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

doi:10.11949/0438-1157.20200446

Abstract

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

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

CLC Number:

TQ 021.1

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.

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.

Figures/Tables 16

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

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	$K g s = 34 C D ε s ε g ρ g v s - v g d s ε g - 2.65 ? ? ? ?, ? ? ? ? ? ? ? C D = 24 ε g R e s 1 + 0.15 ε g R e s 0.687 ?, ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ε s < 0.2 150 ε s 1 - ε g μ g ε g d s 2 + 1.75 ρ g ε s v s - v g d s, ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ε s ≥ 0.2 ? ? ? ?$

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	$K g s = 34 C D ε s ε g ρ g v s - v g d s ε g - 2.65 ? ? ? ?, ? ? ? ? ? ? ? C D = 24 ε g R e s 1 + 0.15 ε g R e s 0.687 ?, ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ε s < 0.2 150 ε s 1 - ε g μ g ε g d s 2 + 1.75 ρ g ε s v s - v g d s, ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ε s ≥ 0.2 ? ? ? ?$

Fig.2 Simplified flowsheet of Euler multiphase flow model

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

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

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

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

Fig.6 Simulation results at different grid sizes

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

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

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

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

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

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

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

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

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