Bubble breakage, turbulence dispersion and mass transfer model considering the joint effects of bubble-induced turbulence and shear turbulence

doi:10.11949/0438-1157.20220465

Abstract

Abstract:

In the gas-liquid bubbling flow represented by the bubble column, there are two turbulence mechanisms, the bubble induced turbulence (BIT) and the shear turbulence, and they both compete and work together in different time and space ranges. There are uncertainties remain in how BIT affects the bubble breakage and coalescence, the interphase interaction forces and the mass transfer, due to the limited understanding of the BIT energy spectrum. Considering the joint effects of bubble-induced turbulence and shear turbulence, we proposed the bubble breakage model and the turbulence dispersion force model in dealing with the global or the local dominance of BIT. For different operating conditions, these models have performed well in capturing the dynamic behaviors of both the gas- and the liquid-phase, which offers fresh insights into understanding the mechanisms of the interphase mass transfer process in the gas-liquid bubbly flows.

Key words: bubble, turbulent flow, mass transfer, population balance, large eddy simulation, gas-liquid flow, bubble column

摘要：

在以鼓泡塔为代表的气液鼓泡流动中，存在着气泡诱导湍流（BIT）和剪切湍流两种湍流机制，并且二者在不同的时间、空间范围内既相互竞争又共同作用。受制于BIT动能能谱的形式和特性不够完整清晰，过去的研究中关于BIT如何对气泡破碎聚并、相间作用力、相间传热传质等相间相互作用过程产生影响的结论比较模糊。因此，本文在具有波数κ^-3特性的BIT能谱的基础上，提出了在不同工况下考虑BIT与剪切湍流共同作用的研究思路。研究结果表明，考虑两种湍流机制的气泡破碎模型和湍流相间扩散模型对BIT在整体或局部占据不同程度主导地位的情况，都能很好地捕捉气液鼓泡流动的动力学特性，为进一步准确揭示气液相间传质过程的内在机理提供了基础。

关键词: 气泡, 湍流, 传质, 种群平衡, 大涡模拟, 气液两相流, 鼓泡塔

CLC Number:

TQ 021.1

Weibin SHI, Shanshan LONG, Xiaogang YANG, Xinyue CAI. Bubble breakage, turbulence dispersion and mass transfer model considering the joint effects of bubble-induced turbulence and shear turbulence[J]. CIESC Journal, 2022, 73(6): 2573-2588.

施炜斌, 龙姗姗, 杨晓钢, 蔡心悦. 计及气泡诱导与剪切湍流的气泡破碎、湍流相间扩散及传质模型[J]. 化工学报, 2022, 73(6): 2573-2588.

Figures/Tables 15

Table 1 Reynolds stress equation model

模型	方程
$ρ u i' u j' ˉ$ 输运方程	$? α l ρ l u i' u j' ˉ ? t + ? α l ρ l u k u i' u j' ˉ ? x k = ? ? x k α l μ l + μ t σ k ? u i' u j' ˉ ? x k + α l P i j + α l ? i j - 23 δ i j α l ρ l ε + α l S i j B I T$ (3)
湍动能产生项	$P i j = - ρ l u i' u k' ˉ ? u j ? x k + u j' u k' ˉ ? u i ? x k$ (4)
压力-应变项	$? i j = ? i j, 1 + ? i j, 2 + ? i j, 1 W + ? i j, 2 W = - C 1 ρ l ε k u i' u j' ˉ - 23 k δ i j - C 2 ρ l ε k P i j - 13 t r P δ i j - C 1 W ρ l ε k u k' u m' ˉ n k n m δ i j - 32 u k' u i' ˉ n k n j - 32 u k' u j' ˉ n k n i k 3 / 2 ε 1 C l y W 2 - C 2 W ? k m, 2 n k n m δ i j - 32 ? i k, 2 n k n j - 32 ? j k, 2 n k n i k 3 / 2 ε 1 C l y W 2$ (5)
湍流耗散率输运方程	$? α l ρ l ε ? t + ? ? x i α l ρ l ε u i = ? ? x j α l μ l + μ t σ ε ? ε ? x j + α l ρ l ε k C 1 ε u' i u' j ˉ ? u i ? x k - C 2 ε ε + α l S ε B I T$ (6)
湍动能	$k = 12 ∑ i = 1,2, 3 u i' u j'$ (7)

