EMMS-based flow regime study of circulating fluidized beds

doi:10.11949/0438-1157.20200062

Abstract

Abstract:

The design, enlargement, and optimization of fluidized beds require a basic understanding of the watershed. However, the division of watersheds for gas-solid systems still has many controversies. In this paper, the state-of-the-art regime studies are summarized with the main disputes highlighted. Inconsistency is found on the demarcation of the fast fluidization. The steady-state EMMS (energy minimization multi-scale) drag model is thus integrated into two-fluid model (TFM) to simulate a circulating fluidized bed (CFB) with a variety of gas velocities and solids holdups. Particle refluxing and slugging are found in the simulation results, whereby bound the fast fluidization regime. A regime diagram is drawn, where the main features of the different regimes in CFBs are presented.

Key words: circulating fluidized bed, regime transition, mesoscale, computational fluid dynamics, EMMS

摘要：

流化床的设计、放大和优化需要对流域有基础的认识，然而气固系统的流域划分至今仍存在诸多争议。总结了气固流化系统流域划分的研究现状，并分析了流域划分的主要争议，发现文献中对快速床的界定存在分歧。通过耦合基于稳态EMMS的曳力模型开展双流体模拟，对不同气速和颗粒浓度下的循环流化床进行了数值研究。模拟结果捕捉到了颗粒回流、节涌等现象，据此确定了快速床的操作边界并绘制了流域图，该流域图能够展示循环床中的各流域形态。

关键词: 循环流化床, 流域转变, 介尺度, 计算流体力学, EMMS

CLC Number:

TQ 021.1

Kaicheng CHEN, Yujie TIAN, Fei LI, Hao WU, Wei WANG. EMMS-based flow regime study of circulating fluidized beds[J]. CIESC Journal, 2020, 71(7): 3018-3030.

陈恺成, 田于杰, 李飞, 吴昊, 王维. 基于EMMS的循环流化床流域研究[J]. 化工学报, 2020, 71(7): 3018-3030.

Figures/Tables 18

Table 1 Regime diagrams in literature

文献	基本变量	流域
第一类
[4]	U_slip-ε_s	鼓泡流化、湍动流化、快速流化、稀相输送
[24]	ε_g-U_g	节涌流化、湍动流化、快速流化、密相输送、气力输送
[13]	G_s-U_g	鼓泡/湍动流化、快速流化、密相输送、稀相输送
[22]	U_slip-U_p	快速流化、环-核稀相流、均匀稀相流
[42]	G_s-U_g	稀相输送、密相输送
[3]	G_s-U_g	鼓泡流化、湍动流化、快速流化、气力输送
[43]	G_s-U_g-ε_s	鼓泡流化、湍动流化、循环湍动床、低密度循环流化床、高密度循环流化床、气力输送
第二类
[31]	(ρ_s-ρ_g)-d_p	A、B、C、D类颗粒
[2]	U_g^*-Ar	固定床、移动床、喷动床、循环床、输送床等
[44]	Ω-Ar	固定床、流化床、输送床
[45]	Re-Ar	鼓泡流、节涌流、湍动流、快速流、稀相流等
第三类
[32]	Re-Ar-H/D	鼓泡流动、非鼓泡流动、节涌流动、稀相输送

Fig.1 Comparison of regime classifications of CFBs in literatures

Table 2 Regime classifications and characteristics in CFBs

文献	流域及其特征
[13]	稀相输送：轴/径向浓度均匀分布	密相输送：由稀相输送向快速流化转变时的过渡流域	快速流化：轴向颗粒浓度分布上稀下浓；径向环-核型颗粒浓度分布
[22]	均匀稀相流：轴/径向浓度均匀分布；无颗粒聚团	环-核稀相流：出现颗粒聚团、径向环-核结构	快速流化：轴向颗粒浓度分布上稀下浓
[43]	气力输送：均匀流动	低密度循环流化床：轴向指数型/S形颗粒浓度分布；径向环-核型颗粒浓度分布	高密度循环流化床：轴向颗粒浓度分布较为均匀；径向颗粒浓度分布呈凹形抛物线

