基于SPH方法的空间碎片超高速碰撞特性及其防护结构设计研究
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摘要
随着航天科技的迅速发展以及航天发射任务的急剧增加,大量的空间碎片散落在近地轨道上,构成了复杂的空间碎片环境,对航天器的安全构成了极大的威胁。如何确保航天器的安全,成为当前航天器设计领域中一个十分重要的问题。由于超高速碰撞问题的复杂性,碰撞碎片云的特性还不是很清楚,防护结构的设计还有待进一步研究。
光滑粒子流体动力学(简称SPH)方法作为最早提出的无网格方法,现在已逐渐被应用到许多流体力学相关领域。它具有逻辑简单,可以避免有限元方法中的网格缠绕和扭曲问题等优点,因而特别适合模拟超高速碰撞问题。
本文系统介绍了SPH方法,并对该方法数值计算相关问题作了较深入的探讨。在此基础上,采用SPH方法对空间碎片超高速碰撞碎片云特性以及Whipple防护结构设计问题作了数值研究。
本文的主要工作及其结论如下:
1、利用Fortran语言自行编写了基于直角坐标系的二维和三维SPH计算程序,并成功引入Johnson-Cook拉伸累积损伤本构模型、Johnson-Cook粘塑性本构模型以及SCG本构模型,由此得到的数值结果与实验较为吻合,说明自编程序能较好的模拟各类碰撞动力学问题,特别是超高速碰撞问题。
2、从计算精度、拉伸不稳定性、虚粒子方法、初始光滑长度和非均匀粒子间距界面等五个方面讨论了SPH方法数值计算相关问题。对三种拉伸不稳定性处理方法作了比较,结果表明,与守恒光滑法相比较,Monaghan型拉伸不稳定处理方法以及基于Lagrangian核函数的稳定化粒子方法能更好地消除拉伸不稳定性。虚粒子方法是处理固壁边界的一种有效方法。然而,如果在对称结构的对称面处(为减少计算量,对称面通常被当作固壁边界处理)采用虚粒子方法,则在对称面附近会存在一个粒子数明显偏少的低密度区域,这显然是不合理的。研究表明,采用XSPH速度纠错公式在一定程度上可以改善计算结果。分析了初始光滑长度对数值模拟结果的影响。结果表明,初始光滑长度越大,弹丸材料表现出的刚性越小,h0的合理取值范围应为d0 3、从碎片云形状、质量、速度和动量等方面研究了超高速正碰撞碎片云特性。结果表明,球形弹丸的碎片云前端呈半球形分布,柱状弹丸的碎片云前端有一锥状突出,当长径比足够小时圆盘形弹丸形成的碎片云内部会产生柱状结构。提出了识别碎片的自然边界判定方法,结合近邻粒子搜索技术,得到了碎片云的质量分布情况。给出了累积碎片百分数与碰撞速度和碎片质量的近似函数关系。通过在SPH程序中加入速度矢量子程序,获得了碎片云速度矢量分布。碎片云速度特性分析表明前端速度与碰撞速度成线性关系。分析了弹丸初始半径范围内的碎片云总动量特性,结果表明球形弹丸的动量衰减幅度大于其它两种弹丸。
4、在超高速正碰撞的基础上,进一步对超高速斜碰撞碎片云特性作了数值研究。球形和柱状弹丸的碎片云形状基本为倾斜的椭球,柱状弹丸形成的椭球形碎片云更加倾斜,圆盘形弹丸形成的碎片云类似于斜锥体。得到了超高速斜碰撞碎片云速度矢量分布。给出了单位面积累积动量MA的获取方法,应用该方法得到了三种弹丸MA分布图。累积动量分布表明,在超高速斜碰撞条件下,柱状弹丸和圆盘形弹丸的破坏能力明显强于球形弹丸,且柱状弹丸的破坏能力最强。
5、讨论了物态方程和本构模型对超高速碰撞数值模拟结果的影响。碎片云形状特征的比较表明,Mie-Grüneisen物态方程得到的碎片云图像与实验图像吻合得较好,而Tillotson物态方程得到的碎片分布则较为分散。从弹坑深度和靶孔直径的角度看,Tillotson物态方程的数值结果更接近实验数据,Mie-Grüneisen物态方程得到的结果则明显大于实验结果。本构模型对碎片的整体空间分布影响较小,在局部区域,Johnson-Cook本构模型得到的碎片分布更加符合物理事实。
6、基于弹道极限方程,分别从缓冲屏和后墙间距、缓冲屏密度、缓冲屏厚度、后墙厚度以及后墙材料等五个方面讨论了Whipple结构的设计问题,给出了相应的结构设计方案,数值结果表明结构设计后的防护结构的防护性能得到了较大提高。通过比较不同长径比的非球形弹丸和等效直径球形弹丸超高速正碰撞和斜碰撞Whipple结构的数值模拟结果,讨论了非球形弹丸对Whipple结构防护性能的影响。结果表明,长径比大于1的柱状弹丸对后墙的破坏能力都明显强于圆盘形弹丸和球形弹丸。
7、通过引入弹道极限质量比的概念,定量地比较了非球形弹丸和等效直径球形弹丸破坏能力的大小。超高速斜碰撞分析表明,后墙受到不同长径比的弹丸超高速碰撞后最有可能发生破坏的位置是不同的,而同一长径比、不同等效直径、不同碰撞速度的非球形弹丸对后墙造成破坏的位置基本相同。通过数据拟合,得到了非球形弹丸对后墙造成破坏的位置LBC的经验表达式。
Along with the quick development of aerospace sci-tech and sharply increment of aerospace mission, a great deal of space debris scatter on low earth orbit. This constitutes the complicated space debris environment which has been threatening the safety of the spacecraft seriously. How insure the safety of the spacecraft, which becomes a very important problem of the current spacecraft design. Because of the complexity of hypervelocity impacts, characteristics of debris clouds are not still clear. Therefore the design of spacecraft shielding structure still needs the further research.
Smoothed particle hydrodynamics(SPH) method is the pioneer of meshless particle methods. Nowadays it has been applied to many realms with related fluid mechanics. It has simple logic, can avoid the mesh enlacement and distort of finite element method. So it is suitable for simulating hypervelocity impacts especially.
