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

Abstract

The most diffused neutronics modeling approach in control-oriented simulators is pointwise 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\ud 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

An Adjoint Proper Orthogonal Decomposition method for a neutronics reduced order model

“…The adopted description allows for the spatial heterogeneity of the system, in particular as far as the thermal reactivity feedbacks are concerned, providing a spatial representation of the neutron flux. On the other hand, it can be employed in control-oriented applications, being accurate in both the reactivity and transient representation (Lorenzi et al, 2015) without an excessive computational cost. This modelling improvement may allow adopting innovative control strategies, whose feasibility in the nuclear field cannot be adequately studied by means of the Point Kinetics approach.…”

“…As test functions, the adjoint functions related to the Modal Method are employed. This method is adopted in (Lorenzi et al, 2015). • Case C. The POD is used for the creation of the spatial basis functions.…”

“…The adoption of Reduced Order Methods (ROMs) (Hesthaven et al, 2016;Rozza et al, 2008) can be suitable for this aim, especially in the areas of process optimization, control or uncertainty quantification (Chinesta et al, 2016;Gunzburger, 2002;Quarteroni et al, 2011). The interest in Reduced Order Methods for the simulation of complex systems in nuclear field is increased in the last years, being applied to Monte Carlo methods (Aufiero et al, 2016;Aufiero and Fratoni, 2017), to the deterministic transport equations (Bang et al, 2015;Buchan et al, 2015), and diffusion problems (Buchan et al, 2013;Gong et al, 2016;Lorenzi et al, 2015;Sartori et al, 2014). The fields of application of ROMs are not limited to the neutronics modelling but they are employed also in sensitivity analysis and uncertainty quantification (Abdel-Khalik et al, 2013;Bang et al, 2012a) and in thermal-hydraulic context (Lorenzi et al, 2017(Lorenzi et al, , 2016.…”