Application Of Polynomial Expansion In Sensitivity Analysis Of Reactor Core Calculation

In recent years,the safety analysis method composed of best estimate safety computer codes and uncertainty analysis has reduced the conservatism of accident analysis,made the operation of reactor more flexible,and has been widely recognized in the international scope.The best estimate safety analysis is gradually replacing accident analysis,become an essential part of nuclear safety analysis.The uncertainty analysis method developed at present is still the Monte Carlo method.However,the Monte Carlo method has a slow convergence rate and is not suitable for the uncertainty analysis with high single running cost.Therefore,it is of great significance to develop a fast convergence analysis method.The polynomial expansion method has the potential of rapid convergence,but in practice,there is a "dimension curse" phenomenon,which is difficult to be used in the middle and high dimensional problem.In this paper,it is found that in polynomial expansion method,the matching between original function,fitting function and numerical integral can effectively alleviate the severity of dimension curse.From the point of view of original function,fitting function and numerical integral,this paper improves the polynomial expansion method.A polynomial truncation method matching sparse node integral is proposed,that is,Smolyak expansion,and three fitting methods are proposed.Integral fitting,partial fitting and partition convergence method.Compared with the traditional polynomial expansion method,the improved polynomial expansion method has faster convergence speed and better computational stability.The improved polynomial expansion method has the potential to be applied in the middle and high dimension problems.In order to reduce the calculation cost of sensitivity analysis,this paper takes the improved polynomial expansion method as the sensitivity analysis method,the subchannel program as the calculation tool,and the 3×3 bar bundle module model as the research object.The sensitivity of core thermal hydraulic calculation is studied and compared with Monte Carlo method.By exploring the one-dimensional function relationship between quality factors and input parameters,the influence of polynomial expansion order and numerical integration on sensitivity analysis results is determined.By exploring the multidimensional function relationship between quality factors and input parameters,the application of polynomial expansion method in medium-dimensional sensitivity analysis is verified.The results show that the improved polynomial expansion method is more reasonable than Monte Carlo method and the analysis cost is lower.By using the physical thermal coupling program and the improved polynomial expansion method,the sensitivity study of the physical thermal coupling calculation of the 3×3 bar beam module model under full power condition is carried out in this paper.Considering the cost of analysis,SI test,which is a sensitivity analysis method based on sampling,are compared.As a result,the improved polynomial expansion method can quantitatively and qualitatively complete the sensitivity analysis of the coupling program through a small number of integral nodes,and the analysis results are more reasonable than the SI test.