基于裂变矩阵的谐波计算及其在气冷微堆功率监测中的应用

Harmonic Calculation Based on Fission Matrix and Its Application in Power Monitoring of Gas-cooled Micro Reactor

气冷微堆受限于堆芯体积及堆内高温高辐照运行环境,仅能布置少量堆外探测器用于功率监测。采用基于裂变矩阵产生高阶谐波的谐波展开法进行堆芯功率重构。通过反应堆蒙特卡罗程序RMC统计裂变矩阵,使用瑞利商迭代法求解特征向量,构造高阶谐波库;将堆芯三维功率分布用高阶谐波展开,结合探测器响应矩阵,实现三维功率在线监测。进一步研究了温度、燃耗、控制棒棒位对功率重构精度的影响,结果表明:温度、燃耗变化的工况下,气冷微堆节块平均功率的重构值与蒙特卡罗模拟参考值之间的均方根相对误差小于3%,最大相对误差小于5%;控制棒棒位变化对重构精度的影响较大,通过采用临近棒位的谐波组进行功率重构,均方根相对误差小于3%。验证结果为气冷微堆在线监测系统的后续研发提供参考。

The development and deployment of an accurate and intelligent core online monitoring system are crucial for advancing micro nuclear reactors.The gas-cooled micro reactor,a prismatic super-safe gas-cooled reactor design for mobile micro nuclear power units,features a compact core capable of achieving megawatt-level thermal power and extended service life.Notably,it possesses inherent safety features such as automatic shutdown based solely on temperature feedback,ensuring safety even in accident conditions.However,due to constraints such as limited core volume and the harsh operating environment characterized by high temperatures and radiation levels within the reactor,the installation of in-core detectors is not feasible.As a result,only a limited number of ex-core detectors are utilized for power monitoring purposes.This study adopted the harmonic expansion method to reconstruct core power for the gas-cooled micro reactor.Initially,the Monte Carlo method was utilized to calculate high-order harmonics due to the complex geometry and energy spectrum.Specifically,the RMC Monte Carlo code constructed a precise 3D reactor model and tallied the fission matrix in criticality calculation mode.Then the eigen vectors of the fission matrix were calculated using the Rayleigh quotient iteration method.The high-order harmonics library of the core was then obtained by expanding the 3D power distribution of the core and selecting the main harmonics.Subsequently,Monte Carlo forward calculations determined the contribution of fission sources from each fuel assembly to external detector readings,yielding the detector response matrix.Based on the contribution rate of harmonics to power distribution reconstruction,suitable high-order harmonic groups were selected.Combining this matrix with the detector response allowed for online monitoring of core power distribution using the harmonic expansion method.The study also investigated the influence of temperature and fuel burnup variations,and control rod positions on power reconstruction accuracy.The results show that considering temperature and fuel burnup variations,the root mean square relative error between reconstructed power distribution and Monte Carlo simulation is below 3%,with a maximum relative error below 5%.The control rod position change has a greater impact on the reconstruction accuracy.By using harmonics from adjacent control rods for power reconstruction,the root mean square relative error is less than 3%.Overall,this study showcases the efficacy of using Monte Carlo methods to generate harmonics for online monitoring of micro reactor power distribution,providing valuable insights for the development of future online monitoring systems tailored for gas-cooled micro reactors.