爆炸流场及容器内爆流固耦合问题计算研究
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摘要
本文研究的两个主要问题是：炸药爆炸流场和受冲击载荷作用的流固耦合问题。数值研究的难点表现为：高温、高压爆炸气体产物的膨胀和结构的动力学响应问题。前者涉及大压比、大密度比和多介质的流体界面追踪和界面边界条件提法，这是当前计算流体动力学的难点问题。后者主要是确定与时间相关的载荷和计算应力、应变场。结构动力学响应计算的准确性依赖于冲击波载荷，而爆炸产物膨胀流场计算的精确程度又决定着冲击波载荷。因此，需要对炸药爆炸、冲击波传播和结构响应全过程进行高精度的数值求解。在此基础上，建立必要的三维计算软件平台，这就是本文研究的目标。鉴于此，本文主要内容介绍如下：
(1)第一章介绍了本文研究背景和相关研究进展，说明了本文主要内容及特色。
(2)在简要描述研究对象及介绍状态方程的基础上，第二章重点介绍数值研究爆源、爆炸流场和结构动力学响应、界面追踪等问题所采用的控制方程，及方程的定解条件和无量纲化，这是本文数值分析的基础。用ALE方程描述具有运动边界的爆炸流场，用虚功原理描述固体结构的动力学响应。爆源分别采用点爆炸模型和有限反应速率模型。前者忽略爆源和近场特性，后者考虑了爆源物理和几何特性以及点火、爆轰过程。爆炸产物气体膨胀与空气的界面用levelset方程描述。本章将高精度的界面追踪技术和内边界条件提法引入到爆源和爆炸流场数值研究中。
(3)第三章主要介绍第二章中控制方程的数值求解方法。自相似解的常微分方程组采用四阶Runge-Kutta方法求解，反应度模型方程和界面levelset方程采用五阶WENO格式求解，ALE方程采用PPM格式求解，虚功原理采用动力有限元求解，针对这些数值方法，分别考核了相关的校核算例，为下一章的数值研究奠定基础。
(4)选择爆炸容器内爆问题作为典型例子，第四章运用第二章的数学模型和第三章数值方法模拟了带平板封头和带椭球封头的容器内爆流场及流固耦合问题。数值结果表明：本文较好地解决了炸药爆炸气体产物膨胀问题，为全过程的数值模拟奠定了基础。还给出了爆源点火与爆轰、爆炸流场的冲击波传播和反射、圆柱壳的应力波传播和透射以及结构振动的计算结果。这些结果真实地反映了爆炸容器的工作过程，也与实验结果符合。本章最后讨论了计算结果的误差来源。
(5)第五章给出本文主要结论，并对开展下一步研究提出建议。
This paper presents the solutions of the two main problems: explosion of the condensed high energy explosives and the fluid-structure interaction with impacts. The main difficulties are how to deal with the expansion of explosion gas products in state of high pressure and temperature, and the interaction of blast waves and structural responses. The former essentially is associated with the problem of interface with big pressure/density proportion and the multi-media tracking or capturing. This is one of the current main problems in computational fluid dynamics. The later is involved with the accurately obtained pressure close to structure for structural analysis. Since explosion field and structure deformation are coupled on boundaries, we have to solve these problems systematically. To setup a 3-d numerical analysis platform, we have conducted the studies listed below:
1) Chapter 1 introduces the background and the progress of related works, at the end of this chapter, we have noted the characteristic of this investigation.
2) Chapter 2 gives a brief description of the problem and the state equations. This chapter introduces the reaction mode, the governing equations, the interface capturing method employed in this work in great detail. Moreover, the non-dimensionalization and the initial conditions as well as boundary conditions were presented. To get the detonation process of explosives, Euler equations with source terms were used. As a simplified method, dot-explosion self-similar solution was also adopted in the computation, which omitted the detonation process. The interface of gas products and ambient air was tracked with the levelset function. ALE (Arbitrary Lagrangian Eulerian) equation was established to obtain the explosion field while the principle of virtual work was used to obtain the structural responses.
3) Chapter 3 presents the numerical methods used to solve the equations given in chapter 2. PPM (Piecewise Parabolic Method) scheme was of 3rd order accuracy used to solve ALE equations in finite volume method. Finite ele- ment method was used to solve the principle of virtual work, Newmark method was adopted in time integration. Levelset equation was solved by the 5th order WENO scheme, and so did the reaction rate equation. The 4th order Runge-Kutta method was chosen to solve the ODE (Ordinary Differential Equation) derived from 1-d spherical Euler equations. Some typical problems were chosen to check the codes.
