Numerical Analysis of Particle Residence Time Distribution Characteristics in Fluidized Bed Based on Orthogonal Test

doi:10.12096/j.2096-4528.pgt.24046

Abstract

Abstract:

Objectives The residence time distribution (RTD) of particles is an important index to evaluate gas-solid mixing degree in fluidized bed, but there are many influencing factors and it is difficult to control. In order to design and optimize the fluidized bed with continuous operation, it is necessary to explore the influence of structure and operation parameters on RTD of particles. Methods Based on the Eulerian-Eulerian two-fluid model coupled with the component transport equation, a three-dimensional numerical calculation model of the particle RTD in a rectangular fluidized bed with continuous operation is established. The orthogonal simulation tests with 25 sets are designed to investigate the effects of the baffle structure, number, flow width, particle inlet mass flow rate, and superficial gas velocity on the particle RTD. Results The inlet mass flow rate of particles has the most significant effect on the average residence time of particles, followed by the superficial gas velocity, and both of them are inversely proportional to the average residence time of particles. However, for the dimensionless variance of RTD, the number of baffles and the mass flow rate are important influencing factors. The increase of them will reduce the dimensionless variance, weaken the backmixing degree of the fluidized bed, and make the flow tend to plug flow, but the number of baffles has a greater impact. Conclusions The average residence time of particles can be effectively controlled by adjusting the mass flow rate of particles. The number of baffles is a key structural parameter for designing fluidized beds.The research results can provide theoretical guidance for the design and optimization of fluidized bed.

Key words: fluidized bed, heat transfer, residence time distribution, orthogonal test, optimal design

CLC Number:

TK 12

Nan TU, Chiyu WANG, Xiaoqun LIU, Jiabin FANG. Numerical Analysis of Particle Residence Time Distribution Characteristics in Fluidized Bed Based on Orthogonal Test[J]. Power Generation Technology, 2025, 46(5): 1032-1040.

Figures/Tables 13

Fig. 1 Overall structure diagram of fluidized bed

Tab. 1 Physical parameters

参数	数值
颗粒密度ρ_s/(kg/m³)	2 600
颗粒粒径d_s/μm	200
示踪颗粒密度ρ_tr/(kg/m³)	1 405
示踪颗粒粒径d_tr/μm	200
空气密度ρ_g/(kg/m³)	1.225
空气黏度μ_g/(Pa·s)	1.789 4×10^-5
临界流化速度U_mf/(m/s)	0.036 8

Fig. 2 Pressure drop of fluidized bed under different grid sizes

Fig. 3 Instantaneous variation curve of mass flow at solid inlet and outlet of fluidized bed

Fig. 4 Comparison of particle RTD results between simulation and experimental data

Fig. 5 Schematic diagram of fluidized bed structures with different baffle designs

Tab. 2 Five factors and five levels of orthogonal simulation test

水平	因素
水平	A(结构)	B(N/个)	C(S_f/mm)	D(G_s/(kg/h))	E(U/(m/s))
1	溢流板	1	2	26.25	4U_mf
2	底流板	5	4	36.25	6U_mf
3	侧流板	9	6	46.25	8U_mf
4	—	13	8	56.25	10U_mf
5	—	—	10	66.25	—

Tab. 3 Mixed orthogonal test scheme and results

试验编号	因素					评价指标		t_av，m/s	(t_m/t_av，m)/%
试验编号	A	B	C	D	E	t_m/s	σ $θ 2$	t_av，m/s	(t_m/t_av，m)/%
1	1	3	3	3	2	161.11	0.173	173.56	92.83
2	2	2	1	5	2	119.87	0.155	127.16	94.27
3	1	2	4	1	3	240.15	0.438	272.63	89.19
4	1	4	4	4	1	150.93	0.085	157.57	95.79
5	1	1	1	1	1	306.47	0.494	348.70	87.89
6	2	1	5	4	4	108.60	0.478	123.05	88.26
7	1	1	3	5	1	127.25	0.386	139.70	91.09
8	2	3	4	5	4	98.26	0.120	102.94	95.46
9	3	3	1	4	3	135.46	0.078	139.51	97.10
10	1	3	5	2	1	219.77	0.167	236.55	96.35
11	3	1	4	2	2	199.48	0.557	228.90	87.15
12	3	2	5	3	1	181.17	0.205	196.06	92.41
13	2	3	2	1	1	316.39	0.143	336.90	93.92
14	3	1	3	1	4	211.35	0.564	247.36	85.44
15	1	2	2	2	4	168.99	0.305	186.08	90.82
16	2	4	3	2	3	187.36	0.106	196.83	95.19
17	2	1	2	3	3	140.21	0.504	161.65	86.74
18	2	1	4	3	1	173.70	0.482	201.56	86.18
19	3	4	2	5	1	132.47	0.042	135.53	97.74
20	1	1	2	4	2	127.70	0.518	148.23	86.15
21	2	4	5	1	2	276.57	0.180	298.91	92.53
22	1	4	1	3	4	138.79	0.089	144.57	96.00
23	1	1	5	5	3	101.14	0.493	115.10	87.87
24	2	2	3	4	1	153.66	0.283	172.05	89.32
25	2	1	1	2	1	220.84	0.451	252.60	87.43

