Numerical simulation of erosion of misaligned W/Cu monoblocks caused by ITER-like type-Iedge localized modes

Huang Yan; Sun Ji-Zhong; Sang Chao-Feng; Wang De-Zhen

doi:10.7498/aps.72.20230281

Abstract

The thermal performance of the divertor W/Cu monoblock tiles under the ITER-like transient events has been one of the main concerns for ITER plasma facing components. Owing to the assembly tolerances during installation, the leading edge caused by misalignment between toroidal neighboring tiles will receive the extremely high cumulative heat flux and be damaged. In this work, we develop a two-dimensional heat conductivity model, including evaporation, radiation, melting process, and coupling cooling water condition, to investigate the thermal erosion of two shapes of tiles of W/Cu monoblock (unshaped and beveled tiles) with misalignment in a range from 0 to 0.3 mm, within the allowable maximum misalignment for ITER. To reflect the geometrical effects of castellated divertor tiles on the properties of its adjacent plasma, the energy flux density distribution arriving at the castellated divertor tile surface is evaluated first by using a two-dimension-in-space and three-dimension-in-velocity particle-in-cell plus Monte Carlo collisions code, and the obtained energy flux distribution is then used as input for the heat conduction model. The simulation results show that the maximum temperature of the unshaped tile with no misalignment is lower than that of the beveled tile under the steady-state inter-ELM heat flux, which increases more quickly than that of the beveled tile with misalignment increasing and will be larger than that of the beveled tile when misalignment is not less than 0.105 mm. Two shapes of the divertor tiles would melt and vaporize under typical heat flux density of a transient event of type-I edge localized modes (ELMs) for ITER, deposition energy of 1 MJ·m^–2 in a duration of 600 μs. The highest temperature, the maximum melting thickness, the maximum vaporization thickness of the unshaped tile with no misalignment are higher than those of the beveled tile except the melting volume ratio. The thermal erosion of the unshaped tile increases more remarkably than that of the beveled tile with misalignment increasing, and the melting volume ratio of the unshaped tile will exceed that of the beveled tile at a misalignment of 0.17 mm. In comparison with the unshaped tile, the beveled tile is more resistant to such a high heat flux of an ELM and misalignment.

Keywords:

Authors and contacts

1.
Department of Basic Courses Teaching, Dalian Polytechnic University, Dalian 116034, China
2.
School of Physics, Dalian University of Technology, Dalian 116024, China

Corresponding author: Sun Ji-Zhong, jsun@dlut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12275040).

