Lattice Boltzmann model for interface capturing of multiphase flows based on Allen-Cahn equation

doi:10.1088/1674-1056/ac11d8

中国物理B ›› 2022, Vol. 31 ›› Issue (2): 24701-024701.doi: 10.1088/1674-1056/ac11d8

Lattice Boltzmann model for interface capturing of multiphase flows based on Allen-Cahn equation

He Wang(王贺)¹, Fang-Bao Tian(田方宝)², and Xiang-Dong Liu(刘向东)^1,3,†

1 Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, China;
2 School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia;
3 College of Electrical, Energy and Power Engineering, Yangzhou University, Yangzhou 225127, China

收稿日期:2021-04-26 修回日期:2021-06-28 接受日期:2021-07-07 出版日期:2022-01-13 发布日期:2022-01-25
通讯作者: Xiang-Dong Liu E-mail:liuxd@yzu.edu.cn

Lattice Boltzmann model for interface capturing of multiphase flows based on Allen-Cahn equation

He Wang(王贺)¹, Fang-Bao Tian(田方宝)², and Xiang-Dong Liu(刘向东)^1,3,†

1 Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, China;
2 School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia;
3 College of Electrical, Energy and Power Engineering, Yangzhou University, Yangzhou 225127, China

Received:2021-04-26 Revised:2021-06-28 Accepted:2021-07-07 Online:2022-01-13 Published:2022-01-25
Contact: Xiang-Dong Liu E-mail:liuxd@yzu.edu.cn

摘要/Abstract

摘要： A phase-field-based lattice Boltzmann model is proposed for the interface capturing of multi-phase flows based on the conservative Allen-Cahn equation (ACE). By adopting the improved form of a relaxation matrix and an equilibrium distribution function, the time derivative ∂_t(φu) induced by recovering the diffusion term in ACE is eliminated. The conducted Chapman-Enskog analysis demonstrates that the correct conservative ACE is recovered. Four benchmark cases including Zalesak's disk rotation, vortex droplet, droplet impact on thin film, and Rayleigh-Taylor instability are investigated to validate the proposed model. The numerical results indicate that the proposed model can accurately describe the complex interface deformation.

关键词: lattice Boltzmann method, phase field, multiphase flow

Abstract: A phase-field-based lattice Boltzmann model is proposed for the interface capturing of multi-phase flows based on the conservative Allen-Cahn equation (ACE). By adopting the improved form of a relaxation matrix and an equilibrium distribution function, the time derivative ∂_t(φu) induced by recovering the diffusion term in ACE is eliminated. The conducted Chapman-Enskog analysis demonstrates that the correct conservative ACE is recovered. Four benchmark cases including Zalesak's disk rotation, vortex droplet, droplet impact on thin film, and Rayleigh-Taylor instability are investigated to validate the proposed model. The numerical results indicate that the proposed model can accurately describe the complex interface deformation.

Key words: lattice Boltzmann method, phase field, multiphase flow

中图分类号: (Computational methods in fluid dynamics)

47.11.-j

47.61.Jd (Multiphase flows) 47.11.Qr (Lattice gas)

He Wang(王贺), Fang-Bao Tian(田方宝), and Xiang-Dong Liu(刘向东). Lattice Boltzmann model for interface capturing of multiphase flows based on Allen-Cahn equation[J]. 中国物理B, 2022, 31(2): 24701-024701.

He Wang(王贺), Fang-Bao Tian(田方宝), and Xiang-Dong Liu(刘向东). Lattice Boltzmann model for interface capturing of multiphase flows based on Allen-Cahn equation[J]. Chin. Phys. B, 2022, 31(2): 24701-024701.

