CFD-DEM simulation of effects of gas density on pressurized fluidization

doi:10.11949/0438-1157.20250381

Abstract

Abstract:

Pressurized gas-solid fluidization has been widely applied recently. Computational fluid dynamics coupled with discrete element model (CFD-DEM) was used to investigate the effect of gas density on pressurized fluidization in terms of the minimum fluidization velocity, minimum bubbling velocity, bubble behaviors and pressure signals. Simulation results show that Group A particles exhibit a uniform fluidization regime across all pressure conditions, with the fluidization index increasing as pressure rises. In contrast, Geldart B particles consistently maintain a fluidization index below 1.1. Further, within Group B particles, an increase in gas density leads to a significant decrease in bubble size and a substantial increase in bubble count. Specifically, an 80-fold increase in gas density results in a 60% reduction in bubble size and a 2.5-fold increase in bubble count in a bed with 300 μm particles. However, in Geldart A particle beds, gas density shows almost no effect on bubble sizes or bubble count. Moreover, as gas density increases, both the standard deviations in the time domain and the amplitudes in the frequency domain of pressure drops decrease, with a more pronounced effect in Group B particle beds. Finally, the competition between gas-solid and solid-solid interactions is analyzed through particle collision forces and drag coefficients, which provides a reasonable framework for understanding the characteristics of pressurized gas-solid fluidization.

Key words: pressurized fluidization, gas density, bubble, discrete element method, two-phase flow, numerical simulation, computational fluid dynamics

摘要：

高压流化床工业应用广泛。利用计算流体力学-离散元耦合模型(CFD-DEM)在1.15~92.0 kg/m³范围内考察了气体密度对A、B类颗粒最小流化速度、最小鼓泡速度、气泡和压降等流体力学行为的影响规律。模拟结果表明，不同压力下A类颗粒均存在散式流化区，流化因子随压力提高而略有增加，B类颗粒的流化因子始终小于1.1。此外，随气体密度增加，B类颗粒中气泡尺寸显著减小、数量显著增加。当气体密度由1.15增加到92.0 kg/m³时，粒径为300 μm的B类颗粒中的气泡尺寸减小了约60%，气泡数量增加了2.5倍。典型A类颗粒中的气泡尺寸与数量几乎不受气体密度影响。床层压降标准差和压力脉动振幅均随气体密度增加而降低，B类颗粒降低更显著。最后，通过对颗粒碰撞力和曳力系数的分析，探讨了气固、固固相互作用的竞争对高压流态化稳定性的影响机制。

关键词: 高压流态化, 气体密度, 气泡, 离散元, 两相流, 数值模拟, 计算流体力学

CLC Number:

TQ 021.1

Zhiyong JIA, Xiankun SHEN, Xiaocheng LAN, Tiefeng WANG. CFD-DEM simulation of effects of gas density on pressurized fluidization[J]. CIESC Journal, 2025, 76(9): 4383-4397.

贾志勇, 沈宪琨, 蓝晓程, 王铁峰. 气体密度对高压流态化影响的CFD-DEM模拟[J]. 化工学报, 2025, 76(9): 4383-4397.

Figures/Tables 17

Table 1 Model equations

方程类别	控制方程
气相质量守恒方程	$∂ ∂ t α g ρ g + ∇ ⋅ α g ρ g v g = 0$
气相动量守恒方程	$∂ ∂ t α g ρ g v g + ∇ ⋅ α g ρ g v g v g = α g ρ g g + ∇ ⋅ τ g - α g ∇ P g - I g m$ $τ g = 2 μ g D g + λ g ∇ ∙ t r D g I$ $D g = 12 ∇ v g + ∇ v g T$
颗粒相运动方程	$d x i d t = v p i$ $m i d v p i d t = m i g + F c i + F d i ∈ k, m$ $I i d ω p i d t = T i$
相间动量传递方程	$F d i ∈ k, m = - ∇ P g x i V m + β m i ∈ k V m α m v g x i - v p i$ $V m = π D m 3 6$ $I g m k = 1 V k ∑ i = 1 N m F d i ∈ k, m K x i, x k$
Gidaspow曳力模型	$β g m = 150 (1 - α g) 2 μ g α g d p 2 + 1.75 (1 - α g) ρ g v g - v p d p, α g ≤ 0.8 34 C D ρ g α g α m v g - v p D m α g - 2.65, α g > 0.8$ $C D = 24 R e 1 + 0.15 R e 0.687, R e < 1000 0.44, R e ≥ 1000$ $R e = ρ g α g v g - v p D m μ g$