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References

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[2]	Bolt H, Barabash V, Krauss W, Linke J, Neu R, Suzuki S, Yoshida N, ASDEX Upgrade Team 2004 J. Nucl. Mater. 329–333 66 Google Scholar
[3]	Pitts R A, Bonnin X, Escourbiac F, Frerichs H, Gunn J P, Hirai T, Kukushkin A S, Kaveeva E, Miller M A, Moulton D, Rozhansk V Y, Senichenkov I, Sytova E, Schmitz O, Stangeby P C, De Temmerman G, Veselova I, Wiesen S 2019 Nucl. Mater. Energy 20 100696 Google Scholar
[4]	Wang B G, Zhu D Z, Ding R, Chen J L 2017 Plasma Sci. Technol. 19 025603 Google Scholar
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[8]	Perkins F W, Post D E, Uckan N A, et al. 1999 Nucl. Fusion 39 2137 Google Scholar
[9]	Loarte A, Saibene G, Sartori R, Riccardo V, Andrew P, Paley J, Fundamenski W, Eich T, Herrmann A, Pautasso G, Kirk A, Counsell G, Federici G, Strohmayer G, Whyte D, Leonard A, Pitts R A, Landman I, Bazylev B, Pestchanyi S 2007 Phys. Scr. T128 222 Google Scholar
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[11]	Bazylev B, Janeschitz G, Landman I S, Pestchanyi S E 2005 Fusion Eng. Des. 75–79 407 Google Scholar
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[13]	Chen X H, Ding F, Mao H M, Luo G N, Hu Z H, Xu F, Niu G J 2016 Fusion Eng. Des.108 98 Google Scholar
[14]	El-Din El-Morshedy S 2021 Nucl. Mater. Energy 28 101035 Google Scholar
[15]	Raffray A R, Federici G J 1997 Nucl. Mater. 244 85 Google Scholar
[16]	Federici G, Loarte A, Strohmayer G 2003 Plasma Phys. Control. Fusion 45 1523 Google Scholar
[17]	Dejarnac R, Gunn J P 2007 J. Nucl. Mater. 363–365 560 Google Scholar
[18]	Gunn J P, Carpentier S C, Dejarnac R, Escourbiac F, Hirai T, Komm M, Kukushkin A, Panayotis S, Pitts R A 2016 Nucl. Mater. Energ. 12 75 Google Scholar
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[27]	Carslaw H W, Jaeger J C 1959 Conduction of Heat in Solids (Oxford: Clarendon) p2
[28]	Behrisch R 2010 J. Surf. Invest-X-Ray 4 549 Google Scholar
[29]	Dittus F W, Boelter L M K 1985 Int. Commun. Heat Mass Transfer 12 3 Google Scholar
[30]	Sieder E N, Tate G E 1936 Ind. Eng. Chem. 28 1429 Google Scholar
[31]	Collier J G, Thome J R 1994 Convective Boiling and Condensation (3rd Ed.) (New York: Clarendon Press) pp109–111
[32]	Chen J C 1966 Ind. Eng. Chem. Process Des. Dev. 5 322 Google Scholar
[33]	Robinson K, Hawley J G, Campbell N A F 2003 Proc. Inst. Mech. Eng. D 217 877 Google Scholar
[34]	Kukushkin A S, Pacher H D, Kotov V, Reiter D, Coster D, Pacher G W 2007 Nucl. Fusion 47 698 Google Scholar
[35]	Aymar R, Barabaschi P, Shimomura Y 2002 Plasma Phys. Control. Fusion 44 519 Google Scholar
[36]	Roth J, Tsitrone E, Loarte A, Loarer Th, Counsell G, Neu R, Philipps V, Brezinsek S, Lehnen M, Coad P, Grisolia Ch, Schmid K, Krieger K, Kallenbach A, Lipschultz B, Doerner R, Causey R, Alimov V, Shu W, Ogorodnikova O, Kirschner A, Federici G, Kukushkin A, EFDA PWI Task Force, ITER PWI Team, Fusion for Energy, ITPA SOL/DIV 2009 J. Nucl. Mater. 390–391 1 Google Scholar
[37]	Dejarnac R, Komm M, Gunn J P, Panek R 2009 J. Nucl. Mater. 390–391 818 Google Scholar
[38]	Miloshevsky G V, Hassanein A 2010 Nucl. Fusion 50 115005 Google Scholar
[39]	Loarte A 2003 Plasma Phys. Control. Fusion 45 1549 Google Scholar
[40]	Escourbiac F, Durocher A, Fedosov A, Hirai T, Pitts R A, Gavila P, Riccardi B, Kuznetcov V, Volodin A, Komarov A 2019 Fusion Eng. Des. 146 2036 Google Scholar

Cited By

图 1 排布位错瓦片结构示意图　(a)直角瓦片; (b)斜边瓦片

Figure 1. Schematic diagram of misalignment tile structure: (a) Unshaped tile; (b) beveled tile.

DownLoad: Full-Size Img PowerPoint

图 2 (a)双倒角瓦片钨材料和铜中间层最高温度模拟结果与现有工作^[7]的对比, 排布误差为2.5 mm, 表面热负荷为1.5 MW·m^–2; (b)四分之一双倒角瓦片结构图

Figure 2. (a) Temporal evolution of the highest temperature of W armor and Cu heat sink materials of dual chamfer tile for misalignment of a 2.5 mm and perpendicular heat flux of 1.5 MW·m^–2. Here the calculated results are represented by the dash lines, and those represented by the solid lines are taken from the work by Li et al.^[7]; (b) schematic diagram of quarter dual chamfer tile.

