基于最优运输无网格法的Whipple屏超高速撞击数值模拟

樊江; 袁圆; 廖祜明; 袁庆浩; 陈高翔; 黎波

doi:10.11883/bzycj-2019-0241

基于最优运输无网格法的Whipple屏超高速撞击数值模拟

doi: 10.11883/bzycj-2019-0241

樊江^1,,
袁圆¹,
廖祜明¹,
袁庆浩¹,
陈高翔¹,
黎波^2, ,

1.
北京航空航天大学能源与动力工程学院，北京 100191
2.
凯斯西储大学机械与航空航天工程学院，美国克利夫兰，OH44106

详细信息

作者简介:
樊　江（1973－　），男，博士，副教授，fanjiang@buaa.edu.cn

通讯作者:
黎　波（1979－　），男，博士，教授，bo.li14@case.edu

中图分类号: O385
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出版历程
- 收稿日期: 2019-06-14
- 修回日期: 2019-02-18
- 刊出日期: 2020-07-01

Numerical simulation of Whipple shield hypervelocity impact based on optimal transportation meshfree method

1.
School of Energy and Power Engineering, Beihang University, Beijng 100191, China
2.
Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland OH44106, USA

摘要

摘要: Whipple屏是航天器防护空间碎片撞击的常用结构。现有的方法在模拟Whipple屏超高速撞击时均存在问题，本文采用最优运输无网格法（optimal transportation meshfree, OTM）对其进行模拟。OTM法是一种拉格朗日无网格法，其特点是运用最优运输理论对时间进行离散，采用带有位置信息的节点和带有材料信息的物质点对空间进行离散，利用局部最大熵（local maximum entropy, LME）方法得到插值函数，基于能量释放率来判断材料是否失效。本文首先用OTM法对铝球超高速撞击单层铝板进行模拟，通过与实验结果和各类SPH法的计算结果对比，验证了OTM法在超高速撞击问题上的适用性；然后采用OTM法对Whipple屏超高速撞击进行模拟，将OTM法预测的缓冲墙与后墙的损伤情况与实验结果进行对比，结果显示OTM法不仅能准确预测缓冲墙的弹孔直径，也能很好地模拟出后墙的剥落、穿透情况和碎片云的形态。
- 最优运输无网格法 /
- 超高速撞击 /
- Whipple屏 /
- 损伤
Abstract: The Whipple shield is often used for protecting spacecraftfrom the impact of space debris. There are a lot of defects in the general numerical simulation methods for hypervelocity impact problems, thus this paper used OTM (optimal transportation meshfree)method to simulate the impacting process. OTM is a Lagrangian meshless method which ischaracterized by applying optimal transportation theory to discretize time, using a set of nodal-points with position information and a set of material-points with material information to discretize space,utilizing LME (local maximum entropy) approximation schemes to get interpolation functions, and simulating the failure of materials by material-point failure method related toenergy release rate. In this paper, OTM method was firstly used to simulate the impact of an aluminum ball on a single aluminum plate. The applicability of OTM method in hypervelocity impact was verified by comparing with the test results and the calculation results of other SPH methods. Then we used OTM method to simulate the hypervelocity impact of Whipple shield. The damage of the outer bumper and the spacecraft wall predicted by the OTM method was compared with the experimental results. It could be seen that the OTM method could not only predict the diameter of the bullet hole of the outer bumper, but also accurately simulate the spalling and penetration of the spacecraft wall, and the shape of the debris cloud.
- optimal transportation meshfree /
- hypervelocity impact /
- whipple shield /
- damage

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图 1 空间离散示意图^[17]

Figure 1. Spatial discrete diagram^[17]

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图 2 评估能量释放率的局部邻域^[15]

Figure 2. The local neighborhood used to estimate the energy-release rate^[15]

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图 3 铝球撞击铝板离散模型

Figure 3. Discrete model of aluminum ball impacting single aluminum plate

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图 4 OTM法与各类SPH方法计算结果对比

Figure 4. Comparison of OTM and various SPH methods’ simulation results

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图 5 实验模型示意图

Figure 5. Schematic diagram of experimental model

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图 6 Whipple屏超高速撞击数值模拟模型

Figure 6. The numerical simulation model of Whipple shield hypervelocity impact

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图 7 缓冲墙损伤对比图(撞击速度5.29 km/s)

