NUMERICAL SIMULATION OF FULL PHASES OF COLLAPSE OF THREE-DIMENSIONAL CYLINDRICAL GRANULAR PILE
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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.Abstract: The collapse of static granular pile under gravity is the basis for understanding many human processes and natural phenomena. There are some difficulties for the traditional simulation methods, such as large number of single particle tracking, obvious rheological characteristics, and complex phase evolution of macro simulation. Based on the physical mechanism of different phases in granular media, the concept of full phases is defined and divided into three regions. According to the stress-strain relationship and volume fraction of granular media, the existing theories describing each phase are effectively combined by determining the coupling relationship and transformation criteria between different phases, and the coupling model theory describing all phase states of granular media is established. Then the physical model of granular media is solved with the strategy of coupling smoothed discrete particle hydrodynamics and discrete element method. The coupling and transformation algorithm between different phase particles is clarified and the particle size independence of the diameter selection of the initial SDPH particles is tested. The numerical simulation of collapse process of granular pile under different aspect ratio is realized. The calculated results are in good agreement with the experimental results. At the same time, compared with the discrete element method, the amount of calculation is controlled. It not only captures the different phenomena of deposition after granular pile collapse under the influence of different parameters, but also obtains the effects of different conditions and parameters on the spreading characteristics of granular pile after collapse are obtained, which provides effective support for revealing the complex motion mechanism of granular media widely existing in industry and nature.
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Key words:
- granular pile /
- collapse /
- all phases /
- numerical simulation
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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 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 $ 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
Method Total number of particles Computing platform Time step Calculation time method in this paper 182484 i9-9900 16 thread parallelism 1 × 10−5 s 4 h 32 min DEM method 182484 i9-9900 16 thread parallelism 2 × 10−6 s 23 h 15 min 
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