横向磁场作用下Taylor-Couette湍流流动的大涡模拟

董帅; 纪祥勇; 李春曦

doi:10.7498/aps.70.20210389

摘要

采用大涡模拟方法对横向磁场作用下导电流体Taylor-Couette湍流流动进行数值模拟, 以研究其运动规律. 计算模型为无限长度, 半径比为1/2. 雷诺数分别选取为3000和5000, 磁场加载方式为全局磁场, 哈特曼数取值0—50. 对磁场作用下泰勒涡的演化过程、速度分布和湍动能分布进行分析, 并与轴向磁场作用下泰勒涡演化过程进行对比. 结果表明: 磁场对流场有显著的抑制作用, 扭曲的泰勒涡在横向磁场的作用下破裂成小尺度涡结构, 并沿磁场方向排列; 在外圆筒和垂直于磁场方向的区域, 磁场抑制效果较强; 随着雷诺数的增加, 磁场抑制效果减弱, 在流场不同区域, 流动呈现出不同的特点. 与轴向磁场相比, 横向磁场对流场的抑制效果较弱, 流场分布呈现出明显的各向异性.

关键词:

Abstract

By the large eddy simulation method, the turbulent Taylor-Couette flow of conducting fluid under a homogenous transverse magnetic field is investigated through using the computational fluid dynamic software ANSYS Fluent 17.0. The flow is confined between two infinitely long cylinders, thus a periodic boundary condition is imposed in the axial direction. The inner cylinder rotates while the outer one is at rest, and their radius ratio is 1/2. Two Reynolds numbers of 3000 and 5000 are considered in the simulations, and the Hartmann number is varied from 0 to 50. In the present study, we assume a lower magnetic Reynolds number $Re_{\rm m} \ll 1$, i.e., the influence of the induced magnetic field on the flow is negligible in comparison with the imposed magnetic field. The evolution of Taylor vortices, velocity profile of mean flow, and turbulent kinetic energy distribution under the transverse magnetic field are analyzed and compared with the results of the axial magnetic field counterpart. It shows that the imposed magnetic field has a significant damping effect on the Taylor-Couette flow. The twisted Taylor vortices break into small-scale vortex structures under the transverse magnetic field and they arrange themselves along the magnetic field. The fluctuations which are perpendicular to the magnetic field are suppressed effectively, while the one which is parallel to the magnetic field is nearly uninfluenced, resulting in quasi-two-dimensional elongated structure in the flow field. As anticipated, in a sufficiently strong magnetic field, the turbulent Taylor-Couette flow may eventually decay to a Couette laminar flow. In the outer cylinder and the area perpendicular to the direction of the magnetic field, the suppression effect is even stronger than those in any other places and fewer vortices are observed in the simulations. The turbulent kinetic energy is transferred firstly from large eddies to intermediate eddies, then to small eddies, and finally dissipated due to the viscous and Joule effect. As the Reynolds number increases, the suppression effect of the magnetic field weakens, and the flow behaves divergently in different areas of the apparatus. Compared with the axial magnetic field, the transverse magnetic field has a weak suppression effect on the flow field, and the profiles of related variables are obviously anisotropic.

Keywords:

作者及机构信息

华北电力大学能源动力与机械工程学院, 保定　071003

通信作者: 李春曦, Leechunxi@163.com

基金项目: 国家自然科学基金(批准号: 12172129, 11302076)、河北省自然科学基金(批准号: A2014502047)和中央高校基本科研业务费专项资金(批准号: 2021MS081)资助的课题

Authors and contacts

School of Energy Power and Mechanical Engineering, North China Electric Power University, Baoding 071003, China

Corresponding author: Li Chun-Xi, Leechunxi@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12172129, 11302076), the Natural Science Foundation of Hebei Province, China (Grant No. A2014502047), and the Fundamental Research Fund for the Central Universities, China (Grant No. 2021MS081)