Table 3 Empirical correlations to outline the fast bed region

文献	关联式	颗粒物性参数	床层几何尺寸
[13]	操作下限： $U F D g D = 0.684 G s D μ ρ s - ρ g ρ g 0.442 (D d p) - 0.96 R e t - 0.344$	31<d_p<325 μm 706<ρ_s<2643 kg/m³	0.03<D<0.30 m
[13]	操作上限： $U T F g D = 1.463 G s D μ ρ s - ρ g ρ g 0.288 (D d p) - 0.69 R e t - 0.2$	54<d_p<1041 μm 703<ρ_s<2666 kg/m³	0.03<D<0.30 m
[22]	操作下限： $V C A g d p = 21.6 A r 0.105 (G s ρ g V C A) 0.542$	31<d_p<325 μm 660<ρ_s<3090 kg/m³	0.02<D<0.19 m 5.5<H<9.0 m
[22]	操作上限： $V C C g d p = 32 R e t - 0.06 (G s ρ g V C C) 0.28$	20<d_p<290 μm 850<ρ_s<2740 kg/m³	0.038<D<0.050 m
[43]	操作下限： $U t p = 2.7555 l n ? U p + 16.029$	未给出	未给出
[43]	操作上限： $U t r = 0.8072 l n ? U p + 5.1746$	20<d_p<1041 μm 660<ρ_s<3090 kg/m³	0.02<D<0.30 m

Table 3 Empirical correlations to outline the fast bed region

文献	关联式	颗粒物性参数	床层几何尺寸
[13]	操作下限： $U F D g D = 0.684 G s D μ ρ s - ρ g ρ g 0.442 (D d p) - 0.96 R e t - 0.344$	31<d_p<325 μm 706<ρ_s<2643 kg/m³	0.03<D<0.30 m
[13]	操作上限： $U T F g D = 1.463 G s D μ ρ s - ρ g ρ g 0.288 (D d p) - 0.69 R e t - 0.2$	54<d_p<1041 μm 703<ρ_s<2666 kg/m³	0.03<D<0.30 m
[22]	操作下限： $V C A g d p = 21.6 A r 0.105 (G s ρ g V C A) 0.542$	31<d_p<325 μm 660<ρ_s<3090 kg/m³	0.02<D<0.19 m 5.5<H<9.0 m
[22]	操作上限： $V C C g d p = 32 R e t - 0.06 (G s ρ g V C C) 0.28$	20<d_p<290 μm 850<ρ_s<2740 kg/m³	0.038<D<0.050 m
[43]	操作下限： $U t p = 2.7555 l n ? U p + 16.029$	未给出	未给出
[43]	操作上限： $U t r = 0.8072 l n ? U p + 5.1746$	20<d_p<1041 μm 660<ρ_s<3090 kg/m³	0.02<D<0.30 m

Fig.2 EMMS-based intrinsic regime diagram of CFBs [42]

Fig.3 Schematic drawing of riser in simulations

Table 4 Material properties and operating conditions in simulations

参数	数值
物性参数
颗粒密度ρ_s/(kg∕m³)	1070
颗粒直径d_p/μm	49
气体密度ρ_g/(kg·m³)	1.225
气体黏度μ_g/(Pa?s)	1.7894×10^-5
操作条件
表观气速U_g/(m/s)	2.2, 3.0, 3.4, 4.0
初始颗粒浓度ε_s0	0.01, 0.03, 0.05, 0.08, 0.10, 0.13, 0.15, 0.20, 0.25, 0.28, 0.30, 0.35

Table 5 Simulation settings

参数	设置
time step size	0.0005 s
max iterations	50
gas-wall shear condition	no-slip
solids-wall specularity coefficient	0.0001
restitution coefficient	0.9
transient formulation	first-order implicit
pressure-velocity coupling	phase coupled SIMPLE
gradient discretization	green-gauss cell based
momentum discretization	second order upwind
volume fraction discretization	QUICK

Fig.4 Radial distribution of solids holdups, particle velocities and gas velocities (axial position: 0.5 m)

Fig.5 Lower boundary of fast bed

Fig.6 Variation of solids flux with time at higher solids holdup

Fig.7 Upper boundary of fast bed

Fig.8 Operating range of fast bed

Fig.9 Variation of solids flux with mean solids holdup at different gas velocities

Fig.11 Dimensionless regime diagram of CFB

Fig.10 Axial and radial distribution of solids holdups in fast bed regime（Ug=4 m·s-1）

