﻿ 非球形颗粒碰撞过程硬颗粒与软颗粒模型比较研究 Comparison of Collision Dynamics of Non-Spherical Particles between the Hard-Particle Model and Soft-Particle Model

Applied Physics
Vol.07 No.04(2017), Article ID:20276,6 pages
10.12677/APP.2017.74014

Comparison of Collision Dynamics of Non-Spherical Particles between the Hard-Particle Model and Soft-Particle Model

Daling Wu1, Nan Gui 2

1Zhejiang Academy of Safety Science and Technology, Hangzhou Zhejiang

2Institute of Nuclear and New Energy Technology, Tsinghua University, Key Laboratory of Advanced Reactor Engineering and Safety, Ministry of Education, Beijing

Received: Apr. 6th, 2017; accepted: Apr. 20th, 2017; published: Apr. 27th, 2017

ABSTRACT

Non-spherical particles and complex non-spherical particle systems are commonly encountered in energy chemical engineering, mineral engineering, and safety manufacturing engineering. The collision dynamics of non-spherical particles are fundamental issues in the investigations of complex particle systems. Discrete element method is the most prevalent models for particle-particle collision of spherical shapes, which incorporates a spring, a dashpot, and a frictional interaction. In this work, a comparative and analytical study on the mathematical models of collision dynamics for non-spherical particles is carried out. The hard non-spherical particle model and the soft-par- ticle model have been compared. It indicates that agreeable simulation results can be found for the two models. The two models have different advantages or disadvantages in accuracy, computational stability, and feasibility, with particular suitability for different cases.

Keywords:Energy Engineering, Chemical Engineering, Safety Manufacturing, Non-Spherical, Collision Model, Discrete Element Method, Hard Particle, Soft-Particle

1浙江省安全生产科学研究院，浙江 杭州

2清华大学核能与新能源技术研究院，先进反应堆工程与安全教育部重点实验室，北京

1. 引言

2. 数值模型及工况

(1)

(2)

(3)

3. 模拟结果对比

3.1. 工况1 (对心碰)

1) 硬颗粒模拟结果(图1(b)左)，颗粒1 (西侧颗粒，下同)平动动能由0.5降到0，颗粒2 (东侧颗粒，下同)平动动能由0增加到约0.45左右，两者的总动能由0.5下降到0.45 (恢复系数0.5，见表1)。表明碰撞过程中颗粒1和颗粒2发生了动量交换，颗粒1将大部分(90%)的动能传递给颗粒2。碰撞过程中发生了10%的动能损失，这是由于恢复系数为0.9导致的；

2) 软颗粒模拟结果(图1(b)右)，颗粒1和颗粒2在碰撞前后的动能变化与硬颗粒的模拟结果是相似的。不同之处在于，碰撞形变过程中，颗粒系统的动能向形变弹性势能转换，总动能降低，至形变最大处发生转折，其后形变逐渐恢复，弹性势能向颗粒动能转化，使得总动能增加，并恢复至0.45 (受恢复系数0.9即非完全弹性形变限制所致)。由于动能和形变弹性势能的相互转换过程持续时间极短(如图1(b)所示，持续不超过0.005 s)，且迅速恢复到碰撞后的速度，故此转换过程对颗粒宏观速度的影响可以忽略。

3.2. 工况2 (偏心碰)

1) 颗粒1只有一部分动量传递给颗粒2，自己保留了一部分。颗粒2发生平动和转动，同时获得了

Table 1. Calculated parameters

Table 2. Operating conditions

(a)(b)

Figure 1. A pair of triangular particles before and after the central collision (a) and related variation of energy (b)

2) 颗粒1大部分平动动能损失转换为颗粒2的转动动能增量和平动动能增量；

3) 硬颗粒和软颗粒模型的模拟结果出现小幅偏差，其主要原因在于：① 硬颗粒模拟结果中颗粒2的转动动能增量要大于平动动能增量，而软颗粒模拟结果中颗粒2的平动动能增量要大于颗粒2转动动能增量；② 硬颗粒模拟结果中颗粒1的动能损失比软颗粒模拟结果中的动能损失要小。

(a)(b)

Figure 2. A pair of triangular particles before and after the off center collision (a) and related variation of energy (b)

4. 结论

1) 对于对心碰撞过程，GHPM和SIPHPM都能够准确预测颗粒碰撞动力学过程，获得近乎相同的颗粒碰撞后的速度；

2) 对于偏心碰撞过程，GHPM和SIPHPM都在原则上能够获得颗粒碰撞后的平动速度和角速度。但碰撞过程中对于平动速度和角速度变化量的分配则受颗粒质量分布的影响。硬颗粒模型认为颗粒质量均匀分布，偏心碰撞过程中转动动能变化占主导；SIPHPM模型认为大部分颗粒质量分布于颗粒边界，偏心碰撞过程中平动动能变化占主导；

3) 从能量分析的角度看，两者均严格符合由恢复系数定义的碰撞能量变化规律；微观上，SIHPM软颗粒模型在碰撞过程中会发生动能和弹性形变势能的相互转化，使得瞬时颗粒体系的动能会出现波动。

Comparison of Collision Dynamics of Non-Spherical Particles between the Hard-Particle Model and Soft-Particle Model[J]. 应用物理, 2017, 07(04): 97-102. http://dx.doi.org/10.12677/APP.2017.74014

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