SPH method is introduced systemically in this paper. And some kinds of problems related with numerical simulations are discussed deeply. The characteristics of debris clouds produced by hypervelocity impacts are studied using SPH method. Hypervelocity impacts of Whipple shields are simulated and analyzed.
The main achievements and conclusions in this paper are presented in the following:
1. Based on Cartesian coordinate system, the 2D and 3D SPH program is composed on one's own. Johnson-Cook tensile cumulative damage constitutive model, Johnson-Cook visco-plastic constitutive model and Steinberg-Cochran-Guinan (SCG) constitutive model are imported in the program successfully. The simulated results obtained by SPH program are in accord with the experiments. This shows that the SPH program is capable of simulating different impact dynamics problems, especially hypervelocity impacts.
2. Five problems related with numerical simulations, such as the computational accuracy, tensile instability, ghost particle method, initial smoothing length and material interface made by different particle spacing, are studied. The three tensile instability treatment methods are compared. The calculated results show that Monaghan method and stable particle methods based on Lagrangian kernels are better than Conservative Smoothing Approach (CSA). The ghost particle method is an effective method to deal with the rigid boundary condition. But a low density region will be produced in the neighborhood of symmetric plane if the ghost particle method is used to deal with the symmetric boundary. This result is unreasonable. The research shows that the simulated results obtain some extent improvement by using the XSPH correction to the velocity of a particle. The effects of initial smoothing lengths on SPH simulated results are analyzed. The results show that the bigger initial smoothing length, the less rigid projectile. And the rational range of initial smoothing length is d0 3. The characteristics of debris clouds obtained by normal hypervelocity impacts, which include sharp, mass, velocity and momentum, are studied. For the spherical projectile, the front of debris clouds shows a hemisphere. And the front of debris clouds has a cone-shaped jag for the rod. The interior of debris clouds produced by the disk will come into being the column structure when its ratio of length to diameter is enough small. A natural boundary judgement approach of the identification of fragments is presented. Combining the neighbour searching method, the mass distribution of debris clouds is achieved. Based on the numerical fit, the cumulative percentage of fragments as a function of the fragment mass and impact velocity is presented. The velocity vector figures of debris clouds are presented through adding the subroutine of velocity vector in SPH program. The analysis of the velocity characteristics shows that the front velocity has a linear change with the impact velocity. The characteristics of the total momentum of debris clouds within initial projectile radius are analyzed. The results show that the attenuation extent of the sphere is larger than that of two other projectiles.
