磁场作用下导电流体的流动稳定性研究进展

doi:10.16085/j.issn.1000-6613.2017-0398

摘要/Abstract

摘要： 磁场作用下导电流体的流动稳定性研究在电磁材料制备过程以及核聚变反应堆冷却系统的设计与制造有重要意义。文中简述了流动稳定性研究的主要方法，分析了正则模态和非正则模态两种方法的利弊，因两类方法所考察的扰动的增长形式不同，其结论往往不一致；对近十几年磁场作用下导电流体在不同形状管道内的流动稳定性研究进展进行了分类和概述，主要介绍了磁场方向、壁面导电率对流动稳定性的影响；针对相关实验的开展、稳定性分析方法以及对转捩机理的研究等提出了可能值得深入研究的方向。

关键词: 磁场, 导电流体, 流动稳定性, 正则模态, 非正则模态

Abstract: The stability of conducting fluid flow is vital to the electromagnetic processing of materials and the design and operating of thermonuclear fusion reactorcooling system.In this paper,the analysis methods for flow stability based on normal modes and non-normal modes are introduced and compared.Different critical parameters threshold are often obtained with these two methods, this is mainly due to different growth mode of perturbations is concerned in each method.The recent experimental and computational results obtained for flows in pipes, ducts and channels in the presence of magnetic field are reviewed, especially the effects of magnetic field and conductivity of the walls are elaborated.The further investigations on the related experiments, stability analysis methods and the transition mechanisms are discussed.

Key words: magnetic field, conducting fluid, stability, normal mode, non-normal mode

中图分类号:

O361.5

董帅, 李爽, 刘立帅, 叶学民. 磁场作用下导电流体的流动稳定性研究进展[J]. 化工进展, 2017, 36(S1): 17-26.

DONG Shuai, LI Shuang, LIU Lishuai, YE Xuemin. Review on the stability of conducting fluid flow under magnetic field[J]. Chemical Industry and Engineering Progress, 2017, 36(S1): 17-26.

