离散纵标六角形节块法及CMFD加速研究
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摘要
离散纵标节块法是一种求解六角形中子输运方程的有效方法。本文基于六角形横向积分离散纵标方程,解析得到横向积分通量出射通量与入射通量的关系,并根据类似于扩散方法的六角形输运节块中子平衡方程形式,得到了一种离散纵标六角形节块法数值迭代策略。由于离散纵标法收敛速度较慢,本文根据粗网有限差分(CMFD)技术导出离散纵标六角形CMFD加速方法。数值计算结果表明,该CMFD加速技术能取得约16倍的加速效果。
Discrete ordinate nodal method is a very effective method for solving the hexagonal neutron transport equation. Based on hexagonal transverse integrated discrete ordinate equation, the relationship of transverse integrated outgoing and incoming fluxes was analytically obtained. With hexagonal transport nodal neutron balance equation analog to diffusion method, a discrete ordinate hexagonal nodal numerical iteration strategy was obtained. Because discrete ordinate method converges slowly, a coarse mesh finite difference(CMFD) method was introduced for acceleration of hexagonal discrete ordinate method. Numerical results indicate that the method can achieve approximately 16 times accelerating effect.
Discrete ordinate nodal method is a very effective method for solving the hexagonal neutron transport equation. Based on hexagonal transverse integrated discrete ordinate equation, the relationship of transverse integrated outgoing and incoming fluxes was analytically obtained. With hexagonal transport nodal neutron balance equation analog to diffusion method, a discrete ordinate hexagonal nodal numerical iteration strategy was obtained. Because discrete ordinate method converges slowly, a coarse mesh finite difference(CMFD) method was introduced for acceleration of hexagonal discrete ordinate method. Numerical results indicate that the method can achieve approximately 16 times accelerating effect.
引文
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[8] 李志勇. 中子平衡节块离散纵标法及CMFD加速技术研究[J]. 原子能科学技术,2015,49(3):497-501. LI Zhiyong. Study on neutron balance nodal discrete ordinate method and CMFD acceleration technique[J]. Atomic Energy Science and Technology, 2015, 49(3): 497-501(in Chinese).
[9] IKEDA H, TAKEDA T. A new nodal SN transport method for three dimensional hexagonal geometry[J]. Journal of Nuclear Science and Technology, 1994, 31(6): 497-509.
[10] 张颖,谢仲生,陈达,等. 穿透概率法求解二维六角形几何多群中子积分输运方程[J]. 西安交通大学学报,2000,34(3):40-44. ZHANG Ying, XIE Zhongsheng, CHEN Da, et al. Numerical solution of multigroup integral neutron transport equation for hexagonal geometry[J]. Journal of Xi’an Jiaotong University, 2000, 34(3): 40-44(in Chinese).
[2] CHO N Z. Fundamentals and recent developments of reactor physics methods[J]. Nuclear Engineering and Technology, 2005, 37(1): 25-78.
[3] ASKEW J R. A characteristics formulation of the neutron transport equation in complicated geometries, AEEW-R-1108[R]. UK: Atomic Energy Authority, 1972.
[4] CARLVIK I. A method of calculating collision probabilities in general cylindrical geometry and application to flux distributions and dancoff factors[C]//Proceedings of 3rd International Conference on PUAE. Vienna: IAEA, 1964.
[5] CARLSON B G. Transport theory discrete ordinate quadrature over the unit sphere, LA-4554[R]. USA: [s. n.], 1970.
[6] MYNATT F R. DOT-Ⅲ, two-dimensional discrete ordinate transport code, ORNL-TM-4280[R]. USA: [s. n.], 1973.
[7] LAWRENCE R D, DORNING J J. A discrete nodal integral transport theory method for multi- dimensional reactor physics and shielding calculations[C]//Advances in Reactor Physics and Shielding. Sun Valley, Idaho: [s. n.], 1980.
[8] 李志勇. 中子平衡节块离散纵标法及CMFD加速技术研究[J]. 原子能科学技术,2015,49(3):497-501. LI Zhiyong. Study on neutron balance nodal discrete ordinate method and CMFD acceleration technique[J]. Atomic Energy Science and Technology, 2015, 49(3): 497-501(in Chinese).
[9] IKEDA H, TAKEDA T. A new nodal SN transport method for three dimensional hexagonal geometry[J]. Journal of Nuclear Science and Technology, 1994, 31(6): 497-509.
[10] 张颖,谢仲生,陈达,等. 穿透概率法求解二维六角形几何多群中子积分输运方程[J]. 西安交通大学学报,2000,34(3):40-44. ZHANG Ying, XIE Zhongsheng, CHEN Da, et al. Numerical solution of multigroup integral neutron transport equation for hexagonal geometry[J]. Journal of Xi’an Jiaotong University, 2000, 34(3): 40-44(in Chinese).