倾斜非均匀磁场下导电方管磁流体管流的数值模拟研究
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摘要
热核聚变反应堆液态金属包层应用中的一个重要问题是液态金属在导电管中流动和强磁场相互作用产生的额外的磁流体动力学压降.这种磁流体动力学压降远远大于普通水力学压降.美国阿贡国家实验室ALEX研究小组,对非均匀磁场下导电管中液态金属磁流体动力学效应进行了实验研究,其实验结果成为液态金属包层数值验证的标准模型之一.液态金属包层在应用中会受到不同方向的磁场作用,本文以ALEX的非均匀磁场下导电方管中液态金属管流实验中的一组参数为基础,保持哈特曼数、雷诺数和壁面电导率不变,采用三维直接数值模拟的方法,研究了外加磁场与侧壁之间的倾角对导电方管内液态金属流动的速度、电流和压降分布的影响.研究结果表明:沿流向相同横截面上的速度、电流以及压力分布均随磁场的倾斜而同向旋转.倾斜磁场均匀段,横截面上的高速区位于平行磁场方向的哈特曼层和平行层交叉位置,压力梯度随磁场倾角的增大先增大后减小.倾斜磁场递减段,在三维磁流体动力学效应作用下,横截面上的高速射流位置向垂直磁场方向偏移.磁场递减段的三维磁流体动力学压降随磁场倾角的增大而增大.随磁场倾斜,截面上的射流峰值逐渐减小,二次流增强,引发层流向湍流的转捩.
An essential issue in the application of liquid metal blanks in thermal nuclear fusion reactors is the additional magnetohydrodynamic(MHD) pressure drop caused by the interaction of the liquid metal flow with a strong magnetic field.The additional MHD pressure drop is much higher than hydrodynamic pressure drop.Argonne liquid metal experiment(ALEX) group in Argonne National Laboratory of American studied the MHD effect of Liquid Metal flow in ducts and pipes subjected to a fringing magnetic field by experiments.The experiments were introduced as one of the benchmark cases to test numerical codes for liquid metal blankets.As the liquid metal blankets would be subjected to the magnetic field with different directions,liquid metal flow in a square duct subjected to an inclined fringing magnetic field has been numerically studied in this paper.The model is based on one of the ALEX's experiments.With constant Hartmann number,Reynolds number and wall conductance ratio,the effects of the angle between the magnetic field and the side wall on the velocity,the electric current,and the pressure distribution have been investigated using three-dimensional direct numerical simulation method.The results show that the distribution of the velocity,the electric current and the pressure on the cross section rotates with the increase of the inclination angle of the magnetic field.In the uniform part of the inclined magnetic field,the velocity jets located at the junction corners of the Hartmann layer and the side layer which are parallel to the external magnetic field.The pressure gradient in the part of the uniform magnetic field increases firstly and decreases with the increase of the inclination angle of the magnetic field.In the decreasing part of the inclined magnetic field,the high-speed velocity jet is transferred to another pair of corners due to the three-dimensional MHD effect along the streamwise direction.The three-dimensional MHD pressure drop at the cross-section of the duct increases with the increase of the inclination angle of the magnetic field.Furthermore,the maximum value of the velocity jets decreases,the second flow increases and the laminar-turbulent transition of the duct flow occurs.
