Numerical simulation of vortex breakdown in a cylindrical tank with rotating bottom and free surface using level set method

doi:10.1016/j.cjche.2024.10.009

中国化学工程学报 ›› 2025, Vol. 77 ›› Issue (1): 293-300.DOI: 10.1016/j.cjche.2024.10.009

Numerical simulation of vortex breakdown in a cylindrical tank with rotating bottom and free surface using level set method

Zepeng Zhao¹, Qin Li¹, Feng Ye¹, Haoliang Wang², Jianfeng Wang³, Hui Yu¹, Xiangyang Li¹, Chao Yang²

1. School of Chemical Engineering, Sichuan University, Chengdu 610065, China;
2. CAS Key Laboratory of Green Process and Engineering, State Key Laboratory of Petroleum Molecular & Process Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China;
3. School of Ecology and Environment, Zhengzhou University, Zhengzhou 450001, China

收稿日期:2024-08-16 修回日期:2024-10-22 接受日期:2024-10-24 出版日期:2025-01-28 发布日期:2024-11-22
通讯作者: Haoliang Wang,E-mail:hlwang17@ipe.ac.cn;Xiangyang Li,E-mail:xyli2065@scu.edu.cn
基金资助:
National Natural Science Foundation of China (22178228, 22178326) are gratefully acknowledged.

Numerical simulation of vortex breakdown in a cylindrical tank with rotating bottom and free surface using level set method

Zepeng Zhao¹, Qin Li¹, Feng Ye¹, Haoliang Wang², Jianfeng Wang³, Hui Yu¹, Xiangyang Li¹, Chao Yang²

1. School of Chemical Engineering, Sichuan University, Chengdu 610065, China;
2. CAS Key Laboratory of Green Process and Engineering, State Key Laboratory of Petroleum Molecular & Process Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China;
3. School of Ecology and Environment, Zhengzhou University, Zhengzhou 450001, China

Received:2024-08-16 Revised:2024-10-22 Accepted:2024-10-24 Online:2025-01-28 Published:2024-11-22
Contact: Haoliang Wang,E-mail:hlwang17@ipe.ac.cn;Xiangyang Li,E-mail:xyli2065@scu.edu.cn
Supported by:
National Natural Science Foundation of China (22178228, 22178326) are gratefully acknowledged.

摘要/Abstract

摘要： A cylindrical chamber with a rotating bottom holds significant potential for application in cell culture bioreactors due to its ability to generate more stable swirling flows. In order to control vortex breakdown within the chamber, this study first establishes a computational fluid dynamics simulation coupled with the level set method. Verified by experimental results in literature, this method accurately simulates the position and shape of vortex breakdown, and also predicts the critical Reynolds numbers for the appearance and detachment of vortex breakdown bubbles from the center. Additionally, it precisely captures the gas—liquid interface and depicts the vortex breakdown phenomenon in the air above the liquid for the first time. Finally, it predicts the impact of physical property of gas—liquid systems on vortex breakdown in response to significant changes in viscosity of microbial process systems.

关键词: Vortex breakdown, Level set, Microbial cultivation, Micro-bioreactor

Abstract: A cylindrical chamber with a rotating bottom holds significant potential for application in cell culture bioreactors due to its ability to generate more stable swirling flows. In order to control vortex breakdown within the chamber, this study first establishes a computational fluid dynamics simulation coupled with the level set method. Verified by experimental results in literature, this method accurately simulates the position and shape of vortex breakdown, and also predicts the critical Reynolds numbers for the appearance and detachment of vortex breakdown bubbles from the center. Additionally, it precisely captures the gas—liquid interface and depicts the vortex breakdown phenomenon in the air above the liquid for the first time. Finally, it predicts the impact of physical property of gas—liquid systems on vortex breakdown in response to significant changes in viscosity of microbial process systems.

Key words: Vortex breakdown, Level set, Microbial cultivation, Micro-bioreactor

Zepeng Zhao, Qin Li, Feng Ye, Haoliang Wang, Jianfeng Wang, Hui Yu, Xiangyang Li, Chao Yang. Numerical simulation of vortex breakdown in a cylindrical tank with rotating bottom and free surface using level set method[J]. 中国化学工程学报, 2025, 77(1): 293-300.

