# Nuclear Science and Techniques

《核技术》(英文版) ISSN 1001-8042 CN 31-1559/TL     2018 Impact factor 0.961

Nuclear Science and Techniques ›› 2019, Vol. 30 ›› Issue (11): 162

• NUCLEAR ENERGY SCIENCE AND ENGINEERING •

### An improved semi-implicit direct kinetic method for transient analysis of nuclear reactors

Roozbeh Vadi, Kamran Sepanloo

1. School of Nuclear Reactors and Safety, Nuclear Science and Technology Research Institute, End of North Karegar Ave., Tehran 14359-836, Iran
• Received:2019-03-05 Revised:2019-03-31 Accepted:2019-06-26
• Contact: Roozbeh Vadi E-mail:roozbehvadi@yahoo.com
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Roozbeh Vadi, Kamran Sepanloo. An improved semi-implicit direct kinetic method for transient analysis of nuclear reactors.Nuclear Science and Techniques, 2019, 30(11): 162

Abstract: Semi-implicit direct kinetics (SIDK) is an innovative method for the temporal discretization of neutronic equations proposed by J. Banfield. The key approximation of the SIDK method is to substitute a timeaveraged quantity for the fission source term in the delayed neutron differential equations. Hence, these equations are decoupled from prompt neutron equations and an explicit analytical representation of precursor groups is obtained, which leads to a significant reduction in computational cost. As the fission source is not known in a time step, the original study suggested using a constant quantity pertaining to the previous time step for this purpose, and a reduction in the size of the time step was proposed to lessen the imposed errors. However, this remedy notably diminishes the main advantage of the SIDK method. We discerned that if the original method is properly introduced into the algorithm of the point-implicit solver along with some modifications, the mentioned drawbacks will be mitigated adequately. To test this idea, a novel multigroup, multi-dimensional diffusion code using the finitevolume method and a point-implicit solver is developed which works in both transient and steady states. In addition to the SIDK, two other kinetic methods, i.e., direct kinetics and higher-order backward discretization, are programmed into the diffusion code for comparison with the proposed model. The final code is tested at different conditions of two well-known transient benchmark problems. Results indicate that while the accuracy of the improved SIDK is closely comparable with the best available kinetic methods, it reduces the total time required for computation by up to 24%.