Ketterhagen William R, Curtis Jennifer S, Wassgren Carl R
School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jun;71(6 Pt 1):061307. doi: 10.1103/PhysRevE.71.061307. Epub 2005 Jun 30.
Collision resolution is one of the key elements in a discrete element method algorithm for modeling granular flows. Several collision models have been proposed for this process. The hard-particle collision approach is typically used for dilute systems, or for those in which the assumption of binary and instantaneous particle-particle contact remains valid. As the solids fraction increases, however, multiple, enduring collisions can occur and a soft-particle approach is more appropriate for resolving the collision dynamics. In this work, the delineation between dilute and dense systems and the suitability of contact models are explored for a range of solid fractions. Stress results for two-dimensional shear flow simulations are compared using several collision models including an event-driven hard-particle model, a hysteretic spring soft-particle collision model following Walton and Braun [J. Rheol. 30, 949 (1986)], and a hybrid hard-particle-with-overlap model following Hopkins and Louge [Phys. Fluids A 3, 47 (1991)]. Results show that stresses are accurately predicted for a range of solids fractions, coefficients of restitution, and friction coefficients by both the hard-particle-with-overlap and soft-particle models so long as a sufficiently large loading stiffness is used for the soft-particle model. Additional results investigating the accuracy of the collision models and the amount of collisional overlap are presented as functions of the simulation time step and model parameters.
碰撞求解是颗粒流离散元方法算法中的关键要素之一。针对此过程已提出了多种碰撞模型。硬颗粒碰撞方法通常用于稀相系统，或用于二元且瞬时颗粒 - 颗粒接触假设仍然有效的系统。然而，随着固体分数增加，可能会发生多次持久碰撞，此时软颗粒方法更适合求解碰撞动力学。在这项工作中，针对一系列固体分数，研究了稀相和密相系统之间的界限以及接触模型的适用性。使用包括事件驱动硬颗粒模型、遵循Walton和Braun [《流变学杂志》30, 949 (1986)]的滞后弹簧软颗粒碰撞模型以及遵循Hopkins和Louge [《物理流体A》3, 47 (1991)]的硬颗粒与重叠混合模型在内的几种碰撞模型，比较了二维剪切流模拟的应力结果。结果表明，只要为软颗粒模型使用足够大的加载刚度，硬颗粒与重叠模型和软颗粒模型都能在一定范围的固体分数、恢复系数和摩擦系数下准确预测应力。还给出了作为模拟时间步长和模型参数函数的、研究碰撞模型准确性和碰撞重叠量的其他结果。
