A New Formulation of the Reconstruction Problem in Neutronics Nodal Methods Based on Maximum Entropy Principle

Abstract

This paper develops a new method for reconstructing neutron flux distribution, that is based on the maximum entropy Principle in information theory. The Probability distribution that maximizes the entropy Provides the most unbiased objective Probability distribution within the known partial information. The partial information are the assembly volume-averaged neutron flux, the surface-averaged neutron fluxes and the surface-averaged neutron currents, that are the results of the nodal calculation. The flux distribution on the boundary of a fuel assembly, which is the boundary condition for the neutron diffusion equation, is transformed into the probability distribution in the entropy expression. The most objective boundary flux distribution is deduced using the results of the nodal calculation by the maximum entropy method. This boundary flux distribution is then used as the boundary condition in a procedure of the imbedded heterogeneous assembly calculation to provide detailed flux distribution. The results of the new method applied to several PWR benchmark problem assemblies show that the reconstruction errors are comparable with those of the form function methods in inner region of the assembly while they are relatively large near the boundary of the assembly. The incorporation of the surface-averaged neutron currents in the constraint information (that is not done in the present study) should provide better results.