Table 1 Reynolds stress equation model

模型	方程
$ρ u i' u j' ˉ$ 输运方程	$? α l ρ l u i' u j' ˉ ? t + ? α l ρ l u k u i' u j' ˉ ? x k = ? ? x k α l μ l + μ t σ k ? u i' u j' ˉ ? x k + α l P i j + α l ? i j - 23 δ i j α l ρ l ε + α l S i j B I T$ (3)
湍动能产生项	$P i j = - ρ l u i' u k' ˉ ? u j ? x k + u j' u k' ˉ ? u i ? x k$ (4)
压力-应变项	$? i j = ? i j, 1 + ? i j, 2 + ? i j, 1 W + ? i j, 2 W = - C 1 ρ l ε k u i' u j' ˉ - 23 k δ i j - C 2 ρ l ε k P i j - 13 t r P δ i j - C 1 W ρ l ε k u k' u m' ˉ n k n m δ i j - 32 u k' u i' ˉ n k n j - 32 u k' u j' ˉ n k n i k 3 / 2 ε 1 C l y W 2 - C 2 W ? k m, 2 n k n m δ i j - 32 ? i k, 2 n k n j - 32 ? j k, 2 n k n i k 3 / 2 ε 1 C l y W 2$ (5)
湍流耗散率输运方程	$? α l ρ l ε ? t + ? ? x i α l ρ l ε u i = ? ? x j α l μ l + μ t σ ε ? ε ? x j + α l ρ l ε k C 1 ε u' i u' j ˉ ? u i ? x k - C 2 ε ε + α l S ε B I T$ (6)
湍动能	$k = 12 ∑ i = 1,2, 3 u i' u j'$ (7)

Table 2 Interphase momentum exchange models

作用力	方程
曳力	$M D = 34 C D d b ρ l α g u g - u l u g - u l$ (15)
升力	$M l i f t = C l ρ l α g u g - u l × ? × u l$ (16)
虚拟质量力	$M V M = C V M ρ l α g d u l d t l - d u g d t g$ (17)

Table 2 Interphase momentum exchange models

作用力	方程
曳力	$M D = 34 C D d b ρ l α g u g - u l u g - u l$ (15)
升力	$M l i f t = C l ρ l α g u g - u l × ? × u l$ (16)
虚拟质量力	$M V M = C V M ρ l α g d u l d t l - d u g d t g$ (17)

Table 3 Comparison of bubble breakage models

项目	Luo and Svendsen模型	考虑BIT的气泡破碎模型
能谱函数	$E κ = C κ ε 23 κ - 53$ $C κ ≈ 1.5$	$E κ = δ l C l ε 23 κ - 53 + δ b C b α g U s l i p ν κ - 3$ (29) $δ l$ 、 $δ b$ 为开关函数 $C l$ 、 $C b$ 取动态变化值
涡旋平均脉动速度	$u ˉ λ = β 12 ε λ 13$ $β ≈$ 2.0	$u ˉ λ = C λ 12 C b α g U s l i p ν λ$ (30)
湍流涡旋数密度	$f λ = C 3 1 - α λ 4$ $C 3 = 15 2 2 π 23 Γ 13 ≈ 0.822$	$f λ = C 3 1 - α λ 4$ (31) $C 3 = 12 π C λ 2 π 2$
涡旋-气泡碰撞概率密度函数	$ω B T d i, λ = C 4 1 - α n i ε d i 13 1 + ξ 2 d i ξ 113$ $C 4 = π 4 C 3 β 12 ≈ 0.923$	$ω B T d i, λ = C 4 1 - α n i 1 + ξ 2 d i ξ 3 C b α g U s l i p ν$ (32) $C 4 = π 4 C 3 C λ C b 12$
平均湍动能	$e ˉ d i, λ = π β 12 ρ l ε d i 23 d i 3 ξ 113$	$e ˉ d i, λ = π 12 C λ ρ l λ 5 C b α g U s l i p ν$ (33)
破碎速率	$Ω B d i ∶ d j = 0.923 1 - α$ × $n i ε d 2 13 ∫ ξ m i n 1 1 + ξ 2 ξ 113 e x p - 12 σ C f β ρ l ε 23 d i 53 ξ 113 d ξ$	$Ω B d i ∶ d j = 0.923 1 - α n i ε d 2 13$ × $∫ Λ d i 1 1 + ξ 2 ξ 113 e x p - 12 σ C f β ρ l ε 23 d i 53 ξ 113 d ξ + C 4 1 - α$ × (34) $n i C b α g U s l i p ν ∫ ξ m i n Λ d i 1 + ξ 2 ξ 3 e x p - 12 σ C f β ρ l C b α g U s l i p ν d i 3 ξ 5 d ξ$

