凸多面体颗粒流动的本构模型研究

Extensive experimental data show that particle shape has a significant impact on particle flow behavior. However, most of existing continuum theories for particle flows are based on the spherical particle assumption, and the effect of particle shape cannot be considered. Therefore, it is of great significance in theory and application to develop a general and unified continuum model for non-spherical particle flows. In the present project, the Discrete Element Method (DEM) is used to simulate granular shear flows of convex polyhedral particles. Based on the simulation results, the effect of particle surface angularity on the microstructure and macroscopic behavior is systematically analyzed, and the connection between particle-level and bulk properties is explored. Further, the constitutive law of stresses and collisional dissipation rate model are developed for non-spherical particles by considering the effect of particle angularity. With the developed models, the continuum governing equations for the granular flow can be closed, so that the continuum modeling of non-spherical particles with significant surface angularity is achieved. The proposed project makes an attempt to develop theories and computational approaches for the flows of real particles (usually non-spherical, angular, and frictional), provide accurate and efficient tools for the analyses of large-scale particle flows in industries, and therefore achieve the process optimization.

大量实验结果表明，颗粒的形状对颗粒物质的流动有显著的影响。然而，现有的颗粒流连续介质理论基本上都是假设颗粒是球形的，不考虑颗粒形状的影响。发展普适的、统一的非球形颗粒流的连续介质模型具有重要的理论和应用价值。本项研究采用离散单元法（Discrete Element Method 或DEM）模拟凸多面体颗粒的剪切流动，系统的分析颗粒表面棱角对颗粒流动微观结构和宏观力学表现的影响，诠释微观颗粒性质和宏观行为的联系，建立考虑颗粒表面棱角影响的非球形颗粒流的应力本构模型，发展颗粒碰撞能量耗散率模型，进而完成颗粒流连续介质方程组的闭合，实现考虑颗粒表面棱角影响的颗粒流的连续介质模拟。本项研究的预期成果将推动真实颗粒（非球形、有棱角、颗粒间存在较大摩擦）流动理论和数值模拟的发展，为涉及颗粒流的工程生产实践提供更加准确、高效的分析工具，实现工业过程的优化设计。

对复杂颗粒流的深入理解和控制，有利于实现工业生产中的节能减排、质量改进和效率提高，也有助于制定有效措施来防控自然灾害和治理空气污染。本项目采用数值模拟方法研究了具有凸几何形状的非球形颗粒流以及柔性可变形颗粒流，得到的主要结果归纳如下：1）颗粒的粒度和粒形分布特征对流动有显著的影响。多粒度系统的应力与混合物内部各成分的单粒度系统的应力成线性关系，多粒形系统的应力是描述颗粒姿态取向一致性的有序参数的函数，在此认识的基础上，发展了多分散颗粒系统的流动应力本构模型。2）凸多面体颗粒的棱角程度影响二次流型从旋涡流向紊流转变的临界压强值，采用球形度和压强-颗粒温度组合项可以得到二次流型相图。颗粒间滑动摩擦系数一定的情况下，多面体颗粒的表观摩擦系数大于球形颗粒；然而，颗粒外形棱角程度或球形度对表观摩擦系数的影响是非单调的。通过用无量纲颗粒温度项来标度表观摩擦系数，不同的多面体颗粒和球形颗粒的流变关系趋向于统一。3）柔性纤维颗粒气固两相流动行为与刚性颗粒存在显著差异。纤维颗粒的主要特性（柔性、长径比、以及颗粒间由于液桥产生的黏性力的作用）对气固流化行为有显著影响。颗粒成团特性对纤维长径比和弯曲模量的依赖具有非单调性，并且受到这两个参数的耦合影响。纤维颗粒快速变形产生的能量耗散，可以增加颗粒接触数目、延长接触时间，导致生成更多、更大的团簇。上述结果有望应用于化工和能源领域非球形颗粒和柔性颗粒（如生物质材料、大分子聚合物和毛发）的化学反应、输运和干燥等过程的流态化设计。