颗粒黏度模型对采用欧拉多相流模型模拟超密相颗粒流动行为的影响

doi:10.11949/0438-1157.20200446

化工学报 ›› 2020, Vol. 71 ›› Issue (11): 4945-4956.DOI: 10.11949/0438-1157.20200446

• 南京大学化工学院院庆专栏 • 上一篇下一篇

颗粒黏度模型对采用欧拉多相流模型模拟超密相颗粒流动行为的影响

姚晶星^1,³(),杨遥^2,³(),黄正梁^2,³,孙婧元^2,³,王靖岱^1,^2,³,阳永荣^1,^2,³

^1.浙江大学化学工程联合国家重点实验室，浙江杭州 310027
^2.浙江省化工高效制造技术重点实验室，浙江杭州 310027
^3.浙江大学化学工程与生物工程学院，浙江杭州 310027

收稿日期:2020-04-29 修回日期:2020-07-03 出版日期:2020-11-05 发布日期:2020-11-05
通讯作者: 杨遥
作者简介:姚晶星（1996—），男，硕士研究生，21828165@zju.edu.cn
基金资助:
国家自然科学基金项目(21808197)

Impact of viscosity model on simulation of condensed particle flow by Euler multiphase flow model

Jingxing YAO^1,³(),Yao YANG^2,³(),Zhengliang HUANG^2,³,Jingyuan SUN^2,³,Jingdai WANG^1,^2,³,Yongrong YANG^1,^2,³

^1.State Key Laboratory of Chemical Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, China
^2.Zhejiang Provincial Key Laboratory of Advanced Chemical Engineering Manufacture Technology, Hangzhou 310027, Zhejiang, China
^3.College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, China

Received:2020-04-29 Revised:2020-07-03 Online:2020-11-05 Published:2020-11-05
Contact: Yao YANG

摘要/Abstract

摘要：

颗粒黏度是欧拉多相流模型计算固体流动的重要参数之一，其数值大小依赖于摩擦压力和径向分布函数。通过与实验值对比，评估了常用的摩擦压力模型（Based、Johnson）和径向分布函数模型（Lun、Syamlal O’Brien）对密相颗粒流动体系的预测能力。模拟结果表明，Johnson模型的固体体积分数预测值低于Based模型；Syamlal O’Brien 模型固体流率的预测值远大于Lun模型。采用根据实验结果修正的欧根系数后，Based-Lun、Johnson-Lun和Johnson-SO模型组合预测的平均压降相对误差分别由68.6%、73.3%和78.2%降低至13.2%、29.7%和42.3%。综合考虑压降、固体出口质量流率、固体体积分数、壁面区域固体速度的模拟结果与实验值的偏差，发现Based-Lun模型组合的平均预测误差最小，适用于气固移动床的欧拉多相流模拟。研究还发现，欧根系数与内摩擦角对固体速度与压降有着显著的影响，而临界固含率对固体速度与压降的影响较小。

关键词: 移动床, 多相流, 颗粒流, 数值模拟, 计算流体力学

Abstract:

Particle viscosity is one of important parameters for the calculation of solid flow in Euler multiphase flow model, and the value depends on the frictional pressure and radial distribution function. The predictive ability of commonly used frictional pressure models (Based, Johnson) and radial distribution function models (Lun, Syamlal O’Brien) were evaluated by comparing them with experimental results. The simulation results show that the solid volume fraction using the Johnson model is lower than that using the Based model, and the solid mass flow rate using the Syamlal O’Brien model is much larger than that using the Lun model. The relative deviations of the average pressure drop can be reduced substantially after the Ergun coefficient correction was applied. The relative predicting deviations of the Based-Lun, Johnson-Lun, and Johnson-SO models were reduced from 68.6%, 73.3%, 78.2% to 13.2%, 29.7% and 42.3%, respectively. Comprehensively considering the pressure drop, the solid mass flow rate at outlet, solid volume fraction and the solid velocity in the near-wall area, the relative average deviations of the Based-Lun model is the smallest, and the Base-Lun model is suitable for simulation of the gas-solid Euler multiphase flow. In addition, this work found the Ergun coefficient and internal friction angle have a significant effect on solid velocity and pressure drop, while the threshold volume fraction for friction has little effect.