Tab. 3 Mixed orthogonal test scheme and results

试验编号	因素					评价指标		t_av，m/s	(t_m/t_av，m)/%
试验编号	A	B	C	D	E	t_m/s	σ $θ 2$	t_av，m/s	(t_m/t_av，m)/%
1	1	3	3	3	2	161.11	0.173	173.56	92.83
2	2	2	1	5	2	119.87	0.155	127.16	94.27
3	1	2	4	1	3	240.15	0.438	272.63	89.19
4	1	4	4	4	1	150.93	0.085	157.57	95.79
5	1	1	1	1	1	306.47	0.494	348.70	87.89
6	2	1	5	4	4	108.60	0.478	123.05	88.26
7	1	1	3	5	1	127.25	0.386	139.70	91.09
8	2	3	4	5	4	98.26	0.120	102.94	95.46
9	3	3	1	4	3	135.46	0.078	139.51	97.10
10	1	3	5	2	1	219.77	0.167	236.55	96.35
11	3	1	4	2	2	199.48	0.557	228.90	87.15
12	3	2	5	3	1	181.17	0.205	196.06	92.41
13	2	3	2	1	1	316.39	0.143	336.90	93.92
14	3	1	3	1	4	211.35	0.564	247.36	85.44
15	1	2	2	2	4	168.99	0.305	186.08	90.82
16	2	4	3	2	3	187.36	0.106	196.83	95.19
17	2	1	2	3	3	140.21	0.504	161.65	86.74
18	2	1	4	3	1	173.70	0.482	201.56	86.18
19	3	4	2	5	1	132.47	0.042	135.53	97.74
20	1	1	2	4	2	127.70	0.518	148.23	86.15
21	2	4	5	1	2	276.57	0.180	298.91	92.53
22	1	4	1	3	4	138.79	0.089	144.57	96.00
23	1	1	5	5	3	101.14	0.493	115.10	87.87
24	2	2	3	4	1	153.66	0.283	172.05	89.32
25	2	1	1	2	1	220.84	0.451	252.60	87.43

Fig. 6 Diffusion cloud diagram of tracer particles in fluidized bed with different baffle structures (T=30 s)

Tab. 4 Range analysis results of orthogonal simulation test

评价指标	极差	因素
评价指标	极差	A	B	C	D	E
颗粒平均停留时间t_m/s	K₁	1 742.33	1 716.79	921.46	1 350.96	1 982.70
	K₂	1 795.53	863.86	885.78	996.47	884.76
	K₃	859.94	931.02	840.75	794.80	804.33
	K₄	—	886.13	862.54	676.37	726.01
	K₅	—	—	887.27	579.01	—
	k₁	174.23	171.67	184.29	270.19	198.27
	k₂	179.55	172.77	177.15	199.29	176.95
	k₃	171.98	186.20	168.15	158.99	160.86
	k₄	—	177.22	172.50	135.27	145.20
	k₅	—	—	177.45	115.80	—
	R	7.56	14.53	16.14	154.39	53.07
	主次顺序	D>E>C>B>A
	最优水平	A₂	B₃	C₁	D₁	E₁
无量纲方差σ $θ 2$	K₁	3.147	4.928	1.268	1.818	2.738
	K₂	2.903	1.385	1.512	1.586	1.583
	K₃	1.446	0.680	1.513	1.454	1.619
	K₄	—	0.503	1.682	1.441	1.556
	K₅	—	—	1.522	1.196	—
	k₁	0.314	0.492	0.253	0.363	0.273
	k₂	0.290	0.277	0.302	0.317	0.316
	k₃	0.289	0.136	0.303	0.290	0.323
	k₄	—	0.100	0.336	0.288	0.311
	k₅	—	—	0.304	0.239	—
	R	0.025	0.392	0.083	0.124	0.050
	主次顺序	B>D>C>E>A
	最优水平	A₂	B₄	C₁	D₅	E₁

