小型棱柱式高温气冷堆k_(eff)不确定度分析

k_(eff) Uncertainty Analysis of Small Prismatic HTGR

在新型反应堆设计中,堆芯重要参数的不确定度分析对设计的可靠性和安全性至关重要。基于小型棱柱式高温气冷堆堆芯设计方案,采用了随机抽样法、敏感性分析法、多项式混沌展开法,分析核数据的不确定度和模型参数的制造公差对k_(eff)不确定度的影响。分析结果显示,核数据引入的k_(eff)不确定度约为511 pcm,除常规的^(235)U和^(238)U核素截面外,石墨和^(28)Si核素的截面对k_(eff)不确定度贡献高达311 pcm。模型参数方面,控制芯块铀装量是工艺参数控制要求的关键,将其他工艺参数与铀装量参数解耦后,25个模型参数引入的k_(eff)不确定度从约1 950 pcm下降到约420pcm。计算方法方面,敏感性分析法、多项式混沌展开法较随机抽样法的计算效率更高,通过多参数联合分析可同时得到所有输入参数的总不确定度和单独不确定度,PCE方法产生代理模型还可用于不同模型参数下的k_(eff)预测。

Uncertainties on results of reactor physics calculations basically originate from uncertainties of solvers,modeling parameters and nuclear data.The uncertainty quantification(UQ) of import core parameters is critical for the safety and reliability of the innovative nuclear reactor designs.In this paper,the UQ of the k_(eff) due to the neutron cross section data and the manufacturing tolerance of modeling parameters for a small prismatic high temperature gas-cooled reactor(HTGR) was reported.The stochastic sampling(SS) method,the sensitivity analysis(SA) method and the polynomial chaos expansion(PCE) method have been adopted during the UQ process.Firstly,the sensitivity analysis of k_(eff) to nuclear data was performed and uncertainties were calculated with sensitivity coefficients and covariance matrix of cross sections.The numerical results show that the k_(eff) uncertainty due to the neutron cross section data is about 511 pcm,among which 311 pcm are introduced by the neutron cross sections of the graphite and ^(28)Si,the considerable fraction of contribution compared to the conventional^(235)U and ^(238)U.In addition,the SS method and PCE method were used to assess k_(eff) uncertainties owing to 25 modeling parameters,including important geometry dimensions and material compositions.A large number of input parameters were sampled and physical calculations were repeatedly conducted for each set of sampled parameters.In the PCE analysis,Legendre basis was used to construct polynomials on the assumption that all modeling parameters followed a uniform distribution and the linear regression method was adopted to solve for the coefficients.The analysis results indicate that the control of the uranium loading is the most critical manufacturing requirement.Although the uncertainties of the sizes of TRISO particles are large due to the manufacturing capacity,as long as the total loading of uranium is cho sen as an individual control parameter and decoupled from other mo deling parameters,k_(eff) uncertainty introduced by 25 modeling parameters can be reduced from about 1 950 pcm to about 420 pcm,among which the thickness of carbon layers of TRISO particles,the total loading and the enrichment of uranium have the most significant contributions.As far as the UQ analysis methods are concerned,the PCE and the SA methods show better efficiency than the SS method,and they can produce the total uncertainty and the individual uncertainty due to each parameter simultaneously.In addition,the PCE method gives a surrogate model at the same time to predict the k_(eff) for different modeling parameters without re solving to the time-consuming design calculations.