参考文献

[1] MOREAU R.Magnetohydrodynamics[M].London:Kluwer Academic Publisher,1990.
[2] VOROBEV A,ZIKANOV O.Instability and transition to turbulence in a free shear layer affected by a parallel magnetic field[J].Journal of Fluid Mechanics,2007,574(574):131-154.
[3] HARTMANN J. Hg-Dynamics I:Theory of the laminar flow of an electrically conductive liquid in a homogeneous magnetic field[J].Kongelige Danske Videnskabernes Selskab,Matematisk-Fysiske Meddelelser,1937,15(6):1-28.
[4] HARTMANN J,LAZARUS F.Hg-Dynamics Ⅱ:Experimental investigations on the flow of mercury in a homogeneous magnetic field[M].Kongelige Danske Videnskabernes Selskab,Matematisk-Fysiske Meddelelser,1937,15(7):1-45.
[5] SHERCLIFF J A.Steady motion of conducting fluids in pipes under transverse magnetic fields[J].Mathematical Proceedings of the Cambridge Philosophical Society,1953,49(1):136-144.
[6] KINET M,KNAEPEN B,MOLOKOV S.Instabilities and transition in magnetohydrodynamic flows in ducts with electrically conducting walls[J].Physical Review Letters,2009,103(15):154501.
[7] DAVIDSON P A.Magnetohydrodynamics in materials processing[J].Annual Review of Fluid Mechanics,1999,31(1):273-300.
[8] 王宝峰,李建超.电磁搅拌技术在连铸生产中的应用[J].鞍钢技术,2009(1):1-5.
[9] MORLEY N B,SMOLENTSEV S,BARLEON L,et al.Liquid magnetohydrodynamics-recent progress and future directions for fusion[J].Fusion Engineering and Design,2000,51:701-713.
[10] SMOLENTSEV S,MOREAU R,BÜHLER L,et al.MHD thermofluid issues of liquid-metal blankets:phenomena and advances[J].Fusion Engineering and Design,2010,85:1196-1205.
[11] BRANOVER H.Magnetohydrodynamic flow in ducts[M].New York:John Wiley,1978.
[12] CHOWDHURY V,BÜHLER L,MISTRANGELO C,et al.Experimental study of instabilities in magnetohydrodynamic boundary layers[J].Fusion Engineering and Design,2015,98:1751-1754.
[13] JIANMEI W,JIANFENG K,YANJUAN Z,et al.Viscosity monitoring and control on oil-filmbearing lubrication with Ferro fluids[J].Tribology International,2014,75(5):61-68.
[14] AL-SHAIKHLI A K,H FATIMA K O,A FADHIL J L.The magnetic field study of a finite solenoid[J].Circuits and Systems,2013,4(3):316-322.
[15] MURGATROYD W.Experiments on magneto-hydrodynamic channel flow[J].Philosophical Magazine,1953,44(359):1348-1354.
[16] LYKOUDIS P S.Transition from laminar to turbulent flow in magneto-fluid mechanic channels[J].Reviews of Modern Physics,1960,32(4):796-798.
[17] BRANOVER G G.Resistance of magnetohydrodynamic channels[J].Magnetohydrodynamics,1967,3(4):1-11.
[18] MORESCO P,ALBOUSSIÉRET.Experimental study of the instability of the Hartmann layer[J].Journal of Fluid Mechanics,2004,504(1):167-181.
[19] CHOWDHURY V,BÜHLER L,MISTRANGELO C,et al.Experimental study of instabilities in magnetohydrodynamic boundary layers[J].Fusion Engineering and Design,2015,98:1751-1754.
[20] SHATROV V,GERBETH G.Marginal turbulent magne-tohydrodynamic flow in a square duct[J].Physics of Fluids,2010,22(8):585-591.
[21] ZHAO Y,ZIKANOV O.Instabilities and turbulence in magnetohydrodynamic flow in a toroidal duct prior to transition in Hartmann layers[J].Journal of Fluid Mechanics,2012,692:288-316.
[22] ZIKANOV O,KRASNOV D,BOECK T,et al.Laminar-turbulent transition in magnetohydrodynamic duct,pipe,and channel flows[J].Applied Mechanics Reviews,2014,66(3):030802.
[23] 杨小龙,符松.直接数值模拟/大涡模拟中数值误差影响的研究[J].应用数学和力学,2008,29(7):790-798.
[24] KOBAYASHI H.Large eddy simulation of magnetohydrod-ynamic turbulent duct flows[J].Physics of Fluids,2008,20(1):015102.
[25] KOBAYASHI H.Large eddy simulation of magnetohydrod-ynamic turbulent channel flows with local subgrid-scale model based on coherent structures[J].Physics of Fluids,2006,18(4):045107.
[26] VOROBEV A,ZIKANOV O.Smagorinsky constant in LES modeling of anisotropic MHD turbulence[J].Theoretical and Computational Fluid Dynamics,2008,22(3):317-325.
[27] ROBERTS P H.An introduction to magnetohydrodynamics[M].London:Longmans,GreenCo,1967.
[28] LUNDQUIST Stig.Studies in magnetohydrodynamics[J].Arkiv für Fysik,1952,5(4):297-347.
[29] LOCK R C.The stability of the flow of an electrically conducting fluid between parallel planes under a transverse magnetic field[J].Proceedings of the Royal Society A:Mathematical Physical & Engineering Sciences,1955,233(1192):105-125.
[30] TAKASHIMA M. The stability of the modified plane Poiseuille flow in the presence of a transverse magnetic field[J].Fluid Dynamics Research,1996,17(6):293-310.
[31] TAKASHIMA M.The stability of the modified plane Couette flow in the presence of a transverse magnetic field[J].Fluid Dynamics Research,1998,22(2):105-121.
[32] LINGWOOD R J,ALBOUSSI?RE T.On the stability of the Hartmann layer[J].Physics of Fluids,1999,11(8):2058-2068.
[33] SCHMID P J,HENNINGSON D S.Stability and transition in shear flows[M].New York:Springer-Verlag,2001.
[34] GERARD-VARET,D.Amplification of small perturbations in a Hartmann layer[J].Physics of Fluids,2002,14(4):1458-1467.
