RESEARCH

Although the rapid growth in computing power has enhanced the feasibility of the practical application of the direct whole core calculations (DWC), it is still challenging to obtain the solution of the neutron transport equation for the commercial reactor core. In case of the advanced power reactor (APR) 1400 pressurized water reactor (PWR) of Korea, for example, the core is loaded with 241 fuel assemblies (FAs) and each FA with 16x16 lattice feature includes 236 fuel rods and 5 guide tubes. Therefore, it requires to perform the multi-dimensional transport calculations for the 56,876 fuel rods, 1,205 guide tubes, and other components including the control rods (CRs), spacer grids, core shroud, pressure vessel, etc., that are discretized into very fine subregions to take account the spatial reaction rate distributions. Furthermore, the energy dependency of the neutron cross-section (XS), especially the resonance behavior of heavy nuclides, renders additional difficulties such as the refined energy group structure, e.g. the HELIOS 47-group and WIMS 69-group, and the resonance treatment to obtain the effective XSs which incorporate the resonance interference and the shielding effect. As a solution to reduce the computing burdens, the practical and commercial reactor core analyses are normally performed by employing pre-generated and simplified data sets known as the group constants (GCs). The approach is so-called the two-step method.

In its first step, the transport calculations with the refined energy groups are performed for an explicitly modeled lattice to generate the GCs. Commonly the method of characteristics (MOC), collision probability method (CPM), and Monte-Carlo (MC) method are employed, and the solutions are used to homogenize the target lattice within an assembly or several pin-cells and to condense the energy groups. For functionalization of the GCs to incorporate various core states, the transport calculations are also performed by changing the conditions like the burn-up exposure, fuel and moderator temperatures, boron concentration, and moderator density. In SNU RPL, the GC generations are carried out by the MOC code nTRACER.

Conventionally, the multi-dimensional full-core analyses are performed by employing the assembly-homogenized few-GCs and the neutron diffusion equation is solved instead of the transport. The nodal methods are used to approximate the intra-node flux distributions and the assembly discontinuity factor (ADF) and the B1 critical leakage correction are widely used to mitigate the errors involved with the homogenization and condensation. The pin power distribution is reconstructed from the homogeneous nodal flux distribution and the heterogeneous form function obtained in the first step. The reactor numerical simulator (RENUS) of SNU RPL is one of the assembly-wise nodal core analysis codes. It solves the diffusion equation based on the source expansion nodal method (SENM) whose accuracy is comparable to that of the analytic nodal method (ANM) and employs the two-level coarse mesh finite difference (CMFD) scheme to accelerate the solution convergence.

On the other hand, the advanced two-step core analysis codes employ the pin-homogenized multi-group constants (MG-GCs) to reduce the errors from the cell-homogenization and the group condensation and to fully utilize the computing power in recent days. The advanced codes perform the finite difference (FD) or nodal calculations based on the simplified PN theory and are aided by the superhomogenization (SPH) factor or discontinuity factor (DF) to take account the pin-homogenization error. The SP3 based Pin-Homogenized Neutronic Core Simulator (SPHINCS) of SNU RPL is one of the pin-level two-step code. It solves either the diffusion or SP3 equations using the finite difference method (FDM) which is chosen to save the computing resources by taking the advantage of small mesh size. The SPH factors are assigned to each pin-cell and energy group to capture the homogenization, condensation, and spatial discretization errors.

Although SP3 has widely used in the second stage of the two-step method, they are employed with ad hoc domain boundary conditions involving the diffusion like first order derivatives in the surface normal direction when applied to piecewise homogeneous regions. With the objective of finding a remedy to these inconsistencies as well as giving a physical basis to the theory, the Generalized SP3 equations (GSP3) have been proposed. These new equations possess a more rigorous subset of boundary condiitions and a particular angular flux distribution. Application of GSP3 is also researched in SNURPL.