A Control-Oriented Modeling Approach to Spatial Neutronics Simulation of a Lead-Cooled Fast Reactor

The most diffused neutronics modeling approach in control-oriented simulators is point-wise kinetics. In the framework of developing control strategies for innovative reactor concepts, such a simplified description is less effective as it prevents the possibility of exploiting the capabilities of advanced control schemes. In the present work, in order to overcome these limitations, a spatial neutronics description based on the modal method has been considered. This method allows separating the spatial and time dependence of the neutron flux, which can be represented as the sum of the eigenfunctions of the neutron diffusion equation weighted by time-dependent coefficients. In this way, the system dynamic behavior is reduced to the study of these coefficients and can be represented by a set of ordinary differential equations (ODEs), reducing the simulation computational burden. In this paper, a test case involving three fuel pins of an innovative lead-cooled fast reactor has been set up and investigated. Once the eigenfunctions are obtained, the set of ODEs for studying the time-dependent coefficients has been derived and then implemented in the DYMOLA environment, developing an object-oriented component based on the reliable, tested, and well-documented Modelica language. In addition, a heat transfer model for the fuel pin has been developed, still drawing on the principles of the object-oriented modeling. Finally, in order to assess the performance of the developed spatial neutronics component, the outcomes have been compared with the reference results obtained from the multigroup diffusion partial differential equations, achieving a satisfactory agreement.