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Exact scaling laws and coarse-grained discrete element modelling of large scale granular systems

DOI：10.7511/jslxCMGM202213

 作者 单位 E-mail 赵婷婷 太原理工大学 机械与运载工程学院, 太原 030024宁波大学 冲击与安全工程教育部重点实验室, 宁波 315211 冯云田 太原理工大学 机械与运载工程学院, 太原 030024斯旺西大学 辛克维奇计算工程中心, 英国斯旺西 SA1 8EN y.feng@swansea.ac.uk

计算效率是制约工程尺度大规模颗粒系统离散元计算发展的重要因素,现有的粗粒化处理方法局限于特定应用并且缺少一般的理论依据。本文采用量纲分析方法,描述了在精确缩尺系统中各物理量应当满足的缩放定律;通过在粗粒化系统和原始系统的代表性体积单元之间建立质量、动量和能量的近似守恒关系,采用多尺度的描述方法得到了粗粒化系统与原始系统之间宏观和细观两种不同尺度的缩放关系,即双尺度粗粒化模型;精确缩尺系统中得到的缩放定律及离散元接触模型处理方法,完全适用于粗粒化系统中细观颗粒层面相关物理量的缩放,通过筒仓侧壁压力和休止角两个算例对精确缩尺模型在粗粒化系统中的有效性进行了验证。

Computational capacities limit the development of discrete element modelling for large scale realistic simulations.Existing coarse-grained methods are proposed mostly for some specific problems which may not be suitable in general.This work describes scaling laws for physical quantities in the exact scaling system using the dimension analysis.The equivalent relations for the RVE of mass,momentum and energy are developed between the coarse-grained and the original systems from the multiscale perspective.A two-scale coarse-graining theory is proposed.Scaling laws and corresponding modifications for contact models in DEM derived in the exact scaling system are found to be still valid for physical quantities at the particle level in the coarse-grained system.Simulations of the wall pressure of a hopper and the repose angle of a granular system considering cohesion are conducted to validate the exact scaling laws used in the coarse-grained system.