力学的物质点法计算模型,采用集中质量法,给出了控制方程的显式求解格式。物质点法采用固定的背景网格,为方便本质边界条件的处理,采用有限元形函数进行位移函数近似;为保证大变形分析时材料标架的客观性,采用焦曼应力率进行应力的更新;在处理冲击波波阵面的强间断性时,引入了人工粘性;为满足显式时间积分算法的条件稳定性,对时间步控制和声速计算等进行了讨论。采用不同的强度模型对冲击碰撞问题进行了研究,结果表明在高速撞击条件下,强度模型对压力的计算结果影响不大。分别采用物质点法、有限元法、光滑粒子流体动力学方法对高速冲击问题进行了数值模拟,从计算效率来看,采用物质点法来求解本文所研究的问题是相对较优的。对超高速碰撞下碎片云的形状进行了数值模拟,计算得到的碎片云形状与实验结果基本一致。
进一步发展了物质点法,提出了多物质物质点计算格式并将其成功应用到固体炸药冲击起爆问题。在本文的计算中,未反应炸药和爆轰产物的状态方程均采用JWL状态方程,炸药的反应速率方程采用点火增长方程。通过物质点内两相介质的热力学平衡假设等给出了合理的两相混合准则,并在此基础上提出了多物质物质点法计算格式。由于爆轰过程燃烧速率过快,采用传统时间步控制方法求解时,计算精度较低,本文提出了通过控制燃烧质量分数增量修正时间步的方法来提高计算精度。对冲击起爆问题进行了数值模拟,通过升降法得到了破片冲击下固体炸药起爆的临界速度,并与实验结果吻合较好。与传统算法进行了比较,物质点法计算的结果与实验结果相比更为接近,并且物质点算法简单,计算方便,物质点法在冲击起爆领域中具有较大的发展潜力和应用前景。
采用冲击波理论推导了在破片冲击下炸药内部冲击波的强度和宽度,对冲击起爆的工程计算方法进行了研究,并用数值模拟结果验证了工程计算方法的有效性,此工程计算方法可与数值模拟方法互为补充。
目前物质点法还处于研究阶段,没有可用的商业软件,本文开发了相应的计算程序,为计算冲击动力学和冲击起爆问题提供了一个全新的数值模拟平台。该程序包括前处理(可划分背景网格和物质点)和主体计算模块,并编制了相应接口导出数据,可采用Tecplot或Origin等科学绘图软件进行后处理分析。
Study on initiation kinetics is very important for military science. Due to its complexity, progress of experimental and theoretical study is very slow. With the rapid development of computer technology, more and more attention was paid on numerical simulation.
The main work of this paper focused on Shock to Detonation Transition (SDT). SDT problems, involving large deformation, chemical kinetics, multiphase coupling and so on, is solved difficultly by traditional grid-based algorithms, such as the finite element method (FEM) and the finite difference method (FDM). For the Lagrangian grids, large deformation will lead to large distortion, it made the time steps became smaller and smaller, which made the whole calculation time extended. And mesh distortion made the accumulated error increscent. For the Eulerian grids,there are advection errors. To overcome these disadvantages of traditional grid-based algorithms, meshfree methods were developed rapidly and became hotspot in Computational Mechanics. The material point method (MPM) is an extension to solid mechanics problems of a hydrodynamics code called FLIP which, in turn, evolved from the particle-in-cell method. MPM, which is a new meshfree method, takes advantage of both Eurlerian and Lagrangian methods and avoids the mesh distortion and tangling issues associated with Lagrangian methods and the advection errors associated with Eulerian methods. The key feature of the MPM is the use of the same set of nodal basis functions for both the mapping from material points to cell nodes, and the mapping from cell nodes to material points. As a result, the use of the single-valued mapping functions yields a natural no-slip contact/impact scheme so that no interpenetration would occur for penetration problems.
Impact dynamics model with material point method was established, and explicit calculation format of MPM was deduced. Fixed background mesh was used, and finite element shape function was used for function approximation. Stress for large deformation material which exhibit elastic-plastic behavior was integrated by Jaumann stress rate. Artificial bulk viscosity was used to treat shock wave. For the stability of explicit time integration, the time step and sound speed was studied. Several impacting problems were computed. Several impacting problems with different strength models were computed, and it shows that Strength model has little effect on the calculation results. MPM method, FEM method, SPH method were used to simulate impact engineering problems, and the comparison of results proved the advantage of MPM from the aspect of precision and cost. At last, a hypervelocity impact problem was study. The shapes of debris cloud obtained by MPM are in agreement with the experimental result.
Material point method was first proposed for SDT problems. JWL Equation of state was used for unreacted explosive and reacted product, and ignition and growth model of explosive initiation was used. According to thermodynamic equilibrium assumption in material points, a two-phase mixture of unreacted explosive and reacted product was proposed. And multi-material material point, which contains unreacted explosive and reacted product in the same time, design procedure was first proposed on that basis. Because of rapid process of explosive detonation, the mass fraction incremental of combustion was controlled to promote accuracy. Simulating some SDT problems, the critical detonating velocities were gained by means of the‘up-down’method. Compared with the traditional algorithm, the superiority of material point method in the calculation of shock initiation problems is obvious.
Duration and value of shock wave in explosive generated due to impact was deduced with shock wave theory. And a method in engineering calculation, which was validated by numerical results, was proposed in this paper. Engineering calculation method and numerical simulation methods complement each other.
Currently, the material point method is still in the research stage, and there is no commercial software. A Computer code was developed, which provide a new numerical simulation platform for impact problem and SDT problem. It contains pre-processing, main calculation and data interface modules, and Tecplot, Origin software can be used for Post-processing.
引文
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