多相流系统的离散玻尔兹曼研究进展

许爱国; 陈杰; 宋家辉; 陈大伟; 陈志华

doi:10.7638/kqdlxxb-2021.0021

多相流系统的离散玻尔兹曼研究进展

doi: 10.7638/kqdlxxb-2021.0021

许爱国^{1, 2, 3,},
陈杰^{1, 4,},
宋家辉^{1, 5},
陈大伟¹,
陈志华⁴

1.
北京应用物理与计算数学研究所，北京　100088
2.
北京大学应用物理与技术研究中心和高能量密度物理数值模拟教育部重点实验室，北京　100871
3.
北京理工大学爆炸科学与技术国家重点实验室，北京　100081
4.
南京理工大学瞬态物理国家重点实验室，南京　210094
5.
北京理工大学宇航学院，北京　100081

基金项目: 国家自然科学基金（11772064，11702028）；中国工程物理研究院创新发展基金创新项目（CX2019033）；计算物理国防重点实验室稳定支持项目（W2018-05）；爆炸科学与技术国家重点实验室开放课题（KFJJ21-16M）

详细信息

作者简介:
许爱国^*（1970-），男，山东人，研究员，研究方向：理论物理，物理力学.E-mail：Xu_Aiguo@iapcm.ac.cn

分子的平均自由程λ与平均分子间距l成正相关，所以克努森数Kn可视为重新标度的平均分子间距，描述的是系统的离散程度，其倒数描述的是系统的连续程度。对于非平衡流动，Kn又可视为两个分子发生碰撞的平均时间间隔与以分子平均速度通过关注的宏观特征尺度所需时间之比，因而可视为重新标度的分子碰撞平均时间间隔。因其与热力学弛豫时间成正相关，所以可进一步视为重新标度的热力学弛豫时间。从这个意义上，Kn描述的是系统偏离热力学平衡的程度。
中图分类号: O359；O411.3
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出版历程
- 收稿日期: 2021-02-25
- 录用日期: 2021-04-08
- 修回日期: 2021-04-05
- 网络出版日期: 2021-06-25
- 刊出日期: 2021-06-25

Progress of discrete Boltzmann study on multiphase complex flows

XU Aiguo^{1, 2, 3
,},
CHEN Jie^{1, 4
,},
SONG Jiahui^{1, 5},
CHEN Dawei¹,
CHEN Zhihua⁴

1.
Institute of Applied Physics and Computational Mathematics, Beijing　100088, China
2.
Center for Applied Physics and Technology, MOE Key Center for High Energy Density Physics Simulations, Peking University, Beijing　100871, China
3.
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing　100081, China
4.
Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing　210094, China
5.
School of Aerospace Engineering, Beijing Institute of Technology, Beijing　100081, China

