A nodal expansion method for solving the multigroup SP3 equations in the reactor code DYN3D

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 new types of reactors are challenging for these standard methods. A nodal expansion method for solving the equations of the simplified P3 approximation (SP3) of the multigroup transport equation was developed to improve the accuracy of the DYN3D code. In this paper, the method used in DYN3D-SP3 is described. It is applied for the pinwise calculation of a steady state of the OECD/NEA and U.S. NRC PWR MOX/UO2 Core Transient Benchmark. The eigenvalue keff, assembly powers and the pin powers are computed. The results calculated with different approaches including diffusion theory are compared with the reference solution obtained from a heterogeneous transport calculation with the code DeCART. Different approaches of the diffusion coefficient used in the SP3 equations are investigated. The SP3 results obtained with the transport cross section of multigroup diffusion theory show the smallest deviations from the reference solution. These deviations are in the same order as the results of the code DORT, whereas the DORT and DYN3D calculations were carried out with the same library of group constants for homogenized pin cells.