Yasuyoshi Kato

A Coarse-Mesh Correction of the Finite Difference Method for Neutron Diffusion Calculations

This study has been undertaken to evaluate an uncertainty in a finite difference method for two-dimensional neutron diffusion calculations and to provide a simple method to eliminate the uncertainty from k/sub eff/, control rod worth, and peak power density. An effect of a condensation of the energy groups is also studied. It is found that errors in k/sub eff/, control rod worth, and peak power density have linear relationships with the square of mesh spacing, and an extrapolation to zero mesh spacing, by using the linear relationships, is possible, eliminating the uncertainties of 0.7 percent ..delta..k/k in k/sub eff/, approximately 8 percent in control rod worth and approximately 2 percent in peak power density in a case of a mesh calculation as coarse as one mesh point per subassembly. When a basic multigroup cross-section set is condensed into a few-group cross-section set, the errors due to the condensation of the cross sections on k/sub eff/ and on control rod worth are shown to have linear relationships with the inverse square of the number of the condensed energy group. These relationships have been confirmed analytically with the application of perturbation theory.

The coarse space-energy mesh rebalancing method for neutron diffusion calculations in fast reactors

This paper reports on the coarse space-energy mesh rebalancing method studied for the purpose of convergence acceleration on two-dimensional multigroup neutron diffusion calculations with a seven-point finite difference scheme, a uniform triangular mesh, and an arbitrary scattering matrix. The rebalancing method provides convergences without numerical instability for a range of fast reactor problems with varying numbers of neutron energy groups and mesh points. The number of outer iterations is decreased with the rebalancing method by a factor of 2 in comparison to the case when only asymptotic fission source extrapolation and successive overrelaxation acceleration techniques are applied. With the rebalancing method. The HIVER code solves the problems 5 to 20 times faster than the existing reference CITATION code. The relative calculation speed of the reference code increases with the problem size.

Decomposition Principle for Refueling Optimization in Fast Breeder Reactors

A decomposition principle has been proposed for refueling optimization in fast breeder reactors (FBRs). In refueling optimization a total multistage decision problem with nonlinear programming is decomposed into many partial problems with solvable size and linear programming by taking advantage of the FBR physics. First, the problem is decomposed into determinations of the number of refueling subassemblies in concentric annular core zones and the subassembly-by-subassembly refueling patterns. Second, the latter process is further decomposed into the determination of the refueling patterns in the equilibrium cycles and the transition cycles. Third, the simultaneous determination of the refueling patterns throughout multicycles over the plant lifetime is decomposed into a consecutive cycle-by-cycle determination. Fourth, the linear programming problems are decomposed into a sequence of smaller ones by using a decomposition algorithm for solving large-size programming. The number of fresh fuel subassemblies added at each cycle in the initial loading core through the equilibrium cycles is optimized in concentric annular refueling zones of the core. The optimization is carried out so as to maximize the average discharge burnup subject to nuclear and thermal constraints by using linear programming with an application of a revised simplex method. The refueling pattern at each cycle is determined by treating each fuel subassembly separately and by minimizing power peaking subject to the number of refueling subassemblies determined in the previous step. After optimizing the refueling patterns in the equilibrium cycles, the transition cycle patterns are determined cycle by cycle to match the equilibrium cycle patterns by means of an implicit enumeration method. An explicit formulation is worked out for the implicit enumeration method, which makes it possible to determine the refueling patterns cycle by cycle. The refueling optimization method based on the decomposition principle was applied to a typical 300-MW(electric) FBR core. It successfully affords the numbers of fresh fuel subassemblies and optimal refueling patterns from the initial loading cycle to the equilibrium cycles. The optimized refueling patterns lower the power-peaking factor by ∼ 5% and increase the average discharge burnup by ∼ 3% compared with a trial-and-error method. This method has the flexibility to handle the unexpected alteration of refueling patterns in the cases of fuel failure and the expected alteration for burnup increase through batch size extension within the transition period of several cycles.