Study on adaptability of scaling law to residence time distribution in bubbling fluidized beds with continuous operation

doi:10.11949/0438-1157.20231195

Abstract

Abstract:

Particles residence time distribution (RTD) in bubbling fluidized beds is important for its performances, and the evaluation of particles RTD in large-scale bubbling fluidized beds is a critical issue. In this study, a diffusion criteria number was introduced based on the scaling law proposed by Glicksman. Then the fluidized bed similarity scaling law that exhibits RTD similarity was obtained, and the transformation relations for the similarity of particles RTD was clarified. The flow behaviors and particles RTD of the scaled-down and original fluidized beds were numerically simulated. The results show that within the specific range of geometric similarity constants (1 < k < 200), the computational time for the scaled-down model could be reduced from 22.8 days to 1.4 days. Moreover, the particles RTD exhibits similarity to that of the original bed, with a maximum error not exceeding 9.24%. Following the similarity transformation, the particles RTD of the scaled-down model demonstrates a favorable ability to predict the particles RTD of the original bed, with a maximum error for key characteristic values of 17.8%. Furthermore, variations in particle flow rate, fluidization velocity, and static bed height do not influence the accuracy of scaled-down model in predicting the particles RTD of the original bed. The maximum error of its key characteristic values does not exceed 10.32%. This confirms the applicability of the similarity scaling law under varying operating conditions. All the results demonstrate the effective of presented similarity scaling law for the rapid and accurate prediction of particles RTD in large-scale fluidized beds.

Key words: bubbling fluidized bed, residence time distribution, scaling law, transformation relations, scaled-down model, numerical simulation

摘要：

以连续进出料鼓泡流化床为研究对象，在Glicksman相似准则的基础上引入了扩散准则数，获得了具备颗粒停留时间分布（RTD）相似性的流化床相似放大准则，并明确了颗粒RTD的相似转换关系。对缩尺流化床模型与原型的流动行为及颗粒RTD进行了数值模拟分析，发现在给定的几何相似常数范围内（1<k<200），缩尺模型计算时长可由22.8天降至1.4天，且颗粒分布规律与原型相似，最大误差不超过9.24%。缩尺模型的颗粒RTD经相似转换后能够较好地预测原型颗粒RTD规律且关键特征值最大误差为17.8%。此外，改变颗粒流量、流化气速及静床高度后，缩尺模型仍能准确预测原型的颗粒RTD，其关键特征值最大误差不超过10.32%，证实了该相似准则在变工况下具有适用性，可用于快速、准确预测大型流化床颗粒RTD。

关键词: 鼓泡流化床, 停留时间分布, 相似准则, 相似转换关系, 缩尺模型, 数值模拟

CLC Number:

TQ 021

Nan TU, Xiaoqun LIU, Chiyu WANG, Jiabin FANG. Study on adaptability of scaling law to residence time distribution in bubbling fluidized beds with continuous operation[J]. CIESC Journal, 2024, 75(2): 543-552.

屠楠, 刘晓群, 王驰宇, 方嘉宾. 连续进出料鼓泡流化床停留时间分布的相似准则研究[J]. 化工学报, 2024, 75(2): 543-552.

Figures/Tables 11

Fig.1 Schematic diagram of the structure of the bubbling fluidized bed with continuous feedstock

Fig.2 Uniform pressure drop at fluidized bed layers with different grid numbers

Fig.3 Comparison of RTD numerical simulation and experimental results

Table 1 The material properties， operation conditions and geometry parameters under different k

k	G_s/ (kg/h)	u/u_mf	H_bed/ mm	L/ mm	H/ mm	W/ mm	d_p/ μm	ρ_s/ (kg/m³)	ρ_tr/ (kg/m³)	ρ_g/ (kg/m³)	μ_g/ (kg/(m·s) )	D_s/ (m²/s)
1	56.25	8	100	450	200	40	200	2600	1405	1.23	1.79×10^-5	2.9×10^-5
10	1.779	8	10	45	20	4	20	26000	14050	12.25	5.66×10^-6	9.1×10^-7
50	0.159	8	2	9	4	0.8	4	130000	70250	61.25	2.53×10^-6	8.1×10^-8
100	0.056	8	1	4.5	2	0.4	2	260000	140500	122.5	1.79×10^-6	2.9×10^-8
125	0.040	8	0.8	3.6	1.6	0.32	1.6	325000	175625	153.1	1.60×10^-6	2.1×10^-8
160	0.028	8	0.625	2.8125	1.25	0.25	1.25	416000	224800	196	1.41×10^-6	1.4×10^-8
200	0.020	8	0.5	2.25	1	0.2	1	520000	281000	245	1.27×10^-6	1.0×10^-8

Table 2 Similar conversion relationships of fluidized bed particle RTDs under different k

物理量	表达式	相似转换关系
C(t)	$C (t) = m t r (t) m t r (t) + m s o l i d (t)$	$C 1 (t 1) = C 2 (t 2)$
E(t)	$E (t) = C (t) ∫ 0 ∞ C (t) d t = G s m t r C (t)$	$E 1 (t 1) = k - 0.5 E 2 (t 2)$
t_m	$t m = ∑ i = 1 n t i E (t i) Δ t i ∑ i = 1 n E (t i) Δ t i$	$t m 1 = k 0.5 t m 2$
σ_t²	$σ t 2 = ∑ i = 1 n t i 2 E (t i) ∑ i = 1 n E (t i) - t m 2$	$σ t 1 2 = k σ t 2 2$
θ	θ=t/t_m	θ₁=θ₂
E(θ)	$E (θ) = E (t) t m$	$E 1 (θ 1) = E 2 (θ 2)$
σ_θ	$σ θ = σ t t m$	$σ θ 1 = σ θ 2$

Table 2 Similar conversion relationships of fluidized bed particle RTDs under different k

物理量	表达式	相似转换关系
C(t)	$C (t) = m t r (t) m t r (t) + m s o l i d (t)$	$C 1 (t 1) = C 2 (t 2)$
E(t)	$E (t) = C (t) ∫ 0 ∞ C (t) d t = G s m t r C (t)$	$E 1 (t 1) = k - 0.5 E 2 (t 2)$
t_m	$t m = ∑ i = 1 n t i E (t i) Δ t i ∑ i = 1 n E (t i) Δ t i$	$t m 1 = k 0.5 t m 2$
σ_t²	$σ t 2 = ∑ i = 1 n t i 2 E (t i) ∑ i = 1 n E (t i) - t m 2$	$σ t 1 2 = k σ t 2 2$
θ	θ=t/t_m	θ₁=θ₂
E(θ)	$E (θ) = E (t) t m$	$E 1 (θ 1) = E 2 (θ 2)$
σ_θ	$σ θ = σ t t m$	$σ θ 1 = σ θ 2$

Fig.4 The distribution of the average solid volume in the fluidized bed under different k

Fig.5 The original RTD curves and the similar conversion RTD curves of the scaled-down and original fluidized beds

Fig.6 The original dimensionless RTD curves of the scaled-down and original fluidized beds

Fig.7 Comparisons of theoretical and simulated eigenvalues of RTDs

Fig.8 Comparisons of the prediction results of the scaled-down model with the experimental results of original model under variable working conditions

Fig.9 Comparisons of the prediction results of the scaled-down model with the the numerical results of original model under variable working conditions

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