DownLoad: Full-Size Img PowerPoint

图 3 偏滤器瓦片表面能流密度分布　(a) δ = 0的直角瓦片; (b) δ = 0.3 mm的直角瓦片; (c) δ = 0的斜边瓦片; (d) δ = 0.3 mm的斜边瓦片; 坐标系原点取在瓦片中心, 距离值表示沿着瓦片表面距离瓦片中心的距离, 向右为正, 向左为负

Figure 3. Energy fluxes received by divertor tile: (a) Unshaped tile for δ = 0; (b) unshaped tile for δ = 0.3 mm; (c) beveled tile for δ = 0; (d) beveled tile for δ = 0.3 mm. Origin of coordinate frame is set at tile center, absolute coordinate value is distance along surface away from center; sign ‘+’ denotes direction to right, and sign ‘–’ to left.

DownLoad: Full-Size Img PowerPoint

图 4 能流密度随时间变化关系曲线, ELMs能流密度峰值为 3333 MW·m^–2, 间隙间能流密度为10 MW·m^–2

Figure 4. Temporal evolution of energy flux of an ELM with peak heat flux of 3333 MW·m^–2 plus an inter-ELM steady-state heat flux of 10 MW·m^–2.

DownLoad: Full-Size Img PowerPoint

图 5 排布误差为0的直角瓦片位置1和位置2处温度随时间的变化

Figure 5. Temporal evolution of temperatures in areas near location 1 and 2 of unshaped tile with no misalignment.

DownLoad: Full-Size Img PowerPoint

图 6 (a) t = 0.37 ms时, 排布误差为0的直角瓦片的温度分布; (b) t = 0.29 ms时, 排布误差为0.3 mm的直角瓦片的温度分布, 图中实线为T = 3683 K等温线

Figure 6. Temperature distribution of unshaped tile with (a) no misalignment at t = 0.37 ms and (b) misalignment of 0.3 mm at t = 0.29 ms. Solid line represents an isotherm of 3683 K.

DownLoad: Full-Size Img PowerPoint

图 7 直角瓦片最高温度随排布误差的变化

Figure 7. Highest temperature of unshaped tile versus misalignment.

DownLoad: Full-Size Img PowerPoint

图 8 排布误差为0的斜边瓦片位置3和位置4处温度随时间的变化

Figure 8. Temporal evolution of temperatures in location 3 and 4 of beveled tile with no misalignment.

DownLoad: Full-Size Img PowerPoint

图 9 (a) t = 0.38 ms时, 排布误差为0的斜边瓦片的温度分布; (b) t = 0.38 ms时, 排布误差为0.3 mm的斜边瓦片的温度分布; 图中洋红色实线为T = 3683 K等温线

Figure 9. Temperature distribution of beveled tile with (a) no misalignment at t = 0.38 ms and (b) misalignment of 0.3 mm at t = 0.38 ms. Solid line represents an isotherm of 3683 K.

DownLoad: Full-Size Img PowerPoint

图 10 斜边瓦片最高温度随排布误差的变化

Figure 10. Highest temperature of beveled tile versus misalignment.

DownLoad: Full-Size Img PowerPoint

图 11 排布误差为0和0.3 mm直角、斜边瓦片熔化体积比随时间的变化

Figure 11. Melting volume ratios of unshaped and beveled tiles with misalignment of 0 and 0.3 mm versus time.

DownLoad: Full-Size Img PowerPoint

图 12 直角和斜边瓦片最大熔化体积比随排布误差的变化

Figure 12. Maximum melting volume ratios of unshaped and beveled tiles versus misalignment.

DownLoad: Full-Size Img PowerPoint

图 13 排布误差为0直角和斜边瓦片汽化体积比随时间的变化

Figure 13. Vaporization volume ratios of unshaped and beveled tiles with no misalignment versus time.

DownLoad: Full-Size Img PowerPoint

图 14 直角和斜边瓦片最大汽化体积比随排布误差的变化

Figure 14. Maximum vaporization volume ratios of unshaped and beveled tiles versus misalignment.