文章全文

参考文献

[1]	Taylor G I 1923 Philos. Trans. R. Soc. A 223 289 Google Scholar
[2]	Andereck C D, Liu S S, Swinney H L 1986 J. Fluid Mech. 164 155 Google Scholar
[3]	叶立, 蔡小舒, 童正明 2012 化工进展 31 1878 Ye L, Cai X S, Tong Z M 2012 Chem. Ind. Eng. Prog. 31 1878
[4]	Dutta P K, Ray A K 2004 Chem. Eng. Sci. 59 5249 Google Scholar
[5]	Collet Y, Magotte O, Van den Bogaert N, Rolinsky R, Loix F, Jacot M, Regnier V, Marie J M, Dupret F 2012 J. Cryst. Growth 360 18 Google Scholar
[6]	Li Y, Ruan D, Imaishi N, Wu S, Peng L, Zeng D 2003 Int. J. Heat Mass Transfer 46 2887 Google Scholar
[7]	Gao X, Kong B, Vigil R D 2015 Bioresour. Technol. 198 283 Google Scholar
[8]	Gil L V G, Singh H, Da Silva J D S, Santos D P D, Suazo C A T 2020 Biochem. Eng. J. 162 107710 Google Scholar
[9]	Kang B K, Song Y H, Park W K, Kwag S H, Lim B S, Kwon S B, Yang W S, Yoon D H 2017 J. Eur. Ceram. Soc. 37 3673 Google Scholar
[10]	Serov A F, Nazarov A D, Mamonov V N, Terekhov V I 2019 Appl. Energy 251 113362 Google Scholar
[11]	Donnelly R J, Ozima M 1962 Proc. R. Soc. A 266 272 Google Scholar
[12]	Tagawa T, Kaneda M 2005 J. Phys.: Conf. Ser. 14 007 Google Scholar
[13]	Leng X Y, Kolesnikov Y B, Krasnov D, Li B W 2018 Phys. Fluids 30 015107 Google Scholar
[14]	Leng X Y, Yu Y, Li B W 2014 Comput. Fluids 105 16 Google Scholar
[15]	Zhao Y R, Tao J J, Zikanov O 2014 Phys. Rev. E 89 33002 Google Scholar
[16]	Kikura H, Aritomi M, Takeda Y 2005 J. Magn. Magn. Mater. 289 342 Google Scholar
[17]	Davidson P A 1995 J. Fluid Mech. 299 153 Google Scholar
[18]	丁明松, 江涛, 刘庆宗, 董维中, 高铁锁, 傅杨奥骁 2020 69 134702 Google Scholar Ding M S, Jiang T, Liu Q Z, Dong W Z, Gao T S, Fu Y A X 2020 Acta Phys. Sin. 69 134702 Google Scholar
[19]	Kakarantzas S C, Benos L T, Sarris I E, Knaepenc B, Grecos A P, Vlachos N S 2017 Int. J. Heat Fluid Flow 65 342 Google Scholar
[20]	Dong S 2007 J. Fluid Mech. 587 373 Google Scholar
[21]	Cheng W, Pullin D I, Samtaney R 2020 J. Fluid Mech. 890 17 Google Scholar
[22]	赵斌娟, 谢昀彤, 廖文言, 韩璐遥, 付燕霞, 黄忠富 2020 机械工程学报 56 216 Google Scholar Zhao B J, Xie Y T, Liao W Y, Han L Y, Fu Y X, Huang Z F 2020 J. Mech. Eng. 56 216 Google Scholar
[23]	杜珩, 阙夏, 刘难生 2014 中国科学技术大学学报 44 761 Google Scholar Du H, Que X, Liu N S 2014 J. Univ. Sci. Technol. China 44 761 Google Scholar
[24]	Leng X Y, Krasnov D, Kolesnikov Y, Li B W 2017 Magnetohydrodynamics 53 159 Google Scholar

施引文献

图 1 物理模型

Fig. 1. Physical model.

下载: 全尺寸图片幻灯片

图 2 平均周向速度分布曲线　(a) Re = 3000; (b) Re = 5000

Fig. 2. Distribution of mean azimuthal velocity: (a) Re = 3000; (b) Re = 5000.

下载: 全尺寸图片幻灯片

图 3 平均角动量分布曲线　(a) Re = 3000; (b) Re = 5000

Fig. 3. Distribution of mean angular momentum (a) Re = 3000; (b) Re = 5000.

下载: 全尺寸图片幻灯片

图 4 平均速度u⁺分布　(a) Re = 3000; (b) Re = 5000

Fig. 4. Distribution of mean velocity profile u⁺: (a) Re = 3000; (b) Re = 5000.

下载: 全尺寸图片幻灯片

图 5 Q = 2000时泰勒涡的演化过程图　(a) Re = 3000; (b) Re = 5000

Fig. 5. Diagram of Taylor vortex evolution process with Q = 2000: (a) Re = 3000; (b) Re = 5000.

下载: 全尺寸图片幻灯片

图 6 Re = 3000工况下子午面平均速度矢量图　(a) x = 0; (b) y = 0

Fig. 6. Diagram of mean velocity in the meridian plane at Re = 3000: (a) x = 0; (b) y = 0.

下载: 全尺寸图片幻灯片

图 7 Re = 5000工况下子午面平均速度矢量图　(a) x = 0; (b) y = 0

Fig. 7. Diagram of mean velocity in the meridian plane at Re = 5000: (a) x = 0; (b) y = 0.

下载: 全尺寸图片幻灯片

图 8 全流场周向速度分布曲线　(a) Re = 3000; (b) Re = 5000

Fig. 8. Distribution of the azimuthal velocity in the whole flow field: (a) Re = 3000; (b) Re = 5000.

下载: 全尺寸图片幻灯片

图 9 x = 0子午面周向速度分布曲线　(a) Re = 3000; (b) Re = 5000

Fig. 9. Distribution of the azimuthal velocity in the vertical plane of x = 0: (a) Re = 3000; (b) Re = 5000.