U_g/ (m/s)	{a₀, a₁, …, a₁₀}	{ε_g1, ε_g2}
2.2	{0.016623, 0.493605, 6.389545, 47.358891, 221.919953, 684.633287, 1402.911209, 1877.571271, 1563.265977, 726.070792, 135.926522}	{0.400000, 0.995492}
3.0	{0.040268, 1.072476, 12.454369, 82.862589, 348.987241, 969.842486, 1796.688320, 2185.896346, 1667.924597, 718.182831, 125.826167}	{0.402399, 0.991664}
3.4	{0.003550, 0.123762, 1.871593, 16.096893, 86.800375, 305.222537, 705.575497, 1053.996368, 969.054176, 491.512368, 97.518733}	{0.400000, 0.997121}
4.0	{0.008547, 0.235299, 2.882084, 20.627771,95.098625, 293.303193, 608.805261, 834.270600, 717.833635, 347.089449, 64.694438}	{0.402399, 0.991364}

项目	方程
连续性方程	$? ? t (ε g ρ g) + ? ? (ε g ρ g u g) = 0$
	$? ? t (ε s ρ s) + ? ? (ε s ρ s u s) = 0$
动量方程	$? ? t (ε g ρ g u g) + ? ? (ε g ρ g u g u g) = - ε g ? p + ? ? τ g + ε g ρ g g - β (u g - u s)$
	$? ? t ε s ρ s u s + ? ? ε s ρ s u s u s = - ε s ? p + ? p s + ? ? τ s + ε s ρ s g + β (u g - u s)$
气相/固相应力	$τ g = ε g μ g ? u g + ? u g T - 23 μ g ε g ? ? u g I$
	$τ s = ε s u s ? u s + ? u s T + ε s (λ s - 23 μ s) ? ? u s I$
颗粒压力	$p s = ε s ρ s Θ s [1 + 2 (1 + e) ε s g 0]$
颗粒黏度	$μ s = μ s, c o l + μ s, k i n + μ s, f r$
	$μ s, c o l = 45 ε s ρ s d p g 0 (1 + e) Θ s / π$
	$μ s, k i n = 10 ρ s d p Θ s π 96 ε s (1 + e) g 0 [1 + 45 (1 + e) ε s g 0] 2$
	$μ s, f r = ρ s s i n ? ? 2 ε s I 2 D$
气相/颗粒体积黏度	$λ g = 0, ? λ s = 43 ε s ρ s d p g 0 (1 + e) Θ s / π$
径向分布函数	$g 0 = [1 - (ε s ε s m) 1 / 3] - 1$

项目	方程
连续性方程	$? ? t (ε g ρ g) + ? ? (ε g ρ g u g) = 0$
	$? ? t (ε s ρ s) + ? ? (ε s ρ s u s) = 0$
动量方程	$? ? t (ε g ρ g u g) + ? ? (ε g ρ g u g u g) = - ε g ? p + ? ? τ g + ε g ρ g g - β (u g - u s)$
	$? ? t ε s ρ s u s + ? ? ε s ρ s u s u s = - ε s ? p + ? p s + ? ? τ s + ε s ρ s g + β (u g - u s)$
气相/固相应力	$τ g = ε g μ g ? u g + ? u g T - 23 μ g ε g ? ? u g I$
	$τ s = ε s u s ? u s + ? u s T + ε s (λ s - 23 μ s) ? ? u s I$
颗粒压力	$p s = ε s ρ s Θ s [1 + 2 (1 + e) ε s g 0]$
颗粒黏度	$μ s = μ s, c o l + μ s, k i n + μ s, f r$
	$μ s, c o l = 45 ε s ρ s d p g 0 (1 + e) Θ s / π$
	$μ s, k i n = 10 ρ s d p Θ s π 96 ε s (1 + e) g 0 [1 + 45 (1 + e) ε s g 0] 2$
	$μ s, f r = ρ s s i n ? ? 2 ε s I 2 D$
气相/颗粒体积黏度	$λ g = 0, ? λ s = 43 ε s ρ s d p g 0 (1 + e) Θ s / π$
径向分布函数	$g 0 = [1 - (ε s ε s m) 1 / 3] - 1$

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