Figure 7. Damage characteristics comparison chart of outer bumper (Impact velocity 5.29 km/s)

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图 8 实验与仿真中的剥落和穿透

Figure 8. Definitions of spalling and penetration in experiments and simulations

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图 9 后墙损伤图(撞击速度5.29 km/s)

Figure 9. Damage characteristics of spacecraft wall (impact velocity is 5.29 km/s)

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图 10 正撞碎片云对比图

Figure 10. Fragment cloud comparison chart of vertical impact

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图 11 斜撞碎片云对比图

Figure 11. Fragment cloud comparison chart of oblique impact

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表 1 LY12材料参数

Table 1. Material parameters of LY12

密度/(kg∙m⁻³)	弹性模量/GPa	泊松比	比热容/(J∙kg⁻¹∙K⁻¹)
2 700	68.9	0.33	896

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表 2 J2黏塑性模型参数

Table 2. Parameters of J2 viscoplasticity model

σ₀/MPa	${\varepsilon }_{0}^{\rm{p}}$	${\dot{\varepsilon } }_{0}^{\rm{p} }$	n	m	q	T_m0/K	$ a $	$ {\gamma }_{0} $
276	$ 5\times {10}^{-4} $	1 000	0.075	0.08	0.5	925	1.5	1.97

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表 3 铝球超高速撞击铝板结果对比

Table 3. Comparison of high-velocity impact results between aluminum projectile and plate

方法	d/mm	ε/%	l/mm	w/mm	l/w	Δ/%
Hiermaier实验	27.5	−	−	−	1.39	−
Hiermaier模拟	35.0	27.3	−	−	1.11	−
SPH法	31.6	14.9	102.8	75.5	1.36	2.2
ASPH法	28.9	5.1	105.1	86.1	1.22	12.2
拟流体SPH法	29.4	6.9	105.7	81.4	1.30	6.5
OTM法	26.2	4.7	104.2	76.7	1.36	2.2

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表 4 实验参数设置

Table 4. Parameters in experiments

实验	弹丸直径/mm	弹丸质量/g	缓冲墙厚度/mm	后墙厚度/mm	撞击速度/(km·s⁻¹)	撞击角/(°)
04-0090	5.00	0.1797	1.92	1.94	5.29	0
04-0092	5.02	0.1826	1.94	1.90	5.52	0
04-0079	5.00	0.1810	1.94	1.92	6.08	0
04-0080	5.00	0.1811	1.92	1.90	6.15	0
04-0084	4.04	0.0972	1.92	1.90	5.95	45
04-0083	4.02	0.0960	1.92	1.94	6.02	45
04-0075	4.02	0.0958	1.92	1.90	4.47	45
04-0077	4.00	0.0940	1.92	1.94	4.74	45

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表 5 缓冲墙弹孔尺寸对比

Table 5. Bullethole size comparison of outer bumper

实验	撞击速度/(km∙s⁻¹)	实验缓冲墙弹孔尺寸/mm	仿真缓冲墙弹孔尺寸/mm	相对误差
04-0090	5.29	11.5	10.5	8.69%
04-0092	5.52	11.7	10.9	6.84%
04-0079	6.08	12.4	11.2	9.68%
04-0080	6.15	12.6	11.8	6.35%
04-0075	4.47	10.6×8.5	10.9×8.99	2.83%×5.76%
04-0077	4.74	10.6×8.7	11.2×9.39	5.66%×7.93%
04-0084	5.95	11.6×10.2	12.3×10.1	6.03%×0.98%
04-0083	6.02	11.6×10.3	12.1×9.75	4.31%×5.34%

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表 6 后墙损伤情况对比

Table 6. Damagecomparison of spacecraft wall

实验	撞击速度/(km∙s⁻¹)	实验后墙损伤情况	仿真后墙损伤情况
04-0090	5.29	3处剥落，无穿透	无剥落，2处穿透
04-0092	5.52	2处剥落，无穿透	5处剥落，2处穿透
04-0079	6.08	无剥落，无穿透	无剥落，无穿透
04-0080	6.15	无剥落，无穿透	无剥落，无穿透
04-0075	4.47	无剥落，2处穿透	无剥落，无穿透
04-0077	4.74	无剥落，无穿透	无剥落，无穿透
04-0084	5.95	1处剥落，1处穿透	无剥落，无穿透
04-0083	6.02	1处剥落，1处穿透	1处剥落，无穿透

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