下载: 全尺寸图片幻灯片

图 10 y = 0子午面周向速度分布曲线　(a) Re = 3000; (b) Re = 5000

Fig. 10. Distribution of the azimuthal velocity in the vertical plane of y = 0: (a) Re = 3000; (b) Re = 5000.

下载: 全尺寸图片幻灯片

图 11 k = 1.01 m²/s²时湍动能分布图　(a) Re = 3000; (b) Re = 5000

Fig. 11. Distribution of turbulent kinetic energy with k = 1.01 m²/s²: (a) Re = 3000; (b) Re = 5000.

下载: 全尺寸图片幻灯片

图 12 Re = 3000工况下湍动能谱　(a) Ha = 0; (b) Ha = 30

Fig. 12. Power energy spectra for u_θ at Re = 3000: (a) Ha = 0; (b) Ha = 30.

下载: 全尺寸图片幻灯片

图 13 Re = 3000工况下泰勒涡在轴向磁场作用下的演化过程图(Q = 2000)

Fig. 13. Diagram of Taylor vortex evolution process under the action of axial magnetic field at Re = 3000, Q = 2000.

下载: 全尺寸图片幻灯片

map

[1]	Taylor G I 1923 Philos. Trans. R. Soc. A 223 289 Google Scholar
[2]	Andereck C D, Liu S S, Swinney H L 1986 J. Fluid Mech. 164 155 Google Scholar
[3]	叶立, 蔡小舒, 童正明 2012 化工进展 31 1878 Ye L, Cai X S, Tong Z M 2012 Chem. Ind. Eng. Prog. 31 1878
[4]	Dutta P K, Ray A K 2004 Chem. Eng. Sci. 59 5249 Google Scholar
[5]	Collet Y, Magotte O, Van den Bogaert N, Rolinsky R, Loix F, Jacot M, Regnier V, Marie J M, Dupret F 2012 J. Cryst. Growth 360 18 Google Scholar
[6]	Li Y, Ruan D, Imaishi N, Wu S, Peng L, Zeng D 2003 Int. J. Heat Mass Transfer 46 2887 Google Scholar
[7]	Gao X, Kong B, Vigil R D 2015 Bioresour. Technol. 198 283 Google Scholar
[8]	Gil L V G, Singh H, Da Silva J D S, Santos D P D, Suazo C A T 2020 Biochem. Eng. J. 162 107710 Google Scholar
[9]	Kang B K, Song Y H, Park W K, Kwag S H, Lim B S, Kwon S B, Yang W S, Yoon D H 2017 J. Eur. Ceram. Soc. 37 3673 Google Scholar
[10]	Serov A F, Nazarov A D, Mamonov V N, Terekhov V I 2019 Appl. Energy 251 113362 Google Scholar
[11]	Donnelly R J, Ozima M 1962 Proc. R. Soc. A 266 272 Google Scholar
[12]	Tagawa T, Kaneda M 2005 J. Phys.: Conf. Ser. 14 007 Google Scholar
[13]	Leng X Y, Kolesnikov Y B, Krasnov D, Li B W 2018 Phys. Fluids 30 015107 Google Scholar
[14]	Leng X Y, Yu Y, Li B W 2014 Comput. Fluids 105 16 Google Scholar
[15]	Zhao Y R, Tao J J, Zikanov O 2014 Phys. Rev. E 89 33002 Google Scholar
[16]	Kikura H, Aritomi M, Takeda Y 2005 J. Magn. Magn. Mater. 289 342 Google Scholar
[17]	Davidson P A 1995 J. Fluid Mech. 299 153 Google Scholar
[18]	丁明松, 江涛, 刘庆宗, 董维中, 高铁锁, 傅杨奥骁 2020 69 134702 Google Scholar Ding M S, Jiang T, Liu Q Z, Dong W Z, Gao T S, Fu Y A X 2020 Acta Phys. Sin. 69 134702 Google Scholar
[19]	Kakarantzas S C, Benos L T, Sarris I E, Knaepenc B, Grecos A P, Vlachos N S 2017 Int. J. Heat Fluid Flow 65 342 Google Scholar
[20]	Dong S 2007 J. Fluid Mech. 587 373 Google Scholar
[21]	Cheng W, Pullin D I, Samtaney R 2020 J. Fluid Mech. 890 17 Google Scholar
[22]	赵斌娟, 谢昀彤, 廖文言, 韩璐遥, 付燕霞, 黄忠富 2020 机械工程学报 56 216 Google Scholar Zhao B J, Xie Y T, Liao W Y, Han L Y, Fu Y X, Huang Z F 2020 J. Mech. Eng. 56 216 Google Scholar
[23]	杜珩, 阙夏, 刘难生 2014 中国科学技术大学学报 44 761 Google Scholar Du H, Que X, Liu N S 2014 J. Univ. Sci. Technol. China 44 761 Google Scholar
[24]	Leng X Y, Krasnov D, Kolesnikov Y, Li B W 2017 Magnetohydrodynamics 53 159 Google Scholar

计量

文章访问数: 5495
PDF下载量: 79
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

横向磁场作用下Taylor-Couette湍流流动的大涡模拟