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为了认识储氚高压容器壁材料的力学性能变化及其导致的容器承载能力变化, 必须研究储氚期间, 容器壁中氚和氦-3浓度的空间分布和随时间的变化. 针对容器外表面为一般传质边界条件和容器内部氚为范德瓦尔斯气体的情况, 同时考虑容器腔内和容器壁中氚的衰变和扩散, 建立求解储氚高压容器壁中氚和氦-3浓度的解析理论模型, 导出了氚和氦-3浓度的理论公式. 通过解析计算给出了器壁中氚和氦-3浓度随外表面传质系数的变化曲线和浓度的时空变化曲线, 提出了氦-3浓度的2 1 + 2 / 2倍定律, 即处于开放空间的储氚球形高压容器, 器壁中氦-3的浓度呈内高外低的分布, 时间越长, 浓度沿径向的梯度越大, 在时间足够长时, 各处浓度逼近时间无限长时的最终值, 也就是各处的最大值, 内表面处的最大值是该处氚初始时刻浓度的2 1 + 2 / 2倍, 这里 1 和 2 为与氚的范德瓦尔斯常数相关的参数. 研究结果为储氚高压容器的强度安全性评估提供了前提.In order to understand the changes of mechanical properties of the wall materials and the carrying capacity of vessel which contains high pressure tritium, the spatiotemporal changes of tritium and helium-3 content in the wall should be studied during tritium storage. Taking into consideration the case that the outer surface of the vessel is with general mass transfer boundary condition and the tritium inside the vessel is van der Waals gas, and also taking into account both decay and permeation of tritium inside the vessel and decay and diffusion of tritium in the wall material, the analytical theoretical models of tritium and helium-3 content in the wall are developed and solved, and relevant theoretical formulas are deduced. Through analytical calculations, the curves of tritium and helium-3 content in the wall versus mass transfer coefficient of the outer surface, storage time and the spatial positions are plotted. Through analysis, a law called 21+2/2 time law of helium-3 content is put forward, where 1 and 2 are the coefficients which are related to van der Waals constant of tritium. The law is proposed: helium-3 content in the wall of the spherical high pressure vessel storing tritium which is in an open space rises along the radius from outer to inner, and the content radial gradient increases with storage time. If storage time is long enough, the helium-3 content at any point will approach to its final value, that is, a maximal value at a relevant point. The ratio of the maximum helium-3 content to the related initial tritium content is 21 + 2/2 at the inner surface. The obtained formulas and understandings can be used as a premise of the safety assessment of tritium stored vessel.
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Keywords:
- steel spherical pressure vessel /
- tritium decay /
- helium-3 /
- diffusion
[1] Marchi C S, Somerday B, Robinson S 2007 WSRC-STI 00579
[2] Wang X L 2009 Journal of Nuclear and Radiochemistry 31 64 (in Chinese) [汪小琳 2009 核化学与放射化学 31 64]
[3] Ma L M, Li Y Y 1988 Acta Metallurgica Sinica 24 B432
[4] Fedov V V, Pokhmursky V I , Dyomina E V , Prusakova M D, Vinogradova N A 1995 Fusion Technology 28 1153
[5] Shiraishi T ,Nishikawa M , Tamaguchi T, Kenmotsu K 1999 J. Nucl. Mater. 273 60
[6] Chen C A, Wu S, Ni R F, Bo C M 2000 Journal of Nuclear and Radiochemistry 22 144 (in Chinese) [陈长安, 武胜, 倪然夫, 柏朝茂 2000 核化学与放射化学 22 144]
[7] Chen C A, Wu S, Ni R F 2000 Atomic Energy Science and Technology 35 20 (in Chinese) [陈长安, 武胜, 倪然夫 2000 原子能科学技术 35 20]
