RESEARCH

Nuclear reactor analyses have been performed mostly with the conventional two-step procedure where the assembly homogenized few-group cross sections generated in the first step are used in the core calculations of the second step. This conventional method developed extensively in 1970s to 1990s has provided the practical estimates of the core characteristics. However, there have been inherent limitations in the prediction accuracy due to the approximations such as spatial homogenization, energy condensation, and approximated governing equations. Higher accuracy of neutronics calculation is required to support life extension and new reactor development. Therefore, the interest of direct whole core calculation has been increased with the rapid development of computing powers. The direct whole core transport calculation requires no prior homogenization of the fuel assemblies or the fuel pins. So direct whole core calculation can reduce the solution error introduced by homogenization, condensation and simplifications introduced in conventional core calculations. In order to achieve accurate direct whole core calculation, the methods for three-dimensional heterogeneous whole core transport calculation, resonance self-shielding treatment are required. SNURPL developed direct whole core transport code nTracer which is based on the planar method of characteristics (MOC) coupled 3-D coarse mesh finite difference (CMFD) method.

The neutron transport equation can be solved by both deterministic methods and stochastic methods. In stochastic methods (Monte Carlo method) particle histories are tracked and averaged. It has great advantage in the usage of continuous energy cross section but it has expensive computational costs. In deterministic methods, there are various methods with different discretization techniques. Sn method discretizes the angle with discrete ordinate and wieghting quadratures while Pn method discretizes the angle with the spherical harmonics. Also MOC can be used to solve the neutron transport equation which reduces a partial differential equation to a family of ordinary differential equations. Though deterministic methods has chipper computational cost, 3D transport calculation still poses the problem of excessive computing time and memory. For practicality, the planar MOC based 3D CMFD formulation was developed to perfrom direct whole core calculation without significant losses of accuracy by making the use of fact that most reactors are radially heterogeneous than axially.

The purpose of resonance treatment is to determine the effective cross section for a broad energy group within which significant self-shielding occurs due to the presence of resonances. Since self-shielding and consequently the effective cross section change are affected by the material composition as well as the geometrical configuration, the self-shielding and the effective cross section must be determined locally at the problem specific condition.

The direct calculation of self-shielding with ultra fine energy groups would be most desirable. However, it is not practical. The subgrouop method which is one of the numerous approximate resonance treatment methods has the advantage of handling complex geometries and space dependent self shielding. Basically, the subgroup method is to approximate the continuous resonance various with a stair-like variation involving step changes. The subgroup parameters consisting of the subgroup levels and weights can be determined properly by preserving the effective cross section at different dilutions. With these subgroup parameters, the effective cross section can be determined in the transport calculation code such as DeCART under the specific problem condition.