DownLoad: Full-Size Img PowerPoint

图 15 直角、斜边瓦片最高温度随排布误差的变化, 其中入射能流密度为10和20 MW·m^–2

Figure 15. Highest temperatures of unshaped and beveled tiles versus misalignment, where the incident heat is 10 and 20 MW·m^–2

DownLoad: Full-Size Img PowerPoint

图 16 直角、斜边瓦片最高温度随能流密度的变化

Figure 16. Highest temperatures of unshaped and beveled tiles versus heat flux.

DownLoad: Full-Size Img PowerPoint

[1]	Federici G, Skinner C H, Brooks J N, Coad J P, Grisolia C, Haasz A A, Hassanein A, Philipps V, Pitcher C S, Roth J, Wampler W R, Whyte D G 2001 Nucl. Fusion 41 1967 Google Scholar
[2]	Bolt H, Barabash V, Krauss W, Linke J, Neu R, Suzuki S, Yoshida N, ASDEX Upgrade Team 2004 J. Nucl. Mater. 329–333 66 Google Scholar
[3]	Pitts R A, Bonnin X, Escourbiac F, Frerichs H, Gunn J P, Hirai T, Kukushkin A S, Kaveeva E, Miller M A, Moulton D, Rozhansk V Y, Senichenkov I, Sytova E, Schmitz O, Stangeby P C, De Temmerman G, Veselova I, Wiesen S 2019 Nucl. Mater. Energy 20 100696 Google Scholar
[4]	Wang B G, Zhu D Z, Ding R, Chen J L 2017 Plasma Sci. Technol. 19 025603 Google Scholar
[5]	Hirai T, Escourbiac F, Carpentier-Chouchana S, Fedosov A, Ferrand L, Jokinen T, Komarov V, Kukushkin A, Merola M, Mitteau R, Pitts R A, Shu W, Sugihara M, Riccardi B, Suzuki S, Villari R 2013 Fusion Eng. Des. 88 1798 Google Scholar
[6]	Missirlian M, Firdaouss M, Richou M, Languille P, Lecocq S, Lipa M 2013 Fusion Eng. Des. 88 1793 Google Scholar
[7]	Li C J, Zhu D Z, Ding R, Wang B G, Chen J L, Gao B F, Le Y 2020 Nucl. Mater. Energy 25 100847 Google Scholar
[8]	Perkins F W, Post D E, Uckan N A, et al. 1999 Nucl. Fusion 39 2137 Google Scholar
[9]	Loarte A, Saibene G, Sartori R, Riccardo V, Andrew P, Paley J, Fundamenski W, Eich T, Herrmann A, Pautasso G, Kirk A, Counsell G, Federici G, Strohmayer G, Whyte D, Leonard A, Pitts R A, Landman I, Bazylev B, Pestchanyi S 2007 Phys. Scr. T128 222 Google Scholar
[10]	Bazylev B, Janeschitz G, Landman I S, Loarte A, Pestchanyi S E 2007 J. Nucl. Mater. 363–365 1011 Google Scholar
[11]	Bazylev B, Janeschitz G, Landman I S, Pestchanyi S E 2005 Fusion Eng. Des. 75–79 407 Google Scholar
[12]	Coenen J W, Bazylev B, Brezinsek S, Philipps V, Hirai T, Kreter A, Linke J, Sergienko G, Pospieszczyk A, Tanabe T, Ueda Y, Samm U, The TEXTOR-Team 2011 J. Nucl. Mater. 415 S78 Google Scholar
[13]	Chen X H, Ding F, Mao H M, Luo G N, Hu Z H, Xu F, Niu G J 2016 Fusion Eng. Des.108 98 Google Scholar
[14]	El-Din El-Morshedy S 2021 Nucl. Mater. Energy 28 101035 Google Scholar
[15]	Raffray A R, Federici G J 1997 Nucl. Mater. 244 85 Google Scholar
[16]	Federici G, Loarte A, Strohmayer G 2003 Plasma Phys. Control. Fusion 45 1523 Google Scholar
[17]	Dejarnac R, Gunn J P 2007 J. Nucl. Mater. 363–365 560 Google Scholar
