Application of the SP3 TPEN Method for Hexagonal Core Transient Analysis

The simplified Pn (SPn) method is one of the best solutions. This method expands the neutron angular flux using the n_th order Legendre polynomial on the cosine of the neutron flight angle in computational reactor physics. The SPn solution is quite accurate compare to the conventional diffusion solution that can be obtained by the P1 method. Also, the formulation of the SPn equations is similar to that of the diffusion equation, so the SPn method is easy to adopt nodal methods for efficient core analysis. With this background, there have been various studies to apply SPn nodal methods with the order of 3 (SP3) and it has been proved that the SP3 application takes significant enhancement on core analysis accuracy especially in SMR, FBR, and some cores where large spatial flux variation is formed such as MOX loaded cores or cores under the ARI condition. Most SP3 researches are, however, limited on the steady-state analysis. Although there are a few studies for SP3 application to core transient analysis, they are available only in rectangular core problems. Since a number of SMRs and FBRs use hexagonal fuel assemblies, it is worth evaluating the effect of the SP3 application in hexagonal core transient analysis. In this work, the time-dependent SP3 TPEN method was developed to attain accurate hexagonal core transient solutions. In the SP3 TPEN approach, each hexagon node was split to 6 triangle nodes and the intra-nodal 2-D SP3 solutions were expressed as a third order polynomial in each triangle node. The effectiveness of the SP3 TPEN method in hexagonal core transient analysis was verified in the VVER440 rod ejection benchmark problem. Considerable difference was observed in core power behaviors and estimated rod worth obtained by the P1 and SP3 methods. The superiority of the SP3 method was proved by comparing P1, SP3, and MC solutions that k-eff and estimated rod worth obtained by SP3 was much closer to the MC reference solutions.