处理多重复杂度中子共振问题的子群方法研究
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摘要
中子共振计算是反应堆物理计算的基本环节，直接影响物理计算的准确度。随着核能形势的快速发展，堆芯设计趋于多样化，不可避免地增加了对复杂几何结构、复杂燃料成分、多共振区的多重复杂度共振问题的计算需求。
传统的基于等价原理的共振计算模型难以满足对复杂共振问题的计算要求，而子群法由于在计算精度、计算速度、复杂几何处理能力等方面都有较好的发展潜力，使其成为了解决这一问题的重要选择。本文以子群法作为研究对象，主要进行了以下研究：
第一，将子群法与特征线法结合，实现了对复杂几何结构共振问题的准确处理。利用拟合法获取子群参数，分析了子群数目对子群参数拟合精度的影响，同时还给出了子群散射矩阵的近似处理方法。
第二，针对子群法不能很好处理共振干涉效应的缺陷，提出了两种不同的共振干涉效应处理方法。其中，随机干涉相关概率法采用随机干涉近似求解相关概率，能够处理多温度、多能群、多核素的共振干涉效应；基于截面修正的方法制作近似考虑共振干涉影响的核截面，在提高共振计算精度的同时不额外增加计算量。
第三，通过制作考虑弹性散射共振效应的核截面，并求解相关的子群分截面，将其应用于子群法，进一步提高了共振计算精度。采用合理的近似方法处理共振核素的散射矩阵，解决了由于引入共振弹性散射截面引起的子群方程中散射截面不一致的问题。
根据上述研究内容，研制开发了子群法-特征线法计算程序SGMOC。通过数值验证表明：SGMOC程序能够准确处理不同复杂程度的共振问题；随机干涉相关概率法和基于截面修正的方法都能提高子群法共振干涉计算的准确度；通过考虑弹性散射的共振效应，能够进一步提高子群法计算精度。最后，通过计算分析，给出了求积组数目以及射线间距的选取原则。
通过本文的研究，改进了子群法不能处理共振干涉效应的缺陷，提高了子群法计算精度，最终形成了能够处理多重复杂度共振问题的先进共振计算模型。
Neutron resonance calculation is a basic part of reactor physics calculation, and itdirectly influences the accuracy of physics calculation. With the fast development ofnuclear power, the design of reactor core is becoming more various, and thecomputation requirement of multiple-complexity resonance problems, with complexgeometry structure, complex fuel composition or multiple resonance regions, isinevitably increased.
It is difficult for the traditional resonance calculation model based on equivalenceprinciple to fulfill the computation requirements of complex resonance problems. Onthe other hand, subgroup method has great potential in calculation accuracy, efficiency,and capability of handling complex geometry. These merits make subgroup method animportant choice to solve the problem. So this thesis focuses on subgroup method, andthe research contents are shown as below.
Firstly, the subgroup method and the method of characteristics are combined toachieve the accurate computation of complex geometry resonance problems. The fittingmethod is used to obtain subgroup parameters, and the influence of subgroup number onfitting accuracy of subgroup parameters is analyzed. The approximate treatment ofsubgroup scattering matrix is also proposed.
Secondly, two different methods for resonance interference effect calculation areproposed, which both improve the performance of subgroup method on handlingresonance interference effect. Stochastic interference correlated-probability method isproposed, which obtains correlated-probability by stochastic interference approximation,in order to extend correlated-probability method to compute resonance interferenceproblems with multi-temperature, multi-group, multi-isotope. The method based oncross-section modification produces nuclear cross-section which taking resonanceinterference effect into account approximately. This method enhances the resonancecalculation accuracy; meanwhile, it costs no additional computation time.
Thirdly, new nuclear cross-section taking resonance effect of elastic scattering intoaccount is produced. Correlative subgroup parameters are obtained and applied tosubgroup method, and then the resonance calculation accuracy is further improved.Reasonable approximate technique is used to handle scattering matrixes of resonance isotopes, which solves the scattering cross-section conflicting problem in subgroupequation brought by the importing of resonance elastic scattering cross-section.
Subgroup method&method of characteristics calculation code SGMOC isdeveloped, utilizing the aforementioned methods. The results of several benchmarksshow that: the SGMOC code is able to handle resonance problems with differentcomplexity degrees; both two correction methods, which are stochastic interferencecorrelated-probability method and the method based on cross-section modification, areable to enhance the accuracy of subgroup resonance interference effect calculation; andthe accuracy of subgroup method is further improved by taking resonance elasticscattering into account. Finally, the selection principle of quadrature set order and rayspacing on resonance calculation is proposed.
This thesis improves the performance of subgroup method on resonanceinterference effect calculation, enhances the calculation accuracy of subgroup method,and finally constructs an advanced resonance calculation model which is able to handlemultiple-complexity resonance problems.
