Analysis of collision frequency of non-spherical particle agglomeration during turbulent agglomeration processes

doi:10.11949/0438-1157.20190512

Abstract

Abstract:

The agglomeration processes and fluidization behavior of cohesive particles in a turbulent agglomerator were simulated based on the coupled model of population balance method (PBM) and computational fluid dynamics (CFD). The agglomeration collision frequency model was improved by introducing the collision agglomeration efficiency and fractal dimension. The agglomeration collision efficiency was introduced by considering the influence of hydrodynamic force and van der Waals force on particle agglomeration. At the same time, the fractal dimension were introduced by considering the influence of the local porosity of non-spherical particle agglomeration increasing gradually in the radial direction. Thus the results of the simulation using the improved model compared with the EDEM simulation results and the experimental results. The volume fraction results show that the average relative error between the EDEM simulation results and the experimental results was 16.34%, while the average relative error between the improved model and the experimental results was only 7.39%. In terms of fraction of the agglomeration number, the average absolute error between the EDEM simulation results and the experimental results was 5.36%, while the average absolute error between the improved model and the experimental results was only 2.28%. Therefore, the improved model simulation results were closer to the experimental results.

Key words: population balance model, collision frequency, agglomeration, collision efficiency, fractal dimension

摘要：

基于群体平衡模型（PBM）和计算流体动力学（CFD）的耦合方法模拟了湍流聚并器中黏性颗粒的聚团过程和流化行为。考虑到流体作用力和范德华力对颗粒聚团的影响，引入了聚团碰撞效率，同时考虑非球形颗粒聚团局部孔隙率沿径向逐渐增大的影响，引入分形维数。通过碰撞效率和分形维数对碰撞频率模型进行了改进。并与EDEM模拟计算结果和实验结果进行了对比。体积分数的结果显示，EDEM模拟的结果与实验结果的平均相对误差为16.34%，而改进模型与实验结果的平均相对误差仅为7.39%。而数量分数方面，EDEM模拟的结果与实验结果的平均绝对误差为5.36%，而改进模型与实验结果的平均绝对误差仅为2.28%。因此改进模型模拟结果更接近实验结果。

关键词: 群体平衡模型, 碰撞频率, 聚团, 碰撞效率, 分形维数

CLC Number:

TQ 028.8

Jianxiang ZHENG, Yukai LI, Xiaonan SUN, Huaichun ZHOU. Analysis of collision frequency of non-spherical particle agglomeration during turbulent agglomeration processes[J]. CIESC Journal, 2019, 70(S2): 228-236.

郑建祥, 李玉凯, 孙笑楠, 周怀春. 湍流聚团过程中非球形颗粒聚团碰撞频率分析研究[J]. 化工学报, 2019, 70(S2): 228-236.

Figures/Tables 8

Table 1 Collision frequency model 碰撞频率模型

聚团类型	碰撞频率模型
布朗聚团
Einstein^[32]	$β b r o (v, u) = B 2 C (v) v 1 / 3 + C (u) u 1 / 3 (v 1 / 3 + u 1 / 3)$	(7)
考虑分形^[32]	$β b r o (v, u) = B 2 1 v f + 1 u f (v f + u f) + B 2 ? ν ρ 0 f - 1 / 3 1 v 2 f + 1 u 2 f (v f + u f)$	(8)
修正	$β b r o (v, u) = ψ i, j B 2 1 v f + 1 u f (v f + u f) + B 2 ? v ρ 0 f - 1 / 3 1 v 2 f + 1 u 2 f (v f + u f)$	(9)
湍流聚团
Saffman和Turner^[37]	$β t u r (v, u) = 9 10 π 1 / 2 ε d ν 1 / 2 (v 1 / 3 + u 1 / 3) 3$	(10)
考虑分形^[34]	$β t u r (v, u) = 9 10 π 1 / 2 ε d ν 1 / 2 v ρ 0 1 - 3 f (v f + u f) 3$	(11)
修正	$β t u r (v, u) = ψ i, j 9 10 π 1 / 2 ε d ν 1 / 2 v ρ 0 1 - 3 f (v f + u f) 3$	(12)
线性相加	$β i, j = β b r o + β t u r$	(13)
均方根	$β i, j = β b r o 2 + β t u r 2$	(14)
DEM^[35]	$β i, j = C i, j ψ i, j$	(15)
	$C i, j = N C i, j P P ν a g g r e g a t i o n N P i N P j t s i m$	(16)
	$ψ i, j = 3 U m a x m p w ˉ 2 + 1 e x p - 3 U m a x m p w ˉ 2$	(17)

