边界局域模引起钨偏滤器靶板侵蚀和形貌变化的数值模拟研究

黄艳; 孙继忠; 桑超峰; 胡万鹏; 王德真

doi:10.7498/aps.66.035201

摘要

钨材料在高瞬时热流作用下的熔化、流动是国际热核聚变实验堆面壁材料最突出的问题.本文将热传导方程与Navier-Stokes方程结合，建立了二维流体动力学模型，研究在边界局域模（ELM）强热流轰击下，钨熔化层在表面张力、压强梯度力、磁场力等作用下的流动，以及偏滤器靶板的侵蚀和形貌演化.结果表明，在ELM过程中，熔化层中的液体不断地向边缘区域流动，在打击点区域形成一个熔池，在熔化层的边缘区域形成类似山峰结构的凸起，加重了钨偏滤器靶板的侵蚀.在空间分布为高斯形状入射能流的作用下，钨熔化层两侧的山峰结构是对称的；当能流密度小于3000 MWm-2时，表面张力对熔化层的流动起主要作用.本文在模型的数值求解中，采用交错网格的方法进行离散，克服了液体表面追踪的算法难点，保证了钨偏滤器靶板侵蚀程度计算的准确性.

关键词:

Abstract

The high-Z material tungsten (W) is a promising candidate of the plasma facing components (PFCs) for the future tokamak reactors due to its high melting point (3683 K), low tritium retention and low sputtering yield. However, there are still many problems about W PFCs. One of them is the material melting under off-normal transient heat fluxesit is one of the most outstanding open questions associated with the use of W divertor targets in international thermonuclear experimental reactor (ITER). This requires us urgently to understand the W melting behavior under high power flux deposition condition. In this paper, a two-dimensional (2D) fluid dynamic model is employed by solving the liquid hydrodynamic Navier-Stokes equation together with the 2D heat conduction equation for studying the erosion of the divertor tungsten targets and its resulting topographical modification during a type I-like edge-localized mode (ELM) in ITER with a Gaussian power density profile heat load. In the present model, major interaction forces, including surface tension, pressure gradient and magnetic force responsible for melt layer motion, are taken into account. The simulation results are first benchmarked with the calculated results by other code to validate the present model and code. Simulations are carried out in a wide range of fusion plasma performance parameters, and the results indicate that the lifetime of W plate is determined mainly by the evolution of the melt layer. As a consequence of the melt layer motion, melted tungsten is flushed to the periphery, a rather deep erosion dent appears, and at the dent edges two humps of tungsten form during the ELM. The humps at both edges are almost at the same height. Calculated results show the topographical modification becomes noticeable when the W plate is exposed to a heat flux of 2000 MWm-2 for 0.8 ms (in the simulation, the parameter k=ə/əT is taken to be -9.010-5 Nm-1K-1, where is the surface tension coefficient and T is the temperature). The values of the humps are both about 2.1 m, and the surface roughness is about 1.1 m. The longer the duration of the ELM, the more rapidly the humps rise. The melt flow may account for the higher surface temperature at the pool periphery, and for the larger melt thickness. It is found that when the energy flux is under 3000 MWm-2 the surface tension is a major driving force for the motion of melt layer. Under the same heat flux, the bigger the k used in the simulation, the more severe the surface topography of the target becomes; while at the same k, the higher the heat flux, the more severe the surface topography of the target becomes. In addition, a modified numerical method algorithm for solving the governing equations is proposed.

Keywords:

作者及机构信息

1.
大连工业大学信息科学与工程学院, 大连 116034;

2.
大连理工大学物理与光电工程学院, 大连 116024

通信作者: 孙继忠, jsun@dlut.edu.cn;wangdez@dlut.edu.cn ; 王德真, jsun@dlut.edu.cn;wangdez@dlut.edu.cn

基金项目: 国家磁约束聚变科学项目（批准号：2013GB109001，2013GB107003）、国家自然科学基金（批准号：11275042，11575039）和辽宁省基本科研项目（批准号：2016J027）资助的课题.

