Development of a Spatial Neutronics Model for Control-Oriented Dynamics Simulation

In control-oriented simulators, the neutronics is usually modeled by implementing the point-wise kinetics. In the framework of the study of the control strategy for innovative reactor concepts, such a simplified description is less effective since prevents the possibility of exploiting the capabilities of advanced control schemes. In order to overcome these limitations, a spatial neutronics model based on Modal Method has been considered. This approach allows separating the spatial and time dependence of the neutron flux, which can be represented as sum of the eigenfunctions of the multi-group neutron diffusion equation weighted by time-dependent coefficients. In this way, the system dynamic behavior is reduced to the study of these time-dependent coefficients and can be represented by a set of Ordinary Differential Equations (ODEs), reducing the 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 obtained the eigenfunctions, the set of ODEs for studying the time dependent coefficients has been implemented in the MATLAB environment [1]. Finally, in order to assess the performance of the developed model, the outcomes have been compared with the results obtained from the neutron diffusion partial differential equation, achieving a satisfactory agreement.