适用欧拉-拉格朗日方法模拟气液泡状流的气泡破碎模型

doi:10.11949/0438-1157.20231145

摘要/Abstract

摘要：

欧拉-拉格朗日方法已被广泛应用于模拟鼓泡塔等气-液反应器内的流型、气泡尺寸（或气含率）及其分布。文献中该方法主要基于临界Weber数观点来描述气泡破碎行为，且破碎后的子气泡尺寸由随机数确定。但现有实验和理论研究表明，临界Weber数约束不能体现气体密度等物性参数和泡内气体重分布对气泡破碎行为的影响。针对这些不足，提出了适用欧拉-拉格朗日框架且考虑泡内气体重分布贡献的气泡破碎机理模型，并利用开源软件OpenFOAM开发了基于新破碎模型的求解器。新模型预测结果能较好地吻合实验测量的时均轴向液速、气泡尺寸及其分布等实验数据。特别地，考虑泡内气体重分布现象的破碎机理模型成功预测了实验观测的气泡尺寸双峰分布特征。

关键词: 欧拉-拉格朗日方法, 数学模拟, 鼓泡塔, 气泡, 破碎, 聚并

Abstract:

The Eulerian-Lagrangian method has been widely used to simulate the flow pattern, bubble size (or gas holdup) and its distribution in gas-liquid reactors. However, this method reported in literature is mainly based on the critical Weber number viewpoint to describe the bubble breaking behavior, and the size of the broken sub-bubbles is determined by random numbers. The existing experimental and theoretical studies have shown that the viewpoint of critical Weber number cannot reflect the influence of physical parameters (e.g. gas density) such as gas density and gas redistribution within the bubble on bubble breakup behavior. In view of above shortcomings, this paper proposes a new bubble breakup model suitable for the Eulerian-Lagrangian framework that considers the contribution of gas redistribution mechanism, and develops a solver based on this new model on the basis of open-source software OpenFOAM. The model predictions are in good agreement with the measured time-averaged axial liquid velocity and bubble size distributions. Particularly, the proposed model considering gas redistribution mechanism successfully predicts the bimodal distribution characteristic of bubble size distribution observed in the experiments.

Key words: Eulerian-Lagrangian method, mathematical modeling, bubble column, bubble, breakup, coalescence

中图分类号:

TQ 028.8

韩东, 高宁宁, 唐新德, 龚升高, 夏良树. 适用欧拉-拉格朗日方法模拟气液泡状流的气泡破碎模型[J]. 化工学报, 2024, 75(2): 553-565.

Dong HAN, Ningning GAO, Xinde TANG, Shenggao GONG, Liangshu XIA. Model development for simulating bubble breakup in gas-liquid bubbly flows with the Eulerian-Lagrangian approach[J]. CIESC Journal, 2024, 75(2): 553-565.

图/表 10

图1 气泡破碎过程

Fig.1 Sketch of the dynamic process of a bubble breakup

图2 气泡破碎模拟实施流程

Fig.2 Flowchart of the bubble breakup simulation

图3 不同网格密度下z = 0.2 m截面的时均轴向液体速度

Fig.3 Time-averaged axial liquid velocity at z = 0.2 m for different grid densities

图4 随时间演变的气泡羽流

Fig.4 Bubble plumes with time evolution

图5 对比不同塔高时均轴向液速的模拟值和实验值

Fig.5 Comparison of the simulation and experimental results of time-averaged axial liquid velocity at different heights

图6 z = 0.25 m截面上的ux ′和uz ′预测值与实验值的对比

Fig.6 Comparison of ux ′ and uz ′ obtained from simulations and experiments at section of z = 0.25 m

图7 z = 0.1575、0.25和0.3375 m截面上沿x方向的时均气含率

Fig.7 Time-averaged gas holdup along the x-direction at sections of z = 0.1575, 0.25, and 0.3375 m

图8 0.015 m/s表观气速下鼓泡塔中部和顶部区域内的气泡尺寸分布

Fig.8 Bubble size distribution for gas superficial velocity of 0.015 m/s

图9 表观气速对鼓泡塔顶部区域内气泡尺寸分布的影响

Fig.9 Influence of superficial gas velocity on the bubble size distribution in the top region of bubble column

图10 0.015m/s表观气速下气体密度对鼓泡塔顶部区域内气泡尺寸分布的影响

Fig.10 Effect of gas density on the bubble size distribution in the top region of bubble column with ug = 0.015 m/s