Table 3 Comparison of bubble breakage models

项目	Luo and Svendsen模型	考虑BIT的气泡破碎模型
能谱函数	$E κ = C κ ε 23 κ - 53$ $C κ ≈ 1.5$	$E κ = δ l C l ε 23 κ - 53 + δ b C b α g U s l i p ν κ - 3$ (29) $δ l$ 、 $δ b$ 为开关函数 $C l$ 、 $C b$ 取动态变化值
涡旋平均脉动速度	$u ˉ λ = β 12 ε λ 13$ $β ≈$ 2.0	$u ˉ λ = C λ 12 C b α g U s l i p ν λ$ (30)
湍流涡旋数密度	$f λ = C 3 1 - α λ 4$ $C 3 = 15 2 2 π 23 Γ 13 ≈ 0.822$	$f λ = C 3 1 - α λ 4$ (31) $C 3 = 12 π C λ 2 π 2$
涡旋-气泡碰撞概率密度函数	$ω B T d i, λ = C 4 1 - α n i ε d i 13 1 + ξ 2 d i ξ 113$ $C 4 = π 4 C 3 β 12 ≈ 0.923$	$ω B T d i, λ = C 4 1 - α n i 1 + ξ 2 d i ξ 3 C b α g U s l i p ν$ (32) $C 4 = π 4 C 3 C λ C b 12$
平均湍动能	$e ˉ d i, λ = π β 12 ρ l ε d i 23 d i 3 ξ 113$	$e ˉ d i, λ = π 12 C λ ρ l λ 5 C b α g U s l i p ν$ (33)
破碎速率	$Ω B d i ∶ d j = 0.923 1 - α$ × $n i ε d 2 13 ∫ ξ m i n 1 1 + ξ 2 ξ 113 e x p - 12 σ C f β ρ l ε 23 d i 53 ξ 113 d ξ$	$Ω B d i ∶ d j = 0.923 1 - α n i ε d 2 13$ × $∫ Λ d i 1 1 + ξ 2 ξ 113 e x p - 12 σ C f β ρ l ε 23 d i 53 ξ 113 d ξ + C 4 1 - α$ × (34) $n i C b α g U s l i p ν ∫ ξ m i n Λ d i 1 + ξ 2 ξ 3 e x p - 12 σ C f β ρ l C b α g U s l i p ν d i 3 ξ 5 d ξ$

Fig.1 Schematic diagram of bubble mass centre movement caused by sub-grid scale liquid fluctuations

Table 4 Experimental details of gas-liquid systems and model selections

Case	实验	塔径/m	高度/m	表观气速/(m/s)	静液位高度/m	测量高度/m	湍流模型	湍流扩散	破碎模型
Case 1	Gemello等^[36-37]	0.4	3.6	0.16	1.6	1.5	RSM	—	Luo and Sevndsen
Case 2	Gemello等^[36-37]	0.4	3.6	0.16	1.6	1.5	RSM	—	Luo and Sevndsen Ω_B’(d_i ∶d_j )=10Ω_B(d_i ∶d_j )
Case 3	Gemello等^[36-37]	0.4	3.6	0.16	1.6	1.5	RSM	—	式(34)
Case 4	Guan等^[38]	0.15	1.6	0.08	1.2	0.8	RSM	—	Luo and Sevndsen
Case 5	Guan等^[38]	0.15	1.6	0.08	1.2	0.8	RSM	—	式(34)
Case 6	Sommerfeld等^[17]	0.14	1.4	0.0029	0.65	0.325	LES	Burns等^[39]	—
Case 7	Sommerfeld等^[17]	0.14	1.4	0.0029	0.65	0.325	LES	式(43)	—

Fig.2 Schematic diagram of mesh set-up

Fig.3 Grid sensitivity test results

Fig.4 Comparison of experimental results with simulation results by different breakage models

Fig.5 Comparison of bubble size distributions by different breakage models

Fig.6 Comparison of gas holdup and bubble size distributions by different breakage models

Fig.7 Axial liquid velocity vectors

Fig.8 Time-averaged radial distribution of bubble rise velocity

Fig.9 Turbulent energy spectrum at middle point of z=325 mm plane by LES

Fig.10 Schematic diagram for mass transfer due to bubble-eddy contact

Fig.11 Comparison of the predicted and measured volumetric mass transfer coefficients

