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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:
- transverse magnetic field /
- Taylor-Couette flow /
- turbulence /
- large eddy simulation
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图 1 物理模型
Figure 1. Physical model.
图 2 平均周向速度分布曲线 (a) Re = 3000; (b) Re = 5000
Figure 2. Distribution of mean azimuthal velocity: (a) Re = 3000; (b) Re = 5000.
图 3 平均角动量分布曲线 (a) Re = 3000; (b) Re = 5000
Figure 3. Distribution of mean angular momentum (a) Re = 3000; (b) Re = 5000.
图 4 平均速度u+分布 (a) Re = 3000; (b) Re = 5000
Figure 4. Distribution of mean velocity profile u+: (a) Re = 3000; (b) Re = 5000.
图 5 Q = 2000时泰勒涡的演化过程图 (a) Re = 3000; (b) Re = 5000
Figure 5. Diagram of Taylor vortex evolution process with Q = 2000: (a) Re = 3000; (b) Re = 5000.
图 6 Re = 3000工况下子午面平均速度矢量图 (a) x = 0; (b) y = 0
Figure 6. Diagram of mean velocity in the meridian plane at Re = 3000: (a) x = 0; (b) y = 0.
图 7 Re = 5000工况下子午面平均速度矢量图 (a) x = 0; (b) y = 0
Figure 7. Diagram of mean velocity in the meridian plane at Re = 5000: (a) x = 0; (b) y = 0.
图 8 全流场周向速度分布曲线 (a) Re = 3000; (b) Re = 5000
Figure 8. Distribution of the azimuthal velocity in the whole flow field: (a) Re = 3000; (b) Re = 5000.
图 9 x = 0子午面周向速度分布曲线 (a) Re = 3000; (b) Re = 5000
Figure 9. Distribution of the azimuthal velocity in the vertical plane of x = 0: (a) Re = 3000; (b) Re = 5000.
图 10 y = 0子午面周向速度分布曲线 (a) Re = 3000; (b) Re = 5000
Figure 10. Distribution of the azimuthal velocity in the vertical plane of y = 0: (a) Re = 3000; (b) Re = 5000.
图 11 k = 1.01 m2/s2时湍动能分布图 (a) Re = 3000; (b) Re = 5000
Figure 11. Distribution of turbulent kinetic energy with k = 1.01 m2/s2: (a) Re = 3000; (b) Re = 5000.
图 12 Re = 3000工况下湍动能谱 (a) Ha = 0; (b) Ha = 30
Figure 12. Power energy spectra for uθ at Re = 3000: (a) Ha = 0; (b) Ha = 30.
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)
Figure 13. Diagram of Taylor vortex evolution process under the action of axial magnetic field at Re = 3000, Q = 2000.
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[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 物理学报 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
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