微观尺度下金属/气体界面RM不稳定性自相似现象的分子动力学模拟

丁雨; 黄生洪

doi:10.11858/gywlxb.20180606

微观尺度下金属/气体界面RM不稳定性自相似现象的分子动力学模拟

doi: 10.11858/gywlxb.20180606

丁雨,
黄生洪^*, ,

中国科学技术大学近代力学系材料力学行为和设计重点实验室，安徽合肥　230026

基金项目: 国家自然科学基金（U1530125）；挑战专题（TZ2016001）

详细信息

作者简介:
丁　雨(1995－)，男，硕士研究生，主要从事极端冲击问题的分子动力学模拟研究. E-mail: dy123@mail.ustc.edu.cn

通讯作者:
黄生洪(1974－)，男，博士，副教授，主要从事极端冲击动力学研究. E-mail: hshnpu@ustc.edu.cn

中图分类号: O354; O357
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出版历程
- 收稿日期: 2018-07-31
- 修回日期: 2018-09-06

Microscale Self-Similarity Phenomenon of RM Instability on the Copper/Helium Interface with Molecular Dynamics Simulation

DING Yu,
HUANG Shenghong^{*
, ,}

CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China

摘要

摘要: 极端冲击加载条件下的RM (Richtmyer-Meshkov)不稳定性在惯性约束核聚变领域有重要的学术价值和工程意义。宏观动力学方法受限于极端条件下的模型和参数准确性而难以直接应用，微观分子动力学方法则受限于计算量而难以直接模拟宏观尺度现象。为了解RM不稳定性微观与宏观规律之间的联系，采用基于嵌入原子多体势（EAM）的分子动力学方法模拟铜-氦微观尺度界面在极端冲击加载条件下（活塞冲击加载速度6～15 km/s）的RM不稳定性现象，对比文献提供的近似条件下宏观模拟结果发现，演化过程在唯象上完全相似。进一步比较了不同尺度（7.3～145.0 nm）、不同冲击加载速度（11.7～20.6 km/s）、不同初始界面扰动（扰动振幅与波长之比0.20～0.05）条件下振幅发展规律，发现在相同冲击动力条件和边界条件下，RM不稳定性的振幅增长规律在计算尺度范围内完全自相似，主要参数的变化特征符合理论预测。尽管理论模型因简化而存在一定偏差，但是微观模拟获得的振幅增长规律与宏观现象有相似的变化特征。
- RM不稳定性 /
- 极端条件 /
- 唯象相似 /
- 自相似 /
- 分子动力学
Abstract: The Richtmyer-Meshkov instability (RMI) under extreme shock conditions has important academic and engineering significance in the field of inertial confinement fusion (ICF). Present macroscopic hydrodynamic methods are difficult to be directly applied to RMI in extreme conditions due to the lack of proper models and parameters in such states, while the microscopic results obtained by molecular dynamics (MD) are also difficult to be applied directly in macroscopic scale simulation due to computational cost. To understand the connection between macroscopic and microscopic RMI, the RMI evolution on copper-helium interface at different micro scales under different piston shock conditions (6–15 km/s) was simulated by the molecular dynamics method based on embedded-atom potential (EAM) models. Firstly, the RMI evolution obtained by MD was compared with available literature macroscopic results under similar conditions. Phenomenological similarity results between macroscopic and microscopic RMI is confirmed. The evolution histories of initial sinusoidal disturbance (amplitude/wave length ratio 0.20–0.05) at different incident shock wave speeds (11.7–20.6 km/s) and different scales (7.3–145.0 nm) from RMI simulations were further compared and analyzed. It is found that all amplitude evolution curves behave with self-similarity under same shock and boundary conditions, all main parameters vary in accordance with prediction of theoretical model. Although there exists some extent of discrepancy, similar amplitude evolution characteristics results are obtained by microscopic and macroscopic simulations.
- Richtmyer-Meshkov instability /
- extreme conditions /
- phenomenological similarity /
- self-similarity /
- molecular dynamics

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图 1 初始Cu-He正弦单模界面模型及参数定义

Figure 1. Initial characteristic parameters of single mode sinusoidal Cu-He interface model

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图 2 宏观流体动力学模拟的单模RMI（左）与MD模拟的微观结果（右）的唯象相似性

Figure 2. Macroscopic hydrodynamics and microscopic molecular dynamics simulations of single mode RMI (left) with similar phenomenological results (right)

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图 3 气泡/尖钉位置-时间图像

Figure 3. Displacement-time histories of bubble/spike position

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图 4 微观RMI现象典型时刻的密度分布与原子分布

Figure 4. Density contours and atom arrangements map of RMI simulations by MD at typical time constants

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图 5 RMI振幅-时间演化图像

Figure 5. Time histories of RMI amplitude evolution

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图 6 不同尺度模型的无量纲振幅-时间曲线

Figure 6. Non-dimensional amplitude evolution histories of different scale simulations

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图 7 不同尺度、相同无量纲时刻的密度等值图

Figure 7. Density contours of different scale simulations with the same non-dimensional time constants

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图 8 不同冲击加载速度下的无量纲振幅-时间曲线

Figure 8. Non-dimensional time histories of amplitude evolution under different V_p

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图 9 不同初始振幅波长比条件下的无量纲振幅-时间曲线

Figure 9. Non-dimensional time histories of amplitude evolution with different initial amplitude/wave length ratio

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表 1 RMI不同尺度计算结果的参数统计

Table 1. Computed statistical results of RMI parameters at different scales

λ/nm	W_i/(km·s^–1)	δ_W_i/%	W_t/(km·s^–1)	δ_W_t/%	U/(km·s^–1)	δ_U/%	V₀/(km·s^–1)	δ_V₀/%	A	δ_A/%
7.3	11.5	0.3	18.1	1.4	11.5	1.8	3.16	2.3	–0.83	1.1
14.5	11.7	2.1	17.6	1.3	11.9	1.5	3.19	1.4	–0.83	1.1
29.0	11.5	0.3	18.2	2.0	11.7	0.1	3.23	0.1	–0.84	0
72.5	11.4	0.5	17.7	0.7	12.1	3.2	3.28	1.3	–0.85	1.1
145.0	11.2	2.2	17.6	1.3	11.4	2.7	3.32	2.5	–0.85	1.1

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表 2 不同冲击加载速度下RMI参数

Table 2. Parameters of RMI under different V_p

V_p/(km·s^–1)	W_i/(km·s^–1)	W_t/(km·s^–1)	U/(km·s^–1)	V₀/(km·s^–1)	A
6	11.7	17.6	11.9	3.22	–0.83
9	14.2	24.4	16.6	3.43	–0.84
12	16.5	33.5	21.9	3.57	–0.85
15	20.6	41.7	28.9	3.74	–0.83

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表 3 不同初始振幅波长比条件下RMI参数

Table 3. Parameters of RMI with different initial amplitude/wave length ratio

a	W_i/(km·s^–1)	W_t/(km·s^–1)	U/(km·s^–1)	V₀/(km·s^–1)	A
0.20	11.7	17.6	11.9	3.22	–0.83
0.10	11.7	17.8	11.8	2.00	–0.85
0.05	11.6	18.0	11.6	1.03	–0.84

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