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三维圆柱型颗粒堆坍塌问题的全相态数值模拟

陈福振 李亚雄 史腾达 严红

陈福振, 李亚雄, 史腾达, 严红. 三维圆柱型颗粒堆坍塌问题的全相态数值模拟. 力学学报, 2022, 54(6): 1572-1589 doi: 10.6052/0459-1879-22-001
引用本文: 陈福振, 李亚雄, 史腾达, 严红. 三维圆柱型颗粒堆坍塌问题的全相态数值模拟. 力学学报, 2022, 54(6): 1572-1589 doi: 10.6052/0459-1879-22-001
Chen Fuzhen, Li Yaxiong, Shi Tengda, Yan Hong. Numerical simulation of full phases of collapse of three-dimensional cylindrical granular pile. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1572-1589 doi: 10.6052/0459-1879-22-001
Citation: Chen Fuzhen, Li Yaxiong, Shi Tengda, Yan Hong. Numerical simulation of full phases of collapse of three-dimensional cylindrical granular pile. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1572-1589 doi: 10.6052/0459-1879-22-001

三维圆柱型颗粒堆坍塌问题的全相态数值模拟

doi: 10.6052/0459-1879-22-001
基金项目: 国家自然科学基金(11902267)和江苏省自然科学基金(BK20201203)资助项目
详细信息
    作者简介:

    陈福振, 副教授, 主要研究方向: 多相流理论、数值计算新方法及其应用. E-mail: chenfuzhen@nwpu.edu.cn

  • 中图分类号: O35

NUMERICAL SIMULATION OF FULL PHASES OF COLLAPSE OF THREE-DIMENSIONAL CYLINDRICAL GRANULAR PILE

  • 摘要: 静态颗粒堆在重力作用下的坍塌问题, 是认识和理解许多人为过程和自然现象的基础. 采用传统方法进行模拟存在单颗粒追踪数量大、宏观模拟流变特性明显和相态演变复杂等计算难点. 本文从颗粒介质表现出不同相态的物理机理出发, 对全相态概念进行了定义并进行了区域划分. 根据颗粒介质的应力-应变关系及体积分数的不同, 通过确定不同相态之间的耦合关系和转化准则, 将描述各相态的现有理论有效结合起来, 建立了描述颗粒介质经历全部相态的耦合模型理论. 采用光滑离散颗粒流体动力学方法和离散单元法相耦合的策略, 对颗粒介质物理模型求解, 实现了对不同长径比下的三维圆柱型颗粒堆坍塌过程的数值模拟. 计算结果与实验结果吻合较好, 同时与离散单元法相比, 计算量得到了控制. 不仅捕捉到了不同参数影响下颗粒堆坍塌后沉积的不同现象, 同时获得了不同条件参数对颗粒堆坍塌后铺展特性的影响规律, 为揭示工业和自然界中广泛存在的颗粒介质复杂运动机理提供有效的支撑.

     

  • 图  1  颗粒介质全相态定义及物理模型示意图

    Figure  1.  Definition and diagram of the physical model of all phases of granular media

    图  2  完全弹性到弹性-微小黏塑性再到完全弹性-黏塑性的过渡过程

    Figure  2.  The transition from complete elastic to elastic-micro viscoplastic and then to complete elastic-viscoplastic

    图  3  浓密颗粒流与稀疏颗粒流之间的过渡转化

    Figure  3.  Transition between dense granular flow and dilute granular flow

    图  4  基于SDPH方法的浓密颗粒介质与稀疏颗粒介质相态转变

    Figure  4.  Phase transition between dense granular media and dilute granular media based on SDPH method

    图  5  基于SDPH方法的浓密颗粒介质与稀疏颗粒介质间相互作用

    Figure  5.  Interaction between dense granular media and dilute granular media based on SDPH method

    图  6  SDPH和DEM算法之间的转化方案

    Figure  6.  Conversion between SDPH and DEM

    图  7  SDPH粒子与DEM颗粒之间的相互作用

    Figure  7.  Interaction between SDPH particle and DEM particle

    图  8  SDPH和DEM粒子边界力施加方法

    Figure  8.  Boundary force on SDPH and DEM particles

    图  9  模型示意图

    Figure  9.  Geometric model of granular pile

    图  10  不同SDPH粒子直径下计算结果与实验[6]对比

    Figure  10.  Comparison between calculated results and experiments[6] under different SDPH particle diameters

    图  11  $ a = 0.55 $工况下颗粒堆坍塌过程与实验[6]对比

    Figure  11.  Comparison of the calculated collapse of the granular column with that of the experiment[6] under the condition of $ a = 0.55 $

    图  12  $ a = 0.9 $工况下颗粒堆坍塌过程与实验[6]对比

    Figure  12.  Comparison of the calculated collapse of the granular column with that of the experiment[6] under the condition of $ a = 0.9 $

    图  13  $ a = 3.0 $工况下颗粒堆坍塌过程与实验[6]对比

    Figure  13.  Comparison of the calculated collapse of the granular column with that of the experiment[6] under the condition of $ a = 3.0 $

    图  14  $ a = 13.8 $工况下颗粒堆坍塌过程与实验[6]对比

    Figure  14.  Comparison of the calculated collapse of the granular column with that of the experiment[6] under the condition of $ a = 13.8 $

    图  15  $ a = 16.7 $工况下颗粒堆最终铺展形态与实验[10]对比

    Figure  15.  Comparison of the calculated final spreading morphology of the granular column with that of experimental results[10] under the condition of $ a = 16.7 $

    图  16  $ a = 16.7 $三维圆柱型颗粒堆坍塌过程不同相态演变(黑色表示颗粒处于浓密态, 红色表示颗粒处于稀疏态, 白色表示颗粒处于超稀疏态)

    Figure  16.  The evolution of different phases during the collapse of cylindrical granular pile (Black indicates that the particles are in dense state, red indicates that the particles are in dilute state, and white indicates that the particles are in ultra-dilute state)

    图  17  颗粒堆铺展范围随着a不同的变化曲线($ a < 1.7 $)

    Figure  17.  The runout range of the granular column as a function of $ a $ ($ a < 1.7 $)

    图  18  不同a值条件下颗粒堆高度与铺展范围半径之间的关系曲线

    Figure  18.  The height of the granular column as a function of spreading radius under different conditions of $ a $

    图  19  颗粒堆铺展范围随时间变化曲线

    Figure  19.  The runout range of the granular column over time

    表  1  本文方法与DEM方法计算耗时对比

    Table  1.   Comparison of calculation time between this method and DEM method

    MethodTotal number of particlesComputing platformTime stepCalculation time
    method in this paper182484i9-9900 16 thread parallelism1 × 10−5 s4 h 32 min
    DEM method182484i9-9900 16 thread parallelism2 × 10−6 s23 h 15 min
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  • 收稿日期:  2022-01-02
  • 录用日期:  2022-04-14
  • 网络出版日期:  2022-04-15
  • 刊出日期:  2022-06-18

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