An essential issue in the application of liquid metal blanks in thermal nuclear fusion reactors is the additional magnetohydrodynamic(MHD) pressure drop caused by the interaction of the liquid metal flow with a strong magnetic field.The additional MHD pressure drop is much higher than hydrodynamic pressure drop.Argonne liquid metal experiment(ALEX) group in Argonne National Laboratory of American studied the MHD effect of Liquid Metal flow in ducts and pipes subjected to a fringing magnetic field by experiments.The experiments were introduced as one of the benchmark cases to test numerical codes for liquid metal blankets.As the liquid metal blankets would be subjected to the magnetic field with different directions,liquid metal flow in a square duct subjected to an inclined fringing magnetic field has been numerically studied in this paper.The model is based on one of the ALEX's experiments.With constant Hartmann number,Reynolds number and wall conductance ratio,the effects of the angle between the magnetic field and the side wall on the velocity,the electric current,and the pressure distribution have been investigated using three-dimensional direct numerical simulation method.The results show that the distribution of the velocity,the electric current and the pressure on the cross section rotates with the increase of the inclination angle of the magnetic field.In the uniform part of the inclined magnetic field,the velocity jets located at the junction corners of the Hartmann layer and the side layer which are parallel to the external magnetic field.The pressure gradient in the part of the uniform magnetic field increases firstly and decreases with the increase of the inclination angle of the magnetic field.In the decreasing part of the inclined magnetic field,the high-speed velocity jet is transferred to another pair of corners due to the three-dimensional MHD effect along the streamwise direction.The three-dimensional MHD pressure drop at the cross-section of the duct increases with the increase of the inclination angle of the magnetic field.Furthermore,the maximum value of the velocity jets decreases,the second flow increases and the laminar-turbulent transition of the duct flow occurs.
引文
1 Kirillov IR,Reed CB,Barleon L,et al.Present understanding of mhd and heat transfer phenomena for liquid metal blankets.Fusion Engineering and Design,1995,27:553-569
2 Smolentsev S,Morley NB,Wong C,et al.MHD and heat transfer considerations for the us DCLL blanket for DEMO and ITER TBM.Fusion Engineering and Design,2008,83(10):1788-1791
3 Smolentsev S,Moreau R,B¨uhler L,et al.MHD therm of luid issues of liquid-metal blankets:Phenomena and advances.Fusion Engineering and Design,2010,85(7):1196-1205
4 Brethouwer G,Duguet Y,Schlatter P.Turbulent-laminar coexistence in wall flows with coriolis,buoyancy or lorentz forces.Journal of Fluid Mechanics,2012,704(2):137-172
5崔光耀,潘翀,高琪等.沟槽方向对湍流边界层流动结构影响的实验研究.力学学报,2017,49(6):1201-1212(Cui Guangyao,Pan Chong,Gao Qi,et al.Flow structure in the turbulent boundary layer over directional riblets surfaces.Chinese Journal of Theoretical and Applied Mechanics,2017,49(6):1201-1212(in Chinese))
6 Xu ZY,Pan CJ,Wei WH,et al.Experimental investigation and theoretical analysis of two-dimensional magnetohydrodynamic effects in a rectangular duct.Fusion Technology,2017,36(1):47-51
7 Buhler L,Mistrangelo C,Koehly C.Layout of an experimental liquid-metal circuit based on MHD considerations.IEEE Transactions on Plasma Science,2012,40(3):590-595