参考文献

[1] P.G. Saffman, Vortex Dynamics, Cambridge University Press, Cambridge, 1992.
[2] A. Spohn, M. Mory, E.J. Hopfinger, Observations of vortex breakdown in an open cylindrical container with a rotating bottom, Exp. Fluid 14(1) (1993) 70-77.
[3] M. Piva, E. Meiburg, Steady axisymmetric flow in an open cylindrical container with a partially rotating bottom wall, Phys. Fluids 17(6) (2005) 063603.
[4] I.V. Naumov, B.R. Sharifullin, V.N. Shtern, Vortex breakdown in the lower fluid of two-fluid swirling flow, Phys. Fluids 32(1) (2020) 014101.
[5] V. Shtern, Cellular Flows: Topological Metamorphoses in Fluid Dynamics, Cambridge University Press, New York, 2018.
[6] P. Yu, T.S. Lee, Y. Zeng, H.T. Low, Fluid dynamics of a micro-bioreactor for tissue engineering, Fluid Dynam. Mater. Process. 1(3) (2005) 235-246.
[7] P. Yu, T.S. Lee, Y. Zeng, H.T. Low, A numerical analysis of effects of vortex breakdown on oxygen transport in a micro-bioreactor, Int. Commun. Heat Mass Tran. 35(9) (2008) 1141-1146.
[8] L. Mununga, K. Hourigan, M.C. Thompson, T. Leweke, Confined flow vortex breakdown control using a small rotating disk, Phys. Fluids 16(12) (2004) 4750-4753.
[9] J. Dusting, J. Sheridan, K. Hourigan, A fluid dynamics approach to bioreactor design for cell and tissue culture, Biotechnol. Bioeng. 94(6) (2006) 1196-1208.
[10] P. Yu, T.S. Lee, Y. Zeng, H.T. Low, Effect of vortex breakdown on mass transfer in a cell culture bioreactor, Mod. Phys. Lett. B 19(28n29) (2005) 1543-1546.
[11] H.U. Vogel, Experimentelle Ergebnisse uber die laminare Stromung in einem zylindrischen Gehause mit darin rotierender Scheibe, Max-Planck-Inst fur Stromungsforschung, Germany, 1968.
[12] M. Piva, reportEstructuras de recirculacio en un contenedor cilindrico, Ph.D. Thesis, Universidad de Buenos Aires, Argentina, 2000.
[13] I.V. Naumov, B.R. Sharifullin, M.A. Tsoy, V.N. Shtern, Dual vortex breakdown in a two-fluid confined flow, Phys. Fluids 32(6) (2020) 061706.
[14] H.J. Lugt, M. Abboud, Axisymmetric vortex breakdown with and without temperature effects in a container with a rotating lid, J. Fluid Mech. 179(1987) 179-200.
[15] J.M. Lopez, Axisymmetric vortex breakdown, Part 1. Confined swirling flow, J. Fluid Mech. 221(1990) 533-552.
[16] G.L. Brown, J.M. Lopez, Axisymmetric vortex breakdown, Part 2. Physical mechanisms, J. Fluid Mech. 221(1990) 553-576.
[17] M. Tsoy, S. Skripkin, I. Litvinov, Two spiral vortex breakdowns in confined swirling flow, Phys. Fluids 35(6) (2023) 061704.
[18] S.J. Cogan, K. Ryan, G.J. Sheard, The effects of vortex breakdown bubbles on the mixing environment inside a base driven bioreactor, Appl. Math. Model. 35(4) (2011) 1628-1637.
[19] L. Carrion, M.A. Herrada, V.N. Shtern, Topology changes in a water-oil swirling flow, Phys. Fluids 29(3) (2017) 032109.
[20] I.V. Naumov, V.G. Glavny, B.R. Sharifullin, V.N. Shtern, Formation of a thin circulation layer in a two-fluid rotating flow, Phys. Rev. Fluids 4(5) (2019) 054702.
[21] J. Sethian, Level Set Methods and Fast Marching Methods, Cambridge University Press, Cambridge, 1999.
[22] X.Y. Li, Y.F. Wang, G.Z. Yu, C. Yang, Z.S. Mao, A volume-amending method to improve mass conservation of level set approach for incompressible two-phase flows, Sci. China, Ser. B: Chem. 51(11) (2008) 1132-1140.
[23] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, 1980.
[24] S. Chen, B. Merriman, S. Osher, P. Smereka, A simple level set method for solving Stefan problems, J. Comput. Phys. 135(1) (1997) 8-29.
[25] C. Yang, Z.S. Mao, An improved level set approach to the simulation of drop and bubble motion, Chin. J. Chem. Eng. 21(3) (2002) 263-272.
[26] S.J.Y. Lee, H. An, P.C. Wang, J.G. Hang, S.C.M. Yu, Effects of liquid viscosity on bubble formation characteristics in a typical membrane bioreactor, Int. Commun. Heat Mass Tran. 120(2021) 105000.
[27] M. Saavedra del Oso, M. Mauricio-Iglesias, A. Hospido, Evaluation and optimization of the environmental performance of PHA downstream processing, Chem. Eng. J. 412(2021) 127687.
[28] L. Nino, R. Gelves, J. Solsvik, Viscous effects on gas-liquid hydrodynamics for bubble size determinations in different Newtonian and non-Newtonian fluids using a CFD-PBM model, Chem. Eng. Sci. 282(2023) 119324.
[29] F. Raymond, J.M. Rosant, A numerical and experimental study of the terminal velocity and shape of bubbles in viscous liquids, Chem. Eng. Sci. 55(5) (2000) 943-955.

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Numerical simulation of vortex breakdown in a cylindrical tank with rotating bottom and free surface using level set method

Numerical simulation of vortex breakdown in a cylindrical tank with rotating bottom and free surface using level set method

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