Key words: moving bed, multiphase flow, granular flow, numerical simulation, CFD

中图分类号:

TQ 021.1

姚晶星,杨遥,黄正梁,孙婧元,王靖岱,阳永荣. 颗粒黏度模型对采用欧拉多相流模型模拟超密相颗粒流动行为的影响[J]. 化工学报, 2020, 71(11): 4945-4956.

Jingxing YAO,Yao YANG,Zhengliang HUANG,Jingyuan SUN,Jingdai WANG,Yongrong YANG. Impact of viscosity model on simulation of condensed particle flow by Euler multiphase flow model[J]. CIESC Journal, 2020, 71(11): 4945-4956.

图/表 16

图1 气固移动床冷模实验装置1—空气压缩机；2—缓冲罐；3—流量计；4—料仓；5—进口阀；6—移动床；7—光源；8—高速相机；9—出口阀；10—差压传感器；11—计算机

Fig.1 Cold-model experimental system for gas-solid moving bed reactor

表1 数学模型方程

Table 1 Mathematical formulas for simulation

Model	Correlation
governing equations
continuity equations	gas： $? ? t ε g ρ g + ? · ε g ρ g u g = 0$
continuity equations	solid： $? ? t ε s ρ s + ? · ε s ρ s u s = 0$
momentum equations	gas： $? ? t ε g ρ g u g + ? · ε g ρ g u g u g = - ε g ? P + ? · τ g + ε g ρ g g + F s g$
momentum equations	solid： $? ? t ε s ρ s u s + ? · ε s ρ s u s u s = - ε s ? P - ? P s + ? · τ s + ε s ρ s g + F g s$
constitutive equation
solid pressure	$P s = ε s ρ s Θ s + 2 ρ s 1 + e s s ε s 2 g 0, s s Θ s$
solid shear viscosity	$μ s = μ s, c o l + μ s, k i n + μ s, f r$
collisional viscosity	$μ s, c o l = 45 ε s ρ s g 0, s s 1 + e s s Θ s π$
kinetic viscosity	$μ s, k i n = 10 ρ s d s Θ s π 96 α s 1 + e s s g 0, s s 1 + 45 g 0, s s α s 1 + e s s 2$
frictional viscosity	$μ s, f r = P s, f r s i n ? 2 I 2 D$
bulk viscosity	$λ s = 43 ε s ρ s d s 1 + e s s Θ s π$
granular conductivity	$k Θ s = 150 ρ s d s Θ π 384 1 + e s s g 0, s s 1 + 65 ε g g 0, s s 1 + e s s 2 + 2 ρ s ε s 2 d s 1 + e s s g 0, s s Θ s π$
gas-solid drag coefficient	$K g s = 34 C D ε s ε g ρ g v s - v g d s ε g - 2.65 ? ? ? ?, ? ? ? ? ? ? ? C D = 24 ε g R e s 1 + 0.15 ε g R e s 0.687 ?, ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ε s < 0.2 150 ε s 1 - ε g μ g ε g d s 2 + 1.75 ρ g ε s v s - v g d s, ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ε s ≥ 0.2 ? ? ? ?$

