Empowering nuclear reactor analysis: OpenNode for accurate 3D core simulation through nodal expansion neutron diffusion equations solving

Abstract

OpenNode is a sophisticated reactor core simulation tool, meticulously designed for educational purposes. Its main function is to solve the complex partial differential equation governing multi-group neutron diffusion in a Cartesian geometry. OpenNode relies on the second- and fourth-order Nodal Expansion Method (NEM) to provide accurate solutions to three-dimensional steady-state problems, encompassing both the direct and adjoint modes. At the heart of this method, the neutron balance equation serves as the fundamental framework for calculating the nodal neutron flux and the effective multiplication factor, enabling the complex evaluation of neutron flux distributions within individual nodes.The NEM methodology, carefully programmed in Fortran-90 in OpenNode, meticulously decomposes the reactor core into nodes of reasonable size. This approach balances computational efficiency and accuracy, achieving outstanding precision even when using a reduced number of computational meshes. To further increase the number of equations while maintaining the balance between unknowns, OpenNode judiciously incorporates two essential approximations: the Weighted Residual Method (WRM) and the Quadratic Transverse Leakage (QTL) approximation.OpenNode transcends simple computational prowess by adopting an intuitive Graphical User Interface (GUI), meticulously developed by combining Python 3, Qt Designer, and Blender software. This Python-powered graphical interface offers users a seamless, user-friendly experience, facilitating tasks such as data entry, execution of complex simulations, calculation of results, data visualization, 3D design of nuclear core geometry, and in-depth analysis of results. One of OpenNode’s key features is its innate flexibility, enabling it to solve problems in both 2D and 3D Cartesian geometries. This adaptability makes it a versatile tool suitable for a wide range of research and power reactor applications, offering users the ability to model and design reactors with unrivaled ease.To substantiate OpenNode’s reliability, comprehensive criticality calculations are carried out in various scenarios, including single-cell verification, BIBLIS, KOEBERG cores in two dimensions (2D), and IAEA cores in three dimensions (3D). The results clearly demonstrate OpenNode’s robustness and reliability in multidimensional criticality analysis. In particular, OpenNode adheres to an open-source philosophy, making it readily available for download. This commitment to open access fosters collaboration and paves the way for wider adoption within the education and research communities, nurturing a thriving ecosystem of shared knowledge and exploration.