参考文献 46

1	Shi W B, Yang J, Li G, et al. Modelling of breakage rate and bubble size distribution in bubble columns accounting for bubble shape variations[J]. Chemical Engineering Science, 2018, 187: 391-405.
2	曹俊雅, 张绅, 张涛, 等. 上流式反应器气液相间传质特性的实验研究[J]. 化工学报, 2019, 70(10): 3914-3923.
	Cao J Y, Zhang S, Zhang T, et al. Experimental study of gas-liquid mass transfer characteristics in up-flow reactor[J]. CIESC Journal, 2019, 70(10): 3914-3923.
3	Krishna R, Sie S T. Design and scale-up of the Fischer-Tropsch bubble column slurry reactor[J]. Fuel Processing Technology, 2000, 64(1/2/3): 73-105.
4	Sen N, Singh K K, Patwardhan A W, et al. CFD-PBM simulations of a pulsed sieve plate column[J]. Progress in Nuclear Energy, 2019, 111: 125-137.
5	万景, 张霖, 樊亚超, 等. 基于介尺度PBM模型的生物反应器放大模拟及实验研究[J]. 化工学报, 2022, 73(6): 2698-2707.
	Wan J, Zhang L, Fan Y C, et al. Bioreactor scale-up simulation and experimental study based on mesoscale PBM model[J]. CIESC Journal, 2022, 73(6): 2698-2707.
6	Xie L, Liu Q, Luo Z H. A multiscale CFD-PBM coupled model for the kinetics and liquid-liquid dispersion behavior in a suspension polymerization stirred tank[J]. Chemical Engineering Research and Design, 2018, 130: 1-17.
7	袁佳琦, 刘政, 黄锐, 等. 泡状入流条件下旋流泵能量转换特性研究[J]. 化工学报, 2023, 74(9): 3807-3820.
	Yuan J Q, Liu Z, Huang R, et al. Investigation on energy conversion characteristics of vortex pump under bubble inflow[J]. CIESC Journal, 2023, 74(9): 3807-3820.
8	Tran B V, Nguyen D D, Ngo S I, et al. Hydrodynamics and simulation of air-water homogeneous bubble column under elevated pressure[J]. AIChE Journal, 2019, 65(10): e16685.
9	张华海, 王铁峰. CFD-PBM耦合模型模拟气液鼓泡床的通用性研究[J]. 化工学报, 2019, 70(2): 487-495.
	Zhang H H, Wang T F. Generality of CFD-PBM coupled model for simulations of gas-liquid bubble column[J]. CIESC Journal, 2019, 70(2): 487-495.
10	王珏, 杨宁. 基于EMMS方法的鼓泡塔反应器CFD及群平衡模拟[J]. 化工学报, 2017, 68(7): 2667-2677.
	Wang J, Yang N. CFD-PBM simulation with EMMS correctors for bubble column reactors[J]. CIESC Journal, 2017, 68(7): 2667-2677.
11	Hoppe F, Breuer M. A deterministic and viable coalescence model for Euler-Lagrange simulations of turbulent microbubble-laden flows[J]. International Journal of Multiphase Flow, 2018, 99: 213-230.
12	Luo H A, Svendsen H F. Theoretical model for drop and bubble breakup in turbulent dispersions[J]. AIChE Journal, 1996, 42(5): 1225-1233.
13	Solsvik J, Jakobsen H A. Single air bubble breakup experiments in stirred water tank[J]. International Journal of Chemical Reactor Engineering, 2015, 13(4): 477-491.
14	Han L C, Gong S G, Ding Y W, et al. Consideration of low viscous droplet breakage in the framework of the wide energy spectrum and the multiple fragments[J]. AIChE Journal, 2015, 61(7): 2147-2168.
15	Lau Y M, Bai W, Deen N G, et al. Numerical study of bubble break-up in bubbly flows using a deterministic Euler-Lagrange framework[J]. Chemical Engineering Science, 2014, 108: 9-22.
16	Darmana D, Deen N G, Kuipers J A M. Parallelization of an Euler-Lagrange model using mixed domain decomposition and a mirror domain technique: application to dispersed gas-liquid two-phase flow[J]. Journal of Computational Physics, 2006, 220(1): 216-248.
17	Sungkorn R, Derksen J J, Khinast J G. Euler-Lagrange modeling of a gas-liquid stirred reactor with consideration of bubble breakage and coalescence[J]. AIChE Journal, 2012, 58(5): 1356-1370.
18	Prince M J, Blanch H W. Bubble coalescence and break-up in air-sparged bubble columns[J]. AIChE Journal, 1990, 36(10): 1485-1499.
19	Martínez-Bazán C, Montañés J L, Lasheras J C. On the breakup of an air bubble injected into a fully developed turbulent flow(Part 1): Breakup frequency[J]. Journal of Fluid Mechanics, 1999, 401: 157-182.
20	Hoppe F, Breuer M. A deterministic breakup model for Euler-Lagrange simulations of turbulent microbubble-laden flows[J]. International Journal of Multiphase Flow, 2020, 123: 103119.
21	Hagesaether L, Jakobsen H A, Svendsen H F. A model for turbulent binary breakup of dispersed fluid particles[J]. Chemical Engineering Science, 2002, 57(16): 3251-3267.
22	Martínez-Bazán C, Montañés J L, Lasheras J C. On the breakup of an air bubble injected into a fully developed turbulent flow(Part 2): Size PDF of the resulting daughter bubbles[J]. Journal of Fluid Mechanics, 1999, 401: 183-207.
