Abstract The safety and optimal performance of nuclear reactors require online monitoring in the core. The present paper describes a method that avoids the solution of the time-dependent neutron diffusion equation, and it uses online readings of the fixed in-core neutron detectors to reconstruct the three-dimensional (3D) neutron flux distribution. The essential idea of the nodal synthesis method is the separation of time and space-dependence of the neutron flux distribution. The time-dependent section of the flux distribution is determined by in-core neutron detector readings, and the space-dependent section is obtained from pre-computed harmonics of the neutron diffusion equation. In online computation, time-dependent coefficients are only computed, and flux distribution is reconstructed by pre-computed harmonics. To calculate the diffusion equation harmonics, the nodal expansion method and the Gram-Schmidt process are used. Online reconstruction of neutron flux distribution in the Bushehr Nuclear Power Plant with VVER-1000/446 reactor type is simulated, and the results are benchmarked by valid results. The maximum relative percent error between reconstructed results and the valid results is about 5%, and the computing time is about 0.5 s.

中文翻译：

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使用在线堆芯中子探测器读数通过节点合成法重建中子通量分布

摘要 核反应堆的安全和最佳性能需要堆芯在线监测。本文描述了一种避免求解瞬态中子扩散方程的方法，它使用固定的堆芯中子探测器的在线读数来重建三维 (3D) 中子通量分布。节点合成法的基本思想是分离中子通量分布的时间和空间依赖性。通量分布的时间相关部分由堆芯中子探测器读数确定，空间相关部分由中子扩散方程的预计算谐波获得。在在线计算中，仅计算瞬态系数，并通过预先计算的谐波重建通量分布。为了计算扩散方程谐波，使用了节点扩展方法和 Gram-Schmidt 过程。模拟了VVER-1000/446型反应堆布什尔核电站中子通量分布在线重建，并以有效结果为基准。重构结果与有效结果的最大相对百分比误差约为5%，计算时间约为0.5 s。