参考文献

[1] Dbouk T and Drikakis D 2020 Phys. Fluids 32 053310
[2] Gao W and Chen Y 2019 Int. J. Heat Mass Tran. 135 158
[3] Gerritsen M G and Durlofsky L J 2005 Annu. Rev. Fluid Mech. 37 211
[4] Wu L Y, Liu L B, Han X T, Li Q W and Yang W B 2019 Chin. Phys. B 28 104702
[5] Gao W, Yu C and Yao F 2020 Chin. Phys. B 29 054702
[6] Gao Y J, Jiang H Q, Li J J, Zhao Y Y, Hu J C and Chang Y H 2017 Acta Phys. Sin. 66 024702 (in Chinese)
[7] Zhao K, She Y Z, Jiang Y L, Qin J and Zhang Z H 2019 Acta Phys. Sin. 68 244401 (in Chinese)
[8] Liu H, Zhang Y and Valocchi A J 2015 Phys. Fluids 27 052103
[9] Ma J, Wang Z, Young J, Lai J C S, Sui Y and Tian F B 2020 J. Comput. Phys. 415 109487
[10] Xu L, Tian F B, Young J and Lai J C S 2018 J. Comput. Phys. 375 22
[11] Zhang Z D, Cao Y T, Sun D K, Xing H, Wang J C and Ni Z H 2020 Chin. Phys. B 29 028103
[12] Gunstensen A K, Rothman D H, Zaleski S and Zanetti G 1991 Phys. Rev. A 43 4320
[13] Liu H, Valocchi A J and Kang Q 2012 Phys. Rev. E 85 069901
[14] Wen Z X, Li Q, Yu Y and Luo K H 2019 Phys. Rev. E 100 023301
[15] Inamuro T, Konishi N and Ogino F 2000 Comput. Phys. Commun. 129 32
[16] Pooley C M and Furtado K 2008 Phys. Rev. E 77 046702
[17] Swift M R, Orlandini E, Osborn W R and Yeomans J M 1996 Phys. Rev. E 54 5041
[18] Li Q, Luo K H and Li X J 2013 Phys. Rev. E 87 053301
[19] Shan X W and Chen H D 1993 Phys. Rev. E 47 1815
[20] Zhang Q Y, Sun D K and Zhu M F 2017 Chin. Phys. B 26 084701
[21] Fakhari A and Rahimian M H 2010 Phys. Rev. E 81 036707
[22] Geier M, Fakhari A and Lee T 2015 Phys. Rev. E 91 063309
[23] He X Y, Chen S Y and Zhang R Y 1999 J. Comput. Phys. 152 642
[24] Lee T and Lin C L 2005 J. Comput. Phys. 206 16
[25] Liang H, Shi B C, Guo Z L and Chai Z H 2014 Phys. Rev. E 89 053320
[26] Ren F, Song B, Sukop M C and Hu H 2016 Phys. Rev. E 94 023311
[27] Zheng H W, Shu C and Chew Y T 2005 Phys. Rev. E 72 056705
[28] Zheng H W, Shu C and Chew Y T 2006 J. Comput. Phys. 218 353
[29] Zu Y Q and He S 2013 Phys. Rev. E 87 043301
[30] Huang H, Huang J J, Lu X Y and Sukop M C 2013 Int. J. Mod. Phys. C 24 1350021
[31] Chai Z, Sun D, Wang H and Shi B 2018 Int. J. Heat Mass Transfer 122 631
[32] Wang H L, Chai Z H, Shi B C and Liang H 2016 Phys. Rev. E 94 033304
[33] Liang H, Xu J, Chen J, Wang H, Chai Z and Shi B 2018 Phys. Rev. E 97 033309
[34] Marié S, Ricot D and Sagaut P 2009 J. Comput. Phys. 228 1056
[35] Xu H, Malaspinas O and Sagaut P 2012 J. Comput. Phys. 231 7335
[36] Xu H and Sagaut P 2011 J. Comput. Phys. 230 5353
[37] Chiu P H and Lin Y T 2011 J. Comput. Phys. 230 185
[38] Huang R and Wu H 2014 J. Comput. Phys. 274 50
[39] Yarin A L 2006 Annu. Rev. Fluid Mech. 38 159
[40] Coppola G, Rocco G and de Luca L 2011 Phys. Fluids 23 022105
[41] Josserand C and Zaleski S 2003 Phys. Fluids 15 1650
[42] Rioboo R, Tropea C and Marengo M 2001 Atomizat. Sprays 11 155
[43] Ramaprabhu P, Dimonte G, Young Y N, Calder A C and Fryxell B 2006 Phys. Rev. E 74 066308
[44] Goncharov V N 2002 Phys. Rev. Lett. 88 134502
[45] Waddell J T, Niederhaus C E and Jacobs J W 2001 Phys. Fluids 13 1263
[46] Ding H, Spelt P D M and Shu C 2007 J. Comput. Phys. 226 2078
[47] Shao J Y and Shu C 2015 Int. J. Numer. Methods Fluids 77 526