References 47

1	Luo H A, Svendsen H F. Theoretical model for drop and bubble breakup in turbulent dispersions[J]. AIChE Journal, 1996, 42(5): 1225-1233.
2	Lehr F, Millies M, Mewes D. Bubble-size distributions and flow fields in bubble columns[J]. AIChE Journal, 2002, 48(11): 2426-2443.
3	Andersson R, Andersson B. Modeling the breakup of fluid particles in turbulent flows[J]. AIChE Journal, 2006, 52(6): 2031-2038.
4	Wang T F, Wang J F, Jin Y. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow[J]. Chemical Engineering Science, 2003, 58(20): 4629-4637.
5	Han L C, Fu J, Li M, et al. A theoretical unsteady-state model for k_L of bubbles based on the framework of wide energy spectrum[J]. AIChE Journal, 2016, 62(4): 1007-1022.
6	Zhao H, Ge W. A theoretical bubble breakup model for slurry beds or three-phase fluidized beds under high pressure[J]. Chemical Engineering Science, 2007, 62(1/2): 109-115.
7	Liao Y X, Rzehak R, Lucas D, et al. Baseline closure model for dispersed bubbly flow: bubble coalescence and breakup[J]. Chemical Engineering Science, 2015, 122: 336-349.
8	Zhang X B, Yan W C, Luo Z H. Numerical simulation of local bubble size distribution in bubble columns operated at heterogeneous regime[J]. Chemical Engineering Science, 2021, 231: 116266.
9	Risso F, Roig V, Amoura Z, et al. Wake attenuation in large Reynolds number dispersed two-phase flows[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2008, 366(1873): 2177-2190.
10	Mercado J M, Gómez D C, van Gils D, et al. On bubble clustering and energy spectra in pseudo-turbulence[J]. Journal of Fluid Mechanics, 2010, 650: 287-306.
11	Riboux G, Risso F, Legendre D. Experimental characterization of the agitation generated by bubbles rising at high Reynolds number[J]. Journal of Fluid Mechanics, 2010, 643: 509-539.
12	Mendez-Diaz S, Serrano-García J C, Zenit R, et al. Power spectral distributions of pseudo-turbulent bubbly flows[J]. Physics of Fluids, 2013, 25(4): 043303.
13	Prakash V N, Martínez Mercado J, van Wijngaarden L, et al. Energy spectra in turbulent bubbly flows[J]. Journal of Fluid Mechanics, 2016, 791: 174-190.
14	Lance M, Bataille J. Turbulence in the liquid phase of a uniform bubbly air-water flow[J]. Journal of Fluid Mechanics, 1991, 222: 95.
15	Roghair I, Mercado J M, van Sint Annaland M, et al. Energy spectra and bubble velocity distributions in pseudo-turbulence: numerical simulations vs. experiments[J]. International Journal of Multiphase Flow, 2011, 37(9): 1093-1098.
16	Riboux G, Legendre D, Risso F. A model of bubble-induced turbulence based on large-scale wake interactions[J]. Journal of Fluid Mechanics, 2013, 719: 362-387.
17	Sommerfeld M, Muniz M, Reichardt T. On the importance of modelling bubble dynamics for point-mass numerical calculations of bubble columns[J]. Journal of Chemical Engineering of Japan, 2018, 51(4): 301-317.
18	Laviéville J, Mérigoux N, Guingo M, et al. A generalized turbulent dispersion model for bubbly flow numerical simulation in NEPTUNE_CFD[J]. Nuclear Engineering and Design, 2017, 312: 284-293.
19	de Bertodano M A L. Two fluid model for two-phase turbulent jets[J]. Nuclear Engineering and Design, 1998, 179(1): 65-74.
20	Drew D. A turbulent dispersion model for particles or bubbles[J]. Journal of Engineering Mathematics, 2001, 41: 259-274.
21	Lucas D, Krepper E, Prasser H M. Prediction of radial gas profiles in vertical pipe flow on the basis of bubble size distribution[J]. International Journal of Thermal Sciences, 2001, 40(3): 217-225.
22	Wang T F, Wang J F. Numerical simulations of gas-liquid mass transfer in bubble columns with a CFD-PBM coupled model[J]. Chemical Engineering Science, 2007, 62(24): 7107-7118.
23	Krishna R, van Baten J M. Mass transfer in bubble columns[J]. Catalysis Today, 2003, 79/80: 67-75.
24	Lamont J C, Scott D S. An eddy cell model of mass transfer into the surface of a turbulent liquid[J]. AIChE Journal, 1970, 16(4): 513-519.
25	Han L C, Luo H A, Liu Y J, et al. A multi-scale theoretical model for gas-liquid interface mass transfer based on the wide spectrum eddy contact concept[J]. AIChE Journal, 2011, 57(4): 886-896.