Table 1 Collision frequency model 碰撞频率模型

聚团类型	碰撞频率模型
布朗聚团
Einstein^[32]	$β b r o (v, u) = B 2 C (v) v 1 / 3 + C (u) u 1 / 3 (v 1 / 3 + u 1 / 3)$	(7)
考虑分形^[32]	$β b r o (v, u) = B 2 1 v f + 1 u f (v f + u f) + B 2 ? ν ρ 0 f - 1 / 3 1 v 2 f + 1 u 2 f (v f + u f)$	(8)
修正	$β b r o (v, u) = ψ i, j B 2 1 v f + 1 u f (v f + u f) + B 2 ? v ρ 0 f - 1 / 3 1 v 2 f + 1 u 2 f (v f + u f)$	(9)
湍流聚团
Saffman和Turner^[37]	$β t u r (v, u) = 9 10 π 1 / 2 ε d ν 1 / 2 (v 1 / 3 + u 1 / 3) 3$	(10)
考虑分形^[34]	$β t u r (v, u) = 9 10 π 1 / 2 ε d ν 1 / 2 v ρ 0 1 - 3 f (v f + u f) 3$	(11)
修正	$β t u r (v, u) = ψ i, j 9 10 π 1 / 2 ε d ν 1 / 2 v ρ 0 1 - 3 f (v f + u f) 3$	(12)
线性相加	$β i, j = β b r o + β t u r$	(13)
均方根	$β i, j = β b r o 2 + β t u r 2$	(14)
DEM^[35]	$β i, j = C i, j ψ i, j$	(15)
	$C i, j = N C i, j P P ν a g g r e g a t i o n N P i N P j t s i m$	(16)
	$ψ i, j = 3 U m a x m p w ˉ 2 + 1 e x p - 3 U m a x m p w ˉ 2$	(17)

Fig.1 Schematic diagram of turbulent aggregation and local grid diagram of computational domain

Fig.2 Comparison between different collision frequencies

Fig.3 Comparison of RMS collision frequency and EDEM/agglomeration simulation results

Fig.4 Particle volume fraction and turbulent

Fig.5 Comparison of volume fractions of experimental results，EDEM simulation results [Eq.(15)] and RMS simulation results [Eq.(14) at Df=2.5]

Table 2 Variation of particle volume fraction in different particle size ranges

d/μm	入口/ %	实验出口/%	出口 (EDEM模拟)		出口 (修正耦合模拟)
d/μm	入口/ %	实验出口/%	体积分数/%	相对误差/%	体积分数/%	相对误差/%
<2.5	12.43	2.25	2.65	17.78	2.15	4.44
2.5~5	31.44	4.55	5.25	15.38	4.15	8.79
5~10	56.13	14.88	17.24	15.86	16.21	8.94
10~20	0	56.24	70.02	7.33	66.53	1.98
>20	0	13.09	4.84	63.03	10.96	16.27

Table 3 Variation of agglomeration number fraction in different particle size ranges

d/μm	入口/ %	实验出口/ %	出口(EDEM模拟)		出口(修正耦合模拟)
d/μm	入口/ %	实验出口/ %	数量分数/%	绝对误差/%	数量分数/%	绝对误差/%
<2.5	70.03	73.16	76.76	3.6	74.55	1.39
2.5~5	27.12	18.60	7.27	11.33	13.45	5.15
5~10	2.85	4.53	5.67	1.14	4.83	0.3
10~20	0	3.42	8.21	4.79	6.22	2.8
>20	0	0.28	2.09	1.81	0.95	0.67

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