Characterization of Rayleigh Convection in Interfacial Mass Transfer by Lattice Boltzmann Simulation and Experimental Verification

Abstract

Abstract: Concentration gradient induced Rayleigh convection can influence effectively interfacial mass transfer processes, but the convection phenomena are known as mesoscopic and complex. In order to investigate this phenomenon, a two-equation Lattice Boltzmann Method (LBM) is proposed to simulate the velocity and the concentra-tion distributions of Rayleigh convection generated in the CO₂ absorption into ethanol liquid. The simulated results on velocity distributions are experimentally verified by PIV (particle image velocimetry technique) measurements. In order to simplify the analysis, the convection in the simulation as well as in the experiment, the Rayleigh convection was manipulated into a single down flow pattern. The simulated results show that the concentration contours agree qualitatively with the schlieren images in the literature. The experimental and simulated results show that the Rayleigh convection under investigation is dominated by the flow in the downward direction and impels exchange of the liquid between the interfacial vicinity and the liquid bulk promoting the renewal of interfacial liquid, and hence enhances mass transfer. The comparison between the simulated and experimental results demonstrated that the proposed LBM is a promising alternative for simulating mass transfer induced Rayleigh convection.

Key words: Rayleigh convection, lattice Boltzmann method, particle image velocimetry, interfacial mass transfer, instantaneous mass flux

摘要： Concentration gradient induced Rayleigh convection can influence effectively interfacial mass transfer processes, but the convection phenomena are known as mesoscopic and complex. In order to investigate this phenomenon, a two-equation Lattice Boltzmann Method (LBM) is proposed to simulate the velocity and the concentra-tion distributions of Rayleigh convection generated in the CO₂ absorption into ethanol liquid. The simulated results on velocity distributions are experimentally verified by PIV (particle image velocimetry technique) measurements. In order to simplify the analysis, the convection in the simulation as well as in the experiment, the Rayleigh convection was manipulated into a single down flow pattern. The simulated results show that the concentration contours agree qualitatively with the schlieren images in the literature. The experimental and simulated results show that the Rayleigh convection under investigation is dominated by the flow in the downward direction and impels exchange of the liquid between the interfacial vicinity and the liquid bulk promoting the renewal of interfacial liquid, and hence enhances mass transfer. The comparison between the simulated and experimental results demonstrated that the proposed LBM is a promising alternative for simulating mass transfer induced Rayleigh convection.

关键词: Rayleigh convection, lattice Boltzmann method, particle image velocimetry, interfacial mass transfer, instantaneous mass flux

FU Bo, YUAN Xigang, LIU Botan, CHEN Shuyong, ZHANG Huishu, ZENG Aiwu, YU Guocong. Characterization of Rayleigh Convection in Interfacial Mass Transfer by Lattice Boltzmann Simulation and Experimental Verification[J]. , 2011, 19(5): 845-854.

付博, 袁希钢, 刘伯潭, 陈淑勇, 张会书, 曾爱武, 余国琮. Characterization of Rayleigh Convection in Interfacial Mass Transfer by Lattice Boltzmann Simulation and Experimental Verification[J]. , 2011, 19(5): 845-854.