8 Xu ZY,Reed CB,Pan CJ,et al.FCI related MHD experimental and the oretic results from SWIP LMEL facility//9th.China-Japan Symposium on Materials for Aolvanced Energy System and Fission&Fission Engineering,2007
9张鑫,黄勇,阳鹏宇等.等离子体激励器诱导射流的湍流特性研究.力学学报,2018,50(4):776-786(Zhang Xin,Huang Yong,Yang Pengyu,et al.Investigation on the turbulent characteristics of the je induced by a plasma actuator.Chinese Journal of Theoretical and Applied Mechanics,2018,50(4):776-786(in Chinese))
10董帅,林殿吉,吕玉坤.哈特曼边界层的初级稳定性分析.力学学报,2016,48(2):327-335(Dong Shuai,Lin Dianji,L¨u Yukun The primary stability analysis of Hartmann boundary layer.Chinese Journal of Theoretical and Applied Mechanics,2016,48(2):327-335(in Chinese))
11 Chaudhary R,Shinn AF,Vanka SP,et al.Direct numerical simulations of transverse and spanwise magnetic field effects on turbulen flow in a 2:1 aspect ratio rectangular duct.Computers&Fluids2011,51(1):100-114
12陈智,张劲柏,李椿萱.低磁雷诺数不可压缩磁流体槽道湍流电场相关特性的直接数值模拟.中国科学:物理学力学天文学,201040(9):1144-1155(Chen Zhi,Zhang Jinbo,Li Chunxuan,Direct numerical simulation of turbulent field correlation in a low magnetic Reynolds number incompressible magnetic fluid channel.Scientia Sinica Phys,Mech and Astron,2010,40(9):1144-1155(in Chinese))
13 Morley NB,Smolentsev S,Barleon L,et al.Liquid magnetohydrodynamics-recent progress and future directions for fusion.Fusion Engineering and Design,2000,51-52:701-713
14 Reed CB,Picologlou BF,Dauzvardis PV.Experimental facility for studying mhd effects in liquid metal cooled blankets.Fusion Technology,1985,8(1):257-263
15 Picologlou BF,Reed CB,Dauzvardis PV.Experimental and analytical investigations of magnetohydrodynamic flows near the entrance to a strong magnetic field.Fusion Technology,1986,10:3(3):860-865
16 Walker JS.Liquid-metal flow in a thin conducting pipe near the end of a region of uniform magnetic field.Journal of Fluid Mechanics1986,167(167):199-217
17 Reed CB,Picologlou BF,Hua TQ.ALEX results:A comparison of measurements from a round and a rectangular duct with 3-D code predictions//Symposium on Fusion Engineering.Presented at the12th Symposium on Fusion Engineering,Monterey,Calif.,1987
18 Picologlou BF,Reed CB.Experimental investigation of 3-D MHDflows at high hartmann number and interaction parameter.Liquid Metal Magnetohydrodynamics.Netherlands:Springer,1988:239-241
19 Hua TQ,Picologlou BF,Reed CB.MHD thermal hydraulic analysis of three-dimensional liquid-metal flows in fusion blanket ducts Fusion Engineering&Design,1989,8(89):241-248
20 Reed CB,Picologlou BF.Sidewall flow instabilities in liquid metal MHD flow under blanket relevant conditions.Fusion Technology,1989,15(2):705-715
21 Votyakov EV,Kassinos X SC.Albets-Chico X.Analyticmodels of heterogenous magnetic fields for liquid metal flow simulations.Theoretical&Computational Fluid Dynamics,2009,23(6):571
22 Albets-Chico X,Votyako EV,Radhakrishnan H,et al.Effects of the consistency of the fringing magnetic field on direct numerical simulations of liquid-metal flow.Fusion Engineering and Design,2011,86:5-14
23 Albets-Chico X,Grigoriadis DGE,Votyakov EV,et al.Direct numerical simulation of turbulent liquid metal flow entering a magnetic field.Fusion Engineering and Design,2013,88(12):3108-3124
24 Kobayashi H,Shionoya H,Okuno Y.Turbulent duct flows in a liquid metal magnetohydrodynamic power generator.Journal of Fluid Mechanics,2012,73:243-270
25 Zhou T,Chen HL,Yang ZY.Effect of fringing magnetic field on magnetohydrodynamic flow in rectangular duct.Fusion Engineering and Design,2011,86:2352-2357
26 Li YQ,Zikanov O.Laminar pipe flow at the entrance into transverse magnetic field.Fusion Engineering and Design,2013,88:195-201
