Development and verification of a nodal approach for solving the multigroup SP3 equations

The core model DYN3D which has been developed for three-dimensional analyses of steady states and transients in thermal reactors with quadratic or hexagonal fuel assemblies is based on nodal methods for the solution of the two-group neutron diffusion equation. Loading cores with higher content of MOX fuel, the increase of the fuel cycle length, and the consideration of new reactor types are challenging for these standard methods. A nodal expansion method for solving the equations of the simplified P3 (SP3) approximation of the multigroup transport equation was developed to improve the accuracy of the DYN3D code. The method described in the paper is verified with pinwise calculations of a steady state of the OECD/NEA and US NRC PWR MOX/UO2 Core Transient Benchmark. The used 16-group cross section library was generated for DORT calculations with homogenized pin cells. Two different approximations of the diffusion coefficient which occurs in the within-group form of the SP3 equations are investigated. Using the transport cross section for the calculation of the diffusion coefficient gives much better results than those obtained with the removal cross section. The improvement of the results in comparison to a pinwise diffusion calculation is shown. The results are compared with the DORT and the heterogeneous reference solution of the code DeCART. Concerning the SP3 calculation using the diffusion coefficient based on the transport cross section (DYN3D-SP3-TR) the deviations of the eigenvalue keff and the assembly powers from the transport solutions of DORT and DeCART are in the same order as those between the two transport solutions themselves. The improvement of the DYN3D-SP3-TR results in comparison to the diffusion calculation is presented. As the DYN3D-SP3-TR and DORT calculations are performed with homogenized pin cells, the pin powers of the two calculations are closer to each other than to the pin powers of the DeCART solution. To estimate the contribution of higher flux-moments, the ratio of the second flux moment to the zeroth flux moment is investigated along a horizontal row of pins. It is shown that it is low in the fuel assemblies with small peaks at the water channels. Considering the baffle and the water reflector regions higher values are obtained in the fast neutron groups.