4. Following the analysis of the normal hypervelocity impact, the characteristics of debris clouds obtained by oblique hypervelocity impacts are simulated. The shapes of debris clouds produced by the sphere and the rod are an inclined ellipsoid. However the ellipsoid formed by the rod is more inclined than the sphere. And debris clouds formed by the disk are similar to an inclined centrum. The velocity vector figure of debris clouds of oblique hypervelocity impacts is presented. The acquisition approach of cumulative momentum unit area MA is presented. The MA distributions of three projectiles are obtained by the approach. The results show that the executions of the disk and the rod are more powerful than that of the sphere. And the execution of the rod is strongest.
5. The effects of equations of state and constitutive models on SPH simulated results are discussed. By comparing the shapes of debris clouds, the results obtained by Mie-Grüneisen EOS agree with the experiments. However debris clouds obtained by Tillotson EOS tend to expanding outwards. In the perspective of the depth of the crater and the diameter of the hole of the target, the simulated results from Tillotson EOS are closer to the experimental data than Mie-Grüneisen EOS. The latter results are larger than the experiment clearly. The constitutive models don’t affect the whole distribution of fragments. However debris clouds obtained by Johnson-Cook constitutive model are more reasonable than SCG constitutive model.
6. Based on ballistic limit equations (BLE), the design of Whipple shields is discussed from five aspects which include shield standoff distance, bumper density, bumper thickness, rear wall thickness and rear wall material. The corresponding design project is presented. The results show that the performance of the shielding structure obtains considerable improvements. The effects of non-spherical projectiles with different ratios of length to diameter on shielding performance are studied. Normal and oblique hypervelocity impacts are simulated. The calculated results of non-spherical projectiles are compared with ballistic limit nerves of the sphere. The results show the executions of the rod are stronger than that of the disk and the sphere.
7. By introducing the conception of ballistic limit mass ratio, the executions of non-spherical projectiles are made a qualitative comparison with that of spherical projectiles. The analysis of oblique hypervelocity impacts show that most possible locations on which the rear wall is destroyed relate to the ratio of length to diameter nearly. The projectiles with same ratio of length to diameter have almost same damage position even if they have different equivalent diameter or impact velocity. An empirical expression of the damage position LBC is presented by fitting simulated results.
