两种大规模燃耗链求解算法对比分析

谭杰; 张鹏

doi:10.11884/HPLPB201830.170293

两种大规模燃耗链求解算法对比分析

doi: 10.11884/HPLPB201830.170293

谭杰,
张鹏^,

武汉大学水力机械过渡过程教育部重点实验室, 武汉 430072

基金项目:

国家自然科学基金项目 11305036

详细信息

作者简介:
谭杰(1992—)，女，硕士，从事反应堆燃耗相关研究; jietan@whu.edu.cn

通讯作者:
张鹏(1985—)，男，博士，从事反应堆物理数值计算方法研究; peng-zhang@whu.edu.cn

中图分类号: TL329.2
计量
- 文章访问数: 1231
- HTML全文浏览量: 320
- PDF下载量: 154
- 被引次数: 0
出版历程
- 收稿日期: 2017-07-14
- 修回日期: 2017-11-27
- 刊出日期: 2018-03-15

Comparison and analysis of two algorithms for solving large depletion chains

Tan Jie,
Zhang Peng^,

Hydraulic Machinery Transients Key Laboratory of Ministry of Education, Wuhan University, Wuhan 430072, China

摘要

摘要: 为严格追踪裂变反应堆中核素成分随燃耗的变化，基于燃耗矩阵法求解燃耗方程，分别采用自主编写的Chebyshev有理近似方法(CRAM)程序和广泛应用的ORIGEN2程序进行大规模燃耗链的点燃耗计算，并对两种算法的相关参数进行对比分析。结果表明：在计算精度方面，CRAM与ORIGEN2程序获得的重要核素的核密度较为一致，个别核素相对误差较大；在计算效率方面，单步燃耗计算ORIGEN2略胜一筹，但CRAM耗时也非常短；在步长稳定性方面，CRAM具有显著优势，而ORIGEN2的统计结果受步长变化的影响较大。
- CRAM /
- ORIGEN2 /
- 大规模燃耗链 /
- 步长稳定性
Abstract: In order to trace strictly the changes of nuclide density with burnup in a fission reactor, the independently developed codes by Chebyshev Rational Approximate Method (CRAM) and widely applied ORIGEN2 were adopted to solve large depletion chains to solve depletion equations based on Burnup Matrix Methods. The values are compared and analyzed with the aspects of computational accuracy, efficiency and step stability. The results show that CRAM can provide similar density solutions of important nuclides with a little slower speed and a much better step stability than those of ORIGEN2.
- CRAM /
- ORIGEN2 /
- large depletion chains /
- step stability

HTML全文

图 1 燃耗矩阵的非零元素分布

Figure 1. Non-zero element distribution of a burnup matrix

下载: 全尺寸图片幻灯片

图 2 负实轴上CRAM计算结果r_{16, 16}(x)与e^x的误差图

Figure 2. Plot of error between e^x and r_{16, 16}(x) based on CRAM on negative real axis

下载: 全尺寸图片幻灯片

图 3 重要核素相对误差

Figure 3. Relative differences of important nuclides

下载: 全尺寸图片幻灯片

图 4 Am和Cm燃耗链

Figure 4. Burnup chains of Am and Cm

下载: 全尺寸图片幻灯片

图 5 Am和Cm的核密度变化

Figure 5. Density changes of Am and Cm

下载: 全尺寸图片幻灯片

图 6 Am和Cm的核密度相对误差变化

Figure 6. Relative error changes of density of Am and Cm

下载: 全尺寸图片幻灯片

图 7 不同燃耗步长对重要核素统计的影响

Figure 7. Influence of different burnup step on important nuclides

下载: 全尺寸图片幻灯片

参考文献(12)

[1]	龚建华. 深度优先搜索算法及其改进[J]. 现代电子技术, 2007, 30 (22): 90-92. https://www.cnki.com.cn/Article/CJFDTOTAL-XDDJ200722034.htm Gong Jianhua. Depth priority algorithm and its improvement. Modern Electronics Technique, 2007, 30 (22): 90-92 https://www.cnki.com.cn/Article/CJFDTOTAL-XDDJ200722034.htm
[2]	吴明宇, 王事喜, 杨勇, 等. 基于线性核素链的燃耗算法与蒙特卡罗程序耦合计算[J]. 强激光与粒子束, 2013, 25 (1): 248-252. doi: 10.3788/HPLPB20132501.0248 Wu Mingyu, Wang Shixi, Yang Yong, et al. Monte Carlo program coupling with depletion code based on linear nuclide chain. High Power Laser and Particle Beams, 2013, 25 (1): 248-252 doi: 10.3788/HPLPB20132501.0248
[3]	李昊, 杨烽, 余纲林, 等. 基于线性子链法的压水堆裂变产物源项一体化计算方法[J]. 强激光与粒子束, 2017, 29: 026002. doi: 10.11884/HPLPB201729.160245 Li Hao, Yang Feng, Yu Ganglin, et al. Integrated calculation method for pressurized water reactor design basis source terms based on linear chain method. High Power Laser and Particle Beams, 2017, 29: 026002 doi: 10.11884/HPLPB201729.160245
[4]	Cetenar J. General solution of Bateman equations for nuclear transmutations[J]. Annuals of Nuclear Energy, 2006, 33 (7): 640-645.
[5]	Pusa M. Rational approximations to the matrix exponential in burnup calculations[J]. Nuclear Science & Engineering the Journal of the American Nuclear Society, 2011, 169 (2): 155-167.
[6]	Cody W J, Meinardus G, Varga R S. Chebyshev rational approximations to e^-x in[0, +∞) and applications to heat-conduction problems[J]. Journal of Approximation Theory, 1969, 2 (1): 50-65.
[7]	Pusa M, Leppänen J. Computing the matrix exponential in burnup calculations[J]. Nuclear Science & Engineering: the Journal of the American Nuclear Society, 2010, 164 (23): 140-150.
[8]	Pusa M. Correction to partial fraction decomposition coefficients for Chebyshev rational approximation on the negative real axis[J/OL]. ArXiv: 1206.2880[math. NA], 2012.
[9]	Gonchar A A, Rakhmanov E A. Equilibrium distributions and rate of rational approximation of analytic functions[J]. Mathematics of the USSR-Sbornik, 1989, 62 (2): 306-352.
[10]	Dehart M D. OECD/NEA burnup credit calculational criticality benchmark phaseI-B results[R]. ORNL-6901, 1996.
[11]	James R B, and Donald J R. Sparse matrix computations[M]. New York: Academic Press, 1976: 3-22.
[12]	Pusa M, Leppänen J. Solving linear systems with sparse Gaussian elimination in the Chebyshev Rational Approximation Method[J]. Nuclear Science and Engineering, 2013, 175 (3): 250-258.