Abstract:
Among the high-fidelity numerical calculation methods in reactor physics, the pin-by-pin two-step method may strike a balance between calculation precision and calculation cost, and is currently a practical and viable high-fidelity numerical calculation method. Different from the traditional two-step calculation, the pin-by-pin two-step method only homogenizes the heterogeneous structure within each pin, retaining the assembly heterogeneous during three-dimensional whole-core calculations. In principle, homogenized group constants can only pre-serve the neutron leakage and reaction rates for the boundary conditions under which they are formed. However, the two-step method cannot predict the exact boundary condition in advance of an assembly in the active core. Currently, the pin-by-pin two-step method continues to apply the traditional single-assembly reflective boundary condition. The size of the homogenization region in the pin-by-pin calculation is nearly equal to the averaged neutron-free path, so the pin-by-pin homogenized parameters are more dependent on the assembly environment than the assembly-homogenized parameters. The traditional single-assembly reflective boundary condition does not account for the real environment of the fuel assemblies in the active core, however, the streaming effect and spectrum interference effect between different assemblies in the active core have a significant impact on the pin-by-pin homogenized parameters. As a result, there is deviation between the pin-by-pin homogenized parameters of the real core environment and the traditional single-assembly reflective boundary condition, leading to calculation errors. To deal with the environmental effect for pin-by-pin two-step method and improve the calculation accuracy of high-fidelity numerical calculation, this paper focused on the errors of the homogenized parameters, and improving the calculation accuracy by correcting the errors of environmental effect for the homogenization parameters. Firstly, this study discovers that the traditional Colorset method will cause the phenomenon of extrapolation of the machine learning model when representing the environmental effect, introducing large biases. So, the entire assembly Colorset and zone model was proposed to evaluate the environmental effect based on research into multi-assembly models for inner core assemblies (typical checkerboard problem) and surrounding reflector assemblies (irregular checkerboard problem). Then this study focused on three types of pin feature: information about the pin’s material and location; information about the surrounding assembly; and information about energy spectrum and leakage. By analyzing the machine learning model’s feature sensitivity, the combination features of pin material, location, surrounding assembly, energy spectrum, and leakage-related information were determined. Finally, a method for predicting pin-by-pin homogenized parameters was proposed: the correction method of pin-by-pin homogenization environmental effect of PWR based on machine learning. In order to numerically analyze the performance of the method, the HPR1000 was evaluated. The results show that, as compared to the typical single-assembly reflecting technique, the suggested method achieves higher precision outcomes in reactivity and pin power dithe stribution: The calculation accuracy of reactivity is increased by about 79%, the average pin power deviation is also greatly reduced, and the calculation accuracy is increased by about 76%. As a result, the method developed in this study may be utilized to mitigate the environmental impact of pin-by-pin homogenization in PWR and increase computation accuracy.