26	Parekh J, Rzehak R. Euler-Euler multiphase CFD-simulation with full Reynolds stress model and anisotropic bubble-induced turbulence[J]. International Journal of Multiphase Flow, 2018, 99: 231-245.
27	de Bertodano M L, Lee S J, Lahey R T, et al. The prediction of two-phase turbulence and phase distribution phenomena using a Reynolds stress model[J]. Journal of Fluids Engineering, 1990, 112(1): 107-113.
28	Shi W B, Yang X G, Sommerfeld M, et al. Modelling of mass transfer for gas-liquid two-phase flow in bubble column reactor with a bubble breakage model considering bubble-induced turbulence[J]. Chemical Engineering Journal, 2019, 371: 470-485.
29	Shi W B, Yang X G, Sommerfeld M, et al. A modified bubble breakage and coalescence model accounting the effect of bubble-induced turbulence for CFD-PBM modelling of bubble column bubbly flows[J]. Flow, Turbulence and Combustion, 2020, 105(4): 1197-1229.
30	Rzehak R, Krepper E. CFD modeling of bubble-induced turbulence[J]. International Journal of Multiphase Flow, 2013, 55: 138-155.
31	Rzehak R, Krepper E. Closure models for turbulent bubbly flows: a CFD study[J]. Nuclear Engineering and Design, 2013, 265: 701-711.
32	Long S S, Yang J, Huang X B, et al. Large-eddy simulation of gas-liquid two-phase flow in a bubble column reactor using a modified sub-grid scale model with the consideration of bubble-eddy interaction[J]. International Journal of Heat and Mass Transfer, 2020, 161: 120240.
33	Clift R, Grace J R, Weber M E. Bubbles, Drops, and Particles [M]. New York: Academic Press, 1978.
34	Tomiyama A. Struggle with computational bubble dynamics [J]. New York: Multiphase Science and Technology, 1998, 10(4): 369-405.
35	Luo H. Coalescence, breakup and liuqid circulation in bubble column reactors [D]. Trondheim, Norway: Norwegian Institute of Technology, 1993.
36	Gemello L, Plais C, Augier F, et al. Hydrodynamics and bubble size in bubble columns: effects of contaminants and spargers[J]. Chemical Engineering Science, 2018, 184: 93-102.
37	Gemello L, Plais C, Augier F, et al. Population balance modelling of bubble columns under the heterogeneous flow regime[J]. Chemical Engineering Journal, 2019, 372: 590-604.
38	Guan X P, Yang N. Bubble properties measurement in bubble columns: from homogeneous to heterogeneous regime[J]. Chemical Engineering Research and Design, 2017, 127: 103-112.
39	Burns A D, Frank T, Hamill I, et al. The favre averaged drag model for turbulent dispersion in Eulerian multi-phase flows[C]// 5th International Conference on Multiphase Flow, ICMF' 04. Yokohama, Japan: ICMF, 2004.
40	Chen P, Duduković M P, Sanyal J. Three-dimensional simulation of bubble column flows with bubble coalescence and breakup[J]. AIChE Journal, 2005, 51(3): 696-712.
41	Chen P, Sanyal J, Duduković M P. Numerical simulation of bubble columns flows: effect of different breakup and coalescence closures[J]. Chemical Engineering Science, 2005, 60(4): 1085-1101.
42	Zhang X B, Yan W C, Luo Z H. CFD-PBM simulation of bubble columns: sensitivity analysis of the nondrag forces[J]. Industrial & Engineering Chemistry Research, 2020, 59(41): 18674-18682.
43	Shi W B, Li G, Yang J, et al. CFD-PBM modelling of gas-liquid two-phase flow in bubble column reactors with an improved breakup kernel accounting for bubble shape variations[C]// Proceedings of the 13th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT2017). Portoroz, Slovenia: HEFAT, 2017.
44	Shi W B, Yang J, Li G, et al. Computational fluid dynamics-population balance modeling of gas-liquid two-phase flow in bubble column reactors with an improved breakup kernel accounting for bubble shape variations[J]. Heat Transfer Engineering, 2020, 41(15/16): 1414-1430.
45	Pope S B. Turbulent Flows [M]. Cambridge: Cambridge University Press, 2000.
46	Terasaka K, Hullmann D, Schumpe A. Mass transfer in bubble columns studied with an oxygen optode[J]. Chemical Engineering Science, 1998, 53(17): 3181-3184.
47	Zhang H H, Guo K Y, Wang Y L, et al. Numerical simulations of the effect of liquid viscosity on gas-liquid mass transfer of a bubble column with a CFD-PBM coupled model[J]. International Journal of Heat and Mass Transfer, 2020, 161: 120229.