Tab. 4 Range analysis results of orthogonal simulation test

评价指标	极差	因素
评价指标	极差	A	B	C	D	E
颗粒平均停留时间t_m/s	K₁	1 742.33	1 716.79	921.46	1 350.96	1 982.70
	K₂	1 795.53	863.86	885.78	996.47	884.76
	K₃	859.94	931.02	840.75	794.80	804.33
	K₄	—	886.13	862.54	676.37	726.01
	K₅	—	—	887.27	579.01	—
	k₁	174.23	171.67	184.29	270.19	198.27
	k₂	179.55	172.77	177.15	199.29	176.95
	k₃	171.98	186.20	168.15	158.99	160.86
	k₄	—	177.22	172.50	135.27	145.20
	k₅	—	—	177.45	115.80	—
	R	7.56	14.53	16.14	154.39	53.07
	主次顺序	D>E>C>B>A
	最优水平	A₂	B₃	C₁	D₁	E₁
无量纲方差σ $θ 2$	K₁	3.147	4.928	1.268	1.818	2.738
	K₂	2.903	1.385	1.512	1.586	1.583
	K₃	1.446	0.680	1.513	1.454	1.619
	K₄	—	0.503	1.682	1.441	1.556
	K₅	—	—	1.522	1.196	—
	k₁	0.314	0.492	0.253	0.363	0.273
	k₂	0.290	0.277	0.302	0.317	0.316
	k₃	0.289	0.136	0.303	0.290	0.323
	k₄	—	0.100	0.336	0.288	0.311
	k₅	—	—	0.304	0.239	—
	R	0.025	0.392	0.083	0.124	0.050
	主次顺序	B>D>C>E>A
	最优水平	A₂	B₄	C₁	D₅	E₁

Fig. 7 Influence trend of each factor on average residence time of particles

Fig. 8 Influence trend of each factor on dimensionless variance of particle residence time

Tab.5 Variance analysis results of orthogonal simulation test

评价指标	方差来源	偏方差和	自由度	均方和	检验统计量F值	显著性	显著性水平
颗粒平均停留时间t_m/s	A	237.718	2	118.859	0.961	0.423	不显著
	B	766.865	3	255.622	2.067	0.183	不显著
	C	729.873	4	182.468	1.476	0.296	不显著
	D	74 930.399	4	18732.6	151.485	<0.001	非常显著
	E	10 851.688	3	3 617.229	29.251	<0.001	非常显著
	误差	989.28	8	123.66	—	—	—
无量纲方差σ $θ 2$	A	0.004	2	0.002	1.23	0.342	不显著
	B	0.708	3	0.236	158.234	<0.001	非常显著
	C	0.018	4	0.004	2.947	0.09	不显著
	D	0.041	4	0.01	6.932	0.01	显著
	E	0.012	3	0.004	2.612	0.123	不显著
	误差	0.012	8	0.001	—	—	—

Tab.5 Variance analysis results of orthogonal simulation test

评价指标	方差来源	偏方差和	自由度	均方和	检验统计量F值	显著性	显著性水平
颗粒平均停留时间t_m/s	A	237.718	2	118.859	0.961	0.423	不显著
	B	766.865	3	255.622	2.067	0.183	不显著
	C	729.873	4	182.468	1.476	0.296	不显著
	D	74 930.399	4	18732.6	151.485	<0.001	非常显著
	E	10 851.688	3	3 617.229	29.251	<0.001	非常显著
	误差	989.28	8	123.66	—	—	—
无量纲方差σ $θ 2$	A	0.004	2	0.002	1.23	0.342	不显著
	B	0.708	3	0.236	158.234	<0.001	非常显著
	C	0.018	4	0.004	2.947	0.09	不显著
	D	0.041	4	0.01	6.932	0.01	显著
	E	0.012	3	0.004	2.612	0.123	不显著
	误差	0.012	8	0.001	—	—	—

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