表1 数学模型方程

Table 1 Mathematical formulas for simulation

Model	Correlation
governing equations
continuity equations	gas： $? ? t ε g ρ g + ? · ε g ρ g u g = 0$
continuity equations	solid： $? ? t ε s ρ s + ? · ε s ρ s u s = 0$
momentum equations	gas： $? ? t ε g ρ g u g + ? · ε g ρ g u g u g = - ε g ? P + ? · τ g + ε g ρ g g + F s g$
momentum equations	solid： $? ? t ε s ρ s u s + ? · ε s ρ s u s u s = - ε s ? P - ? P s + ? · τ s + ε s ρ s g + F g s$
constitutive equation
solid pressure	$P s = ε s ρ s Θ s + 2 ρ s 1 + e s s ε s 2 g 0, s s Θ s$
solid shear viscosity	$μ s = μ s, c o l + μ s, k i n + μ s, f r$
collisional viscosity	$μ s, c o l = 45 ε s ρ s g 0, s s 1 + e s s Θ s π$
kinetic viscosity	$μ s, k i n = 10 ρ s d s Θ s π 96 α s 1 + e s s g 0, s s 1 + 45 g 0, s s α s 1 + e s s 2$
frictional viscosity	$μ s, f r = P s, f r s i n ? 2 I 2 D$
bulk viscosity	$λ s = 43 ε s ρ s d s 1 + e s s Θ s π$
granular conductivity	$k Θ s = 150 ρ s d s Θ π 384 1 + e s s g 0, s s 1 + 65 ε g g 0, s s 1 + e s s 2 + 2 ρ s ε s 2 d s 1 + e s s g 0, s s Θ s π$
gas-solid drag coefficient	$K g s = 34 C D ε s ε g ρ g v s - v g d s ε g - 2.65 ? ? ? ?, ? ? ? ? ? ? ? C D = 24 ε g R e s 1 + 0.15 ε g R e s 0.687 ?, ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ε s < 0.2 150 ε s 1 - ε g μ g ε g d s 2 + 1.75 ρ g ε s v s - v g d s, ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ε s ≥ 0.2 ? ? ? ?$

图2 欧拉多相流颗粒的简化模型流程

Fig.2 Simplified flowsheet of Euler multiphase flow model

图3 单组分颗粒下不同径向分布函数随固含率的变化（εs,max=0.64）

Fig.3 Radial distribution functions at different solid phase volume fraction

图4 Johnson-Lun模型组合预测结果随流动时间的变化

Fig.4 Predicted results of Johnson-Lun model combination varied with flow time

图5 Based-Lun模型组合预测结果随流动时间的变化

Fig.5 Predicted results of Based-Lun model combination varied with flow time

表2 欧拉多相流模拟参数设置

Table 2 Parameters setting of Euler multiphase flow simulations

Parameter	Value
gas flow rate /(m³·h^-1)	1.0
particle-particle coefficient of restitution，e	0.9
internal frictional angle，θ / (°)	22
threshold volume fraction for friction，ε_s,min	0.5
maximum solids packing，ε_s,max	0.57
initial solids packing，ε_s,initial	0.56
gas inlet boundary type	velocity inlet
outlet boundary type	pressure outlet
wall boundary type	no slip

图6 不同网格尺寸模拟结果

Fig.6 Simulation results at different grid sizes

图7 不同模型组合预测的固体速度、体积和气体压降

Fig.7 Gas pressure drop and solid vertical velocity, volume fraction simulated by different model combinations

图8 修正欧根系数后不同模型组合预测的床层压降轴向分布

Fig.8 Axial distribution of pressure drops simulated by different models after Ergun coefficients were modified

图9 不同模型组合预测的中央剖面上固体体积分数分布云图

Fig.9 Distribution of solid phase volume fraction on central section predicted by different model combinations

图10 不同模型预测y=1.5 mm处固体速度与PIV测量速度对比

Fig.10 Comparison of simulated vertical velocities at y=1.5 mm and velocities measured by PIV

图11 不同临界固含率预测的床层压降轴向分布

Fig.11 Axial distribution of pressure drops at different threshold volume fraction for friction

图12 不同临界固含率预测的固体速度分布与质量流率

Fig.12 Distribution of vertical velocity and mass flow at different threshold volume fraction for friction

图13 不同内摩擦角预测的床层压降轴向分布与质量流率

Fig.13 Axial distribution of pressure drops and solid mass flow rate at different internal friction angles

图14 不同内摩擦角对应的出口上方固体体积分布

Fig.14 Distribution of solid phase volume fraction above outlet at different internal friction angles

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颗粒黏度模型对采用欧拉多相流模型模拟超密相颗粒流动行为的影响

Impact of viscosity model on simulation of condensed particle flow by Euler multiphase flow model

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