光滑粒子流体动力学(简称SPH)方法作为最早提出的无网格方法,现在已逐渐被应用到许多流体力学相关领域。它具有逻辑简单,可以避免有限元方法中的网格缠绕和扭曲问题等优点,因而特别适合模拟超高速碰撞问题。
本文系统介绍了SPH方法,并对该方法数值计算相关问题作了较深入的探讨。在此基础上,采用SPH方法对空间碎片超高速碰撞碎片云特性以及Whipple防护结构设计问题作了数值研究。
本文的主要工作及其结论如下:
1、利用Fortran语言自行编写了基于直角坐标系的二维和三维SPH计算程序,并成功引入Johnson-Cook拉伸累积损伤本构模型、Johnson-Cook粘塑性本构模型以及SCG本构模型,由此得到的数值结果与实验较为吻合,说明自编程序能较好的模拟各类碰撞动力学问题,特别是超高速碰撞问题。
2、从计算精度、拉伸不稳定性、虚粒子方法、初始光滑长度和非均匀粒子间距界面等五个方面讨论了SPH方法数值计算相关问题。对三种拉伸不稳定性处理方法作了比较,结果表明,与守恒光滑法相比较,Monaghan型拉伸不稳定处理方法以及基于Lagrangian核函数的稳定化粒子方法能更好地消除拉伸不稳定性。虚粒子方法是处理固壁边界的一种有效方法。然而,如果在对称结构的对称面处(为减少计算量,对称面通常被当作固壁边界处理)采用虚粒子方法,则在对称面附近会存在一个粒子数明显偏少的低密度区域,这显然是不合理的。研究表明,采用XSPH速度纠错公式在一定程度上可以改善计算结果。分析了初始光滑长度对数值模拟结果的影响。结果表明,初始光滑长度越大,弹丸材料表现出的刚性越小,h0的合理取值范围应为d0
4、在超高速正碰撞的基础上,进一步对超高速斜碰撞碎片云特性作了数值研究。球形和柱状弹丸的碎片云形状基本为倾斜的椭球,柱状弹丸形成的椭球形碎片云更加倾斜,圆盘形弹丸形成的碎片云类似于斜锥体。得到了超高速斜碰撞碎片云速度矢量分布。给出了单位面积累积动量MA的获取方法,应用该方法得到了三种弹丸MA分布图。累积动量分布表明,在超高速斜碰撞条件下,柱状弹丸和圆盘形弹丸的破坏能力明显强于球形弹丸,且柱状弹丸的破坏能力最强。
5、讨论了物态方程和本构模型对超高速碰撞数值模拟结果的影响。碎片云形状特征的比较表明,Mie-Grüneisen物态方程得到的碎片云图像与实验图像吻合得较好,而Tillotson物态方程得到的碎片分布则较为分散。从弹坑深度和靶孔直径的角度看,Tillotson物态方程的数值结果更接近实验数据,Mie-Grüneisen物态方程得到的结果则明显大于实验结果。本构模型对碎片的整体空间分布影响较小,在局部区域,Johnson-Cook本构模型得到的碎片分布更加符合物理事实。
6、基于弹道极限方程,分别从缓冲屏和后墙间距、缓冲屏密度、缓冲屏厚度、后墙厚度以及后墙材料等五个方面讨论了Whipple结构的设计问题,给出了相应的结构设计方案,数值结果表明结构设计后的防护结构的防护性能得到了较大提高。通过比较不同长径比的非球形弹丸和等效直径球形弹丸超高速正碰撞和斜碰撞Whipple结构的数值模拟结果,讨论了非球形弹丸对Whipple结构防护性能的影响。结果表明,长径比大于1的柱状弹丸对后墙的破坏能力都明显强于圆盘形弹丸和球形弹丸。
7、通过引入弹道极限质量比的概念,定量地比较了非球形弹丸和等效直径球形弹丸破坏能力的大小。超高速斜碰撞分析表明,后墙受到不同长径比的弹丸超高速碰撞后最有可能发生破坏的位置是不同的,而同一长径比、不同等效直径、不同碰撞速度的非球形弹丸对后墙造成破坏的位置基本相同。通过数据拟合,得到了非球形弹丸对后墙造成破坏的位置LBC的经验表达式。
Along with the quick development of aerospace sci-tech and sharply increment of aerospace mission, a great deal of space debris scatter on low earth orbit. This constitutes the complicated space debris environment which has been threatening the safety of the spacecraft seriously. How insure the safety of the spacecraft, which becomes a very important problem of the current spacecraft design. Because of the complexity of hypervelocity impacts, characteristics of debris clouds are not still clear. Therefore the design of spacecraft shielding structure still needs the further research.