Lattice Boltzmann model for interface capturing of multiphase flows based on Allen-Cahn equation

Lattice Boltzmann model for interface capturing of multiphase flows based on Allen-Cahn equation

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Pei-Feng Lin(林培锋), Xiao Hu(胡箫), and Jian-Zhong Lin(林建忠). Inertial focusing and rotating characteristics of elliptical and rectangular particle pairs in channel flow[J]. 中国物理B, 2022, 31(8): 80501-080501.
[2]	Peichan Wu(吴锫婵), Yuhan Yan(严妤函), Huan Zhu(朱欢), Juan Shi(施娟), and Zhenqian Chen(陈振乾). Hemodynamics of aneurysm intervention with different stents[J]. 中国物理B, 2022, 31(6): 64701-064701.
[3]	Chang-Sheng Zhu(朱昶胜), Zi-Hao Gao(高梓豪), Peng Lei(雷鹏), Li Feng(冯力), and Bo-Rui Zhao(赵博睿). Multi-phase field simulation of competitive grain growth for directional solidification[J]. 中国物理B, 2022, 31(6): 68102-068102.
[4]	Xiaowen Shen(沈晓文) and Qi Wang(王奇). Thermodynamically consistent model for diblock copolymer melts coupled with an electric field[J]. 中国物理B, 2022, 31(4): 48201-048201.
[5]	Le Bai(柏乐), Ming-Lei Shan(单鸣雷), Yu Yang(杨雨), Na-Na Su(苏娜娜), Jia-Wen Qian(钱佳文), and Qing-Bang Han(韩庆邦). Effect of viscosity on stability and accuracy of the two-component lattice Boltzmann method with a multiple-relaxation-time collision operator investigated by the acoustic attenuation model[J]. 中国物理B, 2022, 31(3): 34701-034701.
[6]	Chang-Sheng Zhu(朱昶胜), Ting Wang(汪婷), Li Feng(冯力), Peng Lei(雷鹏), and Fang-Lan Ma(马芳兰). Numerical study of growth competition between twin grains during directional solidification by using multi-phase field method[J]. 中国物理B, 2022, 31(2): 28102-028102.
[7]	Mei-Rong Jiang(姜美荣), Jun-Jie Li(李俊杰), Zhi-Jun Wang(王志军), and Jin-Cheng Wang(王锦程). Effect of interface anisotropy on tilted growth of eutectics: A phase field study[J]. 中国物理B, 2022, 31(10): 108101-108101.
[8]	宋先钊, 李斌, 解立峰. Experimental investigation on the properties of liquid film breakup induced by shock waves[J]. 中国物理B, 2020, 29(8): 86201-086201.
[9]	张庆宇, 孙东科, 章顺虎, 王辉, 朱鸣芳. Modeling of microporosity formation and hydrogen concentration evolution during solidification of an Al-Si alloy[J]. 中国物理B, 2020, 29(7): 78104-078104.
[10]	朱昶胜, 胡震, 王凯明. Multi-bubble motion behavior of uniform magnetic field based on phase field model[J]. 中国物理B, 2020, 29(3): 34702-034702.
[11]	覃章荣, 陈燕雁, 凌风如, 孟令娟, 张超英. A mass-conserved multiphase lattice Boltzmann method based on high-order difference[J]. 中国物理B, 2020, 29(3): 34701-034701.
[12]	张兆栋, 曹宇婷, 孙东科, 邢辉, 王锦程, 倪中华. A numerical study on pattern selection in crystal growth by using anisotropic lattice Boltzmann-phase field method[J]. 中国物理B, 2020, 29(2): 28103-028103.
[13]	朱昶胜, 韩丹, 冯力, 徐升. Multi-bubble motion behavior of electric field based on phase field model[J]. 中国物理B, 2019, 28(3): 34701-034701.
[14]	左鸿, 邓守春, 李海波. Boundary scheme for lattice Boltzmann modeling of micro-scale gas flow in organic-rich pores considering surface diffusion[J]. 中国物理B, 2019, 28(3): 30202-030202.
[15]	朱昶胜, 韩丹, 徐升. Phase field simulation of single bubble behavior under an electric field[J]. 中国物理B, 2018, 27(9): 94704-094704.