References

1 Rayleigh, L., “On convection currents in a horizontal layer of fluid when the higher temperature is on the under side”, Phil. Mag., 32, 529-546 (1916).
2 Grahn, A., “Two-dimensional numerical simulations of MarangoniBénard instabilities during liquid-liquid mass transfer in a vertical gap”, Chem. Eng. Sci., 61, 3586-3592 (2006).
3 Sun, Z.F., Yu, K.T., Wang, S.Y., Miao, Y.Z., “Absorption and desorption of carbon dioxide into and from organic solvents:effect of Rayleigh and Marangoni instability”, Ind. Eng. Chem. Res., 41 (7), 1905-1913 (2002).
4 Arend, B., Dittmar, D., Eggers, R., “Interaction of interfacial convection and mass transfer effects in the system CO₂-water”, Int. J. Heat Mass Transfer, 47, 3649-3657 (2004).
5 Kim, M.C., Yoon, D.Y., Choi, C.K., “Onset of buoyancy-driven instability in gas diffusion systems”, Ind. Eng. Chem. Res., 45, 7321-7328 (2006).
6 Sun, Z.F., Fahmy, M., “Onset of Rayleigh-Bénard-Marangoni convection in gas-liquid mass transfer with two-phase flow:theory”, Ind. Eng. Chem. Res., 45, 6325-6329 (2006).
7 Kutepov, A.M., Pokusaev, B.G., Kazenin, D.A., Karlov, S.P., Vyaz’min, A.V., “Interfacial mass transfer in the liquid-gas system:an optical study”, Theor. Found. Chem. Eng., 35 (3), 213-216 (2001).
8 Okhotsimskiis, A., Hozawa, M., “Schlieren visualization of natural convection in binary gas-liquid systems”, Chem. Eng. Sci., 53 (14), 2547-2573 (1998).
9 Chen, W., “Experimental measurement of gas-liquid interfacial Rayleigh-Bénard-Marangoni convection and mass transfer”, Ph. D. Thesis, Tianjin Univ., China (2010). (in Chinese)
10 Sha, Y., Chen, H.L., Yin, Y.W., Tu, S., Ye, L.Y., Zheng, Y.M., “Characteristics of the Marangoni convection induced in initial quiescent water”, Ind. Eng. Chem. Res., 49, 8770-8777 (2010).
11 Mussa, M.A., Abdullah, S., Nor Azwadi, C.S., Muhamad, N., “Simulation of natural convection heat transfer in an enclosure by the lattice-Boltzmann method”, Computers Fluids, 44, 162-168 (2011).
12 Mohamad, A.A., El-Ganaoui, M., Bennacer, R., “Lattice Boltzmann simulation of natural convection in an open ended cavity”, Int. J. Therm. Sci., 48 (10), 1870-1875 (2009).
13 Ma, C.F., “Lattice BGK simulations of double diffusive natural convection in a rectangular enclosure in the presences of magnetic field and heat source”, Nonlinear Anal. Real World Appl., 10, 2666-2678 (2009).
14 Verhaeghe, F., Blanpain, B., Wollants, P., “Lattice Boltzmann method for double-diffusive natural convection”, Phys. Rev. E, 75 (4), 046705 (2007).
15 Lishchuk, S.V., Halliday, I., Care, C.M., “Multicomponent lattice Boltzmann method for fluids with a density contrast”, Phys. Rev. E, 77 (3), 036702 (2008).
16 He, X.Y., Chen, S.Y., Zhang, R.Y., “A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability”, J. Comput. Phys., 152, 642-663 (1999).
17 Aaltosalmi, U., “Fluid flow in porous media with the lattice-Boltzmann method”, Ph D Thesis, University of Jyv skyl,Finland (2005).
18 Chen, S., “A large-eddy-based lattice Boltzmann model for turbulent flow simulation”, Appl. Math. Comput., 215, 591-598 (2009).
19 Chen, S.Y., Doolen, G.D., “Lattice Boltzmann method for fluid flows”, Annu. Rev. Fluid Mech., 30, 329-364 (1998).
20 Inamuro, T., Yoshino, M., Inoue, H., Mizuno, R., Ogino, F., “A lattice Boltzmann method for a binary miscible fluid mixture and its application to a heat-transfer problem”, J. Comput. Phys., 179, 201-215 (2002).
21 Qian, Y.H., D'Humieres, D., Lallemand, P., “Lattice BGK models for Navier-Stokes equation”, Europhys. Lett., 17 (6), 479-484 (1992).
22 Bhatnagar, P.L., Gross, E.P., Krook, M., “A model for collision processes in gases. I. small amplitude processes in charged and neutral one-component systems”, Phys. Rev., 94 (3), 511-525 (1954).
23 Shan, X.W., “Simulation of Rayleigh-Bénard convection using a lattice Boltzmann method”, Phys. Rev. E, 55 (3), 2780-2788 (1997).
24 Buick, J.M., Greated, C.A., “Gravity in a lattice Boltzmann model”, Physical Review E., 61 (5), 5307-5320 (2000).
25 Sukop, M.C., Thorne, D.T. Jr., Lattice Boltzmann Modeling:An Introduction for Geoscientists and Engineers, Springer, Heidelberg, Netherlands, 1-171 (2006).
26 Shi, Y., Zhao, T.S., Guo, Z.L., “Finite difference-based lattice Boltzmann simulation of natural convection heat transfer in a horizontal concentric annulus”, Computers Fluids, 35, 1-15 (2006).
27 Tan, K.K., Thorpe, R.B., “The onset of convection induced by buoyancy during gas diffusion in deep fluids”, Chem. Eng. Sci., 54, 4179-4187 (1999).
28 Treybal, R.E., Mass Transfer Operations, McGraw-Hill Book Company, New York, 25-26 (1955).
29 Takahashi, M., Kobayashi, Y., “Diffusion coefficients and solubilities of carbon dioxide in binary mixed solvents”, J. Chem. Eng. Data, 27, 328-331 (1982).
30 Phillips, T.W., Murphy, K.P., “Liquid viscosity of halocarbons”, J. Chem. Eng. Data, 15 (2), 304-307 (1970).
31 Ma, Y.G., Yu, G.C., Li, H.Z., “Note on the mechanism of interfacial mass transfer of absorption processes”, Int. J. Heat Mass Transfer, 48, 3454-3460 (2005).
32 Cussler, E.L., Diffusion:Mass Transfer in Fluid Systems, 3rd ed., Cambridge University Press, New York, 26-30 (2009).