摘要

摘要: 针对多相复杂流体系统模拟研究，简要介绍从格子气模型到离散玻尔兹曼方法的发展历程。从统计物理学基本原理出发，通过粗粒化建模思路，给出玻尔兹曼方程；分析Chapman-Enskog多尺度展开方法所蕴含的测量逐步细化的物理图像，给出离散玻尔兹曼建模的基本原则和主要步骤。简要介绍离散玻尔兹曼在相分离、燃烧、流体不稳定性等系统中的应用。对于多相复杂流体系统的动理学建模，技术关键是分子间作用力和化学反应贡献的引入。不同颜色的示踪粒子的引入，使得在单流体理论框架下即可实现混合过程中物质粒子来源的确定；示踪粒子在其速度相空间的分布所形成的结构蕴含丰富的流场信息，为复杂流场研究张开一个全新的视角。在多介质情形，离散玻尔兹曼建模与动理学宏观建模的对应关系是一对多。随着系统非平衡程度加深，相对于动理学宏观建模与模拟思路，离散玻尔兹曼建模与模拟的复杂度上升速度较慢。作为系统行为粗粒化描述的一种物理模型构建方法，离散玻尔兹曼根据研究需求，选取一个视角，研究系统的一组动理学性质，因而要求描述这组性质的动理学矩在模型简化过程中保值；是动理学直接建模方法的一种，为连续介质建模失效或物理功能不足、而分子动力学方法因适用尺度受限而无能为力的介尺度情形提供了一条方便、有效的研究途径。
- 多相流 /
- 复杂物理场 /
- 统计物理 /
- 粗粒化建模 /
- 玻尔兹曼方程 /
- 非平衡 /
- 动理学建模 /
- Chapman-Enskog多尺度分析
Abstract: The development of lattice gas model to discrete Boltzmann method is briefly introduced for modeling multiphase complex fluid systems. Based on the basic principles of statistical physics, the Boltzmann equation is given through the idea of coarse-grained modeling. The physical images of progressively refined measurements contained in the Chapman-Enskog multi-scale expansion method are analyzed, and the basic principles and main steps of Discrete Boltzmann Modeling (DBM) are given. The applications of discrete Boltzmann in phase separation, combustion and hydrodynamic instability systems are briefly reviewed. For the kinetic modeling of multiphase complex fluid systems, the key techniques are the introduction of intermolecular forces and the contribution of chemical reactions. The introduction of tracer particles of different colors makes it possible to determine the source of material particles in the mixing process under the framework of single-fluid theory. The structure formed by the distribution of tracer particles in their velocity space contains rich flow field information, which opens a new perspective for the study of complex flow field. In the case of multi-media, the correspondence between discrete Boltzmann modeling and Kinetic Macro Modeling (KMM) is one-to-several, where KMM means that to derive the macroscopic model equations from kinetic theory. As the degree of non-equilibrium of the system deepens, the complexity of discrete Boltzmann modeling and simulation increases more slowly than that of KMM and simulation. As a coarse-grained physical modeling method, discrete Boltzmann selects a perspective to study a set of kinetic properties of the system according to research requirements, so it is required that the kinetic moments describing this set of properties maintain their values in the process of model simplification. It provides a convenient and effective way to investigate the mesoscale situations where continuum modeling fails or physical functions are insufficient and molecular dynamics method is unable to do so due to the limited applicable scale.
- multiphase flow /
- complex physical field /
- statistical physics /
- coarse-grained modeling /
- Boltzmann equation /
- non-equilibrium /
- kinetic modeling /
- Chapman-Enskog multi-scale analysis
注释:

1) 分子的平均自由程λ与平均分子间距l成正相关，所以克努森数Kn可视为重新标度的平均分子间距，描述的是系统的离散程度，其倒数描述的是系统的连续程度。对于非平衡流动，Kn又可视为两个分子发生碰撞的平均时间间隔与以分子平均速度通过关注的宏观特征尺度所需时间之比，因而可视为重新标度的分子碰撞平均时间间隔。因其与热力学弛豫时间成正相关，所以可进一步视为重新标度的热力学弛豫时间。从这个意义上，Kn描述的是系统偏离热力学平衡的程度。

HTML全文

图 1 质心坐标系中二体碰撞的分子运动轨迹

Figure 1. The molecular trajectory of two-body collision in the centroid coordinate system.

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图 2 三维分子碰撞截面和散射示意图

Figure 2. Schematic of 3D molecular collision cross section and scattering

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图 3 非平衡特征量张开的非平衡相空间

Figure 3. Phase space opened by non-equilibrium characteristic quantities

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图 4 RT与RM不稳定性演化过程中系统内不同类型的非平衡强度与密度、温度、流速不均匀度之间关联程度的对比^{[56, 62]}（更多细节参见文献[62]）

Figure 4. Comparison of the correlation degree between different types of non-equilibrium strength and density, temperature and flow rate unevenness in the evolution of RT and RM instability^{[56, 62]} (see Ref. [62] for more details)

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图 5 RM不稳定性演化过程中热传导对相关度的影响^[62]（更多细节参见文献[62]）

Figure 5. Effect of heat conduction on the degree of correlation in the evolution of RM instability^[62] (see Ref. [62] for more details)

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图 6 RTI与RMI共存系统界面反转现象出现机制的示意图^[62]

Figure 6. The schematic diagram of the collaboration and competition relations between RM and RT instability^[62]

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图 7 RTI与RMI共存系统界面反转现象出现与否的数值模拟密度云图^[62]

Figure 7. Numerical simulation density nephogram of interface inversion in RTI and RMI coexistence system^[62]

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图 8 RTI与RMI共存系统宏观特征^[62]

Figure 8. Macrocharacteristics of the RTI and RMI coexistence system^[62]

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图 9 不同重力场下RTI与RMI共存系统的非平衡行为特征^[62]

Figure 9. Non-equilibrium characteristics of RTI and RMI coexistence system under different gravity fields^[62]