Table 1 Model equations

方程类别	控制方程
气相质量守恒方程	$∂ ∂ t α g ρ g + ∇ ⋅ α g ρ g v g = 0$
气相动量守恒方程	$∂ ∂ t α g ρ g v g + ∇ ⋅ α g ρ g v g v g = α g ρ g g + ∇ ⋅ τ g - α g ∇ P g - I g m$ $τ g = 2 μ g D g + λ g ∇ ∙ t r D g I$ $D g = 12 ∇ v g + ∇ v g T$
颗粒相运动方程	$d x i d t = v p i$ $m i d v p i d t = m i g + F c i + F d i ∈ k, m$ $I i d ω p i d t = T i$
相间动量传递方程	$F d i ∈ k, m = - ∇ P g x i V m + β m i ∈ k V m α m v g x i - v p i$ $V m = π D m 3 6$ $I g m k = 1 V k ∑ i = 1 N m F d i ∈ k, m K x i, x k$
Gidaspow曳力模型	$β g m = 150 (1 - α g) 2 μ g α g d p 2 + 1.75 (1 - α g) ρ g v g - v p d p, α g ≤ 0.8 34 C D ρ g α g α m v g - v p D m α g - 2.65, α g > 0.8$ $C D = 24 R e 1 + 0.15 R e 0.687, R e < 1000 0.44, R e ≥ 1000$ $R e = ρ g α g v g - v p D m μ g$

Table 2 Simulation settings

参数	模拟设置	模型验证设置
网格尺寸	3d_p	3d_p
网格数量(x×y×z)	18×80×2	21×240×2
气体密度/(kg/m³)	1.15~92.00	1.15
气体黏度/(Pa·s)	1.78×10^-5	1.70×10^-5
颗粒粒径/μm	60~300	250
颗粒密度/(kg/m³)	2330	2550
摩擦因数	0.1	0.1
法向弹性系数/(N/m)	7.0	7.0
切向弹性系数/(N/m)	2.0	2.0
恢复系数	0.9	0.9
壁面条件	自由滑移	自由滑移
入口边界条件	速度入口	速度入口
出口边界条件	压力出口	压力出口

Fig.1 Comparison of simulated and experimental bed expansion ratios

Fig.2 Fluidization curves with various spring constants

Fig.3 Axial distribution of bubble size with various spring

Table 3 Experimental conditions of pressurized fluidization and correlation parameters for Umf

流化气体	颗粒种类	颗粒密度/(kg/m³)	颗粒类别	实验压力/MPa	关联式参数		文献
流化气体	颗粒种类	颗粒密度/(kg/m³)	颗粒类别	实验压力/MPa	K₂/(2K₁)	1/K₁	文献
N₂	(1) 煤	1247	A/B	0.1~6.4	28.7	0.0494	[7]
	(2) 焦炭	1116	A/B
	(3) 玻璃球	2472	A/B
N₂	玻璃珠	—	B、D	0.1~4.9	33.95	0.0465	[55]
空气	(1) 石英砂	2497	D	0.5~2.0	22.1	0.0354	[56]
空气	(2) 玻璃珠	2571	D	0.5~2.0	22.1	0.0354	[56]
N₂	聚苯乙烯	1020	B、D	0.1~2.7	27.9	0.0554	[57]
CO₂、N₂	(1)石英砂	2560	B	0.1~1.0	31.56	0.043	[8]
CO₂、N₂	(2)铁粉	7800	B	0.1~1.0	31.56	0.043	[8]
N₂	聚苯乙烯	1200	B/D	0.1~2.5	34.15	0.05916	[58]
空气	(1) 塑料颗粒	1010	D	0.1~0.4	15.69	0.0241	[59]
	(2) 玉米芯	924
	(3) 玻璃珠	2157

Fig.4 Effect of operating pressure on minimum fluidization velocity

Fig.5 Effect of operating pressure on minimum bubbling velocity and fluidization index

Fig.6 Gas holdup contours under different operating pressures for typical Geldart A and B particles

Fig.7 Effect of operating pressure on axial distributions of bubble size (Ug = 2.4Umf)

Fig.8 Effect of operating pressure on axial distributions of bubble number (Ug = 2.4Umf)

Fig.9 Effect of operating pressure on standard deviations of pressure drops (Ug = 1.5 Umf)

Fig.10 Effect of operating pressure on frequency distributions of pressure signals (Ug = 2.4Umf)

Fig.11 Effect of operating pressure on particle Stokes number (Ug/Umf = 1.5)

Fig.12 Effect of operating pressure on particle average drag coefficient (Ug/Umf = 1.5)

Fig.13 Effect of operating pressure on particle collision force distribution (Ug/Umf = 1.5)

Fig.14 Effect of operating pressure on particle collision force distribution (Ug/Umf = 2.4)

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