六组点堆中子动力学方程组的同伦分析解

朱倩; 商学利; 陈文振

doi:10.7498/aps.61.070201

摘要

鉴于目前六组点堆中子动力学方程仍然无法获得解析解, 本文尝试将同伦分析方法应用于六组缓发中子动力方程组的求解, 获得了它的级数解析解, 并对级数解析解算法的有效性进行了检验. 结果表明, 该级数解析解算法从计算时间和精度上都能达到工程应用的要求, 可适宜于反应堆中子动力学控制的设计分析和仿真计算.

关键词:

Homotopy analysis method is a new method to form approximate analytical solution for non-linear system by using various base functions, which is different from traditional analytical methods. So far, the analytical solution of the point reactor neutron kinetics equations with six-group delayed neutrons has not been obtained yet. In this paper the homotopy analysis method is employed for solving the point reactor neutron kinetics equations with six-group delayed neutrons. The series analysis solutions are obtained using the homotopy analysis method, and the relevant algorithm is given and analyzed. The results show that the computation time and accuracy satisfy the engineering requirements. This analysis method can be applied to the design, the analysis and the simulation of reactor control.

Keywords:

作者及机构信息

1.
海军工程大学核能科学与工程系, 武汉 430033

基金项目: 国家自然科学基金 (批准号: 10575131)和海军工程大学自然科学基金资助的课题.

Authors and contacts

1.
Department of Nuclear Energy Science and Engineering, Naval University of Engineering, Wuhan 430033, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10575131), and the Natural Science Foundation of Naval University of Engineering.

参考文献

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施引文献

[1]	Huang Z Q 2007 Kinetics Base of Nuclear Reactor (BeijingPeaking University Press) p174 (in Chinese)[黄祖洽 2007 核反应堆动力学基础 (北京: 北京大学出版社) 第174页]
[2]
[3]	Chen W Z, Kuang B, Guo L F, Chen Z Y, Zhu B 2006 NuclearEngineering and Design 236 1326
[4]
[5]
[6]	Chen W Z, Guo L F, Zhu B, Li H F 2007 Progress in NuclearEnergy 49 290
[7]
[8]	Li H F, ChenWZ, Zhang F, Luo L 2007 Annals of Nuclear Energy34 521
[9]	Zhang F, Chen W Z, Gui X W 2008 Annals of Nuclear Energy 35746
[10]
[11]	Li H F, Shang X L, Chen W Z 2010 Chinese Science Bulletin 554116
[12]
[13]
[14]	Li H F, Chen W Z, Zhang F, Chen Z Y 2010 Progress in NuclearEnergy 52 321
[15]	Li H F, Chen W Z, Zhang F, Shang X L 2010 Acta Phys. Sin. 592375 (in Chinese)[黎浩峰, 陈文振, 张帆, 商学利 2010 物理学报 59 2375]
[16]
[17]	Liao S J 2003 Beyond Perturbation: Introduction to the HomotopyAnalysis Method(Boca Raton: Chapman Hall/CRC Press)p20
[18]
[19]	Yamashita M, Yabushita K, Tsuboi K 2007 J. Phys. 40 8403
[20]
[21]	Liao S J, Tan Y 2007 Stud. Appl. Math. 119 317
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[24]	Zhu Q, Li H F, Luo L, Chen Z Y 2010 Atomic Energy Science andTechnology 44(s1) 303 (in Chinese)[朱倩, 黎浩峰, 罗磊, 陈志云 2010 原子能科学技术 44 (s1) 303]
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[26]	Ye W C, Li B, Wang J 2011 Acta Phys. Sin.60 030207 (in Chinese)[叶望川, 李彪, 王佳 2011 物理学报 60 030207]
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