[8] Wang L B, Lu M Q, Li Y Y 2003 Acta Metallurgica Sinica 39 449 (in Chinese) [王隆保, 吕曼祺, 李依依 2003 金属学报 39 449]
[9] Xie B, WENG K P 2009 Journal of Molecular Science 25 352 (in Chinese) [谢波, 翁葵平 2009 分子科学学报 25 352]
[10] Xie C, Hou Q, Wang J, Sun T Y, Long X G, Luo S Z 2008 Acta Phys. Sin. 57 5159 (in Chinese) [谢朝, 侯氢, 汪俊, 孙铁英, 龙兴贵, 罗顺忠 2008 57 5159]
[11] Zhang B L, Wang J, Hou Q 2011 China. Phys. B 20 036105
[12] Liu Y D, Yin Y H, Tan Y, Sun Y, Mei J 2011 Sci. China Tech. Sci. 54 1521
[13] Wang P X, Song J S 2002 Helium in Materials and the Permeation of Tritium (Beijing: National Defense Industry Press) p53 (in Chinese) [王佩璇, 宋家树 2002 材料中的氦及氚渗透 (北京: 国防工业出版社) 第53页]
[14] Hu X, Lv R D, Liu G J, Hei E C 2007 Physical Chemistry (Beijing: Higher Education Press) p11 (in Chinese) [胡英, 吕瑞东, 刘国杰, 黑恩成 2007 物理化学 (北京: 高等教育出版社) 第11页]
[15] Jiang Y M, Xie H B, Guo F, Liu P, Li J 2005 Acta Phys. Sin. 54 5769 (in Chinese) [蒋益明, 谢亨博, 郭峰, 刘平, 李劲 2005 54 5769]
[16] Chen C A 2003 Ph. D. Dissertation (Mianyang: China Academy of Engineering Physics) (in Chinese) [陈长安 2003 博士学位论文 (绵阳: 中国工程物理研究院)]
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[1] Marchi C S, Somerday B, Robinson S 2007 WSRC-STI 00579
[2] Wang X L 2009 Journal of Nuclear and Radiochemistry 31 64 (in Chinese) [汪小琳 2009 核化学与放射化学 31 64]
[3] Ma L M, Li Y Y 1988 Acta Metallurgica Sinica 24 B432
[4] Fedov V V, Pokhmursky V I , Dyomina E V , Prusakova M D, Vinogradova N A 1995 Fusion Technology 28 1153
[5] Shiraishi T ,Nishikawa M , Tamaguchi T, Kenmotsu K 1999 J. Nucl. Mater. 273 60
[6] Chen C A, Wu S, Ni R F, Bo C M 2000 Journal of Nuclear and Radiochemistry 22 144 (in Chinese) [陈长安, 武胜, 倪然夫, 柏朝茂 2000 核化学与放射化学 22 144]
[7] Chen C A, Wu S, Ni R F 2000 Atomic Energy Science and Technology 35 20 (in Chinese) [陈长安, 武胜, 倪然夫 2000 原子能科学技术 35 20]
[8] Wang L B, Lu M Q, Li Y Y 2003 Acta Metallurgica Sinica 39 449 (in Chinese) [王隆保, 吕曼祺, 李依依 2003 金属学报 39 449]
[9] Xie B, WENG K P 2009 Journal of Molecular Science 25 352 (in Chinese) [谢波, 翁葵平 2009 分子科学学报 25 352]
[10] Xie C, Hou Q, Wang J, Sun T Y, Long X G, Luo S Z 2008 Acta Phys. Sin. 57 5159 (in Chinese) [谢朝, 侯氢, 汪俊, 孙铁英, 龙兴贵, 罗顺忠 2008 57 5159]
[11] Zhang B L, Wang J, Hou Q 2011 China. Phys. B 20 036105
[12] Liu Y D, Yin Y H, Tan Y, Sun Y, Mei J 2011 Sci. China Tech. Sci. 54 1521
[13] Wang P X, Song J S 2002 Helium in Materials and the Permeation of Tritium (Beijing: National Defense Industry Press) p53 (in Chinese) [王佩璇, 宋家树 2002 材料中的氦及氚渗透 (北京: 国防工业出版社) 第53页]
[14] Hu X, Lv R D, Liu G J, Hei E C 2007 Physical Chemistry (Beijing: Higher Education Press) p11 (in Chinese) [胡英, 吕瑞东, 刘国杰, 黑恩成 2007 物理化学 (北京: 高等教育出版社) 第11页]
[15] Jiang Y M, Xie H B, Guo F, Liu P, Li J 2005 Acta Phys. Sin. 54 5769 (in Chinese) [蒋益明, 谢亨博, 郭峰, 刘平, 李劲 2005 54 5769]
[16] Chen C A 2003 Ph. D. Dissertation (Mianyang: China Academy of Engineering Physics) (in Chinese) [陈长安 2003 博士学位论文 (绵阳: 中国工程物理研究院)]
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