基于幂律液固曳力模型流化床内湿颗粒流动特性的研究

doi:10.11949/0438-1157.20230265

摘要/Abstract

摘要：

采用欧拉-欧拉双流体模型(TFM)结合颗粒动理学理论(KTGF)方法，对三维幂律流化床中的液固两相流动行为进行了模拟。基于幂律流体的流变方程以及压降方程，提出了两种幂律液固曳力模型，引入了考虑液膜效应的湿颗粒动态恢复系数模型，计算幂律流体与湿颗粒之间的作用力。将预测固含率分别与文献中测得的实验数据进行比较，结果表明结合动态恢复系数模型的相对误差介于0.45%~1.59%，与实验结果吻合较好。探究了稠度系数K以及流性指数n对颗粒流动特性的影响，结果表明随着流变参数的增大，床层内的颗粒平均浓度降低，湿颗粒表面液膜逐渐变厚，法向恢复系数降低；颗粒拟温度随n的升高先增大后减小，随K的上升而增大；曳力系数、颗粒压力以及颗粒黏度均随流变参数的增大而逐渐减小。颗粒在壁面处的浓度明显高于中心处附近的浓度，且颗粒在中心处向上运动，在壁面处附近回落，在流化床中形成环-核结构。

关键词: 幂律液固曳力模型, 动态恢复系数模型, 流化床, 液膜厚度, 两相流, 数值模拟

Abstract:

The liquid-solid two-phase flow behaviors in the power-law fluidized bed are simulated using the Euler-Euler two-fluid model (TFM) based on the kinetic theory of granular flow (KTGF). Based on the pressure drop equations and rheological equations of power-law fluids, two kinds of power-law liquid-solid drag models are presented. And the dynamic restitution coefficient model of wet particles considering the liquid film effect is introduced to calculate the interaction between power-law fluids and particles. The predicted solid holdups are compared with the experimental values in references, the results show that the relative errors of power-law liquid-solid drag models combining dynamic restitution coefficient model are between 0.45% and 1.59%, which is closer to the experimental results. The influences of the consistency coefficients and the flow behavior indexes on the flow characteristics of the particles are explored, indicating that with the increase of the rheological parameters, the averaged solids holdup in the fluidized bed decreases, and the liquid film covered on the surface of wet particles becomes thicker and the normal restitution coefficient decreases. The granular temperature increases first and then decreases with the increase of flow behavior index, and rises with the increase of consistency coefficient. The drag coefficient, granular pressure, and granular viscosity all gradually decrease as the rheological parameters enhance. The concentration of particles near the wall is obviously higher than that near the center, and the particles move upward at the center and fall in the vicinity of the wall, forming the classic core-annulus structure.

Key words: power-law liquid-solid drag models, dynamic restitution coefficient model, fluidized bed, liquid film thickness, two-phase flow, numerical simulation

中图分类号:

TQ 018

袁子涵, 王淑彦, 邵宝力, 谢磊, 陈曦, 马一玫. 基于幂律液固曳力模型流化床内湿颗粒流动特性的研究[J]. 化工学报, 2023, 74(5): 2000-2012.

Zihan YUAN, Shuyan WANG, Baoli SHAO, Lei XIE, Xi CHEN, Yimei MA. Investigation on flow characteristics of wet particles with power-law liquid-solid drag models in fluidized bed[J]. CIESC Journal, 2023, 74(5): 2000-2012.

图/表 12

图1 孔喉结构示意图

Fig.1 The pore-throat structure

表1 数值模拟参数及文献［15-16］实验值

Table 1 Parameters used in numerical simulations and experiments by Ref.［15-16］

符号	参数	文献[15]	本文模拟参数	文献[16]	本文模拟参数
D_in	流化床直径/mm	90	90	68	68
H	流化床高度/mm	2000	1000	1100	1100
h₀	初始床高/mm	120	120	—	200
ε_s,max	最大颗粒浓度	—	0.63	—	0.63
ε₀	初始颗粒浓度	0.578	0.578	—	0.6
d_p	颗粒直径/mm	4.6	4.6	3	3
ρ_s	颗粒密度/(kg/m³)	2258	2258	2500	2500
ρ_l	流体密度/(kg/m³)	1001	1001	997	997
K	稠度系数/(Pa·s ⁿ )	0.013	0.013	0.0299	0.0299
n	流性指数	0.82	0.82	0.719	0.719
u₀	流体表观速度/(cm/s)	5.35~8.96	Same	2.416~10.436	Same
e	法向恢复系数	—	0.98, e_wet	—	0.98, e_wet
	网格数	—	10×100×10	—	10×100×10

图2 固含率随不同液体表观流速变化的实验对比

Fig.2 Comparison between simulations and experiments at different superficial velocities of liquid

图3 不同曳力模型所得模拟值与实验值的相对误差

Fig.3 The relative errors of different drag models between simulated value and experimental value

图4 不同流变参数下颗粒浓度瞬时分布图(左：干颗粒；右：湿颗粒)

Fig.4 Instantaneous concentration of particles with different flow behavior indexes and consistency coefficients at 50 s (left: dry particles; right: wet particles)

图5 不同流性指数和稠度系数下的床层平均颗粒浓度、湿颗粒法向恢复系数以及液膜厚度

Fig.5 Time-averaged concentration of particles, normal restitution coefficient and liquid film thickness with different flow behavior indexes and consistency coefficients

图6 不同流性指数和稠度系数下同一高度处时均颗粒体积分数的径向分布

Fig.6 Radial distributions of the time-averaged particles concentration with different flow behavior indexes and consistency coefficients at the same height

图7 不同流性指数和稠度系数下同一高度处时均颗粒轴向速度的径向分布

Fig.7 Radial distributions of the time-averaged axial velocity of particles with different flow behavior indexes and consistency coefficients at the same height

图8 不同流性指数和稠度系数下时均曳力系数随颗粒体积分数的变化

Fig.8 Time-averaged drag coefficient as a function of particles concentration under different flow behavior indexes and consistency coefficients

图9 不同流性指数和稠度系数下时均颗粒拟温度随颗粒体积分数的变化

Fig.9 Time-averaged granular temperature as a function of particles concentration under different flow behavior indexes and consistency coefficients

图10 不同流性系数和稠度系数下时均颗粒压力随颗粒体积分数的变化

Fig.10 Time-averaged granular pressure as a function of particles concentration under different flow behavior indexes and consistency coefficients

图11 不同流性指数和稠度系数下时均颗粒黏度随颗粒体积分数的变化

Fig.11 Time-averaged granular viscosity as a function of particles concentration under different flow behavior indexes and consistency coefficients

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