基于EMMS的循环流化床流域研究

doi:10.11949/0438-1157.20200062

化工学报 ›› 2020, Vol. 71 ›› Issue (7): 3018-3030.DOI: 10.11949/0438-1157.20200062

基于EMMS的循环流化床流域研究

陈恺成^1,²(),田于杰¹(),李飞^1,³(),吴昊⁴,王维^1,²

^1.中国科学院过程工程研究所多相复杂系统国家重点实验室，北京 100190
^2.中国科学院大学中丹学院，北京 100049
^3.中国科学院绿色过程制造创新研究院，北京 100190
^4.Department of Chemical and Biochemical Engineering, Technical University of Denmark, 2800 Kongens Lyngby, Denmark

收稿日期:2020-01-15 修回日期:2020-03-12 出版日期:2020-07-05 发布日期:2020-07-05
通讯作者: 李飞
作者简介:陈恺成（1995—），男，硕士研究生，kcchen@ipe.ac.cn|田于杰（1991—），男，博士，助理研究员，tianyj@ipe.ac.cn
基金资助:
国家自然科学基金项目(21625605);国家重点研发计划项目(2017YFB0602700);中国科学院绿色过程制造创新研究院(IAGM-2019-A13)

EMMS-based flow regime study of circulating fluidized beds

Kaicheng CHEN^1,²(),Yujie TIAN¹(),Fei LI^1,³(),Hao WU⁴,Wei WANG^1,²

^1.State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China
^2.Sino-Danish College, University of Chinese Academy of Sciences, Beijing 100049, China
^3.Innovation Academy for Green Manufacture, Chinese Academy of Sciences, Beijing 100190, China
^4.Department of Chemical and Biochemical Engineering, Technical University of Denmark, 2800 KongensLyngby, Denmark

Received:2020-01-15 Revised:2020-03-12 Online:2020-07-05 Published:2020-07-05
Contact: Fei LI

摘要/Abstract

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

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

中图分类号:

TQ 021.1

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.

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.

图/表 18

表1 文献中的流域图总结

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

图1 文献中不同循环床流域划分的比较

Fig.1 Comparison of regime classifications of CFBs in literatures

表2 循环床的流域细分及特征描述

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

表3 界定快速床操作上下限的经验关联式

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

表3 界定快速床操作上下限的经验关联式

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

图2 基于EMMS的循环床本征流域图 [42]

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

图3 模拟采用的几何构体

Fig.3 Schematic drawing of riser in simulations

表4 模拟系统的物性参数与操作条件

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

表5 模拟设置

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

图4 不同操作条件下的径向颗粒浓度与颗粒速度、气体速度分布（床高0.5 m处）

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

图5 快速床的下边界

Fig.5 Lower boundary of fast bed

图6 较大颗粒浓度下通量随时间的变化

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

图7 快速床的上边界

Fig.7 Upper boundary of fast bed

图8 快速床的操作范围

Fig.8 Operating range of fast bed

图9 不同气速下颗粒通量随初始颗粒浓度的变化

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

图11 无量纲化的循环床流域图

Fig.11 Dimensionless regime diagram of CFB

图10 快速床流域内的轴径向颗粒浓度分布（Ug=4 m·s-1）Gs —— 颗粒循环通量，kg/(m2·s)g —— 重力加速度，m/s2g0 —— 径向分布函数H —— 反应器高度，mHd —— 非均匀结构因子p —— 压力，Paq —— 脉动能通量，J/(m2·s)R —— 反应器半径，mr —— 径向位置坐标，mRe —— Reynolds数Ret —— 终端沉降Reynolds数U —— 表观速度，m/sUFD —— 快速床的操作下限[13]，m/sUg* —— 无量纲表观气速[2]Umf —— 最小流化速度，m/sUslip —— 表观滑移速度，m/sUTF —— 快速床的操作上限[13]，m/sUtr —— 湍动床向循环床的转变气速，m/sUtp —— 循环床向输送床的转变气速，m/su —— 真实速度，m/sugy —— 竖直方向上的真实气体速度，m/supy —— 竖直方向上的真实颗粒速度，m/sVCA —— 快速床的操作下限[22]，m/sVCC —— 快速床的操作下限[22]，m/sβ —— 气固相间曳力系数，kg/(m3·s)γ —— 碰撞耗散能，J/(m3·s)ε —— 体积分数Θs —— 颗粒温度，m2/s2κ —— 脉动能传导率，kg/(m·s)λ —— 体积黏度，Pa·sμ —— 动力黏度系数，Pa·sρ —— 密度，kg/m3τ —— 黏性应力张量，PaΩ —— Beranek数下角标g —— 气相p —— 颗粒s —— 固相

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

附表1 非均匀结构因子Hd表达式中的系数 (Appendix 1　Coefficients in expressions of heterogeneity indexesHd)

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}

附表2 双流体模型的控制方程和本构关系 (Appendix 2　Governing equations and constitutive equations in TFM)

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	$g 0 = [1 - (ε s ε s m) 1 / 3] - 1$

附表2 双流体模型的控制方程和本构关系 (Appendix 2　Governing equations and constitutive equations in TFM)

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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基于EMMS的循环流化床流域研究

EMMS-based flow regime study of circulating fluidized beds

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