传统的基于等价原理的共振计算模型难以满足对复杂共振问题的计算要求，而子群法由于在计算精度、计算速度、复杂几何处理能力等方面都有较好的发展潜力，使其成为了解决这一问题的重要选择。本文以子群法作为研究对象，主要进行了以下研究：
第一，将子群法与特征线法结合，实现了对复杂几何结构共振问题的准确处理。利用拟合法获取子群参数，分析了子群数目对子群参数拟合精度的影响，同时还给出了子群散射矩阵的近似处理方法。
第二，针对子群法不能很好处理共振干涉效应的缺陷，提出了两种不同的共振干涉效应处理方法。其中，随机干涉相关概率法采用随机干涉近似求解相关概率，能够处理多温度、多能群、多核素的共振干涉效应；基于截面修正的方法制作近似考虑共振干涉影响的核截面，在提高共振计算精度的同时不额外增加计算量。
第三，通过制作考虑弹性散射共振效应的核截面，并求解相关的子群分截面，将其应用于子群法，进一步提高了共振计算精度。采用合理的近似方法处理共振核素的散射矩阵，解决了由于引入共振弹性散射截面引起的子群方程中散射截面不一致的问题。
根据上述研究内容，研制开发了子群法-特征线法计算程序SGMOC。通过数值验证表明：SGMOC程序能够准确处理不同复杂程度的共振问题；随机干涉相关概率法和基于截面修正的方法都能提高子群法共振干涉计算的准确度；通过考虑弹性散射的共振效应，能够进一步提高子群法计算精度。最后，通过计算分析，给出了求积组数目以及射线间距的选取原则。
通过本文的研究，改进了子群法不能处理共振干涉效应的缺陷，提高了子群法计算精度，最终形成了能够处理多重复杂度共振问题的先进共振计算模型。
Neutron resonance calculation is a basic part of reactor physics calculation, and itdirectly influences the accuracy of physics calculation. With the fast development ofnuclear power, the design of reactor core is becoming more various, and thecomputation requirement of multiple-complexity resonance problems, with complexgeometry structure, complex fuel composition or multiple resonance regions, isinevitably increased.
It is difficult for the traditional resonance calculation model based on equivalenceprinciple to fulfill the computation requirements of complex resonance problems. Onthe other hand, subgroup method has great potential in calculation accuracy, efficiency,and capability of handling complex geometry. These merits make subgroup method animportant choice to solve the problem. So this thesis focuses on subgroup method, andthe research contents are shown as below.
Firstly, the subgroup method and the method of characteristics are combined toachieve the accurate computation of complex geometry resonance problems. The fittingmethod is used to obtain subgroup parameters, and the influence of subgroup number onfitting accuracy of subgroup parameters is analyzed. The approximate treatment ofsubgroup scattering matrix is also proposed.
Secondly, two different methods for resonance interference effect calculation areproposed, which both improve the performance of subgroup method on handlingresonance interference effect. Stochastic interference correlated-probability method isproposed, which obtains correlated-probability by stochastic interference approximation,in order to extend correlated-probability method to compute resonance interferenceproblems with multi-temperature, multi-group, multi-isotope. The method based oncross-section modification produces nuclear cross-section which taking resonanceinterference effect into account approximately. This method enhances the resonancecalculation accuracy; meanwhile, it costs no additional computation time.
Thirdly, new nuclear cross-section taking resonance effect of elastic scattering intoaccount is produced. Correlative subgroup parameters are obtained and applied tosubgroup method, and then the resonance calculation accuracy is further improved.Reasonable approximate technique is used to handle scattering matrixes of resonance isotopes, which solves the scattering cross-section conflicting problem in subgroupequation brought by the importing of resonance elastic scattering cross-section.
Subgroup method&method of characteristics calculation code SGMOC isdeveloped, utilizing the aforementioned methods. The results of several benchmarksshow that: the SGMOC code is able to handle resonance problems with differentcomplexity degrees; both two correction methods, which are stochastic interferencecorrelated-probability method and the method based on cross-section modification, areable to enhance the accuracy of subgroup resonance interference effect calculation; andthe accuracy of subgroup method is further improved by taking resonance elasticscattering into account. Finally, the selection principle of quadrature set order and rayspacing on resonance calculation is proposed.
This thesis improves the performance of subgroup method on resonanceinterference effect calculation, enhances the calculation accuracy of subgroup method,and finally constructs an advanced resonance calculation model which is able to handlemultiple-complexity resonance problems.
引文
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[2] Zhaopeng Zhong, Thomas J. Downar, Yunlin Xu. Continuous-energy multi-dimensional SNtransport for problem-dependent resonance self-shielding calculations. Nuclear Science andEngineering,2006,154:190-201.
