Improvement of the SPH Method for Pin-by-Pin Core Calculations

Abstract

In this paper, improvement of the SPH method (the improved SPH method) is proposed. The SPH method is commonly used in pin-by-pin mesh core calculations to reduce cell-homogenization error. The investigation revealed that the normalization condition of the SPH factor in the conventional SPH method is not appropriate for multi-assembly calculations in which different assembly types are adjacent. Since the conventional normalization condition does not incorporate flux discontinuity between assemblies, cell homogenization error in assembly peripheral region becomes larger. In the improved SPH method, the SPH factor is divided by an averaged ''cell-level'' discontinuity factor obtained in each fuel assembly. Though the SPH factor is somewhat modified from the conventional value, no additional homogenization parameters (e.g. discontinuity factor) is necessary in core calculations. Test calculations were carried out in a simplified one-dimensional slab and two-dimensional PWR colorset geometries that simulate part of actual core geometry. The calculation results showed that the improved SPH method effectively reduce the cell-level homogenization error especially in assembly peripheral region. Since we can easily implement the improved SPH method by slight code modifications, it can be a promising candidate of the cell-homogenization method for pin-by-pin core calculations.

A note on application of superhomogénéisation factors to integro-differential neutron transport equations

“…These errors come from the following facts; the conventional SPH factor method cannot consider the flux discontinuity between different assemblies and the cell-homogenized cross-sections are obtained with a single assembly model. The problem due to the former can be partly overcome by introducing the improved SPH method proposed by Yamamoto et al [10]. In the improved SPH method, the flux discontinuity between assemblies is calculated from the following equation:…”

Static and transient pin-by-pin simulations of a full PWR core with the extended coupled code system DYNSUB

“…Both made efforts to improve their discontinuity factors generated by making them environment dependent (boundary conditions and neutron spectra). Yamamoto and his partners introduced improved SPH factors to better account for flux discontinuities between adjacent fuel assemblies (Yamamoto et al, 2004). The feasibility of utilizing any of the above approaches in DYNSUB is to be determined.…”

A unified generic theory on discontinuity factors in diffusion, SP 3 and transport calculations

“…While when using homogenized pin cells one may be better off not to use discontinuity factor on the assembly boundary, which is the case of using Prime EPDF. However in the reference (Yamamoto et al, 2004;Chiba et al, 2012), it was found that in SP 3 calculation for a typical UO2 checker board problem the renormalized SPH gave better result than the conventional SPH. This is contrary to what Table 3 shows.…”

“…Hence the conventional SPH factor is equivalent to a directionally isotropic Prime EPDF without renormalization. However as suggested in the references (Yamamoto et al, 2004;Chiba et al, 2012) the conventional SPH factor could also be arbitrarily renormalized without affecting the interface boundary condition on cell surfaces except for the assembly boundary surface. It should be mentioned that the renormalized EPDF definition by Eq.…”