Smoothed particle hydrodynamics(SPH) method is the pioneer of meshless particle methods. Nowadays it has been applied to many realms with related fluid mechanics. It has simple logic, can avoid the mesh enlacement and distort of finite element method. So it is suitable for simulating hypervelocity impacts especially.
SPH method is introduced systemically in this paper. And some kinds of problems related with numerical simulations are discussed deeply. The characteristics of debris clouds produced by hypervelocity impacts are studied using SPH method. Hypervelocity impacts of Whipple shields are simulated and analyzed.
The main achievements and conclusions in this paper are presented in the following:
1. Based on Cartesian coordinate system, the 2D and 3D SPH program is composed on one's own. Johnson-Cook tensile cumulative damage constitutive model, Johnson-Cook visco-plastic constitutive model and Steinberg-Cochran-Guinan (SCG) constitutive model are imported in the program successfully. The simulated results obtained by SPH program are in accord with the experiments. This shows that the SPH program is capable of simulating different impact dynamics problems, especially hypervelocity impacts.
2. Five problems related with numerical simulations, such as the computational accuracy, tensile instability, ghost particle method, initial smoothing length and material interface made by different particle spacing, are studied. The three tensile instability treatment methods are compared. The calculated results show that Monaghan method and stable particle methods based on Lagrangian kernels are better than Conservative Smoothing Approach (CSA). The ghost particle method is an effective method to deal with the rigid boundary condition. But a low density region will be produced in the neighborhood of symmetric plane if the ghost particle method is used to deal with the symmetric boundary. This result is unreasonable. The research shows that the simulated results obtain some extent improvement by using the XSPH correction to the velocity of a particle. The effects of initial smoothing lengths on SPH simulated results are analyzed. The results show that the bigger initial smoothing length, the less rigid projectile. And the rational range of initial smoothing length is d0
4. Following the analysis of the normal hypervelocity impact, the characteristics of debris clouds obtained by oblique hypervelocity impacts are simulated. The shapes of debris clouds produced by the sphere and the rod are an inclined ellipsoid. However the ellipsoid formed by the rod is more inclined than the sphere. And debris clouds formed by the disk are similar to an inclined centrum. The velocity vector figure of debris clouds of oblique hypervelocity impacts is presented. The acquisition approach of cumulative momentum unit area MA is presented. The MA distributions of three projectiles are obtained by the approach. The results show that the executions of the disk and the rod are more powerful than that of the sphere. And the execution of the rod is strongest.
5. The effects of equations of state and constitutive models on SPH simulated results are discussed. By comparing the shapes of debris clouds, the results obtained by Mie-Grüneisen EOS agree with the experiments. However debris clouds obtained by Tillotson EOS tend to expanding outwards. In the perspective of the depth of the crater and the diameter of the hole of the target, the simulated results from Tillotson EOS are closer to the experimental data than Mie-Grüneisen EOS. The latter results are larger than the experiment clearly. The constitutive models don’t affect the whole distribution of fragments. However debris clouds obtained by Johnson-Cook constitutive model are more reasonable than SCG constitutive model.
6. Based on ballistic limit equations (BLE), the design of Whipple shields is discussed from five aspects which include shield standoff distance, bumper density, bumper thickness, rear wall thickness and rear wall material. The corresponding design project is presented. The results show that the performance of the shielding structure obtains considerable improvements. The effects of non-spherical projectiles with different ratios of length to diameter on shielding performance are studied. Normal and oblique hypervelocity impacts are simulated. The calculated results of non-spherical projectiles are compared with ballistic limit nerves of the sphere. The results show the executions of the rod are stronger than that of the disk and the sphere.
7. By introducing the conception of ballistic limit mass ratio, the executions of non-spherical projectiles are made a qualitative comparison with that of spherical projectiles. The analysis of oblique hypervelocity impacts show that most possible locations on which the rear wall is destroyed relate to the ratio of length to diameter nearly. The projectiles with same ratio of length to diameter have almost same damage position even if they have different equivalent diameter or impact velocity. An empirical expression of the damage position LBC is presented by fitting simulated results.
引文
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