[1]	Jingwei CHAO, Jiaxing XU, Tingxian LI. Investigation on the heating performance of the tube-free-evaporation based sorption thermal battery [J]. CIESC Journal, 2023, 74(S1): 302-310.
[2]	Mingkun XIAO, Guang YANG, Yonghua HUANG, Jingyi WU. Numerical study on bubble dynamics of liquid oxygen at a submerged orifice [J]. CIESC Journal, 2023, 74(S1): 87-95.
[3]	Keke SHAO, Mengjie SONG, Zhengyong JIANG, Xuan ZHANG, Long ZHANG, Runmiao GAO, Zekang ZHEN. Experimental study on the formation and distribution of trapped air bubbles in horizontal ice slice [J]. CIESC Journal, 2023, 74(S1): 161-164.
[4]	He JIANG, Junfei YUAN, Lin WANG, Guyu XING. Experimental study on the effect of flow sharing cavity structure on phase change flow characteristics in microchannels [J]. CIESC Journal, 2023, 74(S1): 235-244.
[5]	Yitong LI, Hang GUO, Hao CHEN, Fang YE. Study on operating conditions of proton exchange membrane fuel cells with non-uniform catalyst distributions [J]. CIESC Journal, 2023, 74(9): 3831-3840.
[6]	Jiaqi YUAN, Zheng LIU, Rui HUANG, Lefu ZHANG, Denghui HE. Investigation on energy conversion characteristics of vortex pump under bubble inflow [J]. CIESC Journal, 2023, 74(9): 3807-3820.
[7]	Lei XING, Chunyu MIAO, Minghu JIANG, Lixin ZHAO, Xinya LI. Optimal design and performance analysis of downhole micro gas-liquid hydrocyclone [J]. CIESC Journal, 2023, 74(8): 3394-3406.
[8]	Linjing YUE, Yihan LIAO, Yuan XUE, Xuejie LI, Yuxing LI, Cuiwei LIU. Study on influence of pit defects on cavitation flow characteristics of throat of thick orifice plates [J]. CIESC Journal, 2023, 74(8): 3292-3308.
[9]	Yan GAO, Peng WU, Chao SHANG, Zejun HU, Xiaodong CHEN. Preparation of magnetic agarose microspheres based on a two-fluid nozzle and their protein adsorption properties [J]. CIESC Journal, 2023, 74(8): 3457-3471.
[10]	Hai WANG, Hong LIN, Chen WANG, Haojie XU, Lei ZUO, Junfeng WANG. Investigation of enhanced boiling heat transfer on porous structural surfaces by high voltage electric field [J]. CIESC Journal, 2023, 74(7): 2869-2879.
[11]	Jinming GAO, Yujiao GUO, Chenglin E, Chunxi LU. Study on the separation characteristics of a downstream gas-liquid vortex separator in a closed hood [J]. CIESC Journal, 2023, 74(7): 2957-2966.
[12]	Jinbo JIANG, Xin PENG, Wenxuan XU, Rixiu MEN, Chang LIU, Xudong PENG. Study on leakage characteristics and parameter influence of pump-out spiral groove oil-gas seal [J]. CIESC Journal, 2023, 74(6): 2538-2554.
[13]	Yuanyuan ZHANG, Jiangyuan QU, Xinxin SU, Jing YANG, Kai ZHANG. Gas-liquid mass transfer and reaction characteristics of SNCR denitration in CFB coal-fired unit [J]. CIESC Journal, 2023, 74(6): 2404-2415.
[14]	Xin DONG, Yongrui SHAN, Yinuo LIU, Ying FENG, Jianwei ZHANG. Numerical simulation of bubble plume vortex characteristics for non-Newtonian fluids [J]. CIESC Journal, 2023, 74(5): 1950-1964.
[15]	Zedong WANG, Zhiping SHI, Liyan LIU. Numerical simulation and optimization of acoustic streaming considering inhomogeneous bubble cloud dissipation in rectangular reactor [J]. CIESC Journal, 2023, 74(5): 1965-1973.