[3] T. Hazama, A. Shono, K. Sugino. Verification of a nuclear analysis system for fast reactorsusing BFS-62critical experiment. Journal of nuclear science and technology,2004,41:1145-1154.
[4] Taira Hazama, Go Chiba, Kazuteru Sugino. Development of a fine and ultra-fine group cellcalculation code SLAROM-UF for fast reactor analyses. Journal of nuclear science andtechnology,2006,43:908-918.
[5] Naoki Sugimura, Akio Yamamoto. Resonance treatment based on ultra-fine-group spectrumcalculation in the AEGIS code. Journal of nuclear science and Technology,2007,44:958-966.
[6] L. B. Levitt. The probability table method for treating unresolved neutron resonances inMonte Carlo calculations. Nuclear Science and Engineering,1972,49:450-458.
[7] M. N. Nikolaev. Comments on the Probability Table Method. Nuclear Science andEngineering,1976,61:286-293.
[8] Alain Hebert. A review of legacy and advanced self-shielding models for lattice calculations.Nuclear science and engineering,2007,155:310-320.
[9] Nikolaev, M. N. and Phillipov, V. V. Atomic Energy,1963.
[10] Stewart, J. C., J. Quant. Spectrosc. Radiat. Transfer,1964.
[11] Goldstein, R. and Cohen, E. R. Nuclear Science and Engineering,1962,13:132-140.
[12] Goldstein, R. Nuclear Science and Engineering,1972,48:248-257.
[13] Goldstein, R. Trans. Am. Nucl. Soc.,1975,21:493-501.
[14] Cullen, D. E. Nuclear Science and Engineering,1974,55.
[15] Cullen, D. E. Calculation of Probability Table Parameters to Include Intermediate ResonanceSelf-Shielding. UCRL-79762, Lawrence Livermore Laboratory, Livermore, California,1977.
[16] Cullen, D. E. and Pomraning, G. C., J. Quant. Spectrosc. Radiat. Transfer,1980,24.
[17] Hoffinann, A., Jeanpierre, F., Kavenoky, A., Livolant, M., and Lorain, H. APOLLO CodeMultigroupe de Résolution de l’Equation du Transport pour les Neutrons Thermiques etRapides, note CEA-N-1610,1972.
[18] J. R. ASKEW, F. J. FAYERS, and P. B. KEMSHELL. A General Descreption of the LatticeCode WIMS. J. British Energy Soc.,1966.
[19] D. B. Jones, S. P. Baker, K. E. Watkins. CPM-3, A STATE-OF-THE-ART NUCLEAR FUELLATTICE PHYSICS BURNUP CODE. Proceedings of the PHYSOR2000, Pittsburgh,Pennsylvania, USA,2000.
[20] AHLIN, A. and EDENIUS, M. CASMO–a fast transport theory assembly depletion code forLWR analysis. Transactions of the American Nuclear Society,1977,26:604-605.
[21] W. S. Yang, T. A. Taiwo. Status of Reactor Analysis Methods and Codes in the USA.PHYSOR2004, Chicago, Illinois, USA,2004.
[22] Joel Rhodes, Kord Smith, and Deokjung Lee. CASMO-5Development and Applications.PHYSOR2006, ANS Topical Meeting on Reactor Physics, Organized and hosted by theCanadian Nuclear Society. Vancouver, BC, Canada,2006.
[23] C. M. Mildrum, L. T. Mayhue, et al. QUALIFICATION OF THE PHOENIX/POLCANUCLEAR DESIGN AND ANALYSIS PROGRAMS FOR BOILING WATER REACTORS.WCAP-10841,1985.
[24] R. J. J. Stamm’ler and M. J. Abbate. Methods of steady-state reactor physics in nucleardesign. Academic Press, London,1983.
[25]刘旭东等. TPFAP-E程序用户手册.中国核动力研究设计院,1992.
[26] R. Sanchez, J. Mondot, Z. Stankovski, A. Cossic, I. Zmijarevic. APOLLO2: A user-oriented,portable, modular code for multi-group transport assembly calculations. Nuclear Science andEngineering,1988,100:352-362.
[27] J. Marten, F. Clément, V. Marotte, E. Martinolli, S. Misu, S. Thareau, L. Villatte. The newAREVA NP spectral code APOLLO2-A. Jahrestagung Kerntechnik2007, Karlsruhe,Germany,2007.
[28] M. J. Halsall. WIMS8-Speed with Accuracy, ANS Topical Meeting, Long Island, USA,1998.
[29] D. J. Powney, T. D. Newton. Overview of the WIMS9resonance treatment.ANSWERS/WIMS/TR.26Issue1,2004.
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