4) Numerical results are obtained by applying the validated codes to simulate the typical tests. It was shown that our codes have successfully solved the problem of explosion products expansion to air. The given figures have clearly shown the ignition and detonation growth, the blast wave propagation, the fluid-structure interaction processes and the deformation of structures, etc. The results are also in consistent with the experimental data reported. At the end, causes of calculation errors are discussed.
5) Conclusions and suggestions to the future work are given in the final chapter of this paper.
(1)第一章介绍了本文研究背景和相关研究进展，说明了本文主要内容及特色。
(2)在简要描述研究对象及介绍状态方程的基础上，第二章重点介绍数值研究爆源、爆炸流场和结构动力学响应、界面追踪等问题所采用的控制方程，及方程的定解条件和无量纲化，这是本文数值分析的基础。用ALE方程描述具有运动边界的爆炸流场，用虚功原理描述固体结构的动力学响应。爆源分别采用点爆炸模型和有限反应速率模型。前者忽略爆源和近场特性，后者考虑了爆源物理和几何特性以及点火、爆轰过程。爆炸产物气体膨胀与空气的界面用levelset方程描述。本章将高精度的界面追踪技术和内边界条件提法引入到爆源和爆炸流场数值研究中。
(3)第三章主要介绍第二章中控制方程的数值求解方法。自相似解的常微分方程组采用四阶Runge-Kutta方法求解，反应度模型方程和界面levelset方程采用五阶WENO格式求解，ALE方程采用PPM格式求解，虚功原理采用动力有限元求解，针对这些数值方法，分别考核了相关的校核算例，为下一章的数值研究奠定基础。
(4)选择爆炸容器内爆问题作为典型例子，第四章运用第二章的数学模型和第三章数值方法模拟了带平板封头和带椭球封头的容器内爆流场及流固耦合问题。数值结果表明：本文较好地解决了炸药爆炸气体产物膨胀问题，为全过程的数值模拟奠定了基础。还给出了爆源点火与爆轰、爆炸流场的冲击波传播和反射、圆柱壳的应力波传播和透射以及结构振动的计算结果。这些结果真实地反映了爆炸容器的工作过程，也与实验结果符合。本章最后讨论了计算结果的误差来源。
(5)第五章给出本文主要结论，并对开展下一步研究提出建议。
This paper presents the solutions of the two main problems: explosion of the condensed high energy explosives and the fluid-structure interaction with impacts. The main difficulties are how to deal with the expansion of explosion gas products in state of high pressure and temperature, and the interaction of blast waves and structural responses. The former essentially is associated with the problem of interface with big pressure/density proportion and the multi-media tracking or capturing. This is one of the current main problems in computational fluid dynamics. The later is involved with the accurately obtained pressure close to structure for structural analysis. Since explosion field and structure deformation are coupled on boundaries, we have to solve these problems systematically. To setup a 3-d numerical analysis platform, we have conducted the studies listed below:
1) Chapter 1 introduces the background and the progress of related works, at the end of this chapter, we have noted the characteristic of this investigation.
2) Chapter 2 gives a brief description of the problem and the state equations. This chapter introduces the reaction mode, the governing equations, the interface capturing method employed in this work in great detail. Moreover, the non-dimensionalization and the initial conditions as well as boundary conditions were presented. To get the detonation process of explosives, Euler equations with source terms were used. As a simplified method, dot-explosion self-similar solution was also adopted in the computation, which omitted the detonation process. The interface of gas products and ambient air was tracked with the levelset function. ALE (Arbitrary Lagrangian Eulerian) equation was established to obtain the explosion field while the principle of virtual work was used to obtain the structural responses.
3) Chapter 3 presents the numerical methods used to solve the equations given in chapter 2. PPM (Piecewise Parabolic Method) scheme was of 3rd order accuracy used to solve ALE equations in finite volume method. Finite ele- ment method was used to solve the principle of virtual work, Newmark method was adopted in time integration. Levelset equation was solved by the 5th order WENO scheme, and so did the reaction rate equation. The 4th order Runge-Kutta method was chosen to solve the ODE (Ordinary Differential Equation) derived from 1-d spherical Euler equations. Some typical problems were chosen to check the codes.
4) Numerical results are obtained by applying the validated codes to simulate the typical tests. It was shown that our codes have successfully solved the problem of explosion products expansion to air. The given figures have clearly shown the ignition and detonation growth, the blast wave propagation, the fluid-structure interaction processes and the deformation of structures, etc. The results are also in consistent with the experimental data reported. At the end, causes of calculation errors are discussed.
5) Conclusions and suggestions to the future work are given in the final chapter of this paper.
引文
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