On the Effect of Scalar Flux Weighting of Linearly Anisotropic Scattering Matrices in Higher-Order Transport Calculations

Most of the codes available for homogenized group constant generation for deterministic transport calculations apply the approximation of scalar flux weighting during energy group condensation of higher-order anisotropic scattering matrices. In this paper, we point out the bias caused by scalar flux weighting of linearly anisotropic scattering matrices in the result of SP₃ and S₁₂ calculations. An infinite pin cell was homogenized with Serpent 2 and ERANOS ECCO to compare group constants with different energy group condensation options. Serpent 2 applies scalar flux while ERANOS ECCO performs current weighting of the linearly anisotropic scattering matrices. Three simple reactor models were built assuming different core sizes using standard rectangular assemblies with 15 ×15 fuel pins to analyze the effect of the various weighting options. Diffusion, SP₃, and S₁₂ calculations were performed for the three models using group constants generated with Serpent 2 and ERANOS ECCO. The effect of scalar flux weighting of linearly anisotropic scattering matrices in higher-order transport calculations is shown by comparing the decrease in reactivity due to the decreased reactor size and the assembly power distribution to reference results obtained with Serpent 2 Monte Carlo calculations. Analogous results were observed during the extension of our investigations to a VVER-440 benchmark and the Budapest University of Technology and Economics (BME) Training Reactor. We also studied the effect of increasing the number of groups in these examples. Neglecting higher than linearly anisotropic scattering and indirect application of diffusion coefficients in higher-order transport calculations is advised with few-group structures if angular flux-moment spectra-weighted higher-order scattering matrices cannot be generated. Although in few-group calculations, it can lead to more accurate higher-order transport solutions than applying scalar flux–weighted linearly anisotropic scattering matrices, by increasing the number of energy groups, the distorting effect of scalar flux weighting can also be decreased.