Authors and contacts

1.
School of Information Science and Engineering, Dalian Polytechnic University, Dalian 116034, China;

2.
School of Physics and Optoelectronic Engineering, Dalian University of Technology, Dalian 116024, China

Corresponding author: Sun Ji-Zhong, jsun@dlut.edu.cn;wangdez@dlut.edu.cn ; Wang De-Zhen, jsun@dlut.edu.cn;wangdez@dlut.edu.cn

Funds: Project supported by the National Magnetic Confinement Fusion Science Program of China (Grant Nos. 2013GB109001, 2013GB107003), the National Natural Science Foundation of China (Grant Nos. 11275042, 11575039), and the Scientific Research Foundation of the Liaoning Province, China (Grant No. 2016J027).

参考文献

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[3]	Sergienko G, Bazylev B, Huber A, Kreter A, Litnovsky A, Rubel M, Philipps V, Pospieszczyk A, Mertens P, Samm U, Schweer B, Schmitz O, Tokar M, The TEXTOR Team 2007 J. Nucl. Mater. 363 96
[4]	Sergienko G, Bazylev B, Hirai T 2007 Phy. Scr. T128 81
[5]	Coenen J W, Arnoux G, Bazylev B, Matthews G F, Jachmich S, Balboa I, Clever M, Dejarnac R, Coffey I, Corre Y, Devaux S, Frassinetti L, Gauthier E, Horacek J, Knaup M, Komm M, Krieger K, Marsen S, Meigs A, Mertens Ph, Pitts R A, Puetterich T, Rack M, Stamp M, Sergienko G, Tamain P, Thompson V, JET-EFDA Contributors 2015 J. Nucl. Mater. 463 78
[6]	Federici G, Andrew P, Barabaschi P, Brooks J, Doerner R, Geier A, Herrmann A, Janeschitz G, Krieger K, Kukushkin A, Loarte A, Neu R, Saibene G, Shimada M, Strohmayer G, Sugihara M 2003 J. Nucl. Mater. 313 11
[7]	Federici G, Loarte A, Strohmayer G 2003 Plasma Phys. Control. Fusion 45 1523
[8]	Raffray A R, Federici G 1997 J. Nucl. Mater. 244 85
[9]	Federici G, Raffray A R 1997 J. Nucl. Mater. 244 101
[10]	Hassanein A, Konkashbaev I 2000 Fusion Eng. Des. 51 681
[11]	Sizyuk V, Hassanein A 2015 Phy. Plasmas 22 013301
[12]	Litunovsky V N, Kuznetsov V E, Lyublin B V, Ovchinnikov I B, Titov V A, Hassanein A 2000 Fusion Eng. Des. 49 249
[13]	Shi Y, Miloshevsky G, Hassanein A 2011 Fusion Eng. Des. 86 155
[14]	Hassanein A, Konkashbaev I 2003 J. Nucl. Mater. 313 664
[15]	Genco F, Hassanein A 2014 Laser Part. Beams 32 217
[16]	Wurz H, Bazylev B, Landman I, Pestchanyi S, Gross S 2001 Fusion Eng. Des. 56 397
[17]	Bazylev B, Wuerz H 2002 J. Nucl. Mater. 307 69
[18]	Coenen J W, Bazylev B, Brezinsek S 2011 J. Nucl. Mater. 415 S78
[19]	Bazylev B N, Janeschitz G, Landman I S, Pestchanyi S E 2005 Fusion Eng. Des. 75 407
[20]	Bazylev B N, Janeschitz G, Landman I S, Loarte A, Pestchanyi S E 2007 J. Nucl. Mater. 363 1011
[21]	Igitkhanov Y, Bazylev B 2014 IEEE Trans. Plasma Sci. 42 2284
[22]	Huang Y, Sun J Z, Sang C F, Ding F, Wang D Z 2014 Acta Phys. Sin. 63 035204 (in Chinese)[黄艳, 孙继忠, 桑超峰, 丁芳, 王德真2014 63 035204]
[23]	Huang Y, Sun J Z, Hu W P, Sang C F, Wang D Z 2016 Fusion Eng. Des. 102 28
[24]	Miloshevsky G V, Hassanein 2010 Nucl. Fusion 50 115005
[25]	Loarte A 2003 Plasma Phys. Control. Fusion 45 1549
[26]	Hassanein A, Sizyuk T, Konkashbaev I 2009 J. Nucl. Mater. 390 777
[27]	Jiang C B, Zhang Y L, Ding Z P 2007 Computational Fluid Mechanics (the first edition) (Beijing:China Power Press) p211(in Chinese)[江春波, 张永良, 丁则平2007计算流体力学(第一版)(北京:中国电力出版社)第211页]
[28]	Carslaw H W, Jaeger J C 1959 Conduction of Heat in Solids (2nd Ed.) (Oxford:Clarendon Press) pp89-91
[29]	Behrisch R 2010 J. Synch. Investig. 4 549
[30]	Semak V V, Damkroger B, Kempka S 1999 J. Phys. D:Appl. Phys. 32 1819
[31]	Udaykumar H S, Shyy W 1995 Int. J. Heat Mass Transfer 38 2057
[32]	Bazylev B N, Janeschitz G, Landman I S, Pestchanyi S E 2005 J. Nucl. Mater. 337 766
[33]	Udaykumar H S, Shyy W, Rao M M 1996 Int. J. Numer. Methods Fluids 22 691
[34]	Wurz H, Pestchanyi S, Bazylev B, Landman I, Kappler F 2001 J. Nucl. Mater. 290 1138
[35]	Elsholz F, Scholl E, Scharfenorth C, Seewald G, Eichler H J, Rosenfeld A 2005 J. Appl. Phys. 98 103516
[36]	Elsholz F, Scholl E, Rosenfeld A 2004 Appl. Phys. Lett. 84 4167

施引文献

[1]	Xu W, Wan B N, Xie J K 2003 Acta Phys. Sin. 52 1970 (in Chinese)[徐伟, 万宝年, 谢纪康2003 52 1970]
[2]	Coenen J W, Arnoux G, Bazylev B, Matthews G F, Autricque A, Balboa I, Clever M, Dejarnac R, Coffey I, Corre Y, Devaux S, Frassinetti L, Gauthier E, Horacek J, Jachmich S, Komm M, Knaup M, Krieger K, Marsen S, Meigs A, Mertens P, Pitts R A, Puetterich T, Rack M, Stamp M, Sergienko G, Tamain P, Thompson V, JET-EFDA Contributors 2015 Nucl. Fusion 55 023010
[3]	Sergienko G, Bazylev B, Huber A, Kreter A, Litnovsky A, Rubel M, Philipps V, Pospieszczyk A, Mertens P, Samm U, Schweer B, Schmitz O, Tokar M, The TEXTOR Team 2007 J. Nucl. Mater. 363 96
[4]	Sergienko G, Bazylev B, Hirai T 2007 Phy. Scr. T128 81
[5]	Coenen J W, Arnoux G, Bazylev B, Matthews G F, Jachmich S, Balboa I, Clever M, Dejarnac R, Coffey I, Corre Y, Devaux S, Frassinetti L, Gauthier E, Horacek J, Knaup M, Komm M, Krieger K, Marsen S, Meigs A, Mertens Ph, Pitts R A, Puetterich T, Rack M, Stamp M, Sergienko G, Tamain P, Thompson V, JET-EFDA Contributors 2015 J. Nucl. Mater. 463 78
[6]	Federici G, Andrew P, Barabaschi P, Brooks J, Doerner R, Geier A, Herrmann A, Janeschitz G, Krieger K, Kukushkin A, Loarte A, Neu R, Saibene G, Shimada M, Strohmayer G, Sugihara M 2003 J. Nucl. Mater. 313 11
[7]	Federici G, Loarte A, Strohmayer G 2003 Plasma Phys. Control. Fusion 45 1523
[8]	Raffray A R, Federici G 1997 J. Nucl. Mater. 244 85
[9]	Federici G, Raffray A R 1997 J. Nucl. Mater. 244 101
[10]	Hassanein A, Konkashbaev I 2000 Fusion Eng. Des. 51 681
[11]	Sizyuk V, Hassanein A 2015 Phy. Plasmas 22 013301
[12]	Litunovsky V N, Kuznetsov V E, Lyublin B V, Ovchinnikov I B, Titov V A, Hassanein A 2000 Fusion Eng. Des. 49 249
[13]	Shi Y, Miloshevsky G, Hassanein A 2011 Fusion Eng. Des. 86 155
[14]	Hassanein A, Konkashbaev I 2003 J. Nucl. Mater. 313 664
[15]	Genco F, Hassanein A 2014 Laser Part. Beams 32 217
[16]	Wurz H, Bazylev B, Landman I, Pestchanyi S, Gross S 2001 Fusion Eng. Des. 56 397
[17]	Bazylev B, Wuerz H 2002 J. Nucl. Mater. 307 69
[18]	Coenen J W, Bazylev B, Brezinsek S 2011 J. Nucl. Mater. 415 S78
[19]	Bazylev B N, Janeschitz G, Landman I S, Pestchanyi S E 2005 Fusion Eng. Des. 75 407
[20]	Bazylev B N, Janeschitz G, Landman I S, Loarte A, Pestchanyi S E 2007 J. Nucl. Mater. 363 1011
[21]	Igitkhanov Y, Bazylev B 2014 IEEE Trans. Plasma Sci. 42 2284
[22]	Huang Y, Sun J Z, Sang C F, Ding F, Wang D Z 2014 Acta Phys. Sin. 63 035204 (in Chinese)[黄艳, 孙继忠, 桑超峰, 丁芳, 王德真2014 63 035204]
[23]	Huang Y, Sun J Z, Hu W P, Sang C F, Wang D Z 2016 Fusion Eng. Des. 102 28
[24]	Miloshevsky G V, Hassanein 2010 Nucl. Fusion 50 115005
[25]	Loarte A 2003 Plasma Phys. Control. Fusion 45 1549
[26]	Hassanein A, Sizyuk T, Konkashbaev I 2009 J. Nucl. Mater. 390 777
[27]	Jiang C B, Zhang Y L, Ding Z P 2007 Computational Fluid Mechanics (the first edition) (Beijing:China Power Press) p211(in Chinese)[江春波, 张永良, 丁则平2007计算流体力学(第一版)(北京:中国电力出版社)第211页]
[28]	Carslaw H W, Jaeger J C 1959 Conduction of Heat in Solids (2nd Ed.) (Oxford:Clarendon Press) pp89-91
[29]	Behrisch R 2010 J. Synch. Investig. 4 549
[30]	Semak V V, Damkroger B, Kempka S 1999 J. Phys. D:Appl. Phys. 32 1819
[31]	Udaykumar H S, Shyy W 1995 Int. J. Heat Mass Transfer 38 2057
[32]	Bazylev B N, Janeschitz G, Landman I S, Pestchanyi S E 2005 J. Nucl. Mater. 337 766
[33]	Udaykumar H S, Shyy W, Rao M M 1996 Int. J. Numer. Methods Fluids 22 691
[34]	Wurz H, Pestchanyi S, Bazylev B, Landman I, Kappler F 2001 J. Nucl. Mater. 290 1138
[35]	Elsholz F, Scholl E, Scharfenorth C, Seewald G, Eichler H J, Rosenfeld A 2005 J. Appl. Phys. 98 103516
[36]	Elsholz F, Scholl E, Rosenfeld A 2004 Appl. Phys. Lett. 84 4167

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