23	Han L C, Luo H A, Liu Y J. A theoretical model for droplet breakup in turbulent dispersions[J]. Chemical Engineering Science, 2011, 66(4): 766-776.
24	Wilkinson P M, Van Schayk A, Spronken J P M, et al. The influence of gas density and liquid properties on bubble breakup[J]. Chemical Engineering Science, 1993, 48(7): 1213-1226.
25	Keim N C. Perturbed breakup of gas bubbles in water: memory, gas flow, and coalescence[J]. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 2011, 83(5 Pt 2): 056325.
26	Li B B, Zhang H C, Lu J, et al. Experimental investigation of the effect of ambient pressure on laser-induced bubble dynamics[J]. Optics & Laser Technology, 2011, 43(8): 1499-1503.
27	Andersson R, Andersson B. On the breakup of fluid particles in turbulent flows[J]. AIChE Journal, 2006, 52(6): 2020-2030.
28	Ravelet F, Colin C, Risso F. On the dynamics and breakup of a bubble rising in a turbulent flow[J]. Physics of Fluids, 2011, 23(10): 103301.
29	Zhang H H, Wang Y L, Sayyar A, et al. Experimental study on breakup of a single bubble in a stirred tank: effect of gas density and liquid properties[J]. AIChE Journal, 2023, 69(1): e17511.
30	Zhang H H, Wang Y L, Sayyar A, et al. A CFD-PBM coupled model under entire turbulent spectrum for simulating a bubble column with highly viscous media[J]. AIChE Journal, 2023, 69(1): e17473.
31	张华海, 王悦琳, 李邦昊, 等. 湍流中气泡破碎建模与实验研究进展[J]. 化工学报, 2021, 72(12): 5936-5954.
	Zhang H H, Wang Y L, Li B H, et al. Review of bubble breakup modelling and experimental study in turbulent flow[J]. CIESC Journal, 2021, 72(12): 5936-5954.
32	Lehr F, Mewes D. A transport equation for the interfacial area density applied to bubble columns[J]. Chemical Engineering Science, 2001, 56(3): 1159-1166.
33	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.
34	Lehr F, Millies M, Mewes D. Bubble-size distributions and flow fields in bubble columns[J]. AIChE Journal, 2002, 48(11): 2426-2443.
35	Xing C T, Wang T F, Guo K Y, et al. A unified theoretical model for breakup of bubbles and droplets in turbulent flows[J]. AIChE Journal, 2015, 61(4): 1391-1403.
36	Zhang H H, Yang G Y, Sayyar A, et al. An improved bubble breakup model in turbulent flow[J]. Chemical Engineering Journal, 2020, 386: 121484.
37	Xue J, Chen F G, Yang N, et al. Eulerian-Lagrangian simulation of bubble coalescence in bubbly flow using the spring-dashpot model[J]. Chinese Journal of Chemical Engineering, 2017, 25(3): 249-256.
38	Zhang X S, Wang J H, Wan D C. Euler-Lagrange study of bubble breakup and coalescence in a turbulent boundary layer for bubble drag reduction[J]. Physics of Fluids, 2021, 33(3): 037105.
39	Sommerfeld M, Bourloutski E, Bröder D. Euler/Lagrange calculations of bubbly flows with consideration of bubble coalescence[J]. The Canadian Journal of Chemical Engineering, 2003, 81(3/4): 508-518.
40	Jain D, Kuipers J A M, Deen N G. Numerical study of coalescence and breakup in a bubble column using a hybrid volume of fluid and discrete bubble model approach[J]. Chemical Engineering Science, 2014, 119: 134-146.
41	Smagorinsky J. General circulation experiments with the primitive equations[J]. Monthly Weather Review, 1963, 91(3): 99-164.
42	Yan X K, Zheng K X, Jia Y, et al. Drag coefficient prediction of a single bubble rising in liquids[J]. Industrial & Engineering Chemistry Research, 2018, 57(15): 5385-5393.
43	Tomiyama A. Struggle with computational bubble dynamics[J]. Multiphase Science and Technology, 1998, 10(4): 369-405.
44	Deen N G, Solberg T, Hjertager B H. Large eddy simulation of the gas-liquid flow in a square cross-sectioned bubble column[J]. Chemical Engineering Science, 2001, 56(21/22): 6341-6349.
45	Lau Y M, Sujatha K T, Gaeini M, et al. Experimental study of the bubble size distribution in a pseudo-2D bubble column[J]. Chemical Engineering Science, 2013, 98: 203-211.
46	Zhou Y J, Zhao C R, Ji B Q, et al. Numerical simulation of bubbly flow using partially averaged Navier-Stokes simulation and a path oscillation model in the Euler-Lagrange approach[J]. Industrial & Engineering Chemistry Research, 2021, 60(10): 4120-4130.

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