[35] AIRIAU C,CASTETS M.On the amplification of small disturbances in a channel flow with a normal magnetic field[J].Physics of Fluids,2004,16(8):2991-3005.
[36] KRASNOV D S,ZIENICKE E,ZIKANOV O,et al. Numerical study of the instability of the Hartmann layer[J]. Journal of Fluid Mechanics,2004,504:183-211.
[37] ZIENICKE E,KRASNOV D.Parametric study of streak breakdown mechanism in Hartmann flow[J].Physics of Fluids,2005,17(11):114101.
[38] 董帅,林殿吉,吕玉坤.哈特曼边界层的初级稳定性分析[J].力学学报,2016,48(2):327-335.
[39] ZAKIR HUSSAIN.磁场作用下金属流体线性稳定性分析[D].北京:中国科学院大学,2012.
[40] ZAKIR HUSSAIN,刘婵,倪明玖,等.平行平板间导电流体的磁流体动力学稳定性[J].中国科学院研究生院学报,2013,30(3):304-310.
[41] BÜHLER L.Instabilities in quasi-two-dimensional magnet-ohydrodyamic flows[J].Journal of Fluid Mechanics,1996,326:125-150.
[42] 董帅,刘立帅,叶学民.磁场作用下壁面导电率对导电流体流动稳定性的影响[J].华北电力大学学报(自然科学版),2017,(1):103-110.
[43] BOECK T,KRASNOV D,ROSSI M,et al.Transition to turbulence in MHD channel flow with spanwise magnetic field[C]//Proceedings of the Summer Program,2006:363-374.
[44] KRASNOV D,ROSSI M,ZIKANOV O,et al.Optimal growth and transition to turbulence in channel flow with spanwise magnetic field[J].Journal of Fluid Mechanics,2008,596:73-101.
[45] KRASNOV D,PAREPALLI P,ZIKANOV O,et al.Effect of wall conductivity on turbulent channel flow under spanwise magnetic field[J].Proceedings in Applied Mathematics and Mechanics,2010,10(1):515-516.
[46] 董帅,李本文.平行磁场作用下的低雷诺数平板流研究[J].东北大学学报(自然科学版),2012,33(8):1154-1157.
[47] DONG S,KRASNOV D,LI B W,et al.Instability of streaks in channel flow with a streamwise magnetic field[J].Magnetohydrodynamics,2012,48(1):57-67.
[48] DONG S,KRASNOV D,BOECK T.Secondary energy growth and turbulence suppression in conducting channel flow with streamwise magnetic field[J].Physics of Fluids(1994-present),2012,24(7):074101.
[49] MÜLLER U,BÜHLER L.Magnetofluiddynamics in channels and containers[M].Berlin:Springer,2001.
[50] POTHÉRAT A.Quasi-two-dimensional perturbations in duct flows under transverse magnetic field[J].Physics of Fluids(1994-present),2007,19(7):074104.
[51] BIAU D,SOUEID H,BOTTARO A.Transition to turbulence in duct flow[J].Journal of Fluid Mechanics,2008,596:133-142.
[52] KRASNOV D,ZIKANOV O,ROSSI M,et al.Optimal linear growth in magnetohydrodynamic duct flow[J].Journal of Fluid Mechanics,2010,653(1):273-299.
[53] 刘婵,倪明玖,胡军,等.绝缘方腔中MHD流体流动的线性稳定性分析[C]//中国力学学会、西安交通大学.中国力学大会——2013论文摘要集.西安:中国力学学会、西安交通大学,2013.
[54] BOECK T,KRASNOV D,THESS A,et al.Large-scale intermittency of liquid-metal channel flow in a magnetic field[J].Physical Review Letters,2008,101(24):244501.
[55] KRASNOV D,ZIKANOV O,THESS A,et al.Direct numerical simulation of transition in MHD duct flow[J].Proceedings in Applied Mathematics and Mechanics,2011,1(1):659-660.
[56] KRASNOV D,ZIKANOV O,BOECK T.Numerical study of magnetohydrodynamic duct flow at high Reynolds and Hartmann numbers[J].Journal of Fluid Mechanics,2012,704:421-446.
[57] HU J,LIU C,ZHANG N M,et al.Optimal linear growth of MHD flow in a square duct[C]//Simos T E,Tsitouras C.AIP Conference Proceedings.AIP Publishing,2015,1648(1):030025.
[58] PRIEDE J,ALEKSANDROVA S,MOLOKOV S.Linear stability of magnetohydrodynamic flow in a perfectly conducting rectangular duct[J].Journal of Fluid Mechanics,2012,708:111-127.
[59] TATSUMI T,YOSHIMURA T.Stability of the laminar flow in a rectangular duct[J].Journal of Fluid Mechanics,1990,212:437-449.
[60] UHLMANN M,NAGATA M.Linear stability of flow in an internally heated rectangular duct[J].Journal of Fluid Mechanics,2006,551:387-404.
[61] HUNT J C R.Magnetohydrodynamic flow in rectangular ducts[J].ournal of Fluid Mechanics,1965,21(4):577-590.
[62] PRIEDE J,ALEKSANDROVA S,MOLOKOV S.Linear stability of Hunt's flow[J].Journal of Fluid Mechanics,2010,649:115-134.
[63] TING A L,WALKER J S,MOON T J,et al.Linear stability analysis for high-velocity boundary layers in liquid-metal magnetohydrodynamic flows[J].International Journal of Engineering Science,1991,29(8):939-948.
[64] BRAIDEN L,KRASNOV D,MOLOKOV S,et al.Transition to turbulence in Hunt's flow in a moderate magnetic field[J].Europhysics Letters,2016,115(4):44002.
[65] SMOLENTSEV S,MOREAU R,ABDOU M.Characteri-zation of key magnetohydrodynamic phenomena in PbLi flows for the US DCLL blanket[J].Fusion Engineering and Design,2008,83(5):771-783.
[66] VANTIEGHEM S,KNAEPEN B.Numerical simulation of magnetohydrodynamic flow in a toroidal duct of square cross-section[J].International Journal of Heat and Fluid Flow,2011,32(6):1120-1128.
[67] ROBERTS P H.Singularities of Hartmann Layers[J].Proceedings of the Royal Society A,1967,300(1460):94-107.
[68] ÅKERSTEDT H O.Damping of transient energy growth of three-dimensional perturbations in hydromagnetic pipe flow[J].Fluid Dynamics Research,1995,15(5):295-312.
[69] SATAKE S,KUNUGI T,SMOLENTSEV S. Direct numerical simulations of turbulent pipe flow in a transverse magnetic field[J].Journal of Turbulence.2002,3(20):1-12.
[70] MANNEVILLE P.Understanding the sub-critical transition to turbulence in wall flows[J].Pramana,2008,70(6):1009-1021.