27 Yu PX,Qiu JX,Qin Q,et al.Numerical investigation of natural convection in a rectangular cavity under different directions of uniform magnetic field.International Journal of Heat and Mass Transfer,2013,67:1131-1144
28 Chandra SB,Rabindra D,Jana N.Hall effects on MHD flow in a rotating channel in the presence of an inclined magnetic field.Applied Science and Engineering,2014,17(3):243-252
29 Seth GS,Nandkeolyar R,Ansari MdS.Effects of hall current and rotation on unsteady mhd couette flow in the presence of an inclined magnetic field.Applied Fluid Mechanics,2012,5(2):67-74
30 Davidson PA,Belova EV.An Introduction to Magnetohydrodynamics.UK:Cambridge Unirersity Press,2010
31 Molokov S,Moreau R,Moffatt K.Magnetohydrodynamics.Netherlands:Springer,2007
32 Ni MJ,Munipalli R,Morley NB,et al.A current density conservative scheme for incompressible mhd flows at a low magnetic reynolds number.Part I:On a rectangular collocated grid system.Journal of Computational Physics,2007,227(1):174-204
33毛洁,王浩,刘克等.基于OpenFOAM的投影法磁流体求解器开发与验证.核聚变与等离子体物理,2018,38(1):15-20(Mao Jie,Wang Hao,Liu Ke et al.Development and validation of magnetohydrodynamic solver with projection in OpenFOAM environmentNuclear.Fusion and Plasma Physics,2018,38:15-20(in Chinese))
2 Smolentsev S,Morley NB,Wong C,et al.MHD and heat transfer considerations for the us DCLL blanket for DEMO and ITER TBM.Fusion Engineering and Design,2008,83(10):1788-1791
3 Smolentsev S,Moreau R,B¨uhler L,et al.MHD therm of luid issues of liquid-metal blankets:Phenomena and advances.Fusion Engineering and Design,2010,85(7):1196-1205
4 Brethouwer G,Duguet Y,Schlatter P.Turbulent-laminar coexistence in wall flows with coriolis,buoyancy or lorentz forces.Journal of Fluid Mechanics,2012,704(2):137-172
5崔光耀,潘翀,高琪等.沟槽方向对湍流边界层流动结构影响的实验研究.力学学报,2017,49(6):1201-1212(Cui Guangyao,Pan Chong,Gao Qi,et al.Flow structure in the turbulent boundary layer over directional riblets surfaces.Chinese Journal of Theoretical and Applied Mechanics,2017,49(6):1201-1212(in Chinese))
6 Xu ZY,Pan CJ,Wei WH,et al.Experimental investigation and theoretical analysis of two-dimensional magnetohydrodynamic effects in a rectangular duct.Fusion Technology,2017,36(1):47-51
7 Buhler L,Mistrangelo C,Koehly C.Layout of an experimental liquid-metal circuit based on MHD considerations.IEEE Transactions on Plasma Science,2012,40(3):590-595
8 Xu ZY,Reed CB,Pan CJ,et al.FCI related MHD experimental and the oretic results from SWIP LMEL facility//9th.China-Japan Symposium on Materials for Aolvanced Energy System and Fission&Fission Engineering,2007
9张鑫,黄勇,阳鹏宇等.等离子体激励器诱导射流的湍流特性研究.力学学报,2018,50(4):776-786(Zhang Xin,Huang Yong,Yang Pengyu,et al.Investigation on the turbulent characteristics of the je induced by a plasma actuator.Chinese Journal of Theoretical and Applied Mechanics,2018,50(4):776-786(in Chinese))
10董帅,林殿吉,吕玉坤.哈特曼边界层的初级稳定性分析.力学学报,2016,48(2):327-335(Dong Shuai,Lin Dianji,L¨u Yukun The primary stability analysis of Hartmann boundary layer.Chinese Journal of Theoretical and Applied Mechanics,2016,48(2):327-335(in Chinese))
11 Chaudhary R,Shinn AF,Vanka SP,et al.Direct numerical simulations of transverse and spanwise magnetic field effects on turbulen flow in a 2:1 aspect ratio rectangular duct.Computers&Fluids2011,51(1):100-114
12陈智,张劲柏,李椿萱.低磁雷诺数不可压缩磁流体槽道湍流电场相关特性的直接数值模拟.中国科学:物理学力学天文学,201040(9):1144-1155(Chen Zhi,Zhang Jinbo,Li Chunxuan,Direct numerical simulation of turbulent field correlation in a low magnetic Reynolds number incompressible magnetic fluid channel.Scientia Sinica Phys,Mech and Astron,2010,40(9):1144-1155(in Chinese))