[1]	Junhao Wang, Shugang Ma, Peng Chen, Zhipeng Li, Zhengming Gao, J. J. Derksen. Mixing of miscible shear-thinning fluids in a lid-driven cavity [J]. Chinese Journal of Chemical Engineering, 2023, 58(6): 112-123.
[2]	Shidong Xue, Jingkun Han, Xi Xi, Junyi Zhao, Zhong Lan, Rongfu Wen, Xuehu Ma. Rapid velocity reduction and drift potential assessment of off-nozzle pesticide droplets [J]. Chinese Journal of Chemical Engineering, 2022, 46(6): 243-254.
[3]	Huina Wang, Xiaoxia Duan, Xin Feng, Zai-Sha Mao, Chao Yang. Effect of impeller type and scale-up on spatial distribution of shear rate in a stirred tank [J]. Chinese Journal of Chemical Engineering, 2022, 42(2): 351-363.
[4]	Longyun Zheng, Kai Guo, Hongwei Cai, Bo Zhang, Hui Liu, Chunjiang Liu. Investigation of mass transfer model of CO₂ absorption with Rayleigh convection using multi-relaxation time lattice Boltzmann method [J]. Chinese Journal of Chemical Engineering, 2022, 50(10): 130-142.
[5]	Xifan Duan, Zhiguo Yuan, Youzhi Liu, Hangtian Li, Weizhou Jiao. Numerical simulation and experimental study of the characteristics of packing feature size on liquid flow in a rotating packed bed [J]. Chinese Journal of Chemical Engineering, 2021, 34(6): 22-31.
[6]	Saeed Nahidi, Iraj Jafari Gavzan, Seyfolah Saedodin, Mahmoud Salari. Experimental investigation on the effect of surface characterization of electrodes on the gas bubble dynamics in electrolyte flow and performance of FLA batteries by using PIV [J]. Chinese Journal of Chemical Engineering, 2021, 33(5): 30-39.
[7]	Lele Feng, Hai Zhang, Lilin Hu, Yang Zhang, Yuxin Wu, Yuzhao Wang, Hairui Yang. Classification performance of model coal mill classifiers with swirling and non-swirling inlets [J]. Chinese Journal of Chemical Engineering, 2020, 28(3): 777-784.
[8]	Deyu Luan, Yiming Chen, Hong Wang, Yue Wang, Xing Wei. Chaotic characteristics of pseudoplastic fluid induced by 6PBT impeller in a stirred vessel [J]. Chin.J.Chem.Eng., 2019, 27(2): 293-297.
[9]	Lichen He, Weimin Yang, Changfeng Guan, Hua Yan, Lin Zheng, Xiahua Zuo. Experimental investigation on flow characteristics in circular tube inserted with rotor-assembled strand using PIV [J]. Chin.J.Chem.Eng., 2019, 27(1): 1-9.
[10]	Shuli Shu, Ning Yang. Numerical study and acceleration of LBM-RANS simulation of turbulent flow [J]. Chin.J.Chem.Eng., 2018, 26(1): 31-42.
[11]	Weicheng Xu, Yumei Yong, Junbo Xu, Chao Yang. Effect of surface property on mass flux in a variable-section microchannel [J]. , 2017, 25(4): 401-407.
[12]	Guoneng Li, Youqu Zheng, Huawen Yang, Wenwen Guo, Yousheng Xu. Lattice Boltzmann simulation of a laminar square jet in cross flows [J]. Chin.J.Chem.Eng., 2016, 24(11): 1505-1512.
[13]	Wei Chen, Shuyong Chen, Xigang Yuan, Huishu Zhang, Kuotsung Yu. Three-dimensional simulation of interfacial convection in CO₂-ethanol system by hybrid lattice Boltzmann method with experimental validation [J]. , 2015, 23(2): 356-365.
[14]	Abdelmalek Atia, Kamal Mohammedi. Pore-scale study based on lattice Boltzmann method of density driven natural convection during CO₂ injection project [J]. , 2015, 23(10): 1593-1602.
[15]	Mohsen Nazari, Ladan Louhghalam, Mohamad Hassan Kayhani. Lattice Boltzmann simulation of double diffusive natural convection in a square cavity with a hot square obstacle [J]. Chin.J.Chem.Eng., 2015, 23(1): 22-30.