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图 10 马赫数对RTI与RMI共存系统TNE强度、宏观量梯度与非平衡特征相关度的影响^[62]

Figure 10. Influence of Mach number on thermodynamic non-equilibrium strength, macroscopic gradient and non-equilibrium characteristic correlation of RTI and RMI coexistence system^[62]

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图 11 耦合RTKHI系统（$g = 0.005$, ${u_0} = 0.05$）的温度图像、图灵斑图，以及${u_0} = 0.05$ 的纯KHI的图灵斑图 ^[63]

Figure 11. A coupled RTKHI with $g = 0.005$ and ${u_0} = 0.05$. (a) and (b) are the temperature and the corresponding Turing pattern (${T_{th}} = 1.0$) of the RTKHI, respectively. (c) is the temperature Turing pattern of pure KHI with ${u_0} = 0.05$^[63]

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图 12 振幅 A、振幅增长率${{{\rm{d}}A} / {{\rm{d}}t}}$ 和形态边界长度 L 与时间 t 的关系^[63]

Figure 12. Perturbation amplitude A, growth rate ${{{\rm{d}}A} / {{\rm{d}}t}}$, and morphological boundary length L vs time t ^[63]

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图 13 根据温度场的形态分析早期主要机制^[63]

Figure 13. Morphological analysis of the main mechanism in the early stage^[63]

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图 14 RTKHI系统($g = 0.005$, ${u_0} = 0.1$)，不同视角的非平衡特征^[63]

Figure 14. Non-equilibrium characteristics of the RTKHI system ($g = 0.005$, ${u_0} = 0.1$) ^[63]

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图 15 耦合RTKHI系统的非平衡特征在早期主要机理判断和过渡点捕获中的应用^[63]

Figure 15. The applications of non-equilibrium characteristics in the early main mechanism judgment and transition point capture^[63]

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图 16 等温与非等温相分离过程熵产生速率演化特征的对比^[44]

Figure 16. Comparison of entropy generation rate evolution characteristics between isothermal and non-isothermal phase separation processes^[44]

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图 17 热流对热相分离过程中SD阶段持续时间和熵产生速率的影响^[44]

Figure 17. Effect of heat flow on duration of SD stage and entropy generation rate in thermal phase separation^[44]

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图 19 表面张力对热相分离过程中SD阶段持续时间和熵产生速率的影响^[44]

Figure 19. Effect of surface tension on duration of SD stage and entropy generation rate in thermal phase separation process^[44]

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图 18 黏性对热相分离过程中SD阶段持续时间和熵产生速率的影响^[44]

Figure 18. Effect of viscosity on duration of SD stage and entropy generation rate in thermal phase separation^[44]

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图 20 两种熵产生速率幅值之间的关系曲线，图中箭头指向热传导系数（1/Pr）、黏性系数($\tau $)和表面张力系数（K）增大的方向^[44]

Figure 20. The relationship curve between the amplitude of two kinds of entropy production rate, the arrow in the figure points to the increasing direction of heat conduction coefficient (1/Pr), viscosity coefficient ($\tau $) and surface tension coefficient (K) ^[44]

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图 21 四种反应速率系数随温度变化特征图^[70]

Figure 21. Profiles of k in function of temperature for four different cases^[70]

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图 22 非平衡量$\varDelta _{2,xx}^ * $ 与黏性应力张量${\textit{Π}} _{xx}$ 对比图^[70]

Figure 22. Comparisons of non-equilibrium quantity $\varDelta _{2,xx}^ * $ and viscous stress${\textit{Π}} _{xx}$^[70]

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图 23 非平衡量$\varDelta _{3,1,x}^ * $ 与热流$ {{j}_{q,x}} $ 对比图^[70]

Figure 23. Comparisons of non-equilibrium quantity $\varDelta _{3,1,x}^ * $ and heat flux $ {{j}_{q,x}} $^[70]

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图 24 情形1与情形2下的三种局域熵产生率分布^[70]

Figure 24. Three kinds of profiles of entropy productions for case1 and case2^[70]

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图 25 情形3与情形4下的三种局域熵产生率分布^[70]

Figure 25. Three kinds of profiles of entropy productions for case3 and case4^[70]

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图 26 四种反应速率情形下的全局熵产生率^[70]

Figure 26. Three kinds of profiles of global entropy productions for four cases^[70]

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