13 Morley NB,Smolentsev S,Barleon L,et al.Liquid magnetohydrodynamics-recent progress and future directions for fusion.Fusion Engineering and Design,2000,51-52:701-713
14 Reed CB,Picologlou BF,Dauzvardis PV.Experimental facility for studying mhd effects in liquid metal cooled blankets.Fusion Technology,1985,8(1):257-263
15 Picologlou BF,Reed CB,Dauzvardis PV.Experimental and analytical investigations of magnetohydrodynamic flows near the entrance to a strong magnetic field.Fusion Technology,1986,10:3(3):860-865
16 Walker JS.Liquid-metal flow in a thin conducting pipe near the end of a region of uniform magnetic field.Journal of Fluid Mechanics1986,167(167):199-217
17 Reed CB,Picologlou BF,Hua TQ.ALEX results:A comparison of measurements from a round and a rectangular duct with 3-D code predictions//Symposium on Fusion Engineering.Presented at the12th Symposium on Fusion Engineering,Monterey,Calif.,1987
18 Picologlou BF,Reed CB.Experimental investigation of 3-D MHDflows at high hartmann number and interaction parameter.Liquid Metal Magnetohydrodynamics.Netherlands:Springer,1988:239-241
19 Hua TQ,Picologlou BF,Reed CB.MHD thermal hydraulic analysis of three-dimensional liquid-metal flows in fusion blanket ducts Fusion Engineering&Design,1989,8(89):241-248
20 Reed CB,Picologlou BF.Sidewall flow instabilities in liquid metal MHD flow under blanket relevant conditions.Fusion Technology,1989,15(2):705-715
21 Votyakov EV,Kassinos X SC.Albets-Chico X.Analyticmodels of heterogenous magnetic fields for liquid metal flow simulations.Theoretical&Computational Fluid Dynamics,2009,23(6):571
22 Albets-Chico X,Votyako EV,Radhakrishnan H,et al.Effects of the consistency of the fringing magnetic field on direct numerical simulations of liquid-metal flow.Fusion Engineering and Design,2011,86:5-14
23 Albets-Chico X,Grigoriadis DGE,Votyakov EV,et al.Direct numerical simulation of turbulent liquid metal flow entering a magnetic field.Fusion Engineering and Design,2013,88(12):3108-3124
24 Kobayashi H,Shionoya H,Okuno Y.Turbulent duct flows in a liquid metal magnetohydrodynamic power generator.Journal of Fluid Mechanics,2012,73:243-270
25 Zhou T,Chen HL,Yang ZY.Effect of fringing magnetic field on magnetohydrodynamic flow in rectangular duct.Fusion Engineering and Design,2011,86:2352-2357
26 Li YQ,Zikanov O.Laminar pipe flow at the entrance into transverse magnetic field.Fusion Engineering and Design,2013,88:195-201
27 Yu PX,Qiu JX,Qin Q,et al.Numerical investigation of natural convection in a rectangular cavity under different directions of uniform magnetic field.International Journal of Heat and Mass Transfer,2013,67:1131-1144
28 Chandra SB,Rabindra D,Jana N.Hall effects on MHD flow in a rotating channel in the presence of an inclined magnetic field.Applied Science and Engineering,2014,17(3):243-252
29 Seth GS,Nandkeolyar R,Ansari MdS.Effects of hall current and rotation on unsteady mhd couette flow in the presence of an inclined magnetic field.Applied Fluid Mechanics,2012,5(2):67-74
30 Davidson PA,Belova EV.An Introduction to Magnetohydrodynamics.UK:Cambridge Unirersity Press,2010
31 Molokov S,Moreau R,Moffatt K.Magnetohydrodynamics.Netherlands:Springer,2007
32 Ni MJ,Munipalli R,Morley NB,et al.A current density conservative scheme for incompressible mhd flows at a low magnetic reynolds number.Part I:On a rectangular collocated grid system.Journal of Computational Physics,2007,227(1):174-204
33毛洁,王浩,刘克等.基于OpenFOAM的投影法磁流体求解器开发与验证.核聚变与等离子体物理,2018,38(1):15-20(Mao Jie,Wang Hao,Liu Ke et al.Development and validation of magnetohydrodynamic solver with projection in OpenFOAM environmentNuclear.Fusion and Plasma Physics,2018,38:15-20(in Chinese))