A comparative study of high and low order neutronics calculation models in microreactors

Abstract

Microreactors, characterized by their complex geometries, distinctive neutron spectrum and spatial distributions, pose significant challenges for deterministic nuclear reactor core calculations. Conventional simulation methods, such as assembly homogenization techniques, are commonly employed in microreactor simulations but often fail to fully capture their complexities. To obtain high-resolution simulation, this paper explores two different types of neutronics calculation models based on an explicit description of the reactor core geometry: a high-order model that incorporates multi-group cross-sections and neutron transport calculations, and a low-order model that utilizes few-group cross-sections with the Super-homogenization (SPH) correction and neutron diffusion calculations. Initially, an extensive error analysis is conducted on the low-order model by varying the energy group structure and spatial region division. Subsequently, the high-order and low-order models are compared. The findings indicate that the high-order model achieves superior computational accuracy, with a $k_{\mathrm{eff}}$ error of −75 pcm, and maximum relative errors and root mean square relative errors (RRMSE) of power at 3.8% and 1.1%, respectively. In contrast, the initial maximum relative power error and RRMSE using the uncorrected low-order model are 10.1% and 2.7%, respectively. After implementing the SPH method, the low-order model reduces these errors to 7.1% and 1.8%, respectively. Moreover, the low-order model demonstrates substantial improvements in memory usage and computational speed, with enhancements of 385-time and 247-time, respectively. Thus, the low-order model offers a balanced approach by enhancing accuracy compared to conventional diffusion calculation model while maintaining efficient resource usage, achieving higher accuracy in power distribution results at a lower computational cost.

Conventional simulation methods, such as assembly homogenization techniques, are commonly employed in microreactor simulations but often fail to fully capture their complexities. To obtain high-resolution simulation, this paper explores two neutronics calculation models: a high-order model that incorporates multi-group cross-sections and neutron transport calculations, and a low-order model that utilizes few-group cross-sections with the Super-homogenization (SPH) correction and neutron diffusion calculations. The findings indicate that the high-order model achieves superior computational accuracy, with a $k_{\mathrm{eff}}$ error of −75 pcm, and root mean square relative errors of power at 1.1%. After implementing the SPH method, the low-order model reduces the diffusion errors to 102 pcm and 1.8%, respectively. Moreover, the low-order model improves 385-time memory usage and 247-time computational speed. Thus, the low-order model offers a balanced approach by enhancing accuracy compared to conventional diffusion calculation model while maintaining efficient resource usage.