CHARACTERIZATION OF NEAR-WALL PARTICLE DYNAMICS BASED ON DISCRETE ELEMENT METHOD ANDARTIFICIAL NEURAL NETWORK
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摘要: 颗粒与壁面的相互作用往往对颗粒流动具有显著影响. 为研究颗粒与壁面作用机理, 对滚筒内颗粒流动过程进行离散单元法(DEM)数值模拟. 基于模拟结果统计分析靠近壁面处颗粒的运动特征, 结果表明, 小摩擦系数时颗粒平动和旋转速度均近似满足正态分布, 但由于壁面影响, 摩擦系数增大时颗粒沿滚筒轴向的旋转速度偏离正态分布, 颗粒动力学理论推导壁面边界条件时应考虑速度正态分布的修正及速度脉动的各向异性. 采用人工神经网络(ANN)构建了颗粒无因次旋转温度、滑移速度和平动温度之间的函数模型, 进而可以在常规双流模型壁面边界条件中考虑颗粒旋转的影响. 基于DEM模拟及结果分析可以为壁面边界条件的理论构造和半经验修正提供基础数据和封闭模型.Abstract: The interactions between the particles and the walls often have significant effects on the particle flows. In order to study the mechanism of the interactions between the particles and the walls, the discrete element method (DEM) simulations of the particle flow in the rotating drum are carried out. Based on the statistical analysis of the simulation results, the characteristics of the near-wall particle motion are shown. The results indicate that the particle translational and rotational velocity approximately satisfy the normal distribution when the friction coefficient is small. However, due to the wall effects, the axial rotational velocity deviates from the normal distribution when the friction coefficient increasing. The kinetic theory of granular flow should consider the correction of the velocity normal distribution and also the anisotropic of the velocity fluctuation when deriving the wall boundary conditions. An artificial neural network (ANN) is used to construct a function model between dimensionless particle rotational temperature and particle slip velocity and particle translational temperature, and then the influence of particle rotation can be incorporated in the conventional boundary conditions within the two-flow model. Through comprehensive DEM simulation and result analysis could provide basic data and closure models for the theoretical construction and semi-empirical correction of the wall boundary conditions.
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图 3 网格大小与平均颗粒变量的关系
Figure 3. Relationship between mesh size and averaged particle variables
图 6 不同摩擦系数下的近壁颗粒轴向旋转速度分布
Figure 6. Axial rotational velocity distribution of near-wall particles under different friction coefficients
8 无因次旋转温度的模型预测与DEM统计结果对比
8. Comparison of predicted dimensionless rotational temperature with DEM results
图 8 无因次旋转温度的模型预测与DEM统计结果对比(续)
Figure 8. Comparison of predicted dimensionless rotational temperature with DEM results (continued)
表 1 模拟参数
Table 1. Simulation parameters
Parameters Value drum diameter, D/m 0.1 drum length, L/m 0.65 drum fill level/% 35 total number of particles 72000 particle diameter, d/m 0.003 particles density, ρ/(kg·m−3) 2500 Young modulus, E/(N·m−1) 1.0 × 107 Poisson ratio, $ \nu $ 0.29 restitution coefficient, e 0.9 sliding friction coefficient, μ 0.7 rolling friction coefficient, μr 0.01 
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表 2 平动速度分布的标准差和决定系数
Table 2. Standard deviation and determination coefficient of translational velocity distribution
μ 0.3 0.5 0.7 0.9 SDt 0.02377 0.03048 0.03122 0.02929 SDr 0.01312 0.02087 0.02157 0.02168 SDz 0.0189 0.02023 0.02233 0.02215 Rt2 0.93513 0.96393 0.98887 0.99515 Rr2 0.92683 0.93184 0.96179 0.97895 Rz2 0.98524 0.99693 0.99575 0.99548
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表 3 旋转速度分布的标准差和决定系数
Table 3. Standard deviation and determination coefficient of rotational velocity distribution
μ 0.3 0.5 0.7 0.9 SDX 11.90368 18.65482 21.30643 21.80627 SDY 15.86229 22.58676 22.56652 21.88801 SDZ 41.25149 57.33786 51.13313 43.71098 R2X 0.98682 0.99291 0.99569 0.99535 R2Y 0.99072 0.98469 0.98589 0.98491 R2Z 0.97712 0.87048 0.76709 0.72841
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表 4 人工神经网络模型的细节
Table 4. Details of the artificial neural network model
No. Particulars Specifications 1 network type BP neural network 2 activation function sigmoid and linear 3 error calculation MSE 4 number of input layer unit 2 5 input parameters T, Vsilp 6 number of output layer unit 1 7 output parameters λ 8 number of hidden layer unit 8 9 learning rate 0.0002 10 training times 600 11 training set size 2060 12 test set size 560
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