[18]	Gunn J P, Carpentier S C, Dejarnac R, Escourbiac F, Hirai T, Komm M, Kukushkin A, Panayotis S, Pitts R A 2016 Nucl. Mater. Energ. 12 75 Google Scholar
[19]	Gunn J P, Carpentier-Chouchana S, Escourbiac F, Hirai T, Panayotis S, Pitts R A, Corre Y, Dejarnac R, Firdaouss M, Kočan M, Komm M, Kukushkin A, Languille P, Missirlian M, Zhao W, Zhong G 2017 Nucl. Fusion 57 046025 Google Scholar
[20]	Komm M, Ratynskaia S, Tolias P, Cavalier J, Dejarnac R, Gunn J P, Podolnik A 2017 Plasma Phys. Control. Fusion 59 094002 Google Scholar
[21]	Sang C F, Sun J Z, Wang D Z 2011 J. Nucl. Mater. 415 S204 Google Scholar
[22]	Hu W P, Sang C F, Sun Z Y, Wang D Z 2017 Fusion Eng. Des. 116 5 Google Scholar
[23]	黄艳, 孙继忠, 桑超峰, 丁芳, 王德真 2014 物理学报 63 035204 Google Scholar Huang Y, Sun J Z, Sang C F, Ding F, Wang D Z 2014 Acta Phys. Sin. 63 035204 Google Scholar
[24]	Huang Y, Sun J Z, Hu W P, Sang C F, Wang D Z 2016 Fusion Eng. Des. 102 28 Google Scholar
[25]	Birdsall C K, Langdon A B 1985 Plasma Physics via Computer Simulation (New York: McGraw-Hill) pp1–479
[26]	Verboncoeur J P 2005 Plasma Phys. Control. Fusion 47 A231 Google Scholar
[27]	Carslaw H W, Jaeger J C 1959 Conduction of Heat in Solids (Oxford: Clarendon) p2
[28]	Behrisch R 2010 J. Surf. Invest-X-Ray 4 549 Google Scholar
[29]	Dittus F W, Boelter L M K 1985 Int. Commun. Heat Mass Transfer 12 3 Google Scholar
[30]	Sieder E N, Tate G E 1936 Ind. Eng. Chem. 28 1429 Google Scholar
[31]	Collier J G, Thome J R 1994 Convective Boiling and Condensation (3rd Ed.) (New York: Clarendon Press) pp109–111
[32]	Chen J C 1966 Ind. Eng. Chem. Process Des. Dev. 5 322 Google Scholar
[33]	Robinson K, Hawley J G, Campbell N A F 2003 Proc. Inst. Mech. Eng. D 217 877 Google Scholar
[34]	Kukushkin A S, Pacher H D, Kotov V, Reiter D, Coster D, Pacher G W 2007 Nucl. Fusion 47 698 Google Scholar
[35]	Aymar R, Barabaschi P, Shimomura Y 2002 Plasma Phys. Control. Fusion 44 519 Google Scholar
[36]	Roth J, Tsitrone E, Loarte A, Loarer Th, Counsell G, Neu R, Philipps V, Brezinsek S, Lehnen M, Coad P, Grisolia Ch, Schmid K, Krieger K, Kallenbach A, Lipschultz B, Doerner R, Causey R, Alimov V, Shu W, Ogorodnikova O, Kirschner A, Federici G, Kukushkin A, EFDA PWI Task Force, ITER PWI Team, Fusion for Energy, ITPA SOL/DIV 2009 J. Nucl. Mater. 390–391 1 Google Scholar
[37]	Dejarnac R, Komm M, Gunn J P, Panek R 2009 J. Nucl. Mater. 390–391 818 Google Scholar
[38]	Miloshevsky G V, Hassanein A 2010 Nucl. Fusion 50 115005 Google Scholar
[39]	Loarte A 2003 Plasma Phys. Control. Fusion 45 1549 Google Scholar
[40]	Escourbiac F, Durocher A, Fedosov A, Hirai T, Pitts R A, Gavila P, Riccardi B, Kuznetcov V, Volodin A, Komarov A 2019 Fusion Eng. Des. 146 2036 Google Scholar

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