气固系统中颗粒包覆均匀性数值模拟研究进展

doi:10.11949/0438-1157.20251378

摘要/Abstract

摘要：

颗粒包覆过程在药物制备、功能颗粒制备、核燃料颗粒制备等工业领域有着重要应用。颗粒包覆的均匀性是颗粒包覆过程优化控制的主要目的，是一种包覆工艺成熟的主要标志。其一般包括两个主要方面，即颗粒间包覆均匀性（inter-particle coating uniformity）和颗粒内包覆均匀性（intra-particle coating uniformity），文献中均有相关实验和模拟研究报道。本文详细综述颗粒包覆均匀性的数值模拟方法，对其发展历程和演化机理进行分析，并给出未来发展的启示。在颗粒间均匀性数值模拟方面，研究工作涵盖了四种主要方法：基于停留时间分布的统计模型、基于Monte Carlo方法描述的随机沉积模型、耦合流体力学与颗粒运动的CFD-DEM框架，以及多尺度耦合等高保真模型，这些方法旨在全面揭示包覆前驱物质分布、混合特性与颗粒动力学对包覆均匀性的影响；在颗粒内包覆均匀性数值模拟方面，主要包括表面离散化模型、连续场模型、球谐函数模型及颗粒绑定型非均相包覆模型四类，对比分析了其优缺点。颗粒内包覆均匀性是精细调节整体包覆质量的关键环节，目前多是实验规律研究，数学建模和机理研究还很不完善，亟待深入。未来颗粒包覆均匀性数学模拟需要在精确性和复杂性之间取得平衡，构建兼具可计算性与符合物理机制的多尺度耦合框架，以更高效地支撑包覆工艺优化与揭示包覆机理。

关键词: 颗粒包覆, 数值模拟, 颗粒间均匀性, 颗粒内均匀性, 气固系统, 流体力学, 模型

Abstract:

The particle coating process plays a significant role in various industrial applications, including drug preparation, functional particle preparation, and nuclear fuel particle preparation. The uniformity of particle coating is the primary objective in optimizing the coating process and a key indicator of the maturity of the coating technology. It generally involves two main aspects: inter-particle coating uniformity and intra-particle coating uniformity. Both aspects have been extensively studied in the literature through experimental and simulation research. This review provides a detailed overview of numerical simulation methods for particle coating uniformity, analyzes their development trajectory and underlying mechanisms, and offers insights into future development directions. In terms of inter-particle coating uniformity, four methods are developed: statistical models based on residence time distribution, random deposition models described by the Monte Carlo method, the CFD-DEM framework coupling fluid dynamics and particle motion, and high-fidelity models involving multi-mechanism coupling. These methods aim to comprehensively reveal the effects of precursor material distribution, mixing characteristics, and particle dynamics on coating uniformity. For intra-particle coating uniformity, the primary simulation approaches include surface-discretization-based models, continuous-field-based models, spherical-harmonics-based models, and particle-binding-type heterogeneous-layer models, and its own advantages and limitations are compared and summarized. Intra-particle coating uniformity is a critical factor in determining overall coating quality precisely. Current research focuses on experimental studies predominantly, while mathematical modeling and mechanistic understanding remain underdeveloped. Future advancements in numerical simulations of coating uniformity should aim to balance computation precision and complexity, establishing a multi-scale coupled framework that integrates computational feasibility with physical fidelity, thereby providing more efficient support for coating process optimization and mechanism elucidation.

Key words: particle coating, numerical simulation, inter-particle coating uniformity, intra-particle coating uniformity, gas-solid systems, fluid mechanics, model

中图分类号:

TQ 018

兰蕊, 田宇, 刘荣正, 杨旭, 刘兵, 邵友林, 刘马林. 气固系统中颗粒包覆均匀性数值模拟研究进展[J]. 化工学报, DOI: 10.11949/0438-1157.20251378.

Rui LAN, Yu TIAN, Rongzheng LIU, Xu YANG, Bing LIU, Youlin SHAO, Malin LIU. Research progress in numerical simulation of particle coating uniformity in gas-solid systems[J]. CIESC Journal, DOI: 10.11949/0438-1157.20251378.

图/表 13

图 1 颗粒间包覆非均匀性：(a) 聚合物球形颗粒SEM图像[26]; (b) 通过颗粒尺寸分布描述非均匀性的示意图

Fig.1 Inter-particle coating non-uniformity: (a) SEM image of polymer spherical particles [26]; (b) Schematic diagram of non-uniformity characterized by particle size distribution

图 2 颗粒内包覆非均匀性：(a) TRISO燃料颗粒SiC层缺陷的SEM图像; (b) 通过颗粒表面局部包覆描述非均匀性的示意图

Fig.2 Intra-particle coating non-uniformity: (a) SEM image of defects in the SiC layer of a TRISO fuel particle; (b) Schematic diagram of non-uniformity characterized by local coating features on the particle surface

图 3 四种颗粒间包覆均匀性数值模拟方法示意图

Fig.3 Schematic diagram of four numerical methods for inter-particle coating uniformity

图 4 不同颗粒的在“活跃喷动区”累积循环停留时间示意图

Fig.4 Schematic diagram of the cumulative cyclic residence time of different particles within the “active spout zone”

图 5 包覆过程Monte Carlo模型中的“外部输入-抽样-循环更新”框架示意图

Fig.5 Schematic diagram of the “external input–sampling–iterative update” framework of the Monte Carlo model for the coating process

图 6 (a) 单次随机喷涂下的表面沉积分布[57]；(b) 喷涂次数N=10、100、1000、10000 时包覆均匀性的演化

Fig.6 (a) Surface deposition distribution under a single random spraying event[57]; (b) Evolution of coating uniformity at spraying numbers of N = 10, 100, 1000, and 10000

图 7 CFD-DEM-Monte Carlo耦合框架下单颗粒沉积示意图[20]

Fig.7 Schematic diagram of single-particle deposition within the CFD-DEM-Monte Carlo coupling framework

图 8 DEM-DDM耦合框架示意图[58]：(a) 颗粒表面离散化方式；(b) 不同颗粒形状下局部包覆厚度分布差异

Fig.8 Schematic diagram of the DEM-DDM coupled framework[58]: (a) Discretization scheme of the particle surface; (b) Differences in local coating thickness distributions for particles with different shapes

图 9 单颗粒包覆CFD-DDM-PDE耦合示意图[59]

Fig.9 Schematic diagram of single-particle coating within the CFD-DDM-PDE coupling framework[59]

图 10 基于球谐展开的单颗粒包覆厚度分布定量分析示意图[60]

Fig.10 Schematic diagram of the quantitative analysis of single-particle coating thickness distribution using spherical harmonic expansion[60]

图 11 PBT-HL模型及复合颗粒“自均匀化”[61]：(a) PBT-HL模型；(b) 单颗粒包覆均匀性演变

Fig.11 PBT-HL model and “self-uniformization” behavior of composite particles [61]: (a) PBT-HL model; (b) Evolution of single-particle coating uniformity

表 1 颗粒间包覆均匀性数值模拟方法对比

Table 1 Comparative study of numerical methods for inter-particle coating uniformity

模型类型	主要思路	主要优势	主要局限
时间分布模型	基于颗粒群体的停留时间分布或循环频率等宏观统计量预测包覆颗粒均匀性	模型简洁，计算高效；宏观均匀性趋势预测	无法直接量化涂层增量、忽略局部沉积
蒙特卡洛模拟	以概率方式模拟液滴沉积与膜厚随机增长过程	高效预测群体涂层分布，可捕捉不确定性对包覆均匀性差异的影响	依赖实验或物理模型概率分布
离散元模型	追踪单颗粒运动状态，描述群体尺度包覆均匀性	物理真实性、良好可扩展性	计算量大，仅刻画颗粒动力学
多尺度耦合模型	从机理层面解析颗粒包覆演化的动态行为与均匀性调控机制。	能够完整捕捉“气流—液滴—颗粒—沉积-均匀性”全过程	建模复杂、参数多；大规模应用受限

表 2 颗粒内包覆均匀性数值模拟方法对比

Table 2 Comparative study of numerical methods for intra-particle coating uniformity

模型类别	主要思路	主要优势	主要局限
表面离散化模型	颗粒表面划分面元，模拟局部沉积	易量化局部厚度，反映随机性	面元多计算量大，存在高效性与可控性之间的矛盾
连续场模型	包覆视为连续介质，偏微分方程描述沉积演化	捕捉连续物理过程，高保真	难处理复杂几何，沉积机理简化
球谐函数模型	颗粒表面厚度分布投影到球谐函数基上，角功率谱表征多尺度空间不均匀性	离散表面数据的连续谱域解析	计算代价高昂，仅适用于球形或近球形
颗粒绑定非均相包覆模型	包覆颗粒密度动态变化	定量化描述单颗粒包覆层厚度的各向异性	结构简化假设、动力学耦合不足

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