Spatial neutronics modelling to evaluate the temperature reactivity feedbacks in a Lead-cooled Fast Reactor

The qualitative and quantitative assessment of the thermal reactivity feedbacks occurring in a nuclear reactor is a crucial issue for the time-dependent evolution of the system and, in turn, it has a great impact on the development and validation of advanced control techniques. In the present work, in order to overcome the limitations of the classic Point Kinetics adopted in the control simulators, a spatial neutronics model, representing the neutron flux as sum of a spatial basis weighted by time-dependent coefficients, has been considered. The reference reactor is ALFRED, the European demonstrator of the Lead-cooled Fast Reactor technology. Average crosssections for each Fuel Assembly, calculated by means of a Monte Carlo code, have been used to solve the partial differential equations of the neutron diffusion, exploiting the capabilities of the COMSOL software. Once obtained the spatial functions, the set of equations for studying the reactivity effects has been implemented in the MATLAB environment. Among the several temperature reactivity feedbacks, specific attention has been paid to the Doppler effect in the fuel and to the lead density effect. Several spatial bases have been calculated and their capability of representing the reactivity variation have been assessed.