Environmental Effect Treatment Model for PWR pin-by-pin Calculation

With the development of computing technology, an improved scheme named pin-by-pin calculation becomes popular in recent years. Different from the traditional two-step calculation, only the heterogeneous structure within each pin is homogenized, leaving the assembly heterogeneous during the three dimensional whole-core calculation. Alone with the development of the pin-by-pin homogenization technology, the reflective boundary condition used in the process of the pin-by-pin homogenized parameters becomes the main error source. In principle, the homogenized group constants can preserve the neutron leakage and reaction rates only for the boundary conditions at which they are created. However, the exact boundary condition of an assembly in the active core cannot be obtained in advance for the two-step scheme. The size of the homogeniza-tion region in the pin-by-pin calculation is almost equal to the averaged neutron-free path, making the pin-by-pin homogenized parameters more dependent on the assembly environment compared with the assembly-homogenized parameters. Focused on the environment effect of the pin-by-pin homogenization, the errors of the homogenized parameters were analyzed firstly. For a typical checkerboard problem, it can be found that large pin-power errors always occur in the pins close to the interface between two assemblies due to the large spectral mismatch between the single-assembly and full-core conditions in those locations. And the errors of the pin-by-pin homogenized group constants can be negligible except for the pin-cell discontinuity factors (PDF) of thermal group. Secondly, the relative importance of PDF in each group was analyzed, it can be found that the PDF of the thermal group is more important and contribute more to the error than the fast group ones. Finally, the function for the PDF predication was proposed. The least-squares method (LSM) for multivariate polynomial was utilized to functionalize the relation of the thermal group PDF and the core parameters. The PDF predication function would be created with heterogeneous solutions obtained from several single-assembly calculations and several spectral geometry calculations. It is expected to predicate PDF with a whole-core pin-by-pin homogeneous solution. In this work, the polynomial order of the PDF predication function was analyzed, and the selected core parameters are based on the physics underlying core neutronics behavior. In order to numerically analyze the performance of the method, C5G7 and KAIST benchmarks were evaluated. Results of the C5G7 and KAIST benchmarks indicate that the PDF predication of the thermal group can get high precision results of eigen-value, and work effectively in reducing the relative error of pin-cell power, especially for the pins located near the interface